Cover Page
The handle http://hdl.handle.net/1887/25769 holds various files of this Leiden University
dissertation.
Author: Burg, Remco Fanciscus Johannes van der
Title: The distribution of stellar mass in galaxy clusters over cosmic time
Issue Date: 2014-05-14
S`Q27b+?`B7i
i2` p2`F`BD;BM; pM
/2 ;`/ pM .Q+iQ` M /2 lMBp2`bBi2Bi G2B/2MQT ;2x; pM _2+iQ` J;MB}+mb T`Q7X K`X *XCXCXJX aiQHF2`pQH;2Mb #2bHmBi pM ?2i *QHH2;2 pQQ` S`QKQiB2b
i2 p2`/2/B;2M QT rQ2Mb/; R9 K2B kyR9
FHQFF2 Ry,yy mm`
/QQ`
_2K+Q 6XCX pM /2` "m`;
;2#Q`2M i2 G2B/2`/Q`T
BM RN3e
S`QKQiB2+QKKBbbB2
S`QKQiQ`,
*Q@S`QKQiQ`,
S`Q7X /`X EQ2M`/ EmBDF2M
.`X >2MF >Q2Fbi`
Pp2`B;2 H2/2M,
S`Q7X
S`Q7X
S`Q7X
S`Q7X
/`X
/`X
/`X
/`X
JB+?2H "HQ;?
J`BDM 6`Mt
>mm# _ƺii;2`BM;
CQQT a+?v2
Aa"L, Nd3@N9@ek8N@Rk3@3
Ü kyR9 _2K+Q 6XCX pM /2` "m`;
UlX qi2`HQQV
Ǵ.Q MQi 7QHHQr r?2`2 i?2 Ti? Kv H2/XXX
:Q BMbi2/ r?2`2 i?2`2 Bb MQ Ti?- M/ H2p2 i`BHXǴ
@ Jm`B2H ai`Q/2
h?2 +Qp2` b?Qrb +Hmbi2`@b+H2 Qp2`/2MbBiv BM i?2 JBHH2MMBmK bBKmHiBQM
i `2/b?B7i z4RX9 U#+F +Qp2`V- M/ i `2/b?B7i z4y U7`QMi +Qp2`VX
*`2/Bi, aT`BM;2H 2i HX UoB`;Q *QMbQ`iBmKV
M/ i?2 Jt@SHM+F@AMbiBimi2 7Q` bi`QT?vbB+bX
h?2 +QHQm` BK;2b b?Qr Q#b2`piBQMb Q7 +Hmbi2` aT_*a@ReRj i z4yX3d U#+FVM/ +Hmbi2` #2HHe88 i z4yXRj U7`QMiV- r?B+? `2 +2Mi`H iQ i?2 rQ`F BM i?Bb i?2bBbX
*Qp2` /2bB;M, _2K+Q 6XCX pM /2` "m`;
*Qp2` Hv@Qmi, amxMM2 hvHQ` JmxxBM
*QMi2Mib
R AMi`Q/m+iBQM
RXR h?2 biM/`/ +QbKQHQ;B+H KQ/2H X X X X X X X X X
RXk ai`m+im`2 7Q`KiBQM BM i?2 lMBp2`b2 X X X X X X X X
RXj h?2 +?HH2M;2 Q7 bi2HH` Kbb2b X X X X X X X X X X X
RX9 h?2 rQ`H/ Q7 ;HtB2b X X X X X X X X X X X X X X X X
RX8 :HtB2b BM ?B;?@/2MbBiv 2MpB`QMK2Mib X X X X X X X
RXe h?Bb h?2bBb X X X X X X X X X X X X X X X X X X X X X
RXeXR :Htv +Hmbi2`b i z ∼ 1 X X X X X X X X X X
RXeXk :Htv +Hmbi2`b BM i?2 HQ+H lMBp2`b2 X X X
RXeXj S`Q#BM; i?2 2`Hv T?b2b Q7 bi`@7Q`KiBQM
X
X
X
X
X
X
X
X
X
k h?2 2MpB`QMK2MiH /2T2M/2M+2 Q7 i?2 bi2HH` Kbb
i z ∼ 1
kXR AMi`Q/m+iBQM X X X X X X X X X X X X X X X X X X X X X X
kXk aKTH2 .i /2b+`BTiBQM X X X X X X X X X X X X X X
kXkXR h?2 :*Gaa +Hmbi2` bKTH2 X X X X X X X X X
kXkXk aT2+i`Qb+QTv X X X X X X X X X X X X X X X X X
kXkXj S?QiQK2i`B+ .i X X X X X X X X X X X X X X
kXkX9 lHioAah }2H/ `272`2M+2 X X X X X X X X X X
kXj MHvbBb X X X X X X X X X X X X X X X X X X X X X X X X
kXjXR S?QiQK2i`B+ `2/b?B7ib X X X X X X X X X X X X X
kXjXk ai2HH` Kbb2b M/ +QKTH2i2M2bb X X X X X X X
kXjXj _2bi@7`K2 +QHQm`b X X X X X X X X X X X X X X
kXjX9 *Hmbi2` K2K#2` b2H2+iBQM X X X X X X X X X X X
kX9 _2bmHib X X X X X X X X X X X X X X X X X X X X X X X X X
kX9XR h?2 +Hmbi2` bi2HH` Kbb 7mM+iBQM X X X X X X
kX9Xk *Hmbi2` p2`bmb 6B2H/ X X X X X X X X X X X X X
kX9Xj ai`@7Q`KBM; pb ZmB2b+2Mi ;HtB2b X X X X X
p
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
R
R
j
j
9
8
e
e
3
3
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
N
RR
Rj
Rj
R9
Re
Rd
R3
R3
RN
ky
kR
k8
k8
kd
kN
7mM+iBQM
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
pB
*PLh1Lha
kX9X9 LQ`KHBbiBQM Q7 i?2 aJ6 X X X X X X X X X X X
.Bb+mbbBQM X X X X X X X X X X X X X X X X X X X X X X X X
kX8XR h?2 b?T2 Q7 i?2 ;Htv aJ6 X X X X X X X X X
kX8Xk bBKTH2 [m2M+?BM; KQ/2H X X X X X X X X X X X
kXe amKK`v M/ *QM+HmbBQMb X X X X X X X X X X X X X X X
kX .i T`Q+2bbBM; M/ +iHQ;m2 +`2iBQM X X X X X X X X
kXXR S?QiQK2i`B+ /i `2/m+iBQM X X X X X X X X X X
kXXk Sa6 ?QKQ;2MBbiBQM M/ +QHQm` K2bm`2K2Mib
kX" 6B2H/ aJ6 K2bm`2K2Mib 7`QK :*Gaa X X X X X X X
X
X
X
X
X
X
X
X
X
jy
jR
jR
jj
j3
9y
9y
9R
99
j h?2 S?b2 aT+2 M/ ai2HH` SQTmHiBQMb Q7 *Hmbi2` :HtB2b
i z ∼ R
jXR AMi`Q/m+iBQM X X X X X X X X X X X X X X X X X X X X X X X X X X X X
jXk .ib2i X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X
jXj :HtB2b BM i?2 *Hmbi2` S?b2 aT+2 X X X X X X X X X X X X X X X
jX9 aBKmHi2/ *Hmbi2` S?b2 aT+2 X X X X X X X X X X X X X X X X X X
jX8 a1. }iiBM; Q7 SQbibi`#m`bi :HtB2b X X X X X X X X X X X X X X
jXe .Bb+mbbBQM X X X X X X X X X X X X X X X X X X X X X X X X X X X X X
jXd amKK`v M/ PmiHQQF X X X X X X X X X X X X X X X X X X X X X X
9d
9N
8y
8R
8j
83
eR
ej
9 *2Mbmb Q7 ai2HH` Jbb BM Ry JbbBp2 >HQ2b i z ∼ 1
i?2 :*Gaa am`p2v
9XR AMi`Q/m+iBQM X X X X X X X X X X X X X X X X X X X X X X X X
9Xk :*Gaa .i MHvbBb X X X X X X X X X X X X X X X X
9XkXR hQiH ?HQ Kbb2b X X X X X X X X X X X X X X X X X
9XkXk S?QiQK2i`B+ `2/b?B7ib M/ ai2HH` Kbb2b X X X X
9XkXj *Hmbi2` K2K#2`b?BT +Q``2+iBQM X X X X X X X X X X
9Xj *2Mi`H bi2HH` Kbb p2`bmb ?HQ Kbb X X X X X X X X X X
9X9 hQiH bi2HH` Kbb p2`bmb ?HQ Kbb X X X X X X X X X X X
9X9XR *QKT`BbQM iQ Qi?2` bKTH2b X X X X X X X X X X
9X8 _/BH bi2HH` /2MbBiv /Bbi`B#miBQM X X X X X X X X X X X X
9X8XR .Bb+mbbBQM X X X X X X X X X X X X X X X X X X X X X
9X8Xk 1pQHmiBQM iQr`/b HQr2` `2/b?B7i X X X X X X X X X
9Xe amKK`v M/ *QM+HmbBQMb X X X X X X X X X X X X X X X X
e8
ed
eN
dR
dk
dj
d8
dd
3y
3j
38
3e
33
kX8
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
7`QK
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
8 h?2 /Bbi`B#miBQM Q7 bi2HH` Kbb BM ;Htv +Hmbi2`b i z ∼ 0.15 NR
8XR AMi`Q/m+iBQM X X X X X X X X X X X X X X X X X X X X X X X X X X X X Nj
8Xk .i Qp2`pB2r T`Q+2bbBM; X X X X X X X X X X X X X X X X X X X N8
8XkXR S?QiQK2i`v @ J2;*K X X X X X X X X X X X X X X X X X Ne
8XkXk S?QiQK2i`v @ q6* X X X X X X X X X X X X X X X X X X X X N3
8XkXj *iHQ;m2 +QMbi`m+iBQM X X X X X X X X X X X X X X X X X X Ryy
8Xj MHvbBb X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X Ry9
8XjXR J2i?Q/ R @ biiBbiB+H #+F;`QmM/ bm#i`+iBQM X X X X X Ry9
*PLh1Lha
8XjXk J2i?Q/ k @ bT2+i`Qb+QTB+ TT`Q+?
_2bmHib M/ +QKT`BbQM i HQr@z X X X X X X
8X9XR :Htv MmK#2` /2MbBiv T`Q}H2 X X X
8X9Xk ai2HH` Kbb /2MbBiv T`Q}H2 X X X X X
8X8 h?2 2pQHpBM; bi2HH` Kbb /Bbi`B#miBQM X X X
8X8XR a2H2+iBQM 2z2+ib BM :*Gaa X X X X
8Xe amKK`v M/ *QM+HmbBQMb X X X X X X X X X
8X *QMbBbi2M+v +?2+Fb X X X X X X X X X X X X X
8X9
pBB
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
e h?2 lo ;Htv GmKBMQbBiv 6mM+iBQM i z 4j@8 7`QK
*6>h G2;+v am`p2v .22T }2H/b
eXR AMi`Q/m+iBQM X X X X X X X X X X X X X X X X X X X X X X X X X
eXk .i aKTH2b X X X X X X X X X X X X X X X X X X X X X X X
eXkXR h?2 *6>h G2;+v am`p2v .22T X X X X X X X X X X
eXkXk u@- g @- M/ r@/`QTQmi bKTH2b X X X X X X X X X X X
eXkXj _2/b?B7i /Bbi`B#miBQMb *QMiKBMiBQM 7`+iBQMb
eXj MHvbBb @ am`p2v +QKTH2i2M2bb X X X X X X X X X X X X X X
eXjXR JQ/2H ;HtB2b X X X X X X X X X X X X X X X X X X X
eXjXk 1//BM;iQM #Bb X X X X X X X X X X X X X X X X X X X
eXjXj aQm`+2 BMD2+iBQM M/ `2+Qp2`v X X X X X X X X X X X
eXjX9 1z2+iBp2 pQHmK2b X X X X X X X X X X X X X X X X X X
eX9 _2bmHib X X X X X X X X X X X X X X X X X X X X X X X X X X X X
eX9XR h?2 lo GmKBMQbBiv 6mM+iBQM i z 4j@8 X X X X X X
eX9Xk h?2 lo GmKBMQbBiv .2MbBiv M/ a6_ .2MbBiv X X
eX9Xj _Q#mbiM2bb Q7 Qm` `2bmHib X X X X X X X X X X X X X X
eX9X9 h?2 2pQHpBM; ;Htv TQTmHiBQM X X X X X X X X X X
eX8 *QKT`BbQM rBi? T`2pBQmb /2i2`KBMiBQMb X X X X X X X X X
eX8XR *QKT`BbQM i z 4j X X X X X X X X X X X X X X X X X
eX8Xk *QKT`BbQM i z 49 X X X X X X X X X X X X X X X X X
eX8Xj *QKT`BbQM i z 48 X X X X X X X X X X X X X X X X X
eX8X9 *QKT`BbQM Q7 i?2 a6_ /2MbBiv X X X X X X X X X X
eXe amKK`v *QM+HmbBQMb X X X X X X X X X X X X X X X X X X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
Rye
Ryd
Ryd
RRy
RRj
RRe
RRN
Rky
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
Rkj
Rk8
Rkd
Rkd
Rkd
Rk3
RkN
Rjy
RjR
Rjk
Rjj
Rj9
Rj9
RjN
R9R
R98
R98
R9e
R93
R8y
R8y
R8y
i?2
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
"B#HBQ;`T?v
R8j
L2/2`HM/b2 aK2MpiiBM;
Rej
*m``B+mHmK oBi2
ReN
LrQQ`/
RdR
*?Ti2`
R
AMi`Q/m+iBQM
h?2 lMBp2`b2 Bb 7b+BMiBM; TH+2- M/ Qm` T2`+2TiBQM Q7 Bi ?b +?M;2/ Qp2`
i?2 +2Mim`B2bX lMiBH MQ KQ`2 i?M k8 ?mKM ;2M2`iBQMb ;Q- i?2 ;2Q@+2Mi`B+
rQ`H/ KQ/2H- BM r?B+? i?2 1`i? Q++mTB2b i?2 +2Mi`2 Q7 i?2 lMBp2`b2- rb Qm`
}/m+BH T`2b+`BTiBQM Q7 i?2 +QbKQbX aBM+2 i?2M- `2pQHmiBQM`v BMbB;?ib ?p2 H2/
iQ p2`v /Bz2`2Mi TB+im`2- 2bT2+BHHv /m`BM; i?2 kyi? +2Mim`vX h?2 lMBp2`b2 Bb
pbiHv H`;2` i?M T`2pBQmbHv i?Qm;?i- M/ r2 ?mKMb /Q MQi b22K iQ Q++mTv
bT2+BH TH+2 BM Bi- MQ` `2 r2 K/2 Q7 i?2 KQbi +QKKQM 7Q`K Q7 Kii2`X
*`27mH bi`QMQKB+H Q#b2`piBQMb ?p2 #22M F2v BM b?TBM; Qm` mM/2`biM/BM;
Q7 i?2 +QbKQbX h?Bb i?2bBb T`2b2Mib K2bm`2K2Mib QM i?2 bi2HH` +QKTQM2Mi BM
i?2 KQbi KbbBp2 bi`m+im`2b 7Q`K2/ BM i?2 lMBp2`b2- rBi? i?2 TQi2MiBH iQ i2bi
M/ 7m`i?2` 2tTM/ +m``2Mi T?vbB+H KQ/2Hb M/ i?mb Qm` mM/2`biM/BM; Q7 i?2
+QbKQbX 6B`bi- BM i?Bb BMi`Q/m+iBQM- r2 bmKK`Bb2 i?2 b2[m2M+2 Q7 b+B2MiB}+
/Bb+Qp2`B2b i?i H2/ iQ i?2 biM/`/ KQ/2H Q7 +QbKQHQ;v- M/ Hv Qmi QT2M
[m2biBQMb r2 `2 +m``2MiHv 7+BM; BM i?2 }2H/ Q7 2ti`;H+iB+ bi`QMQKvX
.2i2`KBMBM; i?2 ;2- +QKTQbBiBQM- M/ 2pQHmiBQM Q7 i?2 lMBp2`b2 b r?QH2
?p2 #22M +2Mi`H ;QHb BM i?2 bim/v Q7 +QbKQHQ;vX h?2b2 [m2biBQMb ?p2 7b@
+BMi2/ ?mKM KBM/b 7Q` +2Mim`B2b- M/ BM i?2 Rei? +2Mim`v i?2 `2pQHmiBQM`v
>2HBQ@+2Mi`B+ KQ/2H rb 7Q`KmHi2/ #v UKQM; Qi?2`bV LB+QHmb *QT2`MB+mb
M/ :HBH2Q :HBH2BX AM i?Bb KQ/2H- i?2 THM2ib r2`2 /2b+`B#2/ iQ Q`#Bi bi@
iBQM`v amM BM i?2 +2Mi`2 Q7 i?2 aQH` bvbi2K- M/ i?Bb H2/ iQ M 2bB2` M/
KQ`2 2H2;Mi Ki?2KiB+H /2b+`BTiBQM Q7 i?2 KQp2K2Mi Q7 i?2 Qi?2` THM2ibX
q2 MQr FMQr i?i i?2 amM ?b T`QT2`iB2b bBKBH` iQ Qi?2` bi`b BM i?2 }`K@
K2Mi- Hi?Qm;? i?2B` /BbiM+2b iQ mb `2 p2`v /Bz2`2MiX ii2KTib iQ /2b+`B#2
i?2 TQbBiBQM Q7 i?2 amM rBi?BM i?Bb pbiM2bb Q7 bi`b H2/ iQ KQ/2H +HH2/ i?2
ETi2vM lMBp2`b2- BM r?B+? Qm` ;Htv- i?2 JBHFv qv- Bb M BbHM/ lMBp2`b2
R
k
*>Sh1_ RX ALh_P.l*hAPL
Q7 #Qmi 9y-yyy HB;?i v2`b BM bBx2 UETi2vM RNkkVX q?2`2b bi`QMQK2`b BM
i?2 RNkyb ;`22/ i?i i?2 amM /Q2b MQi Q++mTv i?2 +2Mi`2 Q7 i?2 JBHFv qvi?2 [m2biBQM r?2i?2` i?2 M2#mH2 `2 Q7 ;H+iB+ Mim`2 rb iQTB+ Q7 /2#i2X
LQi Km+? Hi2`- Q#b2`piBQMb #v 1/rBM >m##H2 U>m##H2 RNkeV b?Qr2/ i?i
KQbi M2#mH2 `2 ;HtB2b #2vQM/ i?2 JBHFv qv r?B+? KQp2 rv 7`QK mbM/ i?Bb b2iiH2/ i?2 /2#i2X h?2 p2HQ+BiB2b UQ` `2/b?B7iV Q7 i?2b2 ;HtB2b r2`2
7QmM/ iQ #2 T`QTQ`iBQMH iQ i?2B` /BbiM+2b U>m##H2 >mKbQM RNjRVX h?Bb
`2bmHi +K2 b #B; bm`T`Bb2- bBM+2 Bi BKTHB2b i?i i?2 lMBp2`b2 Bb MQi biiB+
#mi 2tTM/BM; Qp2` iBK2X
:HtB2b `2 MQi /Bbi`B#mi2/ `M/QKHv BM bT+2- #mi `2 +Hmbi2`2/ QM `M;2 Q7 b+H2b bm+? b ;Htv ;`QmTb- Q` 2p2M H`;2` ;;HQK2`iBQMb +HH2/
+Hmbi2`bX q?2M 6`Bix wrB+Fv bim/B2/ i?2 KQp2K2Mi Q7 ;HtB2b BM i?2 *QK
+Hmbi2`- ?2 7QmM/ i?i i?2B` `2HiBp2 p2HQ+BiB2b r2`2 bB;MB}+MiHv ?B;?2` i?M
r?i rb 2tT2+i2/ 7`QK i?2 Kii2` Q#b2`p2/ BM i?Bb +Hmbi2` UwrB+Fv RNjjVX
h?Bb rb i?2 }`bi BM/B+iBQM Q7 Kii2` +QKTQM2Mi r2 MQr +HH Ǵ/`F Kii2`Ǵ ivT2 Q7 Kii2` i?i /Q2b MQi 2KBi HB;?i #mi /Q2b BMi2`+i i?`Qm;? ;`pBivX
J2bm`2K2Mib Q7 i?2 `QiiBQM p2HQ+Biv Q7 bi`b BM bTB`H ;HtB2b #v _m#BM 6Q`/ URNdyV HbQ b?Qr2/ i?i KQbi Q7 i?2 ;`pBiiBQMH Kii2` BM ;HtB2b +QmH/
MQi #2 Q#b2`p2/- T`QpB/BM; MQi?2` bB;M Q7 /`F Kii2`X JQ/2`M 2biBKi2b
bm;;2bi i?i HH i?2 2H2K2Mib +Qp2`2/ #v i?2 T2`BQ/B+ bvbi2K i?i r2 r2`2
im;?i i b+?QQH +QMbiBimi2 H2bb i?M kyW Q7 i?2 iQiH Kii2` +QMi2Mi Q7 i?2
lMBp2`b2 U"2MM2ii 2i HX kyRjV- M/ i?i i?2 `2bi Bb BM M mMFMQrM 7Q`K Q7
/`F Kii2`X
h?2 /Bb+Qp2`v i?i i?2 lMBp2`b2 QM H`;2 b+H2b Bb 2tTM/BM; KQiBpi2/ i?2
"B; "M; KQ/2H- TB+im`2 BM r?B+? i?2 lMBp2`b2 Q`B;BMi2/ 7`QK bBM;mH`Biv
BM bT+2 M/ iBK2 M/ ?b #22M 2tTM/BM; bBM+2X q?2`2b HQ;B+H i?Qm;?i
Bb i?i i?2 2tTMbBQM bT22/ Bb /2+`2bBM; /m2 iQ ;`pBiv- bim/v Q7 /BbiMi
bmT2`MQp2 BM i?2 Hi2 RNNyb H2/ iQ bm`T`BbBM; BMbB;?iX h?2 2tTMbBQM Q7 i?2
lMBp2`b2 b22Kb iQ #2 ++2H2`iBM; U_B2bb 2i HX RNN3c S2`HKmii2` 2i HX RNNNVH2/BM; iQ i?2 2tQiB+ i2`K Q7 /`F 2M2`;vX h?Bb 7Q`K Q7 2M2`;v Kv /2b+`B#2 i?2
p+mmK 2M2`;v /2MbBiv Q7 bT+2- M/ rb }`bi ?vTQi?2bBx2/ #v H#2`i 1BMbi2BM
r?Q 2tT`2bb2/ Bi b i?2 +QbKQHQ;B+H +QMbiMi ΛX HiQ;2i?2`- MQ +QbKQHQ;B+H
T`Q#2 ?b #22M b +QMbi`BMBM; Q7 Qm` pB2r Q7 i?2 +QbKQb b i?2 Q#b2`piBQMb Q7
i?2 *QbKB+ JB+`Qrp2 "+F;`QmM/ U*J"V U:KQr RN93c >m q?Bi2 RNNec
"2MM2ii 2i HX kyRjVX h?2 *J" Bb i?2 7i2`;HQr Q7 i?2 "B; "M; `2p2HBM; bKHH
UdT /T ≈ 10−5 V i2KT2`im`2 /Bz2`2M+2b Q7 i?2 ∼ 380 000 v2` QH/ lMBp2`b2X
h?2 "B; "M; KQ/2H- r?B+? ?b #22M iB;?iHv +QMbi`BM2/ #v +QK#BMBM;
HH +QbKQHQ;B+H T`Q#2b- KF2b +QM+`2i2 T`2/B+iBQMb M/ i?mb 7` i?Bb KQ/2H
?b Tbb2/ 2p2`v Q#b2`piBQMH i2biX >Qr2p2`- ;Bp2M i?i /`F Kii2` M/
/`F 2M2`;v KF2 mT i?2 /QKBMMi 2M2`;v +QMi2Mi Q7 i?2 lMBp2`b2 BM i?Bb
KQ/2H- bm#biMiBH Kvbi2`B2b `2KBM `2;`/BM; i?2 Mim`2 Q7 i?2b2 +QKTQM2MibX
b HQM; b i?2B` 2tBbi2M+2 Bb QMHv BM72``2/ BM/B`2+iHv- Hi2`MiBp2 +QbKQHQ;B+H
i?2Q`B2b `2KBM iQ #2 +QMbB/2`2/X
RXkX ah_l*hl_1 6P_JhAPL AL h>1 lLAo1_a1
j
++Q`/BM; iQ i?2 +QbKQHQ;B+H biM/`/ KQ/2H- Dmbi 7i2` i?2 "B; "M;- r?B+?
?TT2M2/ #Qmi RjX3 :v` ;Q- i?2 Kii2` BM i?2 lMBp2`b2 rb `2K`F#Hv
?QKQ;2M2QmbHv /Bbi`B#mi2/X .m2 iQ i?2 7Q`+2 Q7 ;`pBiv- bKHH BMBiBH T2`im`@
#iBQMb BM i?2 T`BKQ`/BH /2MbBiv }2H/ ?p2 #22M `2bTQMbB#H2 7Q` i?2 `B+? /Bp2`@
bBiv Q7 bi`m+im`2b r2 Q#b2`p2 iQ/vX q?2`2b i?2 T`QiQMb M/ 2H2+i`QMb BM i?2
vQmM; lMBp2`b2 r2`2 bmTTQ`i2/ #v i?2`KH T?QiQMb- i?2 /`F Kii2` rb #H2
iQ +QHHTb2 2`HB2`- M/ i?Bb ++2H2`i2/ i?2 7Q`KiBQM Q7 bi`m+im`2bX :Bp2M i?2
T`2bmK2/ +QHHBbBQMH2bb Mim`2 Q7 /`F Kii2`- i?2 bi`m+im`2 7Q`KiBQM T`Q+2bb
+M MQr #2 bim/B2/ mbBM; H`;2 L@#Q/v bBKmHiBQMb U2X;X aT`BM;2H 2i HX kyy8VX
Hi?Qm;? i?2b2 bBKmHiBQMb /Q MQi BM+Hm/2 #`vQMB+ T?vbB+b- i?2v KF2
T`2/B+iBQMb QM i?2 Kii2` /Bbi`B#miBQM i?i ?p2 bm++2bb7mHHv Tbb2/ bQK2 #@
bB+ Q#b2`piBQMH i2bibX 6Q` 2tKTH2- i?2 k@/2;`22@6B2H/ :Htv _2/b?B7i am`@
p2v U*QHH2bb 2i HX kyyRV ?b b?QrM r2#@HBF2 bi`m+im`2 BM i?2 /Bbi`B#miBQM Q7
;HtB2b i?i Bb bBKBH` iQ i?2 /Bbi`B#miBQM Q7 /`F Kii2` ?HQ2b BM L@#Q/v
bBKmHiBQMbX HbQ- Dmbi HBF2 BM i?2 Ki?2KiB+H KQ/2H BMi`Q/m+2/ #v S`2bb
a+?2+?i2` URNd9V- i?2 bBKmHiBQMb bm;;2bi i?i bKHH ;`pBiiBQMHHv #QmM/
bi`m+im`2b 7Q`K }`bi- r?B+? bm#b2[m2MiHv K2`;2 iQ 7Q`K ;HtB2b- M/ H`;2`
2Mb2K#H2b bm+? b ;`QmTb M/ +Hmbi2`b Q7 ;HtB2bX h?Bb H2/b iQ ?HQ Kbb
7mM+iBQM i?i Bb /QKBMi2/ #v HQr@Kbb ?HQ2b U2X;X hBMF2` 2i HX kyy3VX h?2
HmKBMQbBiv /Bbi`B#miBQM Q7 ;HtB2b Ua+?2+?i2` RNdeV ?b bBKBH` b?T2- H@
i?Qm;? #`vQMB+ T?vbB+b THv /QKBMMi `QH2 BM /2i2`KBMBM; i?2 2t+i b?T2
Q7 i?2 HmKBMQbBiv UQ` bi2HH` KbbV /Bbi`B#miBQMX h?2 `/BH /2MbBiv T`Q}H2 Q7
/`F Kii2` ?HQ2b Bb 7QmM/ iQ #2 /2b+`B#2/ #v L6q T`Q}H2b ULp``Q 2i HX
RNNdV- bBKBH` iQ r?i i?2 /Bbi`B#miBQM Q7 ;HtB2b BM ;`QmTb M/ +Hmbi2`b Bb
Q#b2`p2/ iQ #2 UGBM 2i HX kyy9c JmxxBM 2i HX kyydc "m/xvMbFB 2i HX kyRkVX
Hi?Qm;? i?2b2 bBKmHiBQMb ;Bp2 `2bmHib i?i [mHBiiBp2Hv ;`22 rBi? i?2 Q#@
b2`piBQMb- M BKTQ`iMi ;QH BM 2ti`;H+iB+ bi`QMQKv iQ/v Bb iQ T`QpB/2
+QKTH2i2 mM/2`biM/BM; ?Qr #`vQMB+ bi`m+im`2b 7Q`K BM i?Bb /`F@Kii2`
/QKBMi2/ lMBp2`b2X
Hi?Qm;? i?2 KDQ`Biv Q7 i?2 #`vQMB+ Kbb BM i?2 lMBp2`b2 Bb BM i?2 7Q`K Q7
;b- i?2 T`2b2M+2 Q7 bi`b THvb M BKTQ`iMi `QH2 BM i?2 Qp2`HH +v+H2 Q7 #`vQMbX
h?`Qm;? bi2HH` rBM/b M/ bmT2`MQp 2tTHQbBQMb- i?2 ;b2Qmb K2/BmK Bb 2M@
`B+?2/ #v 2H2K2Mib ?2pB2` i?M ?v/`Q;2M M/ ?2HBmKX h?2b2 ?2pv 2H2K2Mib
?p2 #22M BKTQ`iMi BM i?2 7Q`KiBQM Q7 i?2 `Q+Fv THM2ib BM Qm` bQH` bvb@
i2K- M/ 2p2MimHHv T`QpB/2/ i?2 BM;`2/B2Mib 7Q` HB72 QM 1`i?X hQ #2 #H2 iQ
+QMbi`BM i?2 #mBH/@mT Q7 i?2 bi2HH` +QKTQM2Mi BM i?2 lMBp2`b2- bi2HH` Kbb
K2bm`2K2Mib M22/ iQ #2 [mMiB}2/X
9
*>Sh1_ RX ALh_P.l*hAPL
AM i?2 JBHFv qv- Q#b2`piBQMb Q7 #BM`v bi`b ?p2 #22M mb2/ iQ K2@
bm`2 i?2 Kbb2b Q7 bi`b rBi? /Bz2`2Mi bT2+i`H ivT2bX aBKTH2 b+HBM; `2HiBQMb
#2ir22M i?2 Kbb- i2KT2`im`2- HmKBMQbBiv- M/ HB72iBK2b Q7 bi`b ?p2 #22M
Q#iBM2/X 6Q` bi`b `QmM/ bQH` Kbb- i?2 HmKBMQbBiv b+H2b rBi? Kbb
`Qm;?Hv b L ∝ M 4 X AM ivTB+H bi2HH` TQTmHiBQMb- HQr@Kbb bi`b `2 bm#@
biMiBHHv KQ`2 #mM/Mi i?M ?B;?@Kbb bi`bX q?2`2b i?2 iQiH Kbb Q7 bi2HH` TQTmHiBQM Bb i?mb /QKBMi2/ #v i?2 HQr@Kbb bi`b- i?2 iQiH 2M2`;v
QmiTmi Bb /QKBMi2/ #v ?B;?@Kbb bi`bX hQ `2Hi2 i?2 HmKBMQbBiv Q7 bi2HH`
TQTmHiBQM iQ Bib iQiH bi2HH` Kbb- r2 M22/ iQ FMQr Bib Kbb /Bbi`B#miBQM Ui?2
Jbb 6mM+iBQM- J6VX >Qr2p2`- 2bT2+BHHv 7Q` /BbiMi ;HtB2b i?2 J6 Bb MQi
/B`2+iHv Q#b2`p#H2- M/ i?mb mMFMQrM iQ mbX
:Bp2M i?i i?2 HB72iBK2b Q7 ?B;?@Kbb bi`b `2 `2HiBp2Hv b?Q`i UT ∝ M −3 Vi?2 J6 Q7 bi2HH` TQTmHiBQM 2pQHp2b rBi? ;2X A7 r2 +QMbB/2` bi2HH` TQTm@
HiBQM Dmbi 7i2` Bi 7Q`K2/ UBX2X i x2`Q@;2V- r2 `272` iQ i?2 J6 b i?2 AMBiBH
J6 UAJ6VX +`BiB+H bbmKTiBQM BM ivTB+H bim/B2b i?i BMpQHp2 bi2HH` Kbb
K2bm`2K2Mib Bb i?i i?2 AJ6 ?b mMBp2`bH b?T2 U?Qr2p2` b22 "biBM
2i HX UkyRyV 7Q` `2pB2rVX aHT2i2` URN88V 2biBKi2/ i?i i?2 AJ6 +M #2
dN
TT`QtBKi2/ #v TQr2`@Hr dM
∝ M −α - r?2`2 α Bb ivTB+HHv ∼ 2.35X _2@
+2Mi bim/B2b UJBHH2` a+HQ RNdNc E`QmT kyyRc *?#`B2` kyyjV ?p2 bm;;2bi2/
`2}M2K2Mib Q7 i?Bb bBKTH2 TQr2`@Hr- H2/BM; iQ /Bz2`2Mi `2HiBQMb #2ir22M i?2
HmKBMQbBiv M/ bi2HH` Kbb Q7 x2`Q@;2 bi2HH` TQTmHiBQMX b Q7 iQ/v- i?2
b?T2 Q7 i?2 AJ6 i HQr Kbb2b Bb i?2 KBM bvbi2KiB+ mM+2`iBMiv QM bi2HH`
Kbb 2biBKi2b Q7 ;HtB2bX
aBM+2 ?B;?@Kbb bi`b `2 p2`v HmKBMQmb BM i?2 mHi`pBQH2i- i?2 bT2+i`H
2M2`;v /Bbi`B#miBQM Ua1.V Q7 bi2HH` TQTmHiBQM #2+QK2b `2//2` b i?2b2 bi`b
+2b2 iQ 2tBbiX h?2 ;2 Q7 bi2HH` TQTmHiBQM +M #2 2biBKi2/ #v +QMbB/2`BM;
Bib 7mHH a1.- M/ QM+2 i?2 ;2 Bb FMQrM r2 +M 2biBKi2 i?2 +m``2Mi J6 7`QK
i?2 bbmK2/ AJ6X h?2 Kbb@iQ@HB;?i `iBQ UJfGV Q7 ;Htv Bb 2biBKi2/ 7`QK
i?2 J6- M/ i?mb bi2HH` Kbb +M #2 2biBKi2/ 7Q` ;Bp2M HmKBMQbBivX
7m`i?2` +QKTHB+iBQM 7Q` bi2HH` Kbb 2biBKi2b Bb i?i i?2 a1. Q7 ;Htv Bb ivTB+HHv MQi r2HH@/2b+`B#2/ #v bBM;H2@;2 bi2HH` TQTmHiBQMX h?2
bi`b Kv ?p2 7Q`K2/ 7QHHQrBM; ;2M2`H ai` 6Q`KiBQM >BbiQ`v Ua6>VH2/BM; iQ KQ`2 +QKTHB+i2/ J6X HbQ- i?2 T`2b2M+2 Q7 /mbi +M `2//2M i?2
a1.- KBKB+FBM; i?2 2z2+i Q7 ?B;?2` ;2 U2X;X qQ`i?2v RNN9VX :Bp2M i?i i?2
a1. Q7 ;Htv Bb Q#b2`p2/- i?2 a6> M/ /mbi@ii2MmiBQM Q7 ;Htv +M
#2 2biBKi2/ mbBM; ivTB+H a1.@}iiBM; T`Q;`K bm+? b 6ah UE`B2F 2i HX
kyyNVX
"v K2bm`BM; T`QT2`iB2b Q7 ;HtB2b bm+? b i?2B` bi2HH` Kbb2b- +QHQm`b M/
KQ`T?QHQ;B2b- i?2v +M `Qm;?Hv #2 /BpB/2/ BM irQ /BbiBM+i ivT2b- H#2HH2/ 2`Hv@
ivT2b M/ Hi2@ivT2b 7Q` ?BbiQ`B+H `2bQMbX Gi2@ivT2 UXFXX bi`@7Q`KBM;V
RX8X :GsA1a AL >A:>@.1LaAhu 1LoA_PLJ1Lha
8
;HtB2b ;2M2`HHv ?p2 +2Mi`H +QM+2Mi`iBQM Q7 QH/ bi`b- M/ M 2ti2M/2/
/BbF BM r?B+? bi`b `2 7Q`KBM;X 1`Hv@ivT2 UXFXX [mB2b+2MiV ;HtB2b `2 `2/@
/2` bBM+2 i?2v 72im`2 MQ UQ` p2`v HBiiH2V QM@;QBM; bi` 7Q`KiBQM- M/ ;2M2`HHv
?p2 2HHBTbQB/H b?T2b +QKT`2/ iQ i?2 bTB`H Mim`2 Q7 Hi2@ivT2 ;HtB2bX .m2
iQ i?2 /pM+2 Q7 KQ/2`M i2H2b+QT2b M/ BMbi`mK2Mib- ;Htv bim/B2b ?p2 #22M
2tTM/2/ Qp2` i?2 Hbi /2+/2b- M/ K2bm`2K2Mib Q7 i?2 GmKBMQbBiv 6mM+iBQM
UG6V M/ ai2HH` Jbb 6mM+iBQM UaJ6V U2X;X "2HH 2i HX kyyjc Sû`2x@:QMx€H2x
2i HX kyy3c AH#2`i 2i HX kyRyV ?p2 #22M mb2/ b F2v Q#b2`p#H2b Q7 TQTmH@
iBQM Q7 ;HtB2bX h?2 G6 M/ aJ6 /2b+`B#2 i?2 MmK#2` /2MbBiv Q7 ;HtB2b b
7mM+iBQM Q7 i?2B` 2biBKi2/ HmKBMQbBiv M/ bi2HH` Kbb2b- `2bT2+iBp2Hv- M/
`2 ;2M2`HHv T`K2i2`Bx2/ mbBM; i?2 a+?2+?i2` 7mM+iBQM Ua+?2+?i2` RNdeVX
"v +QKT`BM; i?2 ?HQ Kbb 7mM+iBQM rBi? i?2 aJ6- r2 ?p2 H2`M2/ i?i
/`F Kii2` ?HQ2b Q7 /Bz2`2Mi Kbb2b ?p2 /Bz2`2Mi bi2HH` Kbb 7`+iBQMb U2X;X
"2?`QQxB 2i HX kyRjVX h?2 BM2{+B2M+v Q7 HQr@Kbb ?HQ2b BM 7Q`KBM; bi`b Bb
TQbbB#Hv /m2 iQ bmT2`MQp 722/#+F U17bii?BQm kyyyc .HH o2++?B a+?v2
kyy3V- bi2HH` rBM/b- M/ i?2 T`2b2M+2 Q7 T?QiQ@BQMBxBM; #+F;`QmM/ U"2MbQM
2i HX kyykVX AM ?B;?@Kbb ?HQ2b- :L 722/#+F Bb 2tT2+i2/ iQ THv `QH2 BM
`2;mHiBM; i?2 7Q`KiBQM Q7 bi`b Ua+?rBMbFB 2i HX kyydc 6#BM kyRkVX
a2T`iBM; i?2 aJ6 #2ir22M Hi2@ivT2 M/ 2`Hv@ivT2 ;HtB2b- Q#b2`p@
iBQMb ?p2 b?QrM i?i i?2 KQbi KbbBp2 ;HtB2b `2 ;2M2`HHv 2`Hv@ivT2X Ai
Bb HbQ b?QrM i?i i?2B` #mM/M+2 `Bb2b iQr`/b i?2 T`2b2Mi /v +QKT`2/
iQ Hi2@ivT2 ;HtB2bX *QMi``v iQ r?i i?2B` MK2b Kv bm;;2bi- Hi2@ivT2
;HtB2b `2 i?mb `2;`/2/ b i?2 T`Q;2MBiQ`b Q7 2`Hv@ivT2 ;HtB2bX _2+2Mi
bim/B2b UJmxxBM 2i HX kyRjV ?p2 K2bm`2/ M/ +QKT`2/ i?2 mMBp2`bH aJ6
Q7 i?2 irQ ;Htv ivT2b mT iQ z ∼ 4- M/ bm+? K2bm`2K2Mib `2 7mM/K2MiH
Q#b2`p#H2b 7Q` +QMbi`BMBM; i?2 bi`@7Q`KiBQM 2{+B2M+v b 7mM+iBQM Q7 ?HQ
Kbb M/ `2/b?B7i BM T?vbB+H KQ/2Hb U2X;X a+?v2 2i HX kyRyc >2M`B[m2b 2i HX
kyRkc q2BMKMM 2i HX kyRkc *2M kyR9VX `2HiBp2Hv bBKTH2 TT`Q+? iQ i?Bb
Bb i?2 #mM/M+2 Ki+?BM; i2+?MB[m2 U2X;X "2?`QQxB 2i HX kyRyc JQbi2` 2i HX
kyRyc "2?`QQxB 2i HX kyRjc JQbi2` 2i HX kyRjV- BM r?B+? Q#b2`p#H2b bm+? b
i?2 aJ6 M/ +QbKB+ bi` 7Q`KiBQM ?BbiQ`v `2 /B`2+iHv +QK#BM2/ rBi? K2`;2`
i`22b 7`QK /`F Kii2` bBKmHiBQMb iQ T`QpB/2 +QMbi`BMib QM i?2 T`Q+2bb2b i?i
#mBH/ mT i?2 bi2HH` Kbb BM i?2 +2Mi`H ;HtB2b Q7 /`F Kii2` ?HQ2bX
Ai ?b #22M FMQrM 7Q` HQM; iBK2 MQr i?i i?2 T`QT2`iB2b Q7 ;HtB2b /Q
MQi QMHv /2T2M/ QM i?2 Kbb Q7 i?2 ?HQ BM r?B+? i?2v HBp2- #mi HbQ +Q`@
`2Hi2 rBi? i?2 /2MbBiv Q7 i?2B` 2MpB`QMK2Mi U2X;X .`2bbH2` RN3yVX :HtB2b
BM +`Qr/2/ `2;BQMb ;2M2`HHv b?Qr ?B;?2` [mB2b+2Mi 7`+iBQM i?M ;HtB2b
BM bT`b2 2MpB`QMK2MibX a2p2`H T?vbB+H K2+?MBbKb ?p2 #22M T`QTQb2/ iQ
2tTHBM i?2b2 /Bz2`2M+2b- #mi +QMb2Mbmb Bb biBHH KBbbBM;X h?2 aHQM .B;BiH
aFv am`p2v Ua.aaV ?b HHQr2/ bm#biMiBH T`Q;`2bb iQ #2 K/2 BM [mMiB@
e
*>Sh1_ RX ALh_P.l*hAPL
7vBM; i?2 `2HiBQMb?BT #2ir22M ;Htv 2MpB`QMK2Mi M/ ai` 6Q`KiBQM _i2
Ua6_V- KQ`T?QHQ;v- bi2HH` Kbb- M/ K2iHHB+Biv BM i?2 HQ+H lMBp2`b2 U2X;X
EmzKMM 2i HX kyy9c "H/`v 2i HX kyyec S2M; 2i HX kyRyVX >Qr2p2`- bm`p2vb
i?i ?p2 T`QpB/2/ BMbB;?i BMiQ i?2 7`@rv lMBp2`b2 U2X;X *PaJPac a+QpBHH2
2i HX kyydV ivTB+HHv H+F i?2 pQHmK2 iQ bim/v i?2 KQbi 2ti`2K2 Qp2`@/2MbBiB2b
UBX2X ;Htv +Hmbi2`bV i i?2b2 `2/b?B7ib bBM+2 i?2v Q#b2`p2 `2HiBp2Hv bKHH `2b
QM i?2 bFvX
*Hmbi2`b Q7 ;HtB2b `2 i?2 KQbi KbbBp2 ;`pBiiBQMHHv #QmM/ bi`m+im`2b
BM i?2 lMBp2`b2- r?B+? ivTB+HHv +QMiBM ∼ 1000 ;HtB2b M/ ?p2 iQiH Kbb
Q7 ! 1014 J" X :Bp2M i?2B` 2ti`2K2 Qp2`@/2MbBiB2b i Mv 2TQ+?- r2 2tT2+i 2M@
pB`QMK2MiH 2z2+ib QM i?2 2pQHmiBQM Q7 ;HtB2b iQ #2 KQbi T`QKBM2Mi BM i?2b2
bvbi2KbX hQ b2T`i2 i?2b2 2MpB`QMK2MiH 2z2+ib 7`QK ;2M2`H `2/b?B7i 2pQHm@
iBQM- ;Htv +Hmbi2`b HbQ ?p2 iQ #2 bim/B2/ i ?B;?2` `2/b?B7ibX AM bm`p2vb i?i
+Qp2` H`;2 }2H/@Q7@pB2r- i?2b2 bvbi2Kb +M #2 /2i2+i2/ #v i?2B` ?Qi s@`v
2KBiiBM; ;b U2X;X _QbiV- amMv2p@w2HǶ/QpB+? /2+`2K2Mi U2X;X aSh- SHM+FVQ` ;Htv Qp2`@/2MbBiv U2X;X aT_*aV- M/ `2 i?2M bT2+B}+HHv i`;2i2/ 7Q`
7QHHQr@mT Q#b2`piBQMbX
LmK#2` /2MbBiv K2bm`2K2Mib Q7 KbbBp2 ?HQ2b b 7mM+iBQM Q7 `2/b?B7i
`2 HbQ mb2/ iQ +QMbi`BM +QbKQHQ;B+H T`K2i2`b- b i?2b2 ?HQ2b `2 b2MbB@
iBp2 T`Q#2 Q7 i?2 ;`Qri? Q7 bi`m+im`2bX h?2 irQ TTHB+iBQMb Q7 +QbKQHQ;v M/
;Htv 2pQHmiBQM `2 BMiBKi2Hv `2Hi2/- bBM+2 i?2 T`2b2M+2 Q7 #`vQMb +M ?p2
K2bm`#H2 2z2+i QM i?2 b?T2 Q7 i?2 Kii2` TQr2` bT2+i`mK M/ i?2 +Hmbi2`
Kbb 7mM+iBQM- M/ i?2`27Q`2 QM i?2 /2i2`KBM2/ +QbKQHQ;B+H T`K2i2`b U2X;X
pM .H2M 2i HX kyRRc *mbrQ`i? 2i HX kyRjVX AM Q`/2` iQ BMi2`T`2i #mM/M+2
K2bm`2K2Mib Q7 +Hmbi2`b BM +QbKQHQ;B+H +QMi2ti- +QKT`BbQM rBi? }iiBM;
7mM+iBQMb Q#iBM2/ 7`QK bBKmHiBQMb Bb `2[mB`2/ U2X;X hBMF2` 2i HX kyy3VX aQ
7`- i?2b2 bBKmHiBQMb `2 #b2/ QM L@#Q/v +Q/2b- M/ i?mb /Q MQi BM+Hm/2
#`vQMB+ T?vbB+bX AM M 2` BM r?B+? r2 BK iQ /Q T`2+BbBQM +QbKQHQ;v- i?2
BM~m2M+2 Q7 #`vQMb +M MQ HQM;2` #2 B;MQ`2/ BM bBKmHiBQMb M/ i?2B` bb2K#Hv
M22/b iQ #2 #2ii2` +QMbi`BM2/ #v Q#b2`piBQMbX
AM i?Bb i?2bBb- r2 bim/v i?2 /Bbi`B#miBQM Q7 ;HtB2b BM ;Htv +Hmbi2`b Qp2`
+QbKB+ iBK2X "Qi? i?2 aJ6 M/ i?2 bTiBH /Bbi`B#miBQM Q7 ;HtB2b T`QpB/2
BMbB;?ib BM i?2 +QMM2+iBQM #2ir22M /`F Kii2` M/ i?2 bi2HH` +QKTQM2Mi- M/
i?2 i`Mb7Q`KiBQM Q7 ;HtB2b BM ?B;?@/2MbBiv 2MpB`QMK2MibX
z∼1
AM Q`/2` iQ bb2bb i?2 iBK2 2pQHmiBQM Q7 ;HtB2b BM ?B;?@/2MbBiv 2MpB`QMK2Mibr2 bim/v Ry +Hmbi2`b Q#b2`p2/ BM i?2 /BbiMi lMBp2`b2 BM *?Ti2`b k@9- r?2M
i?2 lMBp2`b2 rb #Qmi ?H7 Bib +m``2Mi ;2X h?Bb +Hmbi2` bKTH2 Bb /`rM
7`QK i?2 :2KBMB *Hmbi2` bi`QT?vbB+b aT2+i`Qb+QTB+ am`p2v U:*GaaV- r?B+?
RXeX h>Aa h>1aAa
d
+QMbBbib Q7 Ry Q7 i?2 `B+?2bi +Hmbi2`b BM i?2 `2/b?B7i `M;2 0.86 < z < 1.34
b2H2+i2/ 7`QK i?2 9k b[m`2 /2;`22 aT_*a bm`p2v UJmxxBM 2i HX kyyNc qBHbQM
2i HX kyyNc .2K`+Q 2i HX kyRyVX
AM *?Ti2` k- r2 T`2b2Mi i?2 ;Htv aJ6 Q7 i?2 :*Gaa +Hmbi2`b- M/
+QKT`2 Bi /B`2+iHv iQ i?2 aJ6 Q7 }2H/ ;HtB2b BM i?2 bK2 `2/b?B7i `M;2
iQ bim/v i?2 2z2+i Q7 2MpB`QMK2Mi QM i?Bb 7mM/K2MiH Q#b2`p#H2 i z ∼ 1X
AMi2`2biBM;Hv- r?2M r2 /BbiBM;mBb? T?QiQK2i`B+HHv #2ir22M bi`@7Q`KBM; M/
[mB2b+2Mi ;HtB2b- r2 }M/ i?i i?2 #2bi@}iiBM; a+?2+?i2` T`K2i2`b α M/
M ∗ `2 bBKBH` rBi?BM i?2 mM+2`iBMiB2b 7Q` i?2b2 ;Htv ivT2b rBi?BM i?2 /B7@
72`2Mi 2MpB`QMK2MibX >Qr2p2`- i?2`2 Bb bB;MB}+Mi /Bz2`2M+2 BM i?2 b?T2 M/
MQ`KHBbiBQM Q7 i?2 iQiH aJ6 #2ir22M i?2 +Hmbi2`b M/ i?2 }2H/ bKTH2X h?Bb
/Bz2`2M+2 BM i?2 iQiH aJ6 Bb T`BK`BHv `2~2+iBQM Q7 i?2 BM+`2b2/ 7`+iBQM
Q7 [mB2b+2Mi ;HtB2b BM ?B;?@/2MbBiv 2MpB`QMK2MibX i z ∼ 1 i?2 +Hmbi2`b `2
H`2/v +QKTH2i2Hv /QKBMi2/ #v [mB2b+2Mi ;HtB2bX q2 2KTHQv M/ 2pHmi2
[m2M+?BM; KQ/2H #b2/ QM S2M; 2i HX UkyRyV- r?B+? b2T`i2b i?2 [m2M+?BM;
Q7 ;HtB2b #v irQ /BbiBM+i i`+Fb /m##2/ Kbb@[m2M+?BM; M/ 2MpB`QMK2MiH
[m2M+?BM;- M/ }M/ i?i i?Bb KQ/2H ;Bp2b `2bQM#H2 /2b+`BTiBQM Q7 i?2 /iX
h?2 [m2M+?BM; KQ/2H T`2/B+ib i?2 T`2b2M+2 Q7 ;HtB2b i?i ?p2 `2+2MiHv
#22M #`mTiHv [m2M+?2/X AM *?Ti2` j- r2 7QHHQr i?Bb T`2/B+iBQM #v bim/vBM;
i?2 i`Mb7Q`KiBQM Q7 ;HtB2b i z ∼ 1 BM i?2 :*Gaa +Hmbi2`bX lbBM; i?2
/22T bT2+i`Qb+QTB+ /i pBH#H2 7Q` :*Gaa- r2 B/2MiB7v TQTmHiBQM Q7
TQbi@bi`#m`bi ;HtB2b rBi? MQ QM@;QBM; bi`@7Q`KiBQM- #mi rBi? bT2+i` biBHH
BM/B+iBp2 Q7 vQmM; bi2HH` TQTmHiBQMbX h?2 7+i i?i i?Bb ivT2 Q7 ;Htv Bb
KQ`2 #mM/Mi BM i?2 +Hmbi2`b i?M BM i?2 }2H/ UJmxxBM 2i HX kyRkV bm;;2bib
i?i i?2 `2bTQMbB#H2 T`Q+2bb /2T2M/b QM 2MpB`QMK2MiX q2 }M/ i?i i?2 TQbi@
bi`#m`bi ;HtB2b ?p2 /BbiBM+iBp2 /Bbi`B#miBQM BM T`QD2+i2/ p2HQ+Biv pbX TQ@
bBiBQM T?b2 bT+2- TQbbB#Hv `2Hi2/ iQ [m2M+?BM; T`Q+2bb2b i?i `2 /2T2M/2Mi
QM 2MpB`QMK2MiX lbBM; b2p2`H xQQK bBKmHiBQMb Q7 +Hmbi2`b- r2 }M/ i?i i?Bb
+Q?2`2Mi /Bbi`B#miBQM Q7 TQbi@bi`#m`bi ;HtB2b +M #2 `2bQM#Hv r2HH `2T`Q@
/m+2/ mbBM; bBKTH2 [m2M+?BM; b+2M`BQX h?2 T?b2@bT+2 /Bbi`B#miBQM Q7 i?2b2
;HtB2b +M #2 `2T`Q/m+2/ B7 bi2HHBi2 [m2M+?BM; Q++m`b QM `TB/ iBK2b+H2
UyXR" Tq "yX8 :v`V 7i2` i?2v KF2 i?2B` }`bi Tbb;2 Q7 _ ∼ y.8R200 - r?2`2
R200 Bb /2}M2/ b i?2 `/Bmb i r?B+? i?2 K2M BMi2`BQ` /2MbBiv Bb kyy iBK2b
i?2 +`BiB+H /2MbBiv Q7 i?2 lMBp2`b2X
AM Q`/2` iQ 7m`i?2` +QMbi`BM i?2 `2HiBQM #2ir22M i?2 bb2K#Hv Q7 bi2HH`
Kbb M/ /`F Kii2` BM i?2b2 bvbi2Kb- Qi?2` Q#b2`p#H2b +M #2 2tTHQBi2/X AM
*?Ti2` 9- r2 +QKT`2 i?2 ?HQ Kbb2b Q7 i?2 :*Gaa bvbi2Kb iQ i?2 bi2HH`
Kbb K2bm`2K2Mib Q7 i?2 +2Mi`H ;HtB2b- M/ iQ bi2HH` Kbb K2bm`2K2Mi
Q7 i?2 2MiB`2 TQTmHiBQM Q7 +Hmbi2` ;HtB2bX q?2M r2 bim/v i?2 /Bbi`B#miBQM Q7
bi2HH` Kbb BM i?2 2Mb2K#H2 :*Gaa +Hmbi2`- r2 }M/ i?i Bi Bb r2HH /2b+`B#2/
#v T`QD2+i2/ L6q T`Q}H2- #mi rBi? `2HiBp2Hv ?B;? +QM+2Mi`iBQM T`K2i2`
Q7 c ∼ 7X h?Bb `2bmHi Bb BMi`B;mBM; #2+mb2 Bi b?Qrb i?i i?2 bi2HH` Kbb Bb
bB;MB}+MiHv KQ`2 +QM+2Mi`i2/ i?M i?2 /`F Kii2` BM L@#Q/v bBKmHiBQMb BM
3
*>Sh1_ RX ALh_P.l*hAPL
i?Bb Kbb M/ `2/b?B7i `2;BK2X h?Bb Bb bB;MB}+MiHv /Bz2`2Mi 7`QK i?2 TB+im`2 i
HQr2` `2/b?B7i- r?2M +QKT`2/ iQ bim/B2b BM i?2 HBi2`im`2X >Qr2p2`- /Bz2`2M+2b
rBi? MHvb2b M/ /i b2ib BM i?2 HBi2`im`2 `2 KDQ` +QM+2`M M/ HBKBiiBQMX
"v 2ti2M/BM; i?2 bim/v /2b+`B#2/ #Qp2 iQr`/b HQr2` `2/b?B7i- r2 KF2 i?2
+QKT`BbQM +`Qbb +QbKB+ iBK2 KQ`2 +QMbBbi2Mi M/ Tmi i?2 :*Gaa K2@
bm`2K2Mib BMiQ +QMi2tiX *?Ti2` 8 /2b+`B#2b K2bm`2K2Mi Q7 i?2 bi2HH`
Kbb /Bbi`B#miBQM BM Ry +Hmbi2`b BM i?2 `2/b?B7i `M;2 0.07 < z < 0.26- /`rM
7`QK i?2 JmHiB@1TQ+? L2`#v *Hmbi2` am`p2v UJ1L2*aV M/ i?2 *M/BM
*Hmbi2` *QKT`BbQM S`QD2+i U***SVX h?2 bvbi2Kb ?p2 /vMKB+H Kbb2b Q7
M200,c $ 1015 J" - r?B+? `Qm;?Hv Ki+?2b i?2 2tT2+i2/ /2b+2M/2Mi TQTmH@
iBQM Q7 i?2 :*Gaa bKTH2X q2 }M/ i?i i?2 bi2HH` Kbb /Bbi`B#miBQM Bb r2HH
/2b+`B#2/ #v M L6q T`Q}H2 rBi? +QM+2Mi`iBQM c ∼ 2X h?2 bi2HH` Kbb /Bb@
i`B#miBQM i?mb 2pQHp2b bB;MB}+MiHv bBM+2 z ∼ 1- M/ i?Bb i`2M/ Bb QTTQbBi2 iQ
r?i Bb b22M BM i?2 2pQHmiBQM Q7 i?2 /`F Kii2` +QM+2Mi`iBQM BM bBKmHiBQMbX
q2 +QMbB/2` /Bz2`2Mi 2pQHmiBQM`v b+2M`BQb M/ +QM+Hm/2 i?i i?2 #mBH/@mT
Q7 bi2HH` Kbb BM i?2 BMi`+Hmbi2` HB;?i M/ i?2 +2Mi`H ;Htv- +QK#BM2/ rBi?
QmibB/2 ;`Qri? QMiQ i?2 +Hmbi2`b- +QmH/ 2tTHBM i?2 Q#b2`p2/ 2pQHmiBQMX
1p2M BM ;Htv +Hmbi2`b i z ∼ 1- i?2 ;Htv TQTmHiBQM Bb 2MiB`2Hv /QKBMi2/
#v [mB2b+2Mi ;HtB2bX AM *?Ti2` e- r2 im`M Qm` ii2MiBQM iQr`/b M 2TQ+?
BM r?B+? i?2 bi`@7Q`KBM; 7`+iBQM Q7 ;HtB2b rb +QMbB/2`#Hv ?B;?2`X q2 mb2
i?2 ugriz /i b2i Q7 i?2 *6>h G2;+v am`p2v .22T- r?B+? bTMb 9 b[m`2
/2;`22 bm`p2v `2- iQ K2bm`2 i?2 lo ;Htv G6 i 3 < z < 5X h?2 GvKM@
"`2F :HtB2b UG":bV i?i r2 +QMbB/2` `2 bi`@7Q`KBM; ;HtB2b i?i ?p2
KMv TTHB+iBQMbX h?2v `2 B/2MiB}2/ `2HiBp2Hv 2bBHv i i?Bb `2/b?B7i `M;2#v mbBM; KmHiB@#M/ QTiB+H T?QiQK2i`v iQ T`Q#2 i?2 rp2H2M;i?@TQbBiBQM Q7
i?2 GvKM HBKBiX Pm` bim/v BM *?Ti2` e Bb #b2/ QM Ryy-yyy G":b- M/
;Bp2M i?2 H`;2 bm`p2v `2 +QKT`2/ iQ T`2pBQmb bim/B2b- i?Bb `2M/2`b i?2 bvb@
i2KiB+ mM+2`iBMiv QM i?2 G6 +mb2/ #v +QbKB+ p`BM+2 BMbB;MB}+MiX 6m`@
i?2`KQ`2- r2 `2 #H2 iQ K2bm`2 i?2 G6 /QrM iQ bm+? #`B;?i UM/ i?2`27Q`2
``2V ;HtB2b i?i i?2 BMi2`p2MBM; Kii2` /2MbBiv /Bbi`B#miBQM bB;MB}+MiHv H@
i2`b i?2 Ua+?2+?i2`V b?T2 Q7 i?2 G6X qBi? i?2 FMQrH2/;2 Q7 i?2 BMi`BMbB+ b?T2
Q7 i?2 G6 BM ?M/- i?2b2 G":b +M #2 mb2/ b bQm`+2b BM r2F H2MbBM; K;MB@
}+iBQM bim/B2b U2X;X >BH/2#`M/i 2i HX kyRjc 6Q`/ 2i HX kyRjVX Hi?Qm;? i?2
G":b `2 iQQ bKHH iQ #2 bTiBHHv `2bQHp2/ BM i?Bb /i b2i- K;MB}+iBQM
bim/v QMHv `2[mB`2b K2bm`2K2Mib Q7 i?2B` ~mt2bX aBM+2 i?Bb `2Ht2b i?2 Q#@
b2`piBQMH `2[mB`2K2Mib bm#biMiBHHv- Bi Bb T`QKBbBM; K2i?Q/ 7Q` K2bm`BM;
i?2 iQiH Kbb2b Q7 ;Htv +Hmbi2`b i `2/b?B7ib z ! 1- b b?QrM #v >BH/2#`M/i
2i HX UkyRRV 7Q` i?2 aT_*a +Hmbi2` bKTH2X
*?Ti2`
k
h?2 2MpB`QMK2MiH /2T2M/2M+2
Q7 i?2 bi2HH` Kbb 7mM+iBQM i
z∼1
q2 T`2b2Mi i?2 bi2HH` Kbb 7mM+iBQMb UaJ6bV Q7 bi`@7Q`KBM; M/ [mB2b+2Mi
;HtB2b 7`QK Q#b2`piBQMb Q7 Ry `B+?- `2/@b2[m2M+2 b2H2+i2/- +Hmbi2`b BM i?2
:2KBMB *Hmbi2` bi`QT?vbB+b aT2+i`Qb+QTB+ am`p2v U:*GaaV BM i?2 `2/b?B7i
`M;2 0.86 < z < 1.34X q2 +QKT`2 Qm` `2bmHib rBi? }2H/ K2bm`2K2Mib i
bBKBH` `2/b?B7ib mbBM; /i 7`QK Eb @#M/ b2H2+i2/ +iHQ;m2 Q7 i?2 *Pa@
JPaflHi`oAah }2H/X q2 +QMbi`m+i Eb @#M/ b2H2+i2/ KmHiB@+QHQm` +i@
HQ;m2 7Q` i?2 +Hmbi2`b BM RR T?QiQK2i`B+ #M/b +Qp2`BM; u@3µK- M/ 2biBKi2
T?QiQK2i`B+ `2/b?B7ib M/ bi2HH` Kbb2b mbBM; a1. }iiBM; i2+?MB[m2bX hQ +Q`@
`2+i 7Q` BMi2`HQT2`b BM Qm` +Hmbi2` bKTH2- r2 mb2 i?2 /22T bT2+i`Qb+QTB+ +QK@
TQM2Mi Q7 :*Gaa- r?B+? +QMiBMb bT2+i` 7Q` Rk3k B/2MiB}2/ +Hmbi2` M/ }2H/
;HtB2b iF2M rBi? :2KBMBf:JPaX h?Bb HHQrb mb iQ +Q``2+i +Hmbi2` MmK#2`
+QmMib 7`QK T?QiQK2i`B+ b2H2+iBQM 7Q` 7Hb2 TQbBiBp2 M/ 7Hb2 M2;iBp2 B/2MiB@
}+iBQMbX "Qi? i?2 T?QiQK2i`B+ M/ bT2+i`Qb+QTB+ bKTH2b `2 bm{+B2MiHv /22T
i?i r2 +M T`Q#2 i?2 bi2HH` Kbb 7mM+iBQM /QrM iQ Kbb2b Q7 1010 J" X q2
/BbiBM;mBb? #2ir22M bi`@7Q`KBM; M/ [mB2b+2Mi ;HtB2b mbBM; i?2 `2bi@7`K2
l@o p2`bmb o@C /B;`K- M/ }M/ i?i i?2 #2bi@}iiBM; a+?2+?i2` T`K2i2`b α
M/ M ∗ `2 bBKBH` rBi?BM i?2 mM+2`iBMiB2b 7Q` i?2b2 ;Htv ivT2b rBi?BM i?2
/Bz2`2Mi 2MpB`QMK2MibX >Qr2p2`- i?2`2 Bb bB;MB}+Mi /Bz2`2M+2 BM i?2 b?T2
M/ MQ`KHBbiBQM Q7 i?2 iQiH bi2HH` Kbb 7mM+iBQM #2ir22M i?2 +Hmbi2`b M/
i?2 }2H/ bKTH2X h?Bb /Bz2`2M+2 BM i?2 iQiH bi2HH` Kbb 7mM+iBQM Bb T`BK`BHv
`2~2+iBQM Q7 i?2 BM+`2b2/ 7`+iBQM Q7 [mB2b+2Mi ;HtB2b BM ?B;?@/2MbBiv 2M@
pB`QMK2MibX q2 TTHv bBKTH2 [m2M+?BM; KQ/2H i?i BM+Hm/2b +QKTQM2Mib Q7
Kbb@ M/ 2MpB`QMK2Mi@/`Bp2M [m2M+?BM;- M/ }M/ i?i BM i?Bb TB+im`2 45+4
−3 W
N
Q7 i?2 bi`@7Q`KBM; ;HtB2b- r?B+? MQ`KHHv rQmH/ #2 7Q`KBM; bi`b BM i?2
}2H/- `2 [m2M+?2/ #v i?2 +Hmbi2`X A7 ;HtB2b BM +Hmbi2`b M/ i?2 }2H/ [m2M+?
i?2B` bi` 7Q`KiBQM pB /Bz2`2Mi K2+?MBbKb- i?2b2 T`Q+2bb2b ?p2 iQ +QMbTB`2
BM bm+? rv i?i i?2 b?T2b Q7 i?2 [mB2b+2Mi M/ bi`@7Q`KBM; aJ6 `2KBM
bBKBH` BM i?2b2 /Bz2`2Mi 2MpB`QMK2MibX
_2K+Q 6XCX pM /2` "m`;- /K JmxxBM- >2MF >Q2Fbi`- *?`Bb GB/KM- H2bbM/`Q
_2iim`- :BHHBM qBHbQM- >XEX*X u22- >2M/`BF >BH/2#`M/i- .MBHQ J`+?2bBMB- Jm`Q
ai27MQM- _B+`/Q .2K`+Q- EQM`/ EmBDF2M
bi`QMQKv bi`QT?vbB+b- oQHmK2 88d- R8 UkyRjV
Ry
kXRX ALh_P.l*hAPL
RR
PM2 Q7 i?2 KBbbBM; T`ib BM i?2 i?2Q`v Q7 ;Htv 7Q`KiBQM M/ 2pQHmiBQM Bb /2iBH2/ mM/2`biM/BM; Q7 i?2 #mBH/ mT Q7 bi2HH` Kbb BM i?2 lMBp2`b2X q?BH2
i?2 ?B2``+?B+H ;`Qri? Q7 /`F Kii2` ?HQ2b ?b #22M bim/B2/ BM H`;2 L@#Q/v
bBKmHiBQMb U2X;X aT`BM;2H 2i HX kyy8V- i?2 #`vQMB+ T?vbB+b i?i `2;mHi2b i?2
+QQHBM; Q7 ;b M/ 7Q`KiBQM Q7 bi`b BM i?2b2 ?HQ2b Bb Km+? ?`/2` iQ bBKmHi2
M/ Bb MQi v2i r2HH mM/2`biQQ/X hQ mM/2`biM/ r?B+? T?vbB+H T`Q+2bb2b `2
/QKBMMi BM b?TBM; i?2 bi2HH` +QMi2Mi Q7 ;HtB2b- KQ/2Hb M22/ ;QQ/ Q#b2`p@
iBQMH +QMbi`BMibX PM2 Q7 i?2 KQbi 7mM/K2MiH Q#b2`p#H2b Q7 TQTmHiBQM Q7
;HtB2b Bb i?2B` bi2HH` Kbb 7mM+iBQM UaJ6V- r?B+? /2b+`B#2b i?2 MmK#2` /2M@
bBiv Q7 ;HtB2b b 7mM+iBQM Q7 bi2HH` KbbX J2bm`BM; i?2 aJ6 b 7mM+iBQM
Q7 +QbKB+ iBK2 T`QpB/2b mb27mH +QMbi`BMib QM i?2 T`K2i2`b BM b2KB@MHviB+
KQ/2Hb- M/ i?2b2 KQ/2Hb ?p2 iQ Ki+? M/ T`2/B+i i?2 aJ6 7Q` `M;2 Q7
`2/b?B7ib M/ 2MpB`QMK2MiH /2MbBiB2bX
Hi?Qm;? KQ/2Hb `2 imM2/ iQ Ki+? i?2 Q#b2`piBQMb i z 4y- i?2`2 Bb
BM ;2M2`H biBHH TQQ` ;`22K2Mi #2ir22M Q#b2`piBQMb M/ i?2Q`v i ?B;?2`
`2/b?B7iX JQ/2Hb ;2M2`HHv b?Qr M 2t+2bb Q7 ;HtB2b rBi? bi2HH` Kbb
(J" ) ∼ 1010 J" `QmM/ z =R@k +QKT`2/ iQ Q#b2`piBQMH /i U2X;X "Qr2`
2i HX kyRkc q2BMKMM 2i HX kyRkVX i ?B;?2` `2/b?B7ib i?2 MmK#2` Q7 ?B;?@Kbb
;HtB2b Bb ;2M2`HHv mM/2`T`2/B+i2/ #v i?2 KQ/2HbX 6Q` /2iBH2/ +QKT`BbQM
#2ir22M KQ/2Hb M/ i?2 Q#b2`p2/ aJ6 HbQ b22 J`+?2bBMB 2i HX UkyyNVX
i HQr `2/b?B7ib Uz " 0.2V i?2 aJ6 ?b #22M K2bm`2/ 7`QK rB/2 }2H/
/i M/ bT2+i`Qb+QTB+ BM7Q`KiBQM U*QH2 2i HX kyyRc "2HH 2i HX kyyjV- r?BH2
i ?B;?2` `2/b?B7ib i?2 aJ6 ?b #22M K2bm`2/ 7`QK /22T bm`p2vb #v KFBM;
mb2 Q7 T?QiQK2i`B+ `2/b?B7i 2biBKi2b USû`2x@:QMx€H2x 2i HX kyy3c J`+?2bBMB
2i HX kyyNc AH#2`i 2i HX kyRyVX h?2 ;2M2`H +QMb2Mbmb Bb i?i i?2 iQiH bi2HH`
Kbb /2MbBiv 2pQHp2b bHQrHv #2ir22M 0 < z < 1- r?B+? +M HbQ #2 BM72``2/ 7`QK
i?2 b?`T /2+HBM2 Q7 +QbKB+ bi` 7Q`KiBQM BM i?2 GBHHv@J/m /B;`K UGBHHv
2i HX RNNec J/m 2i HX RNNeV BM i?Bb `2/b?B7i `M;2X h?2 KBM 2pQHmiBQM Bb BM
i?2 MQ`KHBbiBQM Q7 i?2 aJ6- r?2`2b i?2 b?T2 /Q2b MQi b?Qr bm#biMiBH
2pQHmiBQM bBM+2 z ∼ 4 USû`2x@:QMx€H2x 2i HX kyy3VX >Qr2p2`- bBM+2 i?2b2
/22T bm`p2vb ;2M2`HHv T`Q#2 bKHH pQHmK2b- i?2 /QKBMMi bQm`+2 Q7 `M/QK
mM+2`iBMiv Bb Q7i2M +QbKB+ p`BM+2 UaQK2`pBHH2 2i HX kyy9c a+QpBHH2 2i HX kyydc
J`+?2bBMB 2i HX kyyNV- r?B+? Bb 2tT2+i2/ iQ MQi QMHv ?p2 M 2z2+i QM i?2
MQ`KHBbiBQM #mi HbQ QM i?2 b?T2 Q7 i?2 Q#b2`p2/ aJ6 Uh`2MiB aiBp2HHB
kyy3VX P#b2`piBQMb Qp2` H`;2 `2b- Q` +QK#BMiBQM Q7 KmHiBTH2 bB;?i HBM2b`2 mb2/ iQ `2/m+2 i?Bb bQm`+2 Q7 mM+2`iBMivX
"2bB/2b i?2 ;2M2`H iBK2 2pQHmiBQM Q7 i?2 T`QT2`iB2b Q7 ;HtB2b- i?2v `2
HbQ Q#b2`p2/ iQ #2 bi`QM;Hv BM~m2M+2/ #v i?2 /2MbBiv Q7 i?2B` 2MpB`QMK2MiX AM
T`iB+mH`- ;HtB2b BM Qp2`/2Mb2 `2;BQMb b?Qr HQr2` bi` 7Q`KiBQM `i2b- M/ ?B;?2` 7`+iBQM Q7 `2/ ;HtB2bX i HQr `2/b?B7ib- i?2 aHQM .B;BiH aFv am`p2v
?b HHQr2/ mb iQ [mMiB7v i?2b2 +Q``2HiBQMb rBi? ?B;? T`2+BbBQM UEmzKMM
Rk
*>Sh1_ kX h>1 1LoA_PLJ1LhG .1S1L.1L*1 P6 h>1
ah1GG_ Jaa 6lL*hAPL h z ∼ 1
2i HX kyy9c "HQ;? 2i HX kyy9c "HMiQM 2i HX kyy8VX h?2 7`+iBQM Q7 ;HtB2b
i?i `2 `2/ Bb HbQ 7mM+iBQM Q7 i?2B` bi2HH` Kbb- rBi? KQ`2 KbbBp2 ;HtB2b
#2BM; `2//2` M/ 7Q`KBM; 72r2` bi`bX h?2 [m2M+?BM; 7`+iBQM Q7 ;HtB2b #2BM;
7mM+iBQM Q7 #Qi? bi2HH` Kbb M/ 2MpB`QMK2MiH /2MbBiv- bQK2 `2+2Mi bim/B2b
?p2 bm;;2bi2/ i?2 T`Q+2bb2b Q7 ǴKbb [m2M+?BM;Ǵ M/ Ǵ2MpB`QMK2MiH [m2M+?@
BM;Ǵ iQ #2 QT2`iBM; +QKTH2i2Hv BM/2T2M/2MiHv 7`QK 2+? Qi?2` US2M; 2i HX
kyRyc JmxxBM 2i HX kyRkV- 2+? QT2`iBM; QM /Bz2`2Mi iBK2 b+H2bX LBp2Hvr2 rQmH/ 2tT2+i i?2 +QK#BMiBQM Q7 i?2b2 T`Q+2bb2b iQ z2+i i?2 b?T2 Q7 i?2
aJ6X
K2bm`2K2Mi Q7 i?2 aJ6 Q7 ;HtB2b b 7mM+iBQM Q7 2MpB`QMK2MiH
/2MbBiv i?2`27Q`2 T`QpB/2b 7m`i?2` +QMbi`BMib QM i?2 T?vbB+H T`Q+2bb2b i?i
`2 BKTQ`iMi BM i?2b2 /2Mb2 `2;BQMbX 6Q` 2tKTH2- ;HtB2b 7HHBM; BMiQ KbbBp2
;Htv +Hmbi2`b `2 2tT2+i2/ iQ #2 bi`BTT2/ Q7 i?2B` +QH/ ;b +QKTQM2Mi /m2
iQ `K@T`2bbm`2 bi`BTTBM;- M/ H+F Q7 M2r BM~QrBM; +QH/ ;b H2/b iQ ;HtvǶb bi` 7Q`KiBQM #2BM; im`M2/ QzX :HtB2b BM ;`QmTb M/ +Hmbi2`b `2
HbQ 2tT2+i2/ iQ BMi2`+i ;`pBiiBQMHHv i?`Qm;? K2`;2`b M/ 2tT2`B2M+2 bi`QM;
iB/H 7Q`+2b b i?2v 7HH iQr`/b i?2 +Hmbi2` +2Mi`2X
*QK#BMBM; i?2b2 K2bm`2K2Mib /QM2 Qp2` `M;2 Q7 `2/b?B7ib M/ 2MpB`QM@
K2Mib Tmib +QMbi`BMib QM i?2 rv ;HtB2b [m2M+? i?2B` bi` 7Q`KiBQM- bBM+2
Bi HHQrb QM2 iQ b2T`i2 #2ir22M BMi2`MHHv M/ 2ti2`MHHv /`Bp2M T`Q+2bb2bX
aQK2 bim/B2b ?p2 ii2KTi2/ iQ K2bm`2 i?2 aJ6 b 7mM+iBQM Q7 HQ+H 2M@
pB`QMK2Mi i 0.4 " z " 1.2 U2X;X "mM/v 2i HX kyyec "QHxQM2HH 2i HX kyRyc
omH+MB 2i HX kyRR- kyRkc :BQ/BMB 2i HX kyRkVX K2bm`2K2Mi Q7 i?2 aJ6 i
i?2 ?B;?2bi /2MbBiB2b ?b MQi v2i #22M +?B2p2/ BM i?Bb `2/b?B7i `M;2X h?Bb Bb
T`iHv #2+mb2 i?2 /22T UM/ i?2`27Q`2 HBKBi2/ BM `2V bm`p2vb i?i ?p2 #22M
mb2/ 7Q` aJ6 K2bm`2K2Mib UKQbiHv i?2 *PaJPa M/ .11Sk }2H/bV /Q MQi
+QMiBM i?2 2ti`2K2 Qp2`/2MbBiB2b +Q``2bTQM/BM; iQ i?2 KQbi KbbBp2 +Hmbi2`b
Q7 ;HtB2bX
AM i?Bb TT2` r2 T`2b2Mi K2bm`2K2Mi Q7 i?2 aJ6 Q7 ;HtB2b BM Ry `B+?
;Htv +Hmbi2`b i `M;2 Q7 `2/b?B7ib U0.86 < z < 1.34VX h?2b2 +Hmbi2`b r2`2
/2i2+i2/ mbBM; i?2 `2/@b2[m2M+2 K2i?Q/ QM /i 7`QK i?2 aTBix2` /TiiBQM
Q7 i?2 _2/@b2[m2M+2 *Hmbi2` am`p2v UaT_*a- b22 JmxxBM 2i HX kyyNc qBH@
bQM 2i HX kyyNc .2K`+Q 2i HX kyRyV- M/ ?p2 ivTB+H p2HQ+Biv /BbT2`bBQMb Q7
σv = 700 FKfb r?B+? BKTHv ?HQ Kbb2b Q7 Jkyy $ 3 × 1014 J" X q2 +QK#BM2
/22T T?QiQK2i`B+ /i BM RR #M/b rBi? i?2 2ti2MbBp2 /22T bT2+i`Qb+QTB+ +Qp@
2`;2 i?i r2 Q#iBM2/ 7`QK i?2 :2KBMB *Hmbi2` bi`QT?vbB+b aT2+i`Qb+QTB+
am`p2v U:*Gaa- JmxxBM 2i HX kyRkVX h?Bb HHQrb mb iQ 2biBKi2 bi2HH`
Kbb2b 7Q` BM/BpB/mH Q#D2+ib M/ [mMiB7v i?2 KQmMi Q7 BMi2`HQT2`b BM i?2
T?QiQ@z b2H2+i2/ bKTH2 b 7mM+iBQM Q7 Kbb M/ T`QD2+i2/ +Hmbi2`+2Mi`B+
/BbiM+2X q2 mb2 i?2 loC@/B;`K iQ T?QiQK2i`B+HHv b2T`i2 #2ir22M bi`@
7Q`KBM; M/ [mB2b+2Mi ;HtB2b- r?B+? Bb +`BiB+H #2+mb2 i?2 irQ ;Htv ivT2b
bmz2` 7`QK /Bz2`2Mi Q#b2`piBQMH /B{+mHiB2b M/ +QKTH2i2M2bb2bX q2 HbQ
T`QpB/2 +QKT`BbQM #2ir22M i?2 +Hmbi2` `2bmHib M/ i?2 aJ6 K2bm`2/ 7`QK
kXkX aJSG1 .h .1a*_AShAPL
Rj
lHi`oAahf*PaJPa }2H/X
h?2 bi`m+im`2 Q7 i?2 TT2` Bb b 7QHHQrbX AM a2+iX kXk r2 ;Bp2 M Qp2`pB2r Q7
:*Gaa- M/ i?2 bT2+i`Qb+QTB+ M/ T?QiQK2i`B+ /i i?i ?p2 #22M iF2M 7Q`
i?Bb +Hmbi2` bKTH2X q2 HbQ /2b+`B#2 i?2 /i 7`QK i?2 `272`2M+2 lHi`oAah
bm`p2vX AM a2+iX kXj r2 T`2b2Mi Qm` K2bm`2K2Mib Q7 T?QiQK2i`B+ `2/b?B7ibbi2HH` Kbb2b M/ `2bi@7`K2 +QHQm`b iQ /BbiBM;mBb? #2ir22M bi`@7Q`KBM; M/
[mB2b+2Mi ;HtB2bX q2 HbQ 2tTHBM ?Qr r2 +Q``2+i i?2 T?QiQK2i`B+ bKTH2
7Q` BM+QKTH2i2M2bb #v KFBM; mb2 Q7 i?2 bT2+i`Qb+QTB+ /iX AM a2+iX kX9 r2
T`2b2Mi Qm` `2bmHib M/ KF2 +QKT`BbQMb #2ir22M i?2 irQ ;Htv ivT2b- M/
#2ir22M +Hmbi2` 2MpB`QMK2Mib M/ i?2 }2H/X AM a2+iX kX8 r2 /Bb+mbb Qm` `2bmHib
BM i?2 +QMi2ti Q7 ;Htv 2pQHmiBQM`v T`Q+2bb2b M/ BM T`iB+mH` [m2M+?BM;
BM i?2b2 KbbBp2 +Hmbi2`bX q2 bmKK`Bb2 M/ +QM+Hm/2 BM a2+iX kXeX 1ti`
BM7Q`KiBQM +QMbB/2`BM; +QHQm` K2bm`2K2Mib M/ +HB#`iBQM `2 T`2b2Mi2/ BM
i?2 TT2M/B+2bX h?2`2 r2 HbQ +QKT`2 i?2 lHi`oAah }2H/ aJ6 rBi? i?2
}2H/ T`Q#2/ #v :*Gaa QmibB/2 i?2 +Hmbi2`b iQ i2bi 7Q` TQbbB#H2 bvbi2KiB+bX
HH K;MBim/2b r2 [mQi2 `2 BM i?2 " K;MBim/2b bvbi2K M/ r2 /QTi
Λ*.J +QbKQHQ;v rBi? ΩK = 0.3- ΩΛ = 0.7 M/ >y = dy FK b−R JT+−R X
h?2 :*Gaa +Hmbi2` bKTH2 +QMbBbib Q7 Ry Q7 i?2 `B+?2bi +Hmbi2`b BM i?2 `2/b?B7i
`M;2 0.86 < z < 1.34 b2H2+i2/ 7`QK i?2 9k b[m`2 /2;`22 aT_*a bm`p2vb22 h#H2 kXRX *Hmbi2`b BM i?2 aT_*a bm`p2v r2`2 /2i2+i2/ mbBM; i?2 +Hmbi2`
`2/@b2[m2M+2 /2i2+iBQM K2i?Q/ /2p2HQT2/ #v :H//2`b u22 UkyyyV- r?2`2
i?2 z $ − 3.6µK +QHQm` rb mb2/ iQ bKTH2 i?2 4000˚
#`2F i i?2b2 `2/b?B7ib
Ub22 JmxxBM 2i HX kyy3VX 6Q` M 2ti2M/2/ /2b+`BTiBQM Q7 i?2 aT_*a bm`p2v
r2 `272` iQ JmxxBM 2i HX UkyyNV- qBHbQM 2i HX UkyyNV M/ .2K`+Q 2i HX
UkyRyVX h?2 Ry +Hmbi2`b i?i r2`2 b2H2+i2/ 7`QK i?2 aT_*a bm`p2v 7Q` 7m`i?2`
bim/v `2 /2b+`B#2/ BM JmxxBM 2i HX UkyRkV- M/ +M #2 +QMbB/2`2/ b 7B`
`2T`2b2MiiBQM Q7 A_@b2H2+i2/ `B+? +Hmbi2`b rBi?BM i?Bb `2/b?B7i `M;2X
q2 MQi2 i?i i?2`2 Bb TQbbB#H2 b2H2+iBQM #Bb BM 7pQm` Q7 bvbi2Kb rBi?
?B;? MmK#2` Q7 #`B;?i `2/ ;HtB2bX Ai Bb BKTQbbB#H2 iQ b2H2+i +Hmbi2`b #b2/
QM i?2B` iQiH ?HQ Kbb M/ i?2`27Q`2 Mv +Hmbi2` bKTH2 ?b TQi2MiBH b2H2+@
iBQM #Bb2b- r?2i?2` Bi Bb s@`v b2H2+i2/- aw@b2H2+i2/- Q` ;Htv@b2H2+i2/X q2
MQi2 i?i 7QHHQr@mT bim/B2b Q7 s@`v Q` aw@b2H2+i2/ +Hmbi2`b BM i?2 bK2 `2/@
b?B7i `M;2 HbQ b?Qr bB;MB}+Mi Qp2`@/2MbBiv Q7 `2/@b2[m2M+2 ;HtB2b U2X;X
"HF2bH22 2i HX kyyjc JmHHBb 2i HX kyy8VX 6m`i?2`KQ`2- i?2 }2H/ aJ6 i z 4R
b?Qrb U2X;X JmxxBM 2i HX kyRjV i?i 2p2M BM i?2 }2H/- i?2 #`B;?ifKbbBp2 2M/
Q7 i?2 TQTmHiBQM Bb +QKTH2i2Hv /QKBMi2/ #v `2/ ;HtB2bX h?2`27Q`2 Bi b22Kb
mMHBF2Hv i?i `2/@b2[m2M+2 b2H2+iBQM `2bmHib BM bB;MB}+Mi b2H2+iBQM #Bb- i
*>Sh1_ kX h>1 1LoA_PLJ1LhG .1S1L.1L*1 P6 h>1
ah1GG_ Jaa 6lL*hAPL h z ∼ 1
R9
h#H2 kXR, h?2 Ry :*Gaa +Hmbi2`b b2H2+i2/ 7`QK aT_*a 7Q` 7QHHQr@mT bT2+i`Qb+QTB+ M/
T?QiQK2i`B+ Q#b2`piBQMbX h?2b2 +Hmbi2`b 7Q`K i?2 #bBb Q7 i?Bb bim/vX
LK2
zbT2+
aT_*a@yyj9
aT_*a@yyj8
aT_*a@yyje2
aT_*a@ykR8
aT_*a@Ry9d7
aT_*a@Ry8R7
aT_*a@ReRj
aT_*a@ReRe
aT_*a@Rej9
aT_*a@Rej3
yX3ed
RXjj8
yX3eN
RXyy9
yXN8e
RXyj8
yX3dR
RXR8e
RXRdd
RXRNe
_
Ckyyy
yy,j9,9kXy3e
yy,j8,9NXdyy
yy,je,98XyjN
yk,R8,kjXkyy
Ry,9d,jkXN8k
Ry,8R,y8X8ey
Re,Rj,R9Xe9R
Re,Re,9RXkjk
Re,j9,j8X9yk
Re,j3,8RXek8
.2+
Ckyyy
@9j,yd,8jXjey
@9j,Rk,k9XRey
@99,Ry,9NXNRR
@yj,9j,j9X93k
8d,9R,k9Xj9y
83,R3,R8X8ky
8e,9N,kNX8y9
88,98,k8Xdy3
9y,kR,8RX833
9y,j3,9kX3Nj
Eb @#M/ Sa6
6q>J (Ǵ)
RXyR
yX9y
RXkjUCV
RXyy
yXeR
yX3e
yX3R
yX39
yXdd
yXee
EHBK #
(K;" )
kRX8j
kjXey
kkXRRUCV
kRXdj
kkXe3
kkXNe
kkX88
kkXe8
kkX33
kjXyy
J!,HBK +
(J! )
RyX9k
NXNk
RyX8j
RyX98
RyXRd
NXNN
NXNd
RyXjj
RyXR9
RyXRj
HBKBi 7`QK
#+yj/
RyX9j
NXN8
RyX8y
RyX9e
RyXy9
NXNN
RyXyk
RyXky
RyXRj
RyXyN
6Q` 7mHH MK2b r2 `272` iQ JmxxBM 2i HX UkyRkVX
#
3yW +QKTH2i2M2bb HBKBi 7Q` bBKmHi2/ bQm`+2bX
+
*Q``2bTQM/BM; Kbb +QKTH2i2M2bb HBKBi #b2/ QM i?2 ;Htv BM lHi`o@
Aah rBi? i?2 ?B;?2bi JfG }ii2/ i i?Bb `2/b?B7i i EHBK X
/
Jbb HBKBi 7`QK bvMi?2iB+ bT2+i`mK rBi? τ = 10Jv` bi`iBM; i ;2
Q7 mMBp2`b2 i i?i `2/b?B7i rBi? MQ /mbi U"`mxmH *?`HQi kyyjVX
2
6Q` aT_*a@yyje r2 mb2/ iQ C@#M/ b i?2 b2H2+iBQM #M/ bBM+2 Bi Bb
bB;MB}+MiHv /22T2` i?M i?2 Eb @#M/X h?2 BK;2 [mHBiv M/ K;MBim/2
HBKBib `272` iQ i?2 C@#M/ 7Q` i?Bb +Hmbi2`X
7
aBM+2 i?2 "*: Bb Qzb2i 7`QK i?2 +2Mi`2- i?Bb Bb #2ii2` TT`QtBKiBQM
7Q` i?2 +Hmbi2` +2Mi`2 U/Bz2`2Mi 7`QK JmxxBM 2i HX UkyRkVVX
H2bi 7Q` i?2 KQbi KbbBp2 +Hmbi2`b i ;Bp2M `2/b?B7i bm+? b i?2 :*Gaa
bKTH2X
h?2 +Hmbi2`b BM i?2 :*Gaa bKTH2 ?p2 2ti2MbBp2 QTiB+H bT2+i`Qb+QTv- r?B+?
?b #22M iF2M mbBM; i?2 :JPa BMbi`mK2Mib QM :2KBMB@LQ`i? M/ @aQmi?X
6Q` /2iBHb QM i?2b2 K2bm`2K2Mib- i?2 i`;2i b2H2+iBQM M/ M Qp2`pB2r Q7 i?2
`2/m+iBQM Q7 i?2b2 /i- r2 `272` iQ JmxxBM 2i HX UkyRkVX
AM bmKK`v- bT2+i`Qb+QTB+ i`;2ib r2`2 b2H2+i2/ mbBM; +QK#BMiBQM Q7
i?2B` jXeµK ~mt2b- z $ − 3.6µK +QHQm`b- M/ i?2B` T`QD2+i2/ +Hmbi2`+2Mi`B+ `/BBX
h?2 +QHQm` T`BQ`Biv b2H2+iBQM rb +?Qb2M iQ #2 bm{+B2MiHv #`Q/ bQ i?i i?2`2
Bb MQ b2H2+iBQM #Bb ;BMbi #Hm2 ;HtB2b rBi?BM i?2 +Hmbi2`Ƕb `2/b?B7i `M;2X
"2+mb2 i?2 Kbb@iQ@HB;?i `iBQ BM i?2 jXe µK +?MM2H Bb QMHv r2F 7mM+iBQM
kXkX aJSG1 .h .1a*_AShAPL
R8
h#H2 kXk, S`QT2`iB2b Q7 i?2 Ry :*Gaa +Hmbi2`bX
LK2
zbT2+
aT_*a@yyj9
aT_*a@yyj8
aT_*a@yyje
aT_*a@ykR8
aT_*a@Ry9d
aT_*a@Ry8R
aT_*a@ReRj
aT_*a@ReRe
aT_*a@Rej9
aT_*a@Rej3
yX3ed
RXjj8
yX3eN
RXyy9
yXN8e
RXyj8
yX3dR
RXR8e
RXRdd
RXRNe
σv
[FK/b]
700+90
−150
780+80
−120
750+80
−90
640+120
−130
660+70
−120
500+40
−100
1350+100
−100
680+80
−110
790+60
−110
480+50
−100
M200
(1014 J" )
3.6+1.6
−1.9
3.9+1.3
−1.5
4.5+1.6
−1.4
2.6+1.7
−1.3
2.9+1.0
−1.3
1.2+0.3
−0.6
26.1+6.2
−5.4
2.8+1.1
−1.2
4.4+1.1
−1.6
1.0+0.3
−0.5
R200
(JT+)
1.1+0.1
−0.2
0.9+0.1
−0.1
1.1+0.1
−0.1
0.9+0.2
−0.2
1.0+0.1
−0.2
0.7+0.1
−0.1
2.1+0.2
−0.2
0.9+0.1
−0.1
1.0+0.1
−0.1
0.6+0.1
−0.1
Q7 ;Htv ivT2- i?2 i`;2iBM; +QKTH2i2M2bb Bb- iQ }`bi Q`/2`- 7mM+iBQM Q7 `/BH
/BbiM+2 M/ bi2HH` Kbb QMHvX h?2 bbB;M2/ i`;2iBM; T`BQ`Biv Bb ?B;?2bi 7Q`
KbbBp2 Q#D2+ib M2` i?2 +Hmbi2` +2Mi`2b Ub22 JmxxBM 2i HX kyRk- 6B;X 9VX
6Q` i?2b2 Ry +Hmbi2`b i?2`2 `2 Rk3k ;HtB2b BM iQiH rBi? `2/b?B7ib- Q7
r?B+? 98d `2 +Hmbi2` K2K#2`bX 6Q` KQ`2 i?M 90W Q7 i?2 i`;2i2/ Q#D2+ib
rBi? bi2HH` Kbb2b 2t+22/BM; 1010 J" - i?2 HBKBiBM; Kbb Q7 i?2 T?QiQK2i`B+
/i- `2/b?B7i rb K2bm`2/ rBi? ?B;? +QM}/2M+2X LQi2 i?i i?2 i`;2iBM;
T`BQ`BiBxiBQM Bb FMQrM- r2 /Q MQi b2H2+i ;BMbi T`iB+mH` ivT2 Q7 ;HtB2bM/ r2 ?p2 ?B;? bm++2bb `i2 Q7 Q#iBMBM; `2/b?B7ib Qp2` i?2 bi2HH` Kbb
`M;2 r2 bim/vX h?2`27Q`2- Hi?Qm;? i?2 bT2+i`Qb+QTB+ bKTH2 Bb BM+QKTH2i2Bi Bb `2T`2b2MiiBp2 bKTH2 7Q` i?2 mM/2`HvBM; TQTmHiBQM Q7 +Hmbi2` ;HtB2bX
h?2 i`;2iBM; +QKTH2i2M2bb +M #2 [mMiB}2/- M/ BM a2+iX kXjX9 r2 mb2 i?2
bT2+i`Qb+QTB+ bm#@bKTH2 iQ +Q``2+i i?2 7mHH bKTH2 7Q` +Hmbi2` K2K#2`b?BTX
q2 ?p2 T2`7Q`K2/ /vMKB+H MHvbBb UqBHbQM 2i HX- BM T`2TV iQ bim/v
i?2 /Bbi`B#miBQM Q7 HBM2@Q7@bB;?i UGPaV p2HQ+BiB2b Q7 i?2 bT2+i`Qb+QTB+ i`;2ibX
6Q` HH Ry +Hmbi2`b- i?2 /Bbi`B#miBQM Q7 GPa p2HQ+BiB2b TT`QtBKi2b :mbbBM
T`Q}H2- r?B+? Bb M BM/B+iBQM i?i i?2 +Hmbi2`b `2 U+HQb2 iQV pB`BHBb2/X 6`QK
i?Bb /Bbi`B#miBQM r2 K2bm`2 i?2 GPa p2HQ+Biv /BbT2`bBQM (σv ) Q7 i?2 +Hmbi2`bX
h?Bb H2/b iQ 2biBKi2b Q7 R200 - i?2 `/Bmb i r?B+? i?2 K2M BMi2`BQ` /2MbBiv
Bb kyy iBK2b i?2 +`BiB+H /2MbBiv Uρ+`Bi V- M/ M200 - i?2 Kbb +QMiBM2/ rBi?BM
R200 X h?2 +m``2Mi MHvbBb Bb /QM2 bBKBH` iQ .2K`+Q 2i HX UkyRyV- M/ Bb
#b2/ QM M 2tTM/2/ bT2+i`Qb+QTB+ /i b2iX h#H2 kXk b?Qrb i?2 +Hmbi2`
T`QT2`iB2b Q#iBM2/ 7`QK i?Bb MHvbBbX
h?2 +Hmbi2`b ?p2 ivTB+H p2HQ+Biv /BbT2`bBQMb Q7 σv = 700 FKfb r?B+?
BKTHv ?HQ Kbb2b Q7 Jkyy $ 3 × 1014 J" X LQi2 i?i aT_*a@ReRj Bb Km+?
Re
*>Sh1_ kX h>1 1LoA_PLJ1LhG .1S1L.1L*1 P6 h>1
ah1GG_ Jaa 6lL*hAPL h z ∼ 1
KQ`2 KbbBp2- rBi? p2HQ+Biv /BbT2`bBQM Q7 σv = 1350 FKfbX h?Bb ?B;? pHm2
Bb +QMbBbi2Mi rBi? i?2 s@`v i2KT2`im`2 K2bm`2/ 7`QK `2+2Mi *?M/`
Q#b2`piBQM Ub22 1HHBM;bQM- BM T`2TXVX
PTiB+H ugriz /i 7Q` i?2 bBt +Hmbi2`b Q#b2`p#H2 7`QK i?2 LQ`i?2`M bFv r2`2
iF2M rBi? J2;*K i i?2 *M/@6`M+2@>rBB h2H2b+QT2 U*6>hVX 6Q`
i?2 +Hmbi2`b BM i?2 aQmi?- ugri /i r2`2 iF2M rBi? AJ*a i i?2 J;2HHM
i2H2b+QT2b- M/ i?2 z @#M/ /i mbBM; i?2 JPaA*@AA +K2` KQmMi2/ QM
i?2 "HM+Q i2H2b+QT2 i i?2 *2``Q hQHQHQ AMi2`@K2`B+M P#b2`piQ`v U*hAPVX
h?2`2 Bb C@ M/ Eb @#M/ BK;BM; /i 7`QK qA_*K i i?2 *6>h 7Q` i?2
LQ`i?2`M +Hmbi2`b- M/ 7`QK AaSA i i?2 "HM+Q i2H2b+QT2 Q` >qE@A i i?2
o2`v G`;2 h2H2b+QT2 UoGhV lh9 7Q` i?2 aQmi?2`M +Hmbi2`bX LQi2 i?i i?2b2
M2`@A_ /i r2`2 H`2/v T`2b2Mi2/ M/ mb2/ BM GB/KM 2i HX UkyRkV iQ bim/v
i?2 2pQHmiBQM Q7 "*:bX h?2 T?QiQK2i`B+ /i b2i HbQ BM+Hm/2b i?2 jXe- 9X88X3 M/ 3XyµK A_* +?MM2Hb 7`QK aqA_1 UGQMb/H2 2i HX kyyjVX 6Q` ?H7
Q7 i?2 +Hmbi2`b- BM+Hm/BM; i?2 7Qm` i i?2 ?B;?2bi `2/b?B7ib- r2 Q#iBM2/ /22T2`
A_* Q#b2`piBQMb 7`QK i?2 :hP T`Q;`Kb SA.,9yyjj M/ SA.,8yReRX h?2
K2bm`2/ /2Ti?b M/ M Qp2`pB2r Q7 BMbi`mK2Mib i?i r2`2 mb2/ `2 HBbi2/ BM
i?2 TT2M/Bt BM h#H2 kX8X
AM TT2M/Bt kX r2 ;Bp2 +QKT`2?2MbBp2 /2b+`BTiBQM Q7 i?2 T?QiQK2i`B+
/i T`Q+2bbBM; H2/BM; iQ KmHiB@rp2H2M;i? +Qp2`;2 rBi? }2H/ Q7 pB2r Q7
10$ × 10$ +2Mi`2/ QM i?2 aQmi?2`M +Hmbi2`b- M/ 15$ × 15$ }2H/ Q7 pB2r 7Q` i?2
LQ`i?2`M +Hmbi2`bX h?Bb rB/2 }2H/ pB2r T`QpB/2b BM7Q`KiBQM mT iQ b2p2`H JT+
7`QK i?2 +Hmbi2` +2Mi`2b i i?2 `2bT2+iBp2 +Hmbi2` `2/b?B7ib- 2p2M 7Q` +Hmbi2`b i
i?2 HQr2bi `2/b?B7ibX
hQ K2bm`2 i?2 bi2HH` Kbb 7mM+iBQM Bi Bb M2+2bb`v iQ Q#iBM +iHQ;m2
BM r?B+? i?2 ;Htv bKTH2 Bb +QKTH2i2 /QrM iQ FMQrM Kbb i?`2b?QH/BM/2T2M/2Mi Q7 i?2B` bi`@7Q`KiBQM T`QT2`iB2bX AM M A_@rp2H2M;i? #M/ i?2
JfG p`B2b HBiiH2 7Q` /Bz2`2Mi bi` 7Q`KiBQM ?BbiQ`B2b- bQ i?i i?2 HmKBMQbBiv
BM i?Qb2 #M/b Bb ;QQ/ i`+2` 7Q` i?2 iQiH bi2HH` Kbb Q7 ;HtvX
"2+mb2 i?2 A_* +?MM2Hb bmz2` 7`QK H`;2 TQBMi bT`2/ 7mM+iBQM USa6Vb2T`iBM; Q#D2+ib QM i?2 bFv Bb /B{+mHiX b +QKT`QKBb2 #2ir22M ;QQ/ BK;2
[mHBiv M/ /2i2+iBQM BM `2/ }Hi2`- r2 i?2`27Q`2 +?QQb2 i?2 Eb @#M/ b i?2
b2H2+iBQM #M/X q2 mb2 a1ti`+iQ` iQ /2i2+i HH bQm`+2b BM i?2 Eb @#M/ i?i
?p2 8 /D+2Mi TBt2Hb rBi? bB;MB}+M+2 > 2.5σ `2HiBp2 iQ i?2 HQ+H #+F;`QmM/X
q2 Q#iBM +H2M +iHQ;m2 #v 2t+Hm/BM; `2;BQMb M2` #`B;?i bi`b M/
i?2B` /Bz`+iBQM bTBF2b- M/ b2T`i2 bi`b 7`QK ;HtB2b #v mbBM; i?2B` Q#b2`p2/
+QHQm`bX AM i?2 u − C p2`bmb C − E +QHQm` THM2 i?2 /BbiBM+iBQM #2ir22M bi`b
kXkX aJSG1 .h .1a*_AShAPL
Rd
M/ ;HtB2b Bb +H2` Ub22 2X;X q?BiF2` 2i HX kyRRV- M/ r2 }M/ i?i i?2
7QHHQrBM; +QHQm` +`Bi2`BQM +M #2 mb2/ iQ b2H2+i bKTH2 Q7 ;HtB2bX
C − E > 0.18 · (u − C) − 0.70 ∪ C − E > 0.08 · (u − C) − 0.40
UkXRV
hQ K2bm`2 T?QiQK2i`B+ `2/b?B7ib M/ bi2HH` Kbb2b 7Q` i?2 ;HtB2b- ++m`i2
+QHQm` K2bm`2K2Mib `2 M2+2bb`vX h?2 +B`+mKbiM+2b Q7 i?2 iKQbT?2`2 M/
QTiB+H BMbi`mK2Mib +?M;2 +QMiBMmQmbHv- M/ i?2`27Q`2 i?2 b?T2 M/ bBx2 Q7
i?2 Sa6 Bb /Bz2`2Mi #2ir22M i2H2b+QT2b- 2tTQbm`2b M/ }Hi2`bX h?2`27Q`2 Bi Bb
MQM@i`BpBH iQ K2bm`2 +QHQm`b Q7 i?2 bK2 BMi`BMbB+ T`i Q7 ;HtvX +QKKQM
TT`Q+? Bb iQ /2;`/2 i?2 Sa6 Q7 i?2 BK;2b BM HH }Hi2`b iQ i?2 Sa6 Q7 i?2
rQ`bi b22BM;- 7i2` r?B+? i?2 +QHQm`b `2 K2bm`2/ #v +QKT`BM; i?2 ~mt BM
}t2/ T2`im`2b 7Q` HH }Hi2`bX
M Hi2`MiBp2 TT`Q+?- T`QTQb2/ #v EmBDF2M Ukyy3V- Bb iQ T2`7Q`K +QM@
pQHmiBQM Q7 i?2 BK;2b BM 2+? }Hi2` rBi? TQbBiBQM@/2T2M/2Mi +QMpQHmiBQM
F2`M2H iQ KF2 i?2 Sa6 :mbbBM- +B`+mH` M/ mMB7Q`K QM 2+? BK;2X h?2
BK;2b BM i?2 /Bz2`2Mi }Hi2`b `2 MQi `2[mB`2/ iQ b?`2 i?2 bK2 :mbbBM Sa6
bBx2X 6Hmt2b `2 K2bm`2/ BM T2`im`2b rBi? +B`+mH` :mbbBM r2B;?iBM;
7mM+iBQM- r?Qb2 bBx2 Bb /Ti2/ iQ 2Mbm`2 i?i i?2 bK2 T`i Q7 i?2 bQm`+2 Bb
K2bm`2/X "2+mb2 i?2 r2B;?iBM; 7mM+iBQM TT`QtBKi2Hv Ki+?2b i?2 ;Htv
T`Q}H2b- i?Bb i2+?MB[m2 ;2M2`HHv BKT`Qp2b i?2 afL Q7 i?2 K2bm`2K2Mi +QK@
T`2/ iQ MQ`KH iQT@?i b?T2/ T2`im`2- M/ r2 2H#Q`i2 QM i?Bb K2i?Q/
BM TT2M/Bt kXXkX LQi2 i?i i?Bb i2+?MB[m2 Bb MQi bmBi2/ 7Q` K2bm`2K2Mib
Q7 i?2 iQiH ~mt- QMHv iQ Q#iBM +QHQm`b Q7 ;HtvX
h?2 T?QiQK2i`B+ x2`QTQBMib `2 b2i #b2/ QM biM/`/@bi` Q#b2`piBQMbX
q2 BKT`Qp2 i?2 T`2+BbBQM Q7 i?2 x2`QTQBMib BM i?2 ugriz CEb }Hi2`b #v KFBM;
mb2 Q7 i?2 mMBp2`bHBiv Q7 i?2 bi2HH` HQ+mb U>B;? 2i HX kyyNV M/ +QKT`BM;
i?2 K2bm`2/ bi2HH` +QHQm`b BM Qm` BK;2b rBi? `272`2M+2 +iHQ;m2 U*Qp2v
2i HX kyydVX 6m`i?2` /2iBHb +M #2 7QmM/ BM TT2M/Bt kXXkX
AM i?Bb TT2` r2 +QKT`2 i?2 +Hmbi2` `2bmHib iQ K2bm`2K2Mib 7`QK `2T`2@
b2MiiBp2 }2H/ i bBKBH` `2/b?B7ib b i?2 +Hmbi2`bX h?2 Hbi /2+/2 ?b b22M
bm#biMiBH BKT`Qp2K2Mi BM i?2 /2Ti? M/ M BM+`2b2 BM i?2 }2H/@Q7@pB2r Q7
;`QmM/@#b2/ LA_ bm`p2vbX h?2 KQbi `2+2Mi rB/2@}2H/ LA_ bm`p2v Bb lHi`@
oAah UJ+*`+F2M 2i HX kyRkV- r?B+? Bb +QKTQb2/ Q7 /22T uC>Eb BK;2b
iF2M mbBM; i?2 oAah i2H2b+QT2 QM RXe b[m`2 /2;`22 }2H/ i?i Qp2`HTb
rBi? *PaJPaX
h?2 }2H/ bKTH2 BM i?Bb bim/v Bb #b2/ QM Eb @b2H2+i2/ +iHQ;m2 Q7 i?2
*PaJPaflHi`oAah }2H/ 7`QK JmxxBM 2i HX UkyRj#VX h?2 +iHQ;m2 +QM@
R3
*>Sh1_ kX h>1 1LoA_PLJ1LhG .1S1L.1L*1 P6 h>1
ah1GG_ Jaa 6lL*hAPL h z ∼ 1
iBMb Sa6@Ki+?2/ T?QiQK2i`v BM jy T?QiQK2i`B+ #M/b +Qp2`BM; i?2 rp2@
H2M;i? `M;2 yXR8µK @ k9µK M/ BM+Hm/2b i?2 pBH#H2 GALEX UJ`iBM 2i HX
kyy8V- *6>hfam#`m U*TF 2i HX kyydV- lHi`oAah UJ+*`+F2M 2i HX
kyRkV- M/ a@*PaJPa UaM/2`b 2i HX kyydV /ib2ibX aQm`+2b `2 b2H2+i2/
7`QK i?2 ._R lHi`oAah Eb @#M/ BK;BM; UJ+*`+F2M 2i HX kyRkV r?B+?
`2+?2b /2Ti? Q7 Eb = 23.4 i NyW +QKTH2i2M2bbX /2iBH2/ /2b+`BTiBQM Q7
i?2 T?QiQK2i`B+ +iHQ;m2 +QMbi`m+iBQM- T?QiQK2i`B+ `2/b?B7i K2bm`2K2MibM/ bi2HH` Kbb 2biBKi2b Bb T`2b2Mi2/ BM JmxxBM 2i HX UkyRj#VX AM i?2 M2ti
b2+iBQM r2 2biBKi2 i?2b2 T`QT2`iB2b 7Q` i?2 ;HtB2b b2H2+i2/ BM :*Gaa BM
bBKBH` rvX AM TT2M/Bt kX" r2 b?Qr +QKT`BbQM #2ir22M i?2 lHi`o@
Aah }2H/ aJ6 M/ i?2 aJ6 K2bm`2/ BM :*Gaa QmibB/2 Q7 i?2 +Hmbi2`bX
AM ;2M2`H i?2 ;`22K2Mi Bb ;QQ/- 2p2M i?Qm;? i?2 :*Gaa /i `2 Km+?
b?HHQr2` M/ +QMiBM 72r2` }Hi2`bX i i?2 HQr@Kbb 2M/ Q7 i?2 aJ6 i?2`2 `2
bQK2 bKHH /Bz2`2M+2b /m2 iQ BM+QKTH2i2M2bb Q7 :*GaaX q2 mb2 lHi`oAah
iQ +Q``2+i i?Bb M/ T`QpB/2 M mM#Bb2/ K2bm`2 Q7 i?2 a+?2+?i2` T`K2i2`b
BM i?2 }2H/X
q2 2biBKi2 T?QiQK2i`B+ `2/b?B7ib UT?QiQ@z ǶbV mbBM; i?2 Tm#HB+Hv pBH#H2 +Q/2
1wu U"`KK2` 2i HX kyy3VX h?Bb +Q/2 rb i2bi2/ U>BH/2#`M/i 2i HX kyRyV
M/ T2`7Q`Kb p2`v r2HH QM bBKmHi2/
M/ `2H BK;BM; /iX AMTmi iQ i?2
+Q/2 `2 ~mt2b BM i?2 RR pBH#H2
#M/b M/ i?2B` 2``Q`bX
q2 +?2+F2/ 7Q` TQbbB#H2 bvb@
i2KiB+ T`Q#H2Kb BM i?2 T?QiQK2i@
`B+ +HB#`iBQM Q` T?QiQ@z +Q/2 #v
+QKT`BM; i?2 2biBKi2/ T?QiQK2i@
`B+ `2/b?B7ib rBi? bT2+i`Qb+QTB+ `2/@
b?B7ib r?2`2 i?2 bKTH2b Qp2`HT- b22
6B;X kXRX h?2 T2`7Q`KM+2 Bb i?2M
[mMiB}2/ #v i?2 b+ii2`- #Bb M/
QmiHB2` 7`+iBQM Q7 i?Bb +QKT`BbQMX
6B;m`2 kXR, aT2+i`Qb+QTB+ p2`bmb T?QiQK2i`B+
z
−zbT2+
6B`bi r2 +H+mHi2 ∆z = T?Qi
1+zbT2+
`2/b?B7ib 7Q` i?2 Ry :*Gaa +Hmbi2`bX PmiHB2`b7Q` 2+? Q#D2+i rBi? `2HB#H2 bT2+@ Q#D2+ib 7Q` r?B+? ∆z > 0.15- `2 K`F2/ BM
i`Qb+QTB+ `2/b?B7iX 6Q` ?BbiQ`B+H `2@ `2/X h?2 QmiHB2` 7`+iBQM Bb H2bb i?M 5W- i?2
bQMb M/ iQ 7+BHBii2 +QKT`BbQMb b+ii2` Q7 i?2 `2KBMBM; Q#D2+ib Bb σz = 0.036X
rBi? Qi?2` T?QiQ@z bim/B2b- r2 /2}M2 QmiHB2`b b Q#D2+ib 7Q` r?B+? |∆z| > 0.15X
6Q` i?2 `2KBMBM; K2bm`2K2Mib r2 K2bm`2 i?2 K2M Q7 |∆z| M/ i?2 b+i@
kXjX LGuaAa
RN
i2` `QmM/ i?Bb K2M- σz X q2 }M/ i?2 7QHHQrBM; ivTB+H pHm2b, b+ii2` Q7
σz = 0.036- #Bb Q7 |∆z| = 0.005- M/ 72r2` i?M 5W QmiHB2`bX aT2+B}+HHvBM i?2 `2/b?B7i `M;2 Q7 i?2 +Hmbi2`b U0.867 < z < 1.335V- r2 }M/ b+ii2` Q7
σz = 0.035- #Bb Q7 |∆z| < 0.005- M/ #Qmi 8W QmiHB2`bX q2 }M/ i?i i?2
b+ii2` Bb BM i?2 `M;2 0.031 < σz < 0.044 7Q` HH Ry +Hmbi2`b- M/ i?2`27Q`2
i?2 /Bz2`2M+2b BM T?QiQ@z [mHBiv #2ir22M i?2 +Hmbi2`b Bb M2;HB;B#H2X
q?2`2b i?2b2 pHm2b `2 +QKTmi2/ 7Q` i?2 2MiB`2 TQTmHiBQM Q7 ;HtB2b- bm#/BpBbBQM #v ;Htv ivT2 b?Qrb i?i T?QiQ@z 2biBKi2b 7Q` [mB2b+2Mi ;HtB2b
`2 KQ`2 T`2+Bb2 Uσz = 0.030V i?M 7Q` bi`@7Q`KBM; ;HtB2b Uσz = 0.040V
#2+mb2 Q7 i?2 bi`QM;2` 9yyy˚
72im`2 BM i?2 #`Q/@#M/ a1.b Q7 [mB2b+2Mi
;HtB2b- M/ i?2 T`2b2M+2 Q7 2KBbbBQM HBM2b M/ H`;2` /Bp2`bBiv Q7 BMi`BMbB+
a1.b BM i?2 bi`@7Q`KBM; TQTmHiBQMX q2 i?2`27Q`2 KF2 i?2 b2T`iBQM #v
;Htv ivT2 r?2M +Q``2+iBM; 7Q` +Hmbi2` K2K#2`b?BT BM a2+iX kXjX9X h?2 b+ii2`
BM T?QiQ@z 2biBKi2b BM+`2b2b 7Q` 7BMi2` Q#D2+ib- ?Qr2p2` r2 iF2 i?Bb 2z2+i
BMiQ ++QmMi r?2M r2 +Q``2+i 7Q` +Hmbi2` K2K#2`b?BTX
q2 2biBKi2 bi2HH` Kbb2b 7Q` HH Q#D2+ib mbBM; i?2 a1. }iiBM; +Q/2 6ah
UE`B2F 2i HX kyyNVX h?2 `2/b?B7ib `2 }t2/ i i?2 K2bm`2/ bT2+@z - r?2M2p2`
pBH#H2X Pi?2`rBb2 r2 mb2 i?2 T?QiQ@z 7`QK 1wu- M/ i?2 bi2HH` TQTmHiBQM
HB#``B2b 7`QK "`mxmH *?`HQi UkyyjV `2 mb2/ iQ Q#iBM i?2 KQ/2H a1. i?i
;Bp2b i?2 #2bi }i iQ i?2 T?QiQK2i`B+ /iX q2 mb2 T`K2i2`BxiBQM Q7 i?2
bi` 7Q`KiBQM ?BbiQ`v b SF R ∝ e−t/τ - r?2`2 i?2 iBK2@b+H2 τ Bb HHQr2/ iQ
`M;2 #2ir22M Ry Jv` M/ Ry :v`X q2 HbQ bbmK2 *?#`B2` UkyyjV AJ6bQH` K2iHHB+Biv- M/ i?2 *Hx2iiB 2i HX UkyyyV /mbi HrX h?2b2 b2iiBM;b `2
B/2MiB+H iQ i?Qb2 mb2/ 7Q` i?2 K2bm`2K2Mi Q7 bi2HH` Kbb2b BM i?2 lHi`oAah
bKTH2- BM Q`/2` iQ T`QpB/2 7B` +QKT`BbQMX
q2 2biBKi2 i?2 Kbb +QKTH2i2M2bb HBKBib 7Q` 2+? Q7 i?2 +Hmbi2`b BM i?2
7QHHQrBM; rvX 6B`bi r2 K2bm`2 i?2 /2Ti?b Q7 i?2 Eb /2i2+iBQM #M/b #v
T2`7Q`KBM; bBKmHiBQMb BM r?B+? r2 // `iB}+BH bQm`+2b iQ i?2b2 BK;2b 7Q`
`M;2 Q7 K;MBim/2bX q2 i?2M `mM a1ti`+iQ` rBi? i?2 bK2 b2iiBM;b b 7Q`
i?2 +QMbi`m+iBQM Q7 i?2 +iHQ;m2 Ua2+iX kXkXjVX h?2 `2+Qp2`2/ 7`+iBQM b 7mM+iBQM Q7 K;MBim/2 7Q` i?2 bBKmHi2/ bQm`+2b T`QpB/2b M 2biBKi2 7Q` i?2
/2Ti? Q7 i?2 /2i2+iBQM BK;2X LQi2 i?i i?2 +Hmbi2`b i ?B;?2` `2/b?B7i r2`2
T`BQ`BiBx2/ iQ ?p2 HQM;2` 2tTQbm`2 iBK2b M/ i?2`27Q`2 /22T2` /2i2+iBQM #M/bH2/BM; iQ KQ`2 ?QKQ;2M2Qmb /2i2+iBQM HBKBib BM i2`Kb Q7 #bQHmi2 K;MBim/2
M/ bi2HH` KbbX J;MBim/2 pHm2b +Q``2bTQM/BM; iQ i?2 80W `2+Qp2`v HBKBir?B+? `2 ivTB+HHv ∼ kk.8K;" - `2 ;Bp2M BM h#H2 kXRX
q2 2biBKi2 bi2HH` Kbb HBKBib i?i +Q``2bTQM/ iQ i?2b2 80W Eb @#M/ +QK@
TH2i2M2bb HBKBib BM irQ /Bz2`2Mi rvbX h?2 }`bi K2i?Q/ mb2b i?2 lHi`oAah
+iHQ;m2- r?B+? Bb #Qmi K;MBim/2 /22T2` i?M :*Gaa BM i?2 Eb @#M/X
6Q` 2+? +Hmbi2` r2 b2H2+i HH ;HtB2b 7`QK lHi`oAah rBi? T?QiQK2i`B+
ky
*>Sh1_ kX h>1 1LoA_PLJ1LhG .1S1L.1L*1 P6 h>1
ah1GG_ Jaa 6lL*hAPL h z ∼ 1
`2/b?B7i rBi?BM yXy8 7`QK i?2 +Hmbi2` `2/b?B7iX "v +QKT`BM; i?2 iQiH Eb @#M/
K;MBim/2b rBi? 2biBKi2/ bi2HH` Kbb2b BM i?Bb `2/b?B7i `M;2- r2 B/2MiB7v
i?2 ;Htv rBi? i?2 ?B;?2bi Kbb `QmM/ i?2 HBKBiBM; /2i2+iBQM K;MBim/2X
h?Bb Bb i?2 Q#D2+i rBi? i?2 ?B;?2bi Kbb@iQ@HB;?i `iBQ- +Q``2bTQM/BM; iQ i?2
`2//2bi ;Htv BM lHi`oAahX HH ;HtB2b KQ`2 KbbBp2 i?M i?2b2 Kbb HBK@
Bib- r?B+? `2 HBbi2/ BM h#H2 kXR- rBHH #2 /2i2+i2/ rBi? T`Q##BHBiv Q7 > 80W
BM :*GaaX
a2+QM/Hv- iQ T`QpB/2 +QKT`BbQM- r2 HbQ ;Bp2 i?2 Kbb HBKBi +Q``2bTQM/@
BM; iQ KtBKHHv QH/ bi2HH` TQTmHiBQM rBi? MQ /mbi U"`mxmH *?`HQi
kyyjV- i i?2 `2/b?B7i Q7 i?2 +Hmbi2` rBi? ~mt 2[mH iQ i?2 /2i2+iBQM HBKBiX
h?2 Kbb HBKBib `2bmHiBM; 7`QK i?Bb TT`Q+? `2 HbQ ;Bp2M BM h#H2 kXR- M/
`2 bBKBH` iQ i?2 }`bi 2biBKi2b iQ rBi?BM b2p2`H ?mM/`2/i?b Q7 /2t 7Q` KQbi
Q7 i?2 +Hmbi2`bX
LQi2 i?i 7Q` +Hmbi2` aT_*a@yyje r2 mb2 i?2 C@#M/ b i?2 /2i2+iBQM #M/
BMbi2/ Q7 i?2 Eb @#M/ #2+mb2 i?2 Eb @#M/ Bb Q7 Km+? HQr2` [mHBivX "2+mb2
i?2 b22BM; BM i?2 C@#M/ Bb bB;MB}+MiHv #2ii2`- C@#M/ b2H2+iBQM H2/b iQ bi2HH` Kbb /2i2+iBQM HBKBi i?i Bb yXj /2t HQr2` i?M +QmH/ #2 Q#iBM2/ rBi?
Eb @b2H2+iBQMX AM h#H2 kXR r2 i?2`27Q`2 ;Bp2 i?2 2biBKi2b +Q``2bTQM/BM; iQ
i?2 C@#M/X
AM i?2 7QHHQrBM; r2 KF2 b2T`i2 +QKT`BbQM #2ir22M i?2 aJ6 7Q` bi`@
7Q`KBM; M/ [mB2b+2Mi ;HtB2b- M/ +Q``2+i 2+? Q7 i?2 ;Htv ivT2b 7Q` +Hmbi2`
K2K#2`b?BTX qmvib 2i HX UkyydV- qBHHBKb 2i HX UkyyNV M/ Si2H 2i HX UkyRkV
?p2 b?QrM i?i i?2 l@- o@ M/ C@#M/ `2bi@7`K2 ~mt2b Q7 ;HtB2b +M #2
+QK#BM2/ BMiQ loC /B;`K iQ /BbiBM;mBb? [mB2b+2Mi ;HtB2b 7`QK bi`@
7Q`KBM; ;HtB2b- 2p2M B7 i?2 Hii2` TQTmHiBQM Bb `2//2M2/ #v /mbi 2tiBM+iBQMX
7i2` 2biBKiBM; `2/b?B7ib 7Q` HH Q#D2+ib BM i?2 T?QiQK2i`B+ +iHQ;m2- r2
mb2 1wu iQ BMi2`TQHi2 i?2 BMTmi a1. iQ Q#iBM i?2 l@o M/ o@C `2bi@7`K2
+QHQm`b 7Q` 2+? ;HtvX AM 6B;X kXk r2 THQi i?Qb2 +QHQm`b 7Q` HH Eb @#M/ b2H2+i2/
Q#D2+ib rBi? J" > 1010 J" X h?2 ;`2vb+H2 /Bbi`B#miBQM b?Qrb i?2 ;HtB2b BM
:*Gaa i?i `2 BM i?2 `2/b?B7i `M;2 0.85 < z < 1.20- #mi `2 MQi T`i
Q7 i?2 +Hmbi2`b- r?BH2 i?2 `2/ TQBMib b?Qr i?2 Q#D2+ib i?i `2 b2T`i2/ 7`QK
i?2 "*: #v H2bb i?M k `+KBM- M/ ?p2 T?QiQK2i`B+ `2/b?B7i rBi?BM yXR
7`QK i?2 +Hmbi2` `2/b?B7iX q2 b2H2+i b i?2 [mB2b+2Mi TQTmHiBQM ;HtB2b rBi?
(l − o) > R.j ∧ (o − C) < R.e ∧ (l − o) > y.33(o − C) + y.e U2X;X q?BiF2`
2i HX kyRRVX h?Bb /BpB/BM; HBM2 Bb b?QrM BM i?2 };m`2X 6Q` `272`2M+2- i?2 /mbi@
`2//2MBM; p2+iQ` Bb HbQ b?QrM- BM/B+iBp2 Q7 /mbi@BM/2T2M/2Mi b2T`iBQM Q7
[mB2b+2Mi M/ bi`@7Q`KBM; ;HtB2bX
*QKT`BM; i?2 +Hmbi2` M/ }2H/ ;Htv TQTmHiBQMb- r2 }M/ i?i 68W Q7 i?2
+Hmbi2` ;HtB2b BM i?Bb Kbb `M;2 `2 [mB2b+2Mi- r?2`2b QMHv 42W Q7 i?2 }2H/
;HtB2b `2 [mB2b+2MiX h?Bb b?Qrb i?i i?2 +Hmbi2` TQTmHiBQM Bb /QKBMi2/ #v
kXjX LGuaAa
kR
[mB2b+2Mi ;HtB2b- r?2`2b i?2 }2H/ ?b KQ`2 KBt2/ TQTmHiBQM Q7 ;HtB2bX
LQi2- ?Qr2p2`- i?i i?2 /Bbi`B#miBQM Q7 +QHQm`b /m2 iQ /mbi@`2//2MBM; rBi?BM
i?2 b2T`i2 ;Htv ivT2b Bb bBKBH` 7Q` i?2 irQ 2MpB`QMK2MibX
.m2 iQ i?2 b+ii2` BM i?2 T?QiQK2i`B+ `2/b?B7i 2biBKi2b- b2H2+iBM; +Hmbi2` ;Ht@
B2b #b2/ QM T?QiQK2i`B+ `2/b?B7ib rBHH `2bmHi BM i?2 bKTH2 #2BM; +QMiKBMi2/
#v 7Q`2@ M/ #+F;`QmM/ ;HtB2bX AM i?Bb b2+iBQM r2 +QK#BM2 i?2 T?QiQK2i`B+
Eb @#M/ b2H2+i2/ KmHiB@+QHQm` +iHQ;m2 M/ i?2 bm#@bKTH2 Q7 ;HtB2b rBi?
bT2+i`Qb+QTB+ BM7Q`KiBQM iQ b2H2+i +QKTH2i2 bKTH2 Q7 +Hmbi2` K2K#2`bX q2
rBHH mb2 i?2 7QHHQrBM; i2`KBMQHQ;vX "v Ǵ7Hb2 TQbBiBp2Ǵ r2 `272` iQ M Q#D2+i
i?i Bb MQi T`i Q7 i?2 +Hmbi2`- v2i ?b T?QiQ@z i?i Bb +QMbBbi2Mi rBi? i?2
+Hmbi2` `2/b?B7iX Ǵ7Hb2 M2;iBp2Ǵ Bb M Q#D2+i i?i #2HQM;b iQ i?2 +Hmbi2`- #mi
?b T?QiQ@z BM+QMbBbi2Mi rBi? +Hmbi2` K2K#2`b?BTX Ǵb2+m`2 +Hmbi2`Ǵ Q#D2+i
Bb +Q``2+iHv +HbbB}2/ b #2BM; T`i Q7 i?2 +Hmbi2` #b2/ QM i?2 T?QiQ@z - r?BH2
Ǵb2+m`2 }2H/Ǵ Q#D2+i Bb +Q``2+iHv B/2MiB}2/ b #2BM; QmibB/2 Q7 i?2 +Hmbi2`X
:Bp2M i?2 `2HiBp2Hv bKHH }2H/b BM r?B+? r2 K2bm`2 i?2 +Hmbi2` aJ6}2H/@iQ@}2H/ p`BM+2 +QKTHB+i2b 7mHH biiBbiB+H BMi2`HQT2` bm#i`+iBQM i?i
Bb #b2/ bQH2Hv QM T?QiQK2i`B+ /iX >Qr2p2`- QrBM; iQ i?2 2ti2M/2/ bT2+@
i`Qb+QTB+ +Qp2`;2 Q7 :*Gaa- r2 +M 2biBKi2 i?2 }2H/ +QMiKBMiBQM 7`QK
i?2b2 /i rBi?Qmi ?pBM; iQ `2Hv QM i?2 biiBbiB+H bm#i`+iBQM Q7 M 2ti2`MH
}2H/X h?Bb rv r2 iF2 ++QmMi Q7 #Qi? 7Hb2 TQbBiBp2b M/ 7Hb2 M2;iBp2b BM
i?2 T?QiQK2i`B+HHv b2H2+i2/ bKTH2X h?2 Q#D2+ib BM i?2 bT2+i`Qb+QTB+ bKTH2
r2`2 T`BQ`BiBx2/ #v jXeµK A_* ~mt M/ T`QtBKBiv iQ i?2 +Hmbi2` +Q`2- b22
a2+iX kXkXk M/ JmxxBM 2i HX UkyRkVX h?Bb b2H2+iBQM H2/b iQ i`;2iBM; +QK@
TH2i2M2bb i?i Bb- iQ }`bi Q`/2`- 7mM+iBQM Q7 `/BH /BbiM+2 M/ bi2HH` Kbb
QMHvX
6Q` i?2b2 i`;2ib r2 K2bm`2 i?2 /Bz2`2M+2b #2ir22M T?QiQ@z Ƕb M/ i?2
`2/b?B7i 7Q` 2+? +Hmbi2`- M/ #2ir22M bT2+@z Ƕb M/ i?2 `2/b?B7i Q7 i?2 +Hmbi2`X
+QKTQbBi2 7Q` HH Ry +Hmbi2`b Bb b?QrM BM 6B;X kXj- 7i2` b2T`iBM; #2ir22M
[mB2b+2Mi M/ bi`@7Q`KBM; ;HtB2bX h?Bb +M #2 +QMbB/2`2/ b /Bz2`2Mi
`2T`2b2MiiBQM Q7 6B;X kXR- r?2`2 i?2 /i 7Q` HH +Hmbi2`b ?p2 #22M 7QH/2/
QM iQT Q7 2+? Qi?2`X :HtB2b rBi? |∆z| < 0.05 `2 b2H2+i2/ b T`2HBKBM`v
+Hmbi2` K2K#2`b #b2/ QM i?2B` T?QiQK2i`B+ `2/b?B7ibX h?2 `2/ +`Qbb2b b?Qr
7Hb2 TQbBiBp2b- Q`M;2 +`Qbb2b BM/B+i2 7Hb2 M2;iBp2bX :`22M U#Hm2V bvK#QHb
b?Qr Q#D2+ib i?i `2 B/2MiB}2/ b b2+m`2 +Hmbi2` U}2H/V ;HtB2bX LQi2 i?iHi?Qm;? r2 +QmH/ ?p2 bi`i2/ rBi? Mv +mi QM |∆z|- i?2 |∆z| < 0.05 +`Bi2`BQM
+QMp2MB2MiHv vB2H/b MmK#2` Q7 7Hb2 TQbBiBp2b i?i TT`QtBKi2Hv 2[mHb i?i
Q7 7Hb2 M2;iBp2bX
6Q` i?2 Q#D2+ib BM i?2 T?QiQK2i`B+ bKTH2 i?i /Q MQi ?p2 bT2+i`Qb+QTB+
`2/b?B7i- r2 mb2 i?2b2 7`+iBQMb Q7 7Hb2 TQbBiBp2b M/ 7Hb2 M2;iBp2b iQ +Q`@
`2+i i?2 MmK#2` +QmMib 7Q` +Hmbi2` K2K#2`b?BTX hQ KF2 bm`2 i?i i?2 bT2+@z
kk
*>Sh1_ kX h>1 1LoA_PLJ1LhG .1S1L.1L*1 P6 h>1
ah1GG_ Jaa 6lL*hAPL h z ∼ 1
6B;m`2 kXk, _2bi@7`K2 l@o
p2`bmb o@C +QHQm`b 7Q` ;Ht@
B2b rBi? bi2HH` Kbb2b 2t+22/@
BM; 1010 J! iQ /Bz2`2MiBi2
#2ir22M [mB2b+2Mi M/ bi`@
7Q`KBM; ;HtB2bX h?2 ``Qr BM@
/B+i2b i?2 `2//2MBM; p2+iQ` 7Q`
/mbiX *QK#BMBM; #Qi? +QHQm`b
7+BHBii2b /BbiBM+iBQM #2ir22M
#Qi? ;Htv ivT2b- 2p2M r?2M
i?2`2 Bb bB;MB}+Mi `2//2MBM; #v
/mbiX AM ;`2v Bb i?2 /Bbi`B#miBQM
Q7 ;HtB2b 7`QK :*Gaa i?i
`2 #2ir22M 0.85 < z < 1.20#mi QmibB/2 i?2 +Hmbi2`bX `2H@
iBp2 /2MbBiv b+H2 Bb T`QpB/2/X
h?2 `2/ TQBMib b?Qr T?QiQ@z
b2H2+i2/ +Hmbi2` K2K#2`b rBi?
T`QD2+i2/ TQbBiBQM H2bb i?M k
`+KBM 7`QK i?2 +Hmbi2` +2Mi`2bX
6B;m`2 kXj, M /TiiBQM Q7 6B;X kXR- b?QrBM; +QKTQbBi2 THQi Q7 i?2 Ry +Hmbi2`b iQ K2bm`2
i?2 7`+iBQM Q7 7Hb2 TQbBiBp2b M/ 7Hb2 M2;iBp2b- 7i2` b2T`iBM; [mB2b+2Mi M/ bi`@7Q`KBM;
;HtB2bX "v THQiiBM; i?2 /Bz2`2M+2 rBi? `2bT2+i iQ i?2 +Hmbi2` `2/b?B7i- HH +Hmbi2`b `2
2z2+iBp2Hv THQii2/ QM iQT Q7 2+? Qi?2`X h?2 zT?Qi K2bm`2K2Mib 7Q` bi`@7Q`KBM; ;HtB2b
?p2 H`;2` b+ii2` i?M i?2 K2bm`2K2Mib 7Q` [mB2b+2Mi ;HtB2bX q?i Bb MQi b?QrM ?2`2Bb ?Qr i?2 Tm`Biv 7`+iBQMb +?M;2 b 7mM+iBQM Q7 Kbb M/ `/BH /BbiM+2X AM i?2 MHvbBb
r2 HbQ iF2 ++QmMi Q7 i?Bb Kbb M/ `/BH /2T2M/2M+2c b22 6B;X kX9X
kXjX LGuaAa
kj
6B;m`2 kX9, h?2 +Q``2+iBQM 7+iQ`b 7Q` i?2 T?QiQ@z b2H2+i2/ K2K#2`b i?i ?p2 MQ bT2+@z
BM7Q`KiBQM- 2biBKi2/ 7`QK i?2 bm#bKTH2 Q7 Q#D2+ib i?i /Q ?p2 bT2+i`Qb+QTB+ Qp2`HTX b2T`iBQM #v `/BH /BbiM+2 M/ bi2HH` Kbb Bb K/2- M/ i?2b2 7+iQ`b `2 KmHiBTHB2/ iQ
vB2H/ i?2 iQiH +Q``2+iBQM 7+iQ` 7Q` 2+? ;HtvX +Q``2+iBQM 7+iQ` > R BM/B+i2b i?i i?2
MmK#2` Q7 7Hb2 M2;iBp2b 2t+22/b i?2 MmK#2` Q7 7Hb2 TQbBiBp2b BM i?i #BMX AM i?2 #QiiQK
TM2Hb i?2 bT2+i`Qb+QTB+ i`;2iBM; +QKTH2i2M2bb Bb b?QrMX
bm#bKTH2 Bb `2T`2b2MiiBp2 Q7 i?2 T?QiQ@z bKTH2- r2 ?p2 iQ 2biBKi2 i?Bb
+Q``2+iBQM b 7mM+iBQM Q7 `/BH /BbiM+2 M/ bi2HH` KbbX h?Bb b2T`iBQM
2Mbm`2b i?i r2 iF2 ++QmMi Q7 i?2 bT2+i`Qb+QTB+ i`;2iBM; +QKTH2i2M2bb- i?2
Kbb@ M/ `/BHHv@/2T2M/2Mi Qp2`/2MbBiv Q7 i?2 +Hmbi2` +QKT`2/ iQ i?2 }2H/M/ i?2 ~mt /2T2M/2M+2 Q7 i?2 T?QiQ@z [mHBivX AM 6B;X kX9 r2 b?Qr i?2 +Q`@
`2+iBQM 7+iQ`b- b 7mM+iBQM Q7 `/BH /BbiM+2 UH27i TM2HV M/ b 7mM+iBQM
Q7 bi2HH` Kbb U`B;?i TM2HVX 1``Q` #`b ;Bp2 i?2 e3W +QM}/2M+2 `2;BQMb 2biB@
Ki2/ 7`QK b2`B2b Q7 JQMi2@*`HQ bBKmHiBQMb BM r?B+? r2 `M/QKHv /`r MmK#2` 7Q` b2+m`2 +Hmbi2` K2K#2`b- 7Hb2 TQbBiBp2b M/ 7Hb2 M2;iBp2b 7`QK SQBbbQM /Bbi`B#miBQM BM 2+? Kbb@- M/ `/BH #BMX +Q``2+iBQM 7+iQ` > R BM@
/B+i2b i?i i?2 MmK#2` Q7 7Hb2 M2;iBp2b 2t+22/b i?2 MmK#2` Q7 7Hb2 TQbBiBp2b
BM i?i #BMX *Q``2+iBQMb `2 `Qm;?Hv +QMbiMi rBi? J" - /2+`2bBM; bHB;?iHv i
H`;2 `/BB- #mi i?2 b2H2+iBQM Q7 T?QiQ@z K2K#2`b b Q#D2+ib rBi? |∆z| < 0.05
2Mbm`2b i?i i?2 +Q``2+iBQMb `2 bKHH BM ;2M2`HX A7 r2 +?M;2 i?2 +mi iQ yXyjyXyd Q` yXRy- i?Bb H2/b iQ /Bz2`2Mi K2K#2`b?BT +Q``2+iBQMbX >Qr2p2`- 7i2`
i?2b2 +Q``2+iBQMb ?p2 #22M TTHB2/- r2 }M/ i?i i?2b2 +mib ;Bp2 `2bmHib i?i
`2 +QMbBbi2Mi rBi?BM i?2 2``Q`bX
.QrM iQ i?2 Kbb@+QKTH2i2M2bb Q7 i?2 +Hmbi2`b i?2`2 `2 k3j bT2+i`Qb+QT@
k9
*>Sh1_ kX h>1 1LoA_PLJ1LhG .1S1L.1L*1 P6 h>1
ah1GG_ Jaa 6lL*hAPL h z ∼ 1
6B;m`2 kX8, *QKT`BM; i?2 +Hmbi2` aJ6 UH27i TM2HV rBi? bBKBH` `2T`2b2MiiBQM Q7 i?2 }2H/
aJ6 U`B;?i TM2HVX h?2 iQiH aJ6b U#H+F TQBMibV `2 b2T`i2/ #v ;Htv ivT2X _2/ TQBMib
b?Qr i?2 [mB2b+2Mi ;HtB2b M/ i?2 #Hm2 TQBMib b?Qr bi`@7Q`KBM; ;HtB2bX h?2 #2bi@}iiBM;
a+?2+?i2` 7mM+iBQMb `2 Qp2`THQii2/ 7Q` 2+? aJ6 bKTH2X LQi2 i?i i?2 `2/ TQBMib ?p2
#22M Qzb2i #v yXyR /2t 7Q` #2ii2` pBbB#BHBivX AM i?2 #QiiQK TM2H r2 b?Qr i?2 7`+iBQMH
+QMi`B#miBQM Q7 [mB2b+2Mi M/ bi`@7Q`KBM; ;HtB2b iQ i?2 iQiH TQTmHiBQM- M/ i?2 +m`p2b
b?Qr i?2 7`+iBQMH +QMi`B#miBQMb Q7 i?2 a+?2+?i2` 7mM+iBQMbX h?2 `2HiBp2 +QMi`B#miBQM Q7
[mB2b+2Mi ;HtB2b Bb b?QrM iQ #2 ?B;?2` BM i?2 +Hmbi2` i?M BM i?2 }2H/X LQi2 i?i i?2 2``Q`
#`b QM i?2 }2H/ /i `2 bKHH2` i?M i?2 /i TQBMi bvK#QHb- #2+mb2 QMHv SQBbbQMBM 2``Q`b
`2 iF2M BMiQ ++QmMiX
B+HHv +QM}`K2/ +Hmbi2` K2K#2`bX q2 /BpB/2 i?2 k88 T?QiQ@z K2K#2`b 7Q`
r?B+? r2 /Q MQi ?p2 bT2+i` Qp2` k@/BK2MbBQMH ``v Q7 j `/BH #BMb M/ 3
bi2HH` Kbb #BMb- M/ +Q``2+i i?2K 7Q` K2K#2`b?BT #v KmHiBTHvBM; rBi? #Qi?
i?2 `/BH M/ Kbb@/2T2M/2Mi +Q``2+iBQM 7+iQ`b Ub b?QrM BM 6B;X kX9VX "2@
+mb2 i?2 +Q``2+iBQMb `2 `2HiBp2Hv bKHH- i?2 rv r2 #BM i?2 /i QMHv ?b KBMQ` 2z2+i QM i?2 `2bmHibX h?2 /QKBMMi bQm`+2 Q7 mM+2`iBMiv Bb Q7 biiBbiB+H
Mim`2X
kX9X _1alGha
k8
h#H2 kXj, h?2 pHm2b 7Q` i?2 /i TQBMib Q7 i?2 ;Htv aJ6 i?i `2 b?QrM BM 6B;X kX8X
h?2b2 `2 i?2 `r- K2K#2`b?BT@+Q``2+i2/- MmK#2`b Q7 ;HtB2b 7Q` i?2 +Hmbi2`bX hQ Q#iBM i?2
mMBib b?QrM BM i?2 };m`2b 7Q` i?2 +Hmbi2`b- i?2b2 pHm2b M22/ iQ #2 KmHiBTHB2/ #v 8- bBM+2 i?2
#BMbBx2 Bb yXk /2t BM bi2HH` KbbX LmK#2`b BM #`+F2ib b?Qr i?2 iQiH MmK#2` Q7 bT2+i`Qb+QTB+
+Hmbi2` K2K#2`b BM 2+? #BMX LQi2 i?i i?2 bT2+i`Qb+QTB+ +QKTH2i2M2bb Bb ?B;?2bi BM i?2 ?B;?@
Kbb #BMbX 1``Q`b `2T`2b2Mi 1σ mM+2`iBMiB2b 2biBKi2/ 7`QK JQMi2@*`HQ bBKmHiBQMb 7Q` i?2
+Hmbi2` /i- M/ SQBbbQMBM 2``Q`b 7Q` i?2 }2H/ /iX
HQ;(J! )
[J! ]
RyXRy
RyXjy
RyX8y
RyXdy
RyXNy
RRXRy
RRXjy
RRX8y
*Hmbi2` z ∼ 1
hQiH
176+39
−29 [24]
124+20
−18 [20]
114+14
−13 [46]
140+14
−13 [78]
90+11
−10 [63]
51+10
−7 [33]
10+3
−3 [8]
4+2
−2 [4]
LmK#2`
ZmB2b+2Mi
80+24
−21 [9]
87+15
−14 [13]
82+11
−11 [34]
103+11
−10 [63]
75+9
−8 [55]
40+6
−6 [29]
9+3
−3 [7]
4+2
−2 [4]
ai`@7Q`KBM;
96+27
−22 [15]
37+12
−12 [7]
31+8
−8 [12]
36+8
−7 [15]
15+6
−5 [8]
11+7
−4 [4]
1+1
−1 [1]
( y)
6B2H/ z ∼ 1
hQiH
308.6 ± 5.1
260.8 ± 4.7
217.4 ± 4.3
183.0 ± 3.9
112.9 ± 3.1
52.1 ± 2.1
17.6 ± 1.2
3.8 ± 0.6
Φ [10−5 /2t−R
ZmB2b+2Mi
78.9 ± 2.6
91.3 ± 2.8
91.7 ± 2.8
94.9 ± 2.8
72.7 ± 2.5
40.5 ± 1.8
15.3 ± 1.1
3.4 ± 0.5
JT+−j ]
ai`@7Q`KBM;
229.7 ± 4.4
169.5 ± 3.8
125.7 ± 3.3
88.1 ± 2.7
40.2 ± 1.8
11.7 ± 1.0
2.3 ± 0.4
0.4 ± 0.2
q2 K2bm`2 i?2 +Hmbi2` ;Htv aJ6 7`QK i?2 bKTH2 Q7 ;HtB2b BM i?2 Ry
:*Gaa +Hmbi2`b- Q#iBM2/ b /2b+`B#2/ BM a2+iX kXjX9X h?Bb Bb /QM2 #v bmK@
KBM; Qp2` i?2 j `/BH #BMb bQ i?i r2 K2bm`2 i?2 aJ6 Qmi iQ T`QD2+i2/
`/Bmb Q7 R JT+X h?2 bmKKiBQM Bb /QM2 b2T`i2Hv 7Q` [mB2b+2Mi M/ bi`@
7Q`KBM; ;HtB2b- r?B+? r2`2 B/2MiB}2/ mbBM; i?2 loC +`Bi2`BQM Ua2+iX kXjXjVX
h?2 2``Q`b 7`QK i?2 JQMi2@*`HQ bBKmHiBQMb i?i r2 /Bb+mbb2/ BM a2+iX kXjX9
`2 T`QT;i2/X LQi2 ?Qr2p2` i?i i?2 bT2+i`Qb+QTB+ i`;2ib QMHv +QMi`B#mi2
SQBbbQMBM 2``Q`- bBM+2 i?2b2 /Q MQi M22/ iQ #2 biiBbiB+HHv +Q``2+i2/ 7Q`
+Hmbi2` K2K#2`b?BTX
h?2 #Hm2 TQBMib BM i?2 H27i TM2H Q7 6B;X kX8 b?Qr i?2 aJ6 7Q` i?2 bi`@
7Q`KBM; ;HtB2b BM i?2 Ry +Hmbi2`b- r?BH2 i?2 `2/ TQBMib b?Qr i?2 [mB2b+2Mi
TQTmHiBQM BM i?2 +Hmbi2`bX h?2 iQiH ;Htv aJ6 Bb i?2 bmK Q7 i?2 irQ ;Htv
ivT2b- M/ Bb b?QrM BM #H+FX h?2 7`+iBQM Q7 [mB2b+2Mi M/ bi`@7Q`KBM; ;Ht@
B2b iQ i?2 iQiH MmK#2` Q7 ;HtB2b Bb b?QrM BM i?2 #QiiQK TM2HX h?2 /i
TQBMib `2 HbQ ;Bp2M BM h#H2 kXjX LQi2 i?i i?2 [mB2b+2Mi TQTmHiBQM /QK@
BMi2b i?2 aJ6 Q7 i?2 +Hmbi2` ;HtB2b Qp2` HKQbi i?2 2MiB`2 Kbb `M;2 r2
bim/vX h?2 "*:b `2 MQi BM+Hm/2/ BM i?Bb THQi- MQ` BM i?2 `2bi Q7 i?2 MHv@
bBb BM i?Bb TT2`X Hi?Qm;? i?2 bi2HHBi2b BM i?2 ;Htv +Hmbi2`b `2 #2HB2p2/ iQ
Q`B;BMi2 7`QK M BM7HHBM; TQTmHiBQM Q7 +2Mi`Hb BM i?2 }2H/- i?2 "*:b `2 i?2
+2Mi`H ;HtB2b BM KbbBp2 +Hmbi2` ?HQ2b M/ /Q MQi ?p2 }2H/ +QmMi2`T`iX
ke
*>Sh1_ kX h>1 1LoA_PLJ1LhG .1S1L.1L*1 P6 h>1
ah1GG_ Jaa 6lL*hAPL h z ∼ 1
*QMb2[m2MiHv- "*:b /Q MQi 7QHHQr i?2 a+?2+?i2` 7mM+iBQM i?i /2b+`B#2b i?2
`2bi Q7 i?2 +Hmbi2` ;HtB2bX 6Q` bim/v Q7 i?2 bi2HH` Kbb 2pQHmiBQM Q7 "*:b
r2 `272` iQ GB/KM 2i HX UkyRkVX
"2+mb2 i?2 b2H2+iBQM #M/b Q7 bQK2 Q7 i?2 +Hmbi2`b `2 MQi bm{+B2MiHv /22T
iQ T`Q#2 i?2 aJ6 /QrM iQ 1010 J" Ub22 h#H2 kXRV- i?2 HQr2bi irQ bi2HH`@Kbb
#BMb `2 +QKTQb2/ Q7 ;HtB2b b2H2+i2/ 7`QK e M/ d +Hmbi2`b- `2bT2+iBp2HvX
h?2b2 irQ #BMb r2`2 b+H2/ mT #v bbmKBM; i?2 `B+?M2bb2b Q7 i?2 +Hmbi2`b `2
bBKBH`- BX2X KmHiBTHvBM; i?2B` pHm2b rBi? 7+iQ` Q7 10
M/ 10
- `2bT2+iBp2HvX
6
7
`Qm;? 2biBKi2 Q7 i?2 `B+?M2bb2b Q7 i?2 BM/BpB/mH ;Htv +Hmbi2`b b?Qrb i?i
i?2b2 +Q``2+iBQMb 7+iQ`b `2 ++m`i2 iQ rBi?BM RyWX
q2 T2`7Q`K bKHH //BiBQMH +QKTH2i2M2bb +Q``2+iBQM #b2/ QM +QKT`@
BbQM Q7 i?2 }2H/ aJ6 K2bm`2/ 7`QK lHi`oAah M/ i?2 T`ib Q7 :*Gaa
i?i `2 QmibB/2 i?2 +Hmbi2`b UBX2X i?2 }2H/ aJ6 7`QK :*Gaac b22 TT2M/Bt
kX"VX "2+mb2 Q7 i?2 /2Ti? Q7 Bib T?QiQK2i`v- lHi`oAah Bb +QKTH2i2 i
J" > 1010 J" BM i?2 `2/b?B7i `M;2 0.85 < z < 1.20X q2 +QKT`2 i?2 }2H/ 2b@
iBKi2b BM TT2M/Bt kX" M/ }M/ i?i i?2`2 Bb ;QQ/ [mMiBiiBp2 ;`22K2Mi
BM #Qi? i?2 b?T2 M/ MQ`KHBbiBQM Q7 i?2 }2H/ aJ6 #2ir22M i?2 bm`p2vb i
i?Bb bi2HH` Kbb `M;2- 2t+2Ti 7Q` i?2 HQr2bi i?`22 Kbb TQBMibX h?Bb bm;;2bib
i?i i?2`2 Kv #2 `2bB/mH BM+QKTH2i2M2bb BM :*Gaa i?i z2+ib i?2 HQr2bi
Kbb TQBMibX bbmKBM; i?i i?Bb BM+QKTH2i2M2bb z2+ib i?2 +Hmbi2` M/ }2H/
/i Q7 :*Gaa BM bBKBH` rv- r2 +Q``2+i i?2 :*Gaa +Hmbi2` aJ6 TQBMib
7Q` i?2 bi`@7Q`KBM; M/ [mB2b+2Mi ;HtB2b rBi? bKHH 7+iQ`b- mT iQ 37W i i?2
HQr2bi Kbb #BM 7Q` i?2 [mB2b+2Mi ;HtB2bX h?Bb +Q``2+iBQM +?M;2b i?2 #2bi@}i
a+?2+?i2` T`K2i2`b 7Q` i?2 +Hmbi2` }ib BM i?2 7QHHQrBM; rvX M ∗ BM+`2b2b
#v yXyR- yXRy M/ yXy3 /2t M/ α #2+QK2b KQ`2 M2;iBp2 #v yXyd- yXjj M/
yXke 7Q` i?2 iQiH- bi`@7Q`KBM; M/ [mB2b+2Mi TQTmHiBQM- `2bT2+iBp2HvX h?2b2
+?M;2b /Q MQi z2+i Mv Q7 i?2 [mHBiiBp2 `2bmHib BM i?Bb TT2`- MQ` +?M;2
i?2 +QM+HmbBQM BM Mv rvX
q2 }i a+?2+?i2` Ua+?2+?i2` RNdeV 7mM+iBQM iQ i?2 #BMM2/ /i TQBMibX
h?Bb 7mM+iBQM Bb T`K2i2`Bx2/ b
!
"
!
"
∗
∗
Φ(M ) = HM(10)Φ∗ 10(M −M )(1+α) · 2tT −10(M −M ) ,
UkXkV
rBi? M ∗ #2BM; i?2 +?`+i2`BbiB+ Kbb- α i?2 HQr@Kbb bHQT2- M/ φ∗ i?2 iQiH
Qp2`HH MQ`KHBbiBQMX Pm` /i +MMQi `mH2 Qmi /Bz2`2Mi 7mM+iBQMH 7Q`K
i i?2 HQr@Kbb 2M/X h?2`27Q`2 r2 rBHH /Bb+mbb i?2 /Bz2`2M+2b BM i?2 aJ6b
#2ir22M i?2 +Hmbi2` M/ }2H/ BM i?2 +QMi2ti Q7 i?2 a+?2+?i2` 7mM+iBQM }iX KQ`2 [mMiBiiBp2 bb2bbK2Mi rQmH/ `2[mB`2 K2bm`2K2Mib i HQr2` Kbb2bX
"2+mb2 i?2 MmK#2` Q7 bQm`+2b BM i?2 #`B;?i2` bi2HH` Kbb #BMb Bb HQr- r2
`2 BM i?2 `2;BK2 r?2`2 2``Q`b +MMQi #2 `2T`2b2Mi2/ #v :mbbBM /Bbi`B#m@
iBQM M/ i?2`27Q`2 Q`/BM`v χ2 KBMBKBbiBQM Bb MQi TT`QT`Bi2X *QMb2[m2MiHvr2 iF2 ;2M2`H KtBKmK HBF2HB?QQ/ TT`Q+? r?2`2 r2 mb2 i?2 T`Q##BHBiv
7mM+iBQMb QM 2+? /i TQBMi Q#iBM2/ 7`QK i?2 JQMi2@*`HQ bBKmHiBQMbX h?Bb
kX9X _1alGha
kd
rv r2 +QKTmi2 i?2 HBF2HB?QQ/ 7mM+iBQM L QM j /BK2MbBQMH ;`B/ Q7 a+?2+?i2`
T`K2i2`bX h?2 #2bi }iiBM; T`K2i2`b M ∗ M/ α- +Q``2bTQM/BM; iQ LKt `2 HBbi2/ BM h#H2 kX9 M/ i?2 +Q``2bTQM/BM; a+?2+?i2` 7mM+iBQM Bb b?QrM BM
i?2 H27i TM2H Q7 6B;X kX8 U#H+F +m`p2VX h?2 a+?2+?i2` 7mM+iBQM T`QpB/2b `2bQM#H2 }i iQ i?2 /i- rBi? :QQ/M2bb Q7 6Bi U:Q6V Q7 kXRkX q2 HbQ ;Bp2
i?2 e3XjW +QM}/2M+2 H2p2Hb QM 2+? T`K2i2` 7i2` K`;BMHBbBM; Qp2` i?2
Qi?2` irQ T`K2i2`bX q2 iF2 i?Bb +QM}/2M+2 BMi2`pH iQ #2 i?2 `2;BQM r?2`2
2 HM(LKt /L) ≤ 1X >Qr2p2`- bBM+2 i?2b2 T`K2i2`b `2 FMQrM iQ #2 /2;2M@
2`i2- r2 b?Qr +QM}/2M+2 `2;BQMb BM 6B;X kXdX h?2 #H+F +m`p2b +Q``2bTQM/ iQ
e3XjW M/ N8X9W +QM}/2M+2 H2p2Hb 7i2` K`;BMHBbBM; QMHv Qp2` φ∗ X
AM ;2M2`H- mM+2`iBMiB2b QM BM/BpB/mH Kbb K2bm`2K2Mib Q7 i?2 ;HtB2b
H2/ iQ #Bb BM i?2 b?T2 Q7 i?2 aJ6 M/ i?2 #2bi }iiBM; a+?2+?i2` T`K2i2`b
U1//BM;iQM RNRjc h22`BFQ`TB kyy9VX 1bT2+BHHv 7Q` ?B;? Kbb2b- r?2`2 i?2
bHQT2 Q7 i?2 aJ6 Bb bi22T- i?2 b?T2 Q7 i?2 aJ6 +M #2 #Bb2/ #2+mb2 Q7
;HtB2b b+ii2`BM; iQ /D+2Mi #BMbX hQ bim/v i?2 K;MBim/2 Q7 i?Bb 2z2+i
QM Qm` MHvbBb- r2 M22/ iQ 2biBKi2 i?2 bi2HH` Kbb b+ii2` Q7 ;HtB2b BM
2+? #BM Q7 i?2 aJ6X hQ /Q i?Bb r2 +`2i2/ Ryy JQMi2 *`HQ `2HBbiBQMb Q7
i?2 T?QiQK2i`B+ +iHQ;m2- BM r?B+? r2 `M/QKHv T2`im`# i?2 T2`im`2 ~mt2b
7QHHQrBM; i?2 2biBKi2/ biiBbiB+H 2``Q`b QM i?2b2 K2bm`2K2MibX h?2M r2
2biBKi2 T?QiQ@z Ƕb M/ bi2HH` Kbb2b 7Q` i?2 2Mi`B2b Q7 i?2b2 +iHQ;m2b BM bBKBH` rv b 7Q` i?2 biM/`/ MHvbBbX i i?2 ?B;?@Kbb 2M/- r?2`2 i?2
a1. }iiBM; Bb KQbiHv bmTTQ`i2/ #v bT2+@z Ƕb Ub22 6B;X kX9 Q` h#H2 kXjV- i?2
b+ii2` Bb #Qmi yXy8 /2t BM bi2HH` KbbX 6Q` HQr2` Kbb2b i?2 b+ii2` BM+`2b2b
iQr`/b yXy3 UyXRyV /2t BM bi2HH` Kbb 7Q` [mB2b+2Mi Ubi`@7Q`KBM;V ;HtB2bX
1p2M B7 HH ;HtB2b rQmH/ b+ii2` iQ ?B;?2` Kbb2b- i?2 #Bb BM i?2 a+?2+?i2`
T`K2i2` M ∗ rQmH/ #2 yXy8 /2tX AM `2HBiv α KB;?i HbQ +?M;2 bHB;?iHv /m2
iQ 1//BM;iQM #Bb U2X;X pM /2` "m`; 2i HX kyRyV- #mi r2 2tT2+i i?2 #Bb Q7 i?2
+QK#BMiBQM Q7 a+?2+?i2` T`K2i2`b iQ #2 bm#biMiBHHv bKHH2` i?M i?2 bBx2
Q7 i?2 R@σ biiBbiB+H 2``Q` +QMiQm`b BM 6B;X kXdX :Bp2M HbQ i?i i?2 bvbi2KiB+
mM+2`iBMiB2b /m2 iQ bbmKTiBQMb `2;`/BM; i?2 AJ6- KQ/2Hb QM i?2 bi2HH`
TQTmHiBQMb- bi`@7Q`KiBQM ?BbiQ`B2b M/ K2iHHB+Biv- `2 bm#biMiBHHv H`;2`
U2X;X J`+?2bBMB 2i HX kyyNV- r2 /Q MQi ii2KTi iQ +Q``2+i 7Q` i?Bb #Bb BM i?2
+m``2Mi MHvbBbX
q2 +QKT`2 i?2 +Hmbi2` `2bmHib rBi? i?2 }2H/ ;Htv aJ6 #v b2H2+iBM; HH
;HtB2b rBi? T?QiQK2i`B+ `2/b?B7i BM i?2 `M;2 0.85 < z < 1.20 7`QK i?2
lHi`oAah bm`p2vX aBM+2 i?2 lHi`oAah bm`p2v Bb bmT2`BQ` BM /2Ti? +QK@
T`2/ iQ :*Gaa- i?2 aJ6 +M #2 K2bm`2/ /QrM iQ 1010 J" BM i?Bb `2/b?B7i
`M;2X h?2 `B;?i TM2H Q7 6B;X kX8 b?Qrb i?2 }2H/ iQiH aJ6 BM #H+F- r?B+? Bb
+QKTQb2/ Q7 Rjejj ;HtB2b BM i?Bb Kbb M/ `2/b?B7i `M;2X h?2 #2bi }iiBM;
a+?2+?i2` 7mM+iBQM 7Q` i?2 }2H/ bKTH2 Bb 7QmM/ #v KBMBKBxBM; χ2 QM j /BK2M@
k3
*>Sh1_ kX h>1 1LoA_PLJ1LhG .1S1L.1L*1 P6 h>1
ah1GG_ Jaa 6lL*hAPL h z ∼ 1
6B;m`2 kXe, :Htv aJ6b 7Q` /Bz2`2Mi ;Htv ivT2b M/ 2MpB`QMK2MibX G27i TM2H, i?2 iQiH
;Htv TQTmHiBQM BM i?2 +Hmbi2` U#H+FV M/ i?2 }2H/ UK;2MiVX JB//H2 TM2H, i?2 +Hmbi2`
M/ }2H/ aJ6 7Q` i?2 bm#b2i Q7 bi`@7Q`KBM; ;HtB2bX _B;?i TM2H, i?2 bm#b2i Q7 [mB2b+2Mi
;HtB2bX h?2 }2H/ /i ?p2 #22M b+H2/ p2`iB+HHv iQ Ki+? i?2 +Hmbi2` aJ6 i M ∗ Q7 i?2
+Hmbi2`X 1``Q` #`b b?Qr i?2 68W +QM}/2M+2 `2;BQMb 7`QK JQMi2@*`HQ bBKmHiBQMb UQM i?2
+Hmbi2` /iV- Q` SQBbbQM 2``Q` #`b U}2H/ /iVX
6B;m`2 kXd, h?2 e3W M/ N8W HBF2HB?QQ/ +QMiQm`b 7Q` i?2 a+?2+?i2` T`K2i2`b M ∗ M/
α- 7i2` K`;BMHBbBM; Qp2` i?2 φ∗ T`K2i2`X "H+F HBM2b b?Qr i?2 +Hmbi2` +QMiQm`b- r?BH2
K;2Mi HBM2b b?Qr i?2 +QMiQm`b 7Q` i?2 }2H/ /iX +@bB;Mb b?Qr i?2 bBM;H2 #2bi }i a+?2+?i2`
T`K2i2`bX h?2 `2;BQMb +Q``2bTQM/BM; iQ i?2 +Hmbi2` aJ6 r2`2 Q#iBM2/ mbBM; KtBKmK@
HBF2HB?QQ/ }iiBM; Q7 i?2 JQMi2@*`HQ bBKmHi2/ /iX
kX9X _1alGha
kN
h#H2 kX9, +QKT`BbQM #2ir22M i?2 #2bi }iiBM; a+?2+?i2` T`K2i2`b M/ i?2B` e3W
+QM}/2M+2 BMi2`pHb 7Q` i?2 /Bz2`2Mi ;Htv ivT2b M/ 2MpB`QMK2MibX
:Htv ivT2
hQiH
hQiH
ai`@7Q`KBM;
ai`@7Q`KBM;
ZmB2b+2Mi
ZmB2b+2Mi
1MpB`QMK2Mi
*Hmbi2`
6B2H/
*Hmbi2`
6B2H/
*Hmbi2`
6B2H/
HQ;(M ∗ /J" )
10.72+0.09
−0.02
10.83+0.01
−0.02
10.87+0.28
−0.18
10.65+0.02
−0.01
10.71+0.04
−0.10
10.77+0.01
−0.01
α
−0.46+0.08
−0.26
−1.01+0.04
−0.02
−1.38+0.38
−0.35
−1.13+0.02
−0.05
−0.28+0.33
−0.14
−0.43+0.02
−0.04
GoF 2.12
4.66
1.44
4.15
1.21
1.39
:QQ/M2bb Q7 6Bi U:Q6V /2}M2/ b χ2 //Q7 7Q` i?2 }2H/ bm`p2v Ur2 bbmK2/
:mbbBM biiBbiB+b QrBM; iQ i?2 H`;2 MmK#2` +QmMib BM i?Bb bm`p2vVX 6Q` i?2
+Hmbi2` }ib r2 mb2/ M MHQ;Qmb 2tT`2bbBQM 7`QK i?2 JtBKmK HBF2HB?QQ/
}iiBM; K2i?Q/X
bBQMH ;`B/ Q7 a+?2+?i2` T`K2i2`b- M/ Bb `2T`2b2Mi2/ #v i?2 #H+F +m`p2 BM
i?2 `B;?i TM2H Q7 6B;X kX8X 6Q` +QKT`2?2MbBp2 +QKT`BbQM #2ir22M i?2 aJ6
7`QK lHi`oAah M/ Qi?2` }2H/ 2biBKi2b r2 `272` iQ JmxxBM 2i HX UkyRjVX
h?2`2 Bi Bb b?QrM i?i i?2 aJ6 Q7 i?2 2MiB`2 ;Htv TQTmHiBQM- K2bm`2/ rBi?
i?Bb +iHQ;m2- Bb BM ;QQ/ ;`22K2Mi rBi? T`2pBQmb K2bm`2K2MibX
hQ #2ii2` +QKT`2 i?2 b?T2 Q7 i?2 iQiH aJ6 BM i?2 irQ 2MpB`QMK2Mib- r2
`272` iQ i?2 H27i TM2H Q7 6B;X kXe- r?2`2 i?2 K;2Mi TQBMib b?Qr i?2 ;Htv
aJ6 7`QK lHi`oAah- M/ i?2 #H+F TQBMib b?Qr i?2 aJ6 7Q` i?2 +Hmbi2`
;HtB2bX h?2 }2H/ /i ?p2 #22M b+H2/ bm+? i?i i?2 a+?2+?i2` 7mM+iBQMb Q7
i?2 +Hmbi2` M/ }2H/ BMi2`b2+i i i?2 +?`+i2`BbiB+ Kbb M ∗ Q7 i?2 +Hmbi2`X h?2
#2bi }iiBM; pHm2b 7Q` i?2 α M/ M ∗ T`K2i2`b `2 ;Bp2M BM h#H2 kX9- rBi?
i?2B` e3XjW +QM}/2M+2 H2p2HbX "2+mb2 r2 QMHv BM+Hm/2/ SQBbbQMBM 2``Q`b QM
i?2 }2H/ aJ6 /i- i?2 :Q6 Q7 i?2 a+?2+?i2` }ib `2 `i?2` ?B;? UmT iQ 9Xee
7Q` i?2 iQiH ;Htv TQTmHiBQMVX i i?Bb H2p2H Q7 /2iBH Bi Bb HbQ TQbbB#H2 i?i
i?2 a+?2+?i2` 7mM+iBQM Bb MQ HQM;2` M /2[mi2 /2b+`BTiBQM Q7 i?2 /iX h?2
K;2Mi +QMiQm`b BM i?2 H27i TM2H Q7 6B;X kXd b?Qr i?2 k@/ +QM}/2M+2 +QMiQm`b
7Q` i?2 }2H/X
q2 b2T`i2 i?2 lHi`oAah ;Htv +iHQ;m2 #2ir22M [mB2b+2Mi ;HtB2b M/
bi`@7Q`KBM; ;HtB2b #v mbBM; i?2B` 2biBKi2/ `2bi@7`K2 l@o M/ o@C +QHQm`bb rb MHQ;QmbHv /QM2 7Q` i?2 +Hmbi2` ;HtB2b BM a2+iX kXjXjX q2 +QKT`2 i?2
b?T2b Q7 i?2 aJ6 7Q` 2+? ;Htv ivT2 #2ir22M i?2 /Bz2`2Mi 2MpB`QMK2MibX
AM i?2 KB//H2 TM2H Q7 6B;X kXe r2 b?Qr i?2 b?T2 Q7 i?2 aJ6 7Q` bi`@
7Q`KBM; ;HtB2b BM i?2 }2H/ UK;2MiV M/ i?2 +Hmbi2` U#H+FV- iQ;2i?2` rBi?
i?2B` #2bi@}iiBM; a+?2+?i2` 7mM+iBQMbX h?2 }2H/ /i ?p2 #22M MQ`KHBb2/ bQ
jy
*>Sh1_ kX h>1 1LoA_PLJ1LhG .1S1L.1L*1 P6 h>1
ah1GG_ Jaa 6lL*hAPL h z ∼ 1
i?i i?2 a+?2+?i2` 7mM+iBQMb BMi2`b2+i i i?2 +?`+i2`BbiB+ Kbb M ∗ 7Q` bi`@
7Q`KBM; ;HtB2b BM i?2 +Hmbi2`X h?2 +Q``2bTQM/BM; e3W M/ N8W +QM}/2M+2
`2;BQMb 7Q` i?2 a+?2+?i2` T`K2i2`b α M/ M ∗ `2 b?QrM BM i?2 KB//H2 TM2H
Q7 6B;X kXdX h?2 #2bi@}iiBM; a+?2+?i2` T`K2i2`b M/ i?2B` 2``Q` #`b `2 HbQ
;Bp2M BM h#H2 kX9X
h?2 /i TQBMib BM 6B;X kXe `2 `#Bi``BHv MQ`KHBb2/ iQ T`QpB/2 7Q` M 2bv
+QKT`BbQM Q7 i?2 b?T2b Q7 i?2 aJ6 #2ir22M i?2 }2H/ M/ +Hmbi2` bKTH2bX b
+QMb2[m2M+2- i?2 φ∗ T`K2i2`b +Q``2bTQM/BM; iQ i?2 #2bi }iiBM; a+?2+?i2`
7mM+iBQM ?p2 MQ /B`2+i K2MBM;X LQ`KHBb2/ #v pQHmK2 i?2 +Hmbi2` Bb- #v
/2}MBiBQM- bm#biMiBHHv Qp2`/2Mb2 +QKT`2/ iQ i?2 }2H/X hQ #2 #H2 iQ #2ii2`
BMi2`T`2i i?2 /Bz2`2M+2b Q7 i?2 aJ6 #2ir22M i?2 }2H/ M/ +Hmbi2` 2MpB`QMK2Mi
BM a2+iX kX8- r2 i?2`27Q`2 MQ`KHBb2 i?2 aJ6 #v i?2 iQiH KQmMi Q7 Kii2` BM
2+? `2bT2+iBp2 T`i Q7 i?2 lMBp2`b2X
6Q` i?2 lHi`oAah }2H/ `272`2M+2 r2 iF2 i?2 iQiH +QKQpBM; pQHmK2
rBi?BM `2/b?B7i `M;2 0.85 < z < 1.20 M/ M mMKbF2/ bm`p2v `2 Q7 RXek
b[m`2 /2;`22 UJmxxBM 2i HX kyRj#VX 7i2` KmHiBTHvBM; i?2 pQHmK2 +Q``2bTQM/@
BM; iQ i?Bb `2 BM i?Bb `2/b?B7i `M;2- 5.9 · 106 JT+3 - #v i?2 p2`;2 Kii2`
/2MbBiv Q7 i?2 lMBp2`b2- #2BM; kX3 ·10−30 ; +K−3 BM Qm` +QbKQHQ;v- r2 }M/ i?i
i?2 iQiH KQmMi UBX2X /`F Kii2` Y #`vQMB+V Q7 Kii2` BM i?Bb pQHmK2 Bb
#Qmi 2.4 · 1017 J" X
:Bp2M i?2 pHm2b 7Q` M200 - r?B+? `2 T`2b2Mi2/ BM h#H2 kXk M/ `2 #b2/
QM i?2 /vMKB+H MHvbBb Q7 i?2 :*Gaa bT2+i`- r2 2biBKi2 i?2 +QM+2M@
i`iBQM T`K2i2` +Q``2bTQM/BM; iQ i?2 L6q T`Q}H2b ULp``Q 2i HX RNNdV
7Q` i?2b2 bvbi2Kb 7`QK .mzv 2i HX Ukyy3VX q2 BMi2;`i2 i?2b2 L6q T`Q}H2b
HQM; i?2 GPa M/ Qmi iQ T`QD2+i2/ `/Bmb Q7 R JT+- vB2H/BM; iQiH Kbb
Q7 5.6 × 1015 J" 7Q` i?2 Ry +Hmbi2`bX aBM+2 a?2H/QM 2i HX UkyyNV M/ >Q2Fbi`
2i HX UkyyyV ?p2 b?QrM i?i- Hi?Qm;? +Hmbi2` +2Mi`2b `2 /QKBMi2/ #v Hm@
KBMQmb Kii2`- i?2 Kbb iQ HB;?i `iBQ UJfGV Q7 +Hmbi2`b rBi?BM /BbiM+2 Q7
R JT+ Bb bBKBH` iQ i?2 +Hmbi2` JfG rBi?BM H`;2` /BbiM+2b- i?Bb 2Mbm`2b i?i
r2 K2bm`2 M/ MQ`KHBb2 i?2 aJ6 BM `2T`2b2MiiBp2 pQHmK2X
6B;X kX3 b?Qrb i?2 iQiH aJ6 7Q` i?2 +Hmbi2` M/ i?2 }2H/- 7i2` MQ`KHBbBM;
#v i?2 iQiH Kbb2b 2biBKi2/ #Qp2X LQi2 i?i i?2`2 Bb- T2` mMBi iQiH Kbb bi`QM; Qp2`/2MbBiv Q7 ;HtB2b i HH bi2HH` Kbb2b r2 T`Q#2 BM i?2 +Hmbi2`
2MpB`QMK2MibX AM i?2 bi2HH` Kbb `M;2 r2 bim/v- i?2 Qp2`/2MbBiv `M;2b 7`QK
KBMBKmK 7+iQ` Q7 RXj i 1010 J" iQ KtBKmK 7+iQ` Q7 jXk i 1011.1 J" X
h?Bb b?Qrb i?i i?2 +Hmbi2`b +QMiBM p2`v #Bb2/ TQTmHiBQM Q7 ;HtB2b- r?2`2
`2HiBp2Hv ?B;? 7`+iBQM Q7 i?2 iQiH #`vQMB+ Kbb Bb i`Mb7Q`K2/ BMiQ bi`bX
h?2 }2H/- BM +QMi`bi- +QMiBMb `2;BQMb bm+? b pQB/b- r?2`2 i?2 bi` 7Q`KiBQM
2{+B2M+v Bb p2`v HQrX
kX8X .Aa*laaAPL
jR
6B;m`2 kX3, aK2 b i?2 H27i
TM2H Q7 6B;X kXe- #mi MQ`@
KHBb2/ #v i?2 iQiH Kbb
U/`F Kii2` Y #`vQMB+V BM
i?2 }2H/ bKTH2 UK;2MiV
M/ +Hmbi2` bKTH2 U#H+FVX
S2` mMBi Q7 iQiH Kbb i?2
+Hmbi2` ?b +H2` Qp2`/2MbBiv
i HH bi2HH` Kbb2b r2 T`Q#2X
1``Q` #`b b?Qr i?2 68W +QM@
}/2M+2 `2;BQMb 7`QK JQMi2@
*`HQ bBKmHiBQMb UQM i?2 +Hmb@
i2` /iV- Q` SQBbbQM 2``Q` #`b
U}2H/ /iVX AM i?2 H27i TM2H
Q7 6B;X kXe r2 T`QpB/2/ M 2b@
B2` +QKT`BbQM Q7 i?2 b?T2b
Q7 i?2 irQ aJ6bX
AM i?Bb b2+iBQM r2 /Bb+mbb i?2 BKTHB+iBQMb Q7 i?2 `2bmHib 7`QK a2+iX kX9X q2
/Bb+mbb BM a2+iX kX8XR i?2 b?T2 Q7 i?2 aJ6 7Q` bi`@7Q`KBM; ;HtB2b- [mB2b+2Mi
;HtB2b- M/ i?2 iQiH ;Htv TQTmHiBQMX q2 KF2 +QKT`BbQM #2ir22M
i?2 +Hmbi2` M/ }2H/- M/ HbQ +QKT`2 Qm` `2bmHib iQ K2bm`2K2Mib 7`QK i?2
HBi2`im`2X q2 T`Q+22/ iQ TTHv bBKTH2 KQ/2H i?i S2M; 2i HX UkyRyV b?Qr2/
iQ ;Bp2 ;QQ/ }i iQ i?2 aJ6 K2bm`2/ i z = 0 7`QK a.aa /iX S2M; 2i HX
UkyRyV +QmH/ MQi 2tTHQ`2 i?2 `2 Q7 ?B;?@z +Hmbi2`b rBi? *PaJPa M/ a.aa
/i- bQ r2 +QM7`QMi Qm` `2bmHib i z = 1 rBi? i?2 T`2/B+iBQMb Q7 i?2B` KQ/2HX
6B;X kXe b?Qrb i?i i?2 b?T2 Q7 i?2 ;Htv aJ6 7Q` i?2 bm#b2i Q7 loC@b2H2+i2/
bi`@7Q`KBM; ;HtB2b Bb bBKBH` #2ir22M i?2 +Hmbi2`b 7`QK :*Gaa M/ i?2
}2H/ 7`QK lHi`oAahX ZmMiBiiBp2Hv- 6B;X kXd BM/B+i2b i?i i?2 +QK#BMiBQM
Q7 #2bi@}iiBM; a+?2+?i2` T`K2i2`b /Bz2`b #v #Qmi 1σ X h?2 HQr@Kbb bHQT2 α
+0.02
Bb −1.38+0.38
−0.35 7Q` i?2 +Hmbi2` p2`bmb −1.13−0.05 BM i?2 }2H/X h?2 +?`+i2`BbiB+
+0.28
+0.02
∗
Kbb M Bb 10.87−0.18 M/ 10.65−0.01 7Q` i?2 +Hmbi2` M/ }2H/- `2bT2+iBp2HvX
q2 /Q MQi KF2 [mMiBiiBp2 +QKT`BbQM #2ir22M i?2 HBi2`im`2 M/ Qm`
K2bm`2K2Mib Q7 i?2 aJ6 7Q` bi`@7Q`KBM; ;HtB2b #2+mb2 i?2 rv i?2b2
jk
*>Sh1_ kX h>1 1LoA_PLJ1LhG .1S1L.1L*1 P6 h>1
ah1GG_ Jaa 6lL*hAPL h z ∼ 1
bi`@7Q`KBM; bKTH2b `2 b2H2+i2/ Bb /Bz2`2Mi 7Q` /Bz2`2Mi bim/B2bX q?2`2b r2
b2H2+i bm#b2i Q7 bi`@7Q`KBM; ;HtB2b #b2/ QM i?2 loC@/B;`K- KQbi Qi?2`
bim/B2b mb2 2Bi?2` bBM;H2 +QHQm` Q` KQ`T?QHQ;B+H b2H2+iBQMX LQM2i?2H2bb- i?2
}M/BM; i?i i?2 b?T2 Q7 i?2 bi`@7Q`KBM; aJ6 Bb BM/2T2M/2Mi Q7 2MpB`QMK2Mi
Bb [mHBiiBp2Hv +QMbBbi2Mi rBi? HQr2` `2/b?B7i K2bm`2K2Mib T`2b2Mi2/ #v 2X;X
"QHxQM2HH 2i HX UkyRyVX LQi2 ?Qr2p2` i?i i?2 +Hmbi2`b BM :*Gaa +QMbiBimi2
Km+? ?B;?2` Qp2`/2MbBiB2b i?M i?2 ?B;?2bi /2MbBiB2b BM i?2 *PaJPa }2H/b
mb2/ #v "QHxQM2HH 2i HX UkyRyVX h?2 b?T2 Q7 i?2 bi`@7Q`KBM; ;Htv aJ6 Bb
HbQ K2bm`2/ iQ #2 `Qm;?Hv +QMbiMi rBi? +QbKB+ iBK2 U2X;X AH#2`i 2i HX kyRyc
"`KK2` 2i HX kyRRVX h?Bb b?Qrb i?i- r?i2p2` T`Q+2bb2b `2 `2bTQMbB#H2
7Q` i?2 [m2M+?BM; Q7 bi` 7Q`KiBQM BM ;HtB2b- i?2v ?p2 iQ QT2`i2 BM bm+? rv i?i i?2 aJ6 Q7 bi`@7Q`KBM; ;HtB2b /Q2b MQi +?M;2 b?T2- 2p2M BM i?2
?B;?2bi /2MbBiv 2MpB`QMK2MibX h?Bb Bb 7mM/K2MiH bbmKTiBQM 7Q` i?2 S2M;
2i HX UkyRyV [m2M+?BM; KQ/2H i?i r2 2KTHQv BM a2+iX kX8XkX
6B;X kXe b?Qrb i?i 7Q` i?2 b2H2+iBQM Q7 [mB2b+2Mi ;HtB2b #b2/ QM i?2 loC
+`Bi2`BQM- i?2 b?T2 Q7 i?2 aJ6 7Q` i?Qb2 ;HtB2b Bb HbQ bBKBH` BM i?2 /Bz2`2Mi
2MpB`QMK2Mib T`Q#2/ #v :*Gaa M/ lHi`oAahX h?2 #2bi }iiBM; α 7Q` i?2
+0.02
+Hmbi2`b Bb −0.28+0.33
−0.14 p2`bmb −0.43−0.04 BM i?2 }2H/X :Bp2M i?2 /2;2M2`+v
#2ir22M α M/ M ∗ - i?2 +QK#BMiBQM Q7 i?2b2 a+?2+?i2` T`K2i2`b- b b?QrM
BM 6B;X kXd- HbQ ;`22b iQ #2ii2` i?M 1σ #2ir22M i?2 }2H/ M/ +Hmbi2`X Ai b22Kb
`2K`F#H2 i?i- r?i2p2` [m2M+?BM; T`Q+2bb2b `2 `2bTQMbB#H2 7Q` i?2 #mBH/@
mT Q7 i?2 [mB2b+2Mi TQTmHiBQM BM i?2b2 +QMi`biBM; 2MpB`QMK2Mib- i?2v rQ`F
BM bm+? rv i?i i?2 `2bmHiBM; aJ6 7Q` [mB2b+2Mi ;HtB2b i J" > RyRy J"
?b bBKBH` b?T2 BM #Qi? 2MpB`QMK2MibX
_m/MB+F 2i HX UkyyNV K2bm`2/ i?2 +Hmbi2` ;Htv HmKBMQbBiv 7mM+iBQM Q7
`2/ b2[m2M+2 ;HtB2b BM i?2 `2/b?B7i `M;2 0.4 < z < 0.8 M/ +QKT`2/
i?2B` K2bm`2K2Mib rBi? i?2 }2H/ HmKBMQbBiv 7mM+iBQMX h?2v HbQ 7QmM/ HBiiH2
/Bz2`2M+2 BM i?2 b?T2 Q7 i?2 [mB2b+2Mi HmKBMQbBiv 7mM+iBQM #2ir22M i?2 irQ
2MpB`QMK2MibX _m/MB+F 2i HX UkyyNV HbQ 7QmM/ ?BMi Q7 b?HHQr2` HQr@Kbb
bHQT2 BM i?2 +Hmbi2` +QKT`2/ iQ i?2 }2H/X LQi2 i?i i?2v mb2 /Bz2`2Mi
b2H2+iBQM Q7 `2/ ;HtB2b- bQ i?i i?2B` `2/ b2[m2M+2 b2H2+i2/ bKTH2 KB;?i #2
+QMiKBMi2/ #v `2//2M2/ bi`@7Q`KBM; ;HtB2bX
q?2`2b i?2 aJ6 7Q` 2+? Q7 i?2 ;Htv ivT2b TT2`b iQ #2 bBKBH` BM i?2
/Bz2`2Mi 2MpB`QMK2Mib T`Q#2/ #v :*Gaa M/ lHi`oAah- 6B;bX kXe kXd
b?Qr i?i i?2 aJ6 7Q` i?2 iQiH ;Htv TQTmHiBQM Bb bB;MB}+MiHv /Bz2`2MiX
h?Bb Bb #2+mb2 i?2 7`+iBQM Q7 [mB2b+2Mi ;HtB2b Bb ?B;?2` BM i?2 +Hmbi2`X h?i
KF2b i?2 HQr@Kbb bHQT2 Q7 i?2 iQiH aJ6 b?HHQr2` BM i?2 +Hmbi2` +QKT`2/
kX8X .Aa*laaAPL
jj
iQ i?2 }2H/ Ub22 6B;X kXeVX h?Bb `2bmHi Bb HbQ +QMbBbi2Mi rBi? i?2 K2bm`2K2Mib
b?QrM 7Q` KQ`2 KQ/2`i2 Qp2`/2MbBiB2b BM i?2 *PaJPa }2H/ #v "QHxQM2HH
2i HX UkyRyVX q2 +QKT`2 Qm` `2bmHib iQ i?2 HBi2`im`2 `2bmHib 7`QK i?2 qAL:aA*"a M/ 1.Bb*a +Hmbi2`b T`Q#2/ BM omH+MB 2i HX UkyRjV- Hi?Qm;? Qm` bKTH2
Bb mMB[m2 BM i?Bb +QK#BMiBQM Q7 `2/b?B7i `M;2 M/ T?QiQK2i`B+ /2Ti?X
omH+MB 2i HX UkyRjV bbmK2/ E`QmT UE`QmT kyyRV AJ6- r?B+? vB2H/b
bi2HH` Kbb2b +QMbBbi2Mi rBi? *?#`B2` iQ rBi?BM b2p2`H yXyR /2tX 6Q` i?2 bK@
TH2 Q7 qAL:a +Hmbi2`b U0.04 < z < 0.07V i?2v K2bm`2 a+?2+?i2` T`K2i2`b
M ∗ = 10.82 ± 0.13 M/ α = −0.88 ± 0.31X Hi?Qm;? i?2 `2/b?B7i /Bbi`B#miBQM
Bb p2`v /Bz2`2Mi 7`QK i?2 :*Gaa bKTH2- i?2v ;`22 rBi?BM 1 − σ rBi? i?2
+QMiQm`b b?QrM BM 6B;X kXdX h?2 K2bm`2/ a+?2+?i2` T`K2i2`b 7Q` i?2 A*"a
+Hmbi2`b U0.3 < z < 0.45V `2 M ∗ = 11.37 ± 0.28 M/ α = −1.29 ± 0.41X LQi2
i?i i?Bb TQBMi HB2b BM i?2 /B`2+iBQM Q7 i?2 +Q``2HiBQM #2ir22M M ∗ M/ α- b Bb
b?QrM BM 6B;XkXdX h?2 bK2 Bb i`m2 7Q` i?2 1.Bb*a +Hmbi2`b U0.4 < z < 0.8V7Q` r?B+? omH+MB 2i HX UkyRjV `2TQ`i a+?2+?i2` T`K2i2`b M ∗ = 11.15±0.07
M/ α = −1.03 ± 0.08X
MQi?2` 7mM/K2MiH Q#b2`p#H2 Q7 TQTmHiBQM Q7 ;HtB2b- #2bB/2b i?2B`
aJ6- Bb i?2 /Bbi`B#miBQM Q7 bT2+B}+ bi` 7Q`KiBQM `i2b Uba6_bVX q2ix2H 2i HX
UkyRkV bim/B2/ i?2 /Bbi`B#miBQM Q7 ba6_b 7Q` +2Mi`H M/ bi2HHBi2 ;HtB2b b
7mM+iBQM Q7 bi2HH` Kbb BM `M;2 Q7 2MpB`QMK2MibX h?2v b?Qr i?i i?2
/Bbi`B#miBQM Q7 ba6_b Bb +H2`Hv #BKQ/H- rBi? +H2` TQTmHiBQMb Q7 +iBp2 M/
TbbBp2 ;HtB2bX AMi2`2biBM;Hv- i?2v b?Qr i?i i?2 HQ+iBQM M/ b?T2 7Q` 2+?
Q7 i?2 irQ T2Fb Bb BM/2T2M/2Mi Q7 2MpB`QMK2Mi- M/ i?i QMHv i?2 `2HiBp2
KQmMib Q7 bi`@7Q`KBM; M/ [mB2b+2Mi ;HtB2b Q++mTvBM; i?2 T2Fb /Bz2` b
7mM+iBQM Q7 2MpB`QMK2MiX GBF2rBb2- JmxxBM 2i HX UkyRkV b?Qr i?i 7Q` i?2
:*Gaa /i i?2 ba6_ Q7 bi`@7Q`KBM; ;HtB2b BM ;Bp2M Kbb #BM Bb HbQ
BM/2T2M/2Mi Q7 2MpB`QMK2MiX h?2b2 `2bmHib `2 MHQ;Qmb iQ Qm` K2bm`2K2Mib
7Q` i?2 aJ6- r?B+? +M HbQ #2 +QMbB/2`2/ b bmK Q7 i?2 [mB2b+2Mi ;Htv
aJ6 M/ i?2 bi`@7Q`KBM; ;Htv aJ6X >pBM; /Bz2`2Mi 7`+iBQM Q7 [mB2b+2Mi
;HtB2b BM QTTQbBM; 2MpB`QMK2Mib- i?2 iQiH ;Htv aJ6 rBHH HQQF /Bz2`2Mi
r?2`2b i?2 aJ6 7Q` 2+? ;Htv ivT2 Bb bBKBH`- MHQ;Qmb iQ r?i q2ix2H
2i HX UkyRkV 7QmM/ 7Q` i?2 /Bbi`B#miBQM Q7 ba6_bX
Ai ?b #22M FMQrM 7Q` b2p2`H /2+/2b i?i i?2 7`+iBQM Q7 [mB2b+2Mi ;Ht@
B2b BM+`2b2b rBi? #Qi? bi2HH` Kbb M/ 2MpB`QMK2MiH /2MbBiv U2X;X "H/`v
2i HX kyyeVX >Qr2p2`- `2+2Mi bim/B2b U2X;X S2M; 2i HX kyRyc JmxxBM 2i HX
kyRkV ?p2 bm;;2bi2/ i?i i?2 [m2M+?BM; Q7 bi`@7Q`KBM; ;HtB2b +M #2 7mHHv
b2T`i2/ BM irQ /BbiBM+i [m2M+?BM; i`+Fb- /m##2/ ǴKbb [m2M+?BM;Ǵ M/ Ǵ2M@
pB`QMK2MiH [m2M+?BM;ǴX h?2 bbmKTiBQM i?i i?2 b?T2 Q7 i?2 ;Htv aJ6
7Q` bi`@7Q`KBM; ;HtB2b Bb mMBp2`bH- r?B+? Bb bmTTQ`i2/ #v Qm` K2bm`2K2MibTH+2b +QMbi`BMib QM i?2 rv i?2b2 [m2M+?BM; T`Q+2bb2b QT2`i2X
j9
*>Sh1_ kX h>1 1LoA_PLJ1LhG .1S1L.1L*1 P6 h>1
ah1GG_ Jaa 6lL*hAPL h z ∼ 1
hQ BMi2`T`2i Qm` Q#b2`p2/ /i BM i?Bb +QMi2ti r2 +QMbB/2` i?2 bBKTH2 KQ/2H
T`QTQb2/ #v S2M; 2i HX UkyRyVX h?Bb KQ/2H Bb #b2/ QM i?2 Q#b2`p2/ +QMbiM+v
BM i?2 b?T2 Q7 i?2 aJ6 7Q` bi`@7Q`KBM; ;HtB2b rBi? `2/b?B7iX S2M; 2i HX
UkyRyV mb2 +QK#BMiBQM Q7 Kbb [m2M+?BM; M/ 2MpB`QMK2MiH [m2M+?BM;T`Q+2bb2b r?B+? i?2v bbmK2 iQ +i BM/2T2M/2MiHv Q7 2+? Qi?2`- iQ #mBH/ mT
i?2 [mB2b+2Mi TQTmHiBQMX h?2 #bB+ /2b+`BTiBQMb 7Q` i?2b2 [m2M+?BM; i`+Fb `2
/2KM/2/ iQ QT2`i2 bm+? i?i i?2 b?T2 Q7 i?2 aJ6 7Q` bi`@7Q`KBM; ;HtB2b
Bb BM/2T2M/2Mi Q7 2MpB`QMK2MiX
"2+mb2 bi`@7Q`KBM; ;HtB2b `2 7Q`KBM; bi`b i `i2 i?i b+H2b `Qm;?Hv
HBM2`Hv rBi? i?2B` bi2HH` Kbb Ui?2 Q#b2`p2/ ba6_ 7Q` i?Bb TQTmHiBQM Bb
`Qm;?Hv BM/2T2M/2Mi Q7 Kbb ULQ2bF2 2i HX kyydVV- Kbb [m2M+?BM; Bb bmT@
TQb2/ iQ T`272`2MiBHHv [m2M+? ?B;? Kbb ;HtB2b BM Q`/2` iQ F22T i?2 aJ6 7Q`
bi`@7Q`KBM; ;HtB2b mM+?M;2/X h?2`27Q`2 i?2 `2bmHiBM; ;Htv aJ6 7Q` i?Bb
[m2M+?2/ TQTmHiBQM Bb 2tT2+i2/ iQ +QMiBM M 2t+2bb Q7 ?B;? Kbb ;HtB2b
M/ ?2M+2 ?b b?HHQr HQr@Kbb bHQT2X AM ?B;?@/2MbBiv 2MpB`QMK2Mib i?2
7`+iBQM Q7 [mB2b+2Mi ;HtB2b BM+`2b2b +QKT`2/ iQ HQr@/2MbBiv 2MpB`QMK2MibX
S2M; 2i HX UkyRyV bbmK2 i?i i?Bb BM+`2b2 Bb +mb2/ #v i?2 T`Q+2bb Q7 2MpB@
`QMK2MiH [m2M+?BM;X h?2 2MpB`QMK2MiH [m2M+?BM; 2{+B2M+v Bb bbmK2/ iQ
#2 BM/2T2M/2Mi Q7 Kbb- bQ i?i i?2 `2bmHiBM; aJ6 Q7 i?2 2MpB`QMK2MiHHv@
[m2M+?2/ ;HtB2b ?b i?2 bK2 b?T2 b i?2 bi`@7Q`KBM; ;Htv aJ6X qBi?
bQK2 //BiBQMH [m2M+?BM; /m2 iQ- r?i i?2v T`2bmK2 iQ #2- K2`;2` T`Q+2bb2bS2M; 2i HX UkyRyV b?Qr2/ i?i i?Bb KQ/2H rQ`Fb p2`v r2HH i `2T`Q/m+BM;
i?2 aJ6 K2bm`2/ BM i?2 `2/b?B7i `M;2 0.02 < z < 0.085 7`QK a.aa ._d
U#xDBM 2i HX kyyNV /iX h?2 `2;BK2 Q7 z ∼ 1 +Hmbi2`b ?Qr2p2` ?b MQi v2i
#22M i2bi2/ ;BMbi i?2B` KQ/2H- bBM+2 i?Bb `M;2 Bb MQi T`Q#2/ #v *PaJPaX
h?2 KQ/2H- ?Qr2p2`- KF2b T`2/B+iBQMb 7Q` i?2 aJ6 i ?B;?2` `2/b?B7ib
Qp2` `M;2 Q7 2MpB`QMK2MiH /2MbBiB2b US2M; 2i HX kyRy- 6B;X RjV- M/ r2
+QKT`2 i?2b2 T`2/B+iBQMb i z = 1 iQ i?2 aJ6b K2bm`2/ 7`QK :*Gaa
M/ lHi`oAahX h?2 T`2/B+iBQMb 7`QK i?2B` KQ/2H `2 b2T`i2/ #v 2MpB@
`QMK2MiH /2MbBiv BM 7Qm` [m`iBH2b- rBi? .R U.9V +Q``2bTQM/BM; iQ i?2 HQr2bi
U?B;?2biV /2MbBiv [m`iBH2X h?2 U2bT2+BHHv 2MpB`QMK2MiHHvV [m2M+?2/ ;HtB2b
+QMi`B#mi2 KQ`2 bm#biMiBHHv iQ i?2 iQiH ;Htv TQTmHiBQM BM .9 +QKT`2/
iQ .R- H2/BM; iQ ?B;?2` 7`+iBQM Q7 [mB2b+2Mi ;HtB2bX h?2 H27i TM2H Q7
6B;X kXN +QKT`2b i?2 T`2/B+iBQM Q7 i?2 ?B;?2bi 2MpB`QMK2MiH /2MbBiv [m`@
iBH2 U.9V rBi? i?2 K2bm`2K2Mi Q7 i?2 +Hmbi2` ;Htv aJ6 7`QK :*GaaX q2
}ii2/ i?2 iQiH MQ`KHBbiBQM b 7`22 T`K2i2`- #mi H27i i?2 `2HiBp2 MQ`@
KHBbiBQMb Q7 bi`@7Q`KBM; M/ [mB2b+2Mi ;HtB2b mM+?M;2/X LQi2 i?i i?2
:*Gaa +Hmbi2`b +QMbiBimi2 i?2 KQbi KbbBp2 bi`m+im`2b `QmM/ z = 1 M/
i?2`27Q`2 +QMiBM ?B;?2` Qp2`/2MbBiB2b i?M i?2 .9 `272`2M+2X L2p2`i?2H2bb- i?2
.9 KQ/2H T`QpB/2b `2bQM#H2 }i iQ i?2 /i- r?2`2 i?2 [mB2b+2Mi 7`+iBQM Q7
;HtB2b #2ir22M i?2 KQ/2H M/ i?2 /i Bb r2HH Ki+?2/X AM 7mim`2 bim/B2b Bi
rQmH/ #2 BMi2`2biBM; iQ +QKT`2 i?2 S2M; 2i HX UkyRyV KQ/2H 7Q` i?2 mTT2` 8W
BM 2MpB`QMK2MiH /2MbBiv iQ i?2 +Hmbi2` /i- r?B+? rQmH/ #2 +HQb2` Ki+?
kX8X .Aa*laaAPL
j8
6B;m`2 kXN, h?2 H27i TM2H +QKT`2b i?2 S2M; 2i HX UkyRyV KQ/2H T`2/B+iBQM BM i?2 2MpB`QM@
K2MiH /2MbBiv [m`iBH2 .9 rBi? Qm` :*Gaa +Hmbi2` aJ6 K2bm`2K2Mib- r?B+? r2`2 H`2/v
T`2b2Mi2/ BM 6B;X kX8 M/ h#H2 kXjX b2T`iBQM #2ir22M i?2 irQ [m2M+?BM; T`Q+2bb2b Bb
K/2X h?2 `B;?i TM2H KF2b bBKBH` +QKT`BbQM #2ir22M i?2 KQ/2H BM [m`iBH2 .R rBi? i?2
lHi`oAah }2H/ /iX LQi2 i?i i?2 `2HiBp2 MQ`KHBbiBQMb Q7 bi`@7Q`KBM; M/ [mB2b+2Mi
TQTmHiBQMb `2 }t2/- M/ i?i i?2 TQTmHiBQMb `2 }ii2/ bBKmHiM2QmbHvX
6B;m`2 kXRy, h?2 +Hmbi2` /ir?B+? r2`2 H`2/v ;Bp2M BM h@
#H2 kXj- rBi? i?2 T`2/B+iBQMb 7`QK
bBKTH2 [m2M+?BM; KQ/2H #b2/
QM S2M; 2i HX UkyRyV BM Bib KQbi
#bB+ 7Q`K- mbBM; lHi`oAah b
bi`iBM; TQBMiX Jbb [m2M+?@
BM; M/ 2MpB`QMK2MiH [m2M+?BM;
`2 bbmK2/ iQ +i BM/2T2M/2MiHvX
h?2 #Hm2 a+?2+?i2` 7mM+iBQM Bb i?2
#2bi }i iQ i?2 bi`@7Q`KBM; ;Htv
TQTmHiBQM M/ i?2 `2/ bQHB/ HBM2
;Bp2b i?2 #2bi }i iQ i?2 [mB2b+2Mi
TQTmHiBQMX h?2 `2/ HBM2 Bb +QK@
TQb2/ Q7 Kbb [m2M+?2/ TQT@
mHiBQM U/Qii2/ `2/ HBM2V- M/ M
2MpB`QMK2MiHHv [m2M+?2/ TQTm@
HiBQM U/b?2/ HBM2VX h?Bb KQ/2H
M22/b 98W //BiBQMH 2MpB`QM@
K2MiH [m2M+?BM; +QKT`2/ iQ
i?2 }2H/ iQ vB2H/ i?2 #2bi }i iQ
i?2 /iX LQi2 i?i i?2 `2/ TQBMib
?p2 #22M Qzb2i #v yXyR /2t 7Q`
#2ii2` pBbB#BHBivX
je
*>Sh1_ kX h>1 1LoA_PLJ1LhG .1S1L.1L*1 P6 h>1
ah1GG_ Jaa 6lL*hAPL h z ∼ 1
iQ i?2B` /2MbBivX
h?2 lHi`oAah }2H/ Bb 2tT2+i2/ iQ +QMiBM `M;2 Q7 2MpB`QMK2MiH
/2MbBiB2bX h?2 K2bm`2/ aJ6 7`QK i?2b2 /i b?QmH/ i?2`27Q`2 #2 Ki+?2/
iQ +QK#BMiBQM Q7 i?2 [email protected] KQ/2HbX >Qr2p2`- i?2 `B;?i TM2H Q7 6B;X kXN
b?Qrb i?i 2p2M i?2 HQr2bi 2MpB`QMK2MiH /2MbBiv [m`iBH2 .R Qp2`T`2/B+ib i?2
[mB2b+2Mi 7`+iBQM Q7 ;HtB2b BM i?2 }2H/ Q7 lHi`oAah i z = 1X h?2 +p2i
Bb i?i i?2 b2T`iBQM Q7 bi`@7Q`KBM; M/ [mB2b+2Mi ;HtB2b Bb /QM2 /Bz2`2MiHv
#2ir22M i?2 /i M/ i?2 KQ/2HX Pm` bKTH2 Q7 loC@b2H2+i2/ bi`@7Q`KBM;
;HtB2b BM+Hm/2b bi`@7Q`KBM; ;HtB2b i?i `2 b22M 2/;2@QM M/ i?2`27Q`2
`2//2M2/ #v /mbi- r?2`2b `2bi@7`K2 Ul@"V +QHQm` b2H2+iBQM- b TTHB2/ BM
S2M; 2i HX UkyRyV- B/2MiB}2b i?2b2 Q#D2+ib b #2BM; QM i?2 `2/ b2[m2M+2X
hQ `2+QM+BH2 i?2 TT`2Mi /Bb;`22K2Mi #2ir22M i?2 /i M/ i?2 S2M;
2i HX UkyRyV KQ/2H BM T`2/B+iBM; i?2 [mB2b+2Mi 7`+iBQM Q7 ;HtB2b- r2 +QMbB/2`
i?2 7QHHQrBM; bBKTHB}2/ MHviB+H KQ/2H r?2`2 r2 QMHv bbmK2 Kbb [m2M+?@
BM; M/ 2MpB`QMK2MiH [m2M+?BM;- M/ MQ //BiBQMH K2`;BM;X q2 TTHv i?Bb
bBKTHB}2/ KQ/2H- #b2/ QM i?2 bK2 T`BM+BTH2b b S2M; 2i HX UkyRyV- iQ i?2
:*Gaa +Hmbi2` /i- #mi mb2 i?2 a+?2+?i2` }ib iQ i?2 lHi`oAah /i b bi`iBM; TQBMiX lHi`oAah Bb i?2 HBKBiBM; +b2 r?2`2 i?2 /QKBMMi [m2M+?BM;
T`Q+2bb Bb Kbb@[m2M+?BM;X
q2 }i i?2 +Hmbi2` /i #v +QK#BMiBQM Q7 i?`22 7mM+iBQMb i?i /2b+`B#2
TQTmHiBQMb Q7 bi`@7Q`KBM; ;HtB2b- Kbb@[m2M+?2/ [mB2b+2Mi ;HtB2b M/
2MpB`QMK2MiHHv@[m2M+?2/ [mB2b+2Mi ;HtB2bX hrQ Q7 i?2b2 7mM+iBQMb `2 ;Bp2M
#v i?2 a+?2+?i2` }ib i?i r2`2 K2bm`2/ 7Q` i?2 lHi`oAah }2H/ TQTmHiBQMX
h?2 [mB2b+2Mi TQTmHiBQM Q7 lHi`oAah Bb 2tT2+i2/ iQ #2 T`BK`BHv Kbb@
[m2M+?2/ i i?2 bi2HH` Kbb `M;2 r2 bim/v- bQ r2 iF2 i?2 b?T2 Q7 i?Bb
aJ6 7Q` i?2 Kbb@[m2M+?2/ TQTmHiBQM M/ HHQr i?2 MQ`KHBbiBQM iQ #2
/Dmbi2/ #v i?2 }iX h?2 aJ6 7Q` bi`@7Q`KBM; ;HtB2b Bb HbQ iF2M 7`QK
lHi`oAah- M/ bBM+2 i?2 7mM+iBQMH 7Q`K Q7 i?Bb /Bbi`B#miBQM Bb bbmK2/ iQ
#2 BM/2T2M/2Mi Q7 2MpB`QMK2Mi- r2 mb2 i?2 b?T2 Q7 i?Bb aJ6 M/ HHQr 7Q` +?M;2 BM i?2 MQ`KHBbiBQMX h?2 i?B`/ aJ6- i?i /2b+`B#2b i?2 TQTmHiBQM Q7
2MpB`QMK2MiHHv@[m2M+?2/ ;HtB2b- Bb bbmK2/ iQ ?p2 i?2 bK2 b?T2 b i?2
aJ6 Q7 bi`@7Q`KBM; ;HtB2b- #mi i?2 MQ`KHBbiBQM +M #2 /Ti2/ BM i?2 }iX
h?2 bmK Q7 i?2 7mM+iBQMb 7Q` #Qi? [m2M+?2/ TQTmHiBQMb Bb }ii2/ iQ i?2 /i
TQBMib i?i /2b+`B#2 i?2 aJ6 7Q` [mB2b+2Mi ;HtB2bX
LQr i?i i?2 7mM+iBQMH 7Q`Kb Q7 i?2 i?`22 TQTmHiBQMb i?i r2 }i `2
/2}M2/- i?2 MQ`KHBbiBQMb `2 /Ti2/ #v }iiBM; irQ 7`22 T`K2i2`b BM i?2
7QHHQrBM; rvX PM2 7`22 T`K2i2` x /2b+`B#2b ?Qr i?2 i?`22 7mM+iBQMb KQp2
`2HiBp2 iQ 2+? Qi?2`- M/ +QMbi`BMb i?2 T2`+2Mi;2 Q7 bi`@7Q`KBM; ;HtB2b
i?i Bb 2MpB`QMK2MiHHv [m2M+?2/ #v i?2 +Hmbi2`X h?Bb ;Bp2b `Bb2 iQ TQTmHiBQM
Q7 2MpB`QMK2MiHHv@[m2M+?2/ ;HtB2b rBi? MQ`KHBbiBQM Q7 x +QKT`2/ iQ
i?2 bi`@7Q`KBM; ;HtB2bX h?2 bi`@7Q`KBM; ;HtB2b `2 `2/m+2/ #v 7+iQ`
Q7 (1 − x)X q2 /Q MQi +?M;2 i?2 `2HiBp2 KQmMi Q7 Kbb@[m2M+?2/ ;HtB2bX
h?2 b2+QM/ 7`22 T`K2i2` /2b+`B#2b i?2 iQiH MQ`KHBbiBQM Q7 i?2b2 i?`22
kX8X .Aa*laaAPL
jd
7mM+iBQMb M/ ?b MQ /B`2+i K2MBM; #2+mb2 i?2 +Hmbi2` M/ }2H/ `2 `#Bi``BHv
MQ`KHBb2/ rBi? `2bT2+i iQ 2+? Qi?2`X
q2 T2`7Q`K KtBKmK@HBF2HB?QQ/ }i iQ i?2 /i TQBMib 7Q` i?2 bi`@
7Q`KBM; M/ [mB2b+2Mi ;HtB2b bBKmHiM2QmbHv- r?2`2 r2 /Ti i?2b2 irQ T@
`K2i2`b- M/ }M/ #2bi }iiBM; pHm2 Q7 x = 0.45+0.04
−0.03 X bbmKBM; i?Bb bBKTH2
TB+im`2 r2 i?2`27Q`2 }M/ i?i- #2bB/2b i?2 [m2M+?BM; T`Q+2bb2b i?i HbQ ?T@
T2M BM i?2 }2H/- i?2 +Hmbi2` 2MpB`QMK2Mi ?b iQ [m2M+? M //BiBQMH 98W Q7
i?2 ;HtB2b iQ vB2H/ i?2 #2bi }iX AM i?2 S2M; .9 KQ/2H i?Bb 2MpB`QMK2MiH
[m2M+?BM; 7`+iBQM `M;2b 7`QK yXRd i 1010 J" iQ yXkk i 1011 J" X 6B;X kXRy
b?Qrb i?2 #2bi }i iQ i?2 Q#b2`p2/ aJ6 BM i?2 +Hmbi2` #b2/ QM i?Bb bBKTH2
KQ/2HX h?2 #Hm2 M/ `2/ bQHB/ HBM2b ;Bp2 i?2 bBKmHiM2Qmb #2bi }i iQ #Qi?
;Htv ivT2b- 7Q` i?2 bi`@7Q`KBM; M/ [mB2b+2Mi TQTmHiBQMb `2bT2+iBp2HvX h?2
`2/ HBM2 Bb +QKTQb2/ Q7 Kbb@[m2M+?2/ TQTmHiBQM U/Qii2/ `2/ HBM2V- M/
M 2MpB`QMK2MiHHv@[m2M+?2/ TQTmHiBQM U/b?2/ HBM2VX h?2 [mB2b+2Mi TQTm@
HiBQM i ?B;? U> 1010.2 J" V Kbb2b Bb /QKBMi2/ #v Kbb@[m2M+?2/ ;HtB2br?BH2 i?2 TQTmHiBQM i HQr2` bi2HH` Kbb2b Bb /QKBMi2/ #v 2MpB`QMK2MiHHv@
[m2M+?2/ ;HtB2bX
h?2 #2bi@}iiBM; KQ/2H /Q2b MQi vB2H/ T2`72+i `2T`2b2MiiBQM Q7 i?2 /ibBM+2 i?2 KQ/2H bB;MB}+MiHv Qp2`T`2/B+ib i?2 MmK#2` Q7 [mB2b+2Mi ;HtB2b BM
i?2 HQr Kbb `2;BK2 U< 1010.6 J" VX i BMi2`K2/Bi2 Kbb2b `QmM/ 1010.9 J"
i?2 KQ/2H T`2/B+ib #Qmi jyW H2bb ;HtB2b i?M i?2 /i b?QrX h?2 Qp2`HH
:QQ/M2bb@Q7@6Bi 7Q` i?Bb KQ/2H Bb kXk T2` /2;`22 Q7 7`22/QKX S2M; 2i HX UkyRyV
+FMQrH2/;2 i?i MQi?2` i2`K- /m2 iQ K2`;2` [m2M+?BM;- Bb `2[mB`2/ iQ }i i?2
/i BM a.aa M/ x*PaJPaX
q2 FMQr i?i K2`;2`b Q++m` BM +Hmbi2`b U2X;X pM .QFFmK 2i HX RNNNVM/ i?i i?2 BMi`@+Hmbi2` HB;?i #mBH/b mT Qp2` iBK2- T`Q##Hv #v /Bb`mTiBQMb
Q7 `2HiBp2Hv HQr Kbb ;HtB2b UJ`i2H 2i HX kyRkVX HbQ r2 FMQr i?i "*:b
?p2 iQ ;`Qr BM bi2HH` Kbb Qp2` iBK2 U2X;X GB/KM 2i HX kyRkV- HBF2Hv #v
+QMbmKBM; BM7HHBM; ;HtB2bX Ai Bb TQbbB#H2 i?i i?2b2 K2`;BM; T`Q+2bb2b `2
`2[mB`2/ iQ `2+QM+BH2 i?2 /Bb;`22K2Mi #2ir22M i?2 /i M/ i?Bb KQ/2HX
h?2 BMi`B;mBM; bBKBH`Biv BM i?2 b?T2 Q7 i?2 [mB2b+2Mi aJ6 #2ir22M i?2
+Hmbi2` M/ }2H/ 2MpB`QMK2Mib i z ∼ 1 bm;;2bib i?i i?2`2 KB;?i #2 bBKTH2`
2tTHMiBQM i?M i?2 S2M; 2i HX UkyRyV KQ/2H i?i /Q2b MQi BMpQHp2 H`;2
KQmMi Q7 K2`;2`bX bBKBH` BMi2`MHHv@/`Bp2M [m2M+?BM; K2+?MBbK KB;?i
#2 `2bTQMbB#H2 7Q` i?2 #mBH/@mT [mB2b+2Mi TQTmHiBQM BM #Qi? 2MpB`QMK2MibX
q2 FMQr i?i i?2 ;2 Q7 [mB2b+2Mi ;Htv i ;Bp2M bi2HH` Kbb /Q2b MQi
bB;MB}+MiHv /2T2M/ QM Bib 2MpB`QMK2Mi Uh?QKb 2i HX kyRyc JmxxBM 2i HX
kyRkVX >Qr2p2`- 7Q` ;HtB2b i ;Bp2M bi2HH` Kbb- i?2B` mM/2`HvBM; /`F
Kii2` Ubm#@V?HQ2b i i?2 iBK2 Q7 7Q`KiBQM KB;?i #2 /Bz2`2Mi #2ir22M i?2
+Hmbi2`b M/ i?2 }2H/X Ǵ1MpB`QMK2Mi [m2M+?BM;Ǵ +QmH/ i?2`27Q`2 `272` iQ M
BMi2`MHHv /`Bp2M T`Q+2bb i?i Bb ++2H2`i2/ BM +Hmbi2` bm#@?HQ2b +QKT`2/ iQ
i?2 }2H/X h?2 }M/BM; i?i i?2 +Hmbi2` 2MpB`QMK2Mi ?b H`2/v 7Q`K2/ H`;2
bi2HH` Kbb +QMi2Mi #v z ∼ 1 Ub22 6B;X kX3V +QKT`2/ iQ i?2 }2H/- M/ i?i i?2
j3
*>Sh1_ kX h>1 1LoA_PLJ1LhG .1S1L.1L*1 P6 h>1
ah1GG_ Jaa 6lL*hAPL h z ∼ 1
7`+iBQM Q7 [mB2b+2Mi ;HtB2b Bb ?B;?2` BM i?2 +Hmbi2` i?M BM i?2 }2H/- +QmH/ #2
+mb2/ #v /Bz2`2Mi 2pQHmiBQM Q7 i?2 mM/2`HvBM; /`F Kii2` ?HQ2bX
/2iBH2/ bim/v Q7 i?2 2pQHmiBQM Q7 i?2 Ubm#@V?HQ Kbb 7mM+iBQM- +QKT`2/
#2ir22M +Hmbi2` M/ }2H/- Bb `2[mB`2/ iQ HQQF BMiQ i?2 /Bz2`2Mi [m2M+?BM; b+2@
M`BQbX Ai Bb `2[mB`2/ iQ i`+2 #+F i?2 Ubm#@V?HQ2b i?i ?Qbi i?2 ;HtB2b r2
bim/v iQ BMp2biB;i2 ?Qr i?2B` T`Q;2MBiQ`b K2`;2 M/ ++`2i2 /m`BM; i?2B` 7Q`@
KiBQM ?BbiQ`vX am+? bim/v +QmH/ #2 mb27mH iQ #2ii2` mM/2`biM/ i?2 T`Q+2bb
Q7 2MpB`QMK2MiH [m2M+?BM;X
AM i?Bb TT2` r2 K2bm`2/ M/ +QKT`2/ i?2 ;Htv aJ6 i z ∼ 1 BM i?2 ?B;?@
/2MbBiv 2MpB`QMK2Mib T`Q#2/ #v :*Gaa M/ i?2 }2H/ 2MpB`QMK2Mi 7`QK lH@
i`oAahX h?2 :*Gaa bKTH2 Bb +QKTQb2/ Q7 Ry `B+?- `2/@b2[m2M+2 b2H2+i2/
+Hmbi2`b BM i?2 `2/b?B7i `M;2 0.86 < z < 1.34X h?2 Eb @#M/ b2H2+i2/ +iHQ;m2
#b2/ QM Q#b2`piBQMb BM RR T?QiQK2i`B+ }Hi2`b HHQr2/ mb iQ 2biBKi2 T?QiQ@
K2i`B+ `2/b?B7ib M/ bi2HH` Kbb2b 7Q` ;HtB2b BM i?2 bim/B2/ `2/b?B7i `M;2
/QrM iQ bi2HH` Kbb Q7 1010 J" X h?2 2ti2MbBp2 bT2+i`Qb+QTB+ bKTH2 Q7
:*Gaa +Qp2`b i?2 KDQ`Biv Q7 i?2 +Hmbi2` K2K#2`b- M/ Bb +`BiB+H iQ ++QmMi
7Q` +QMiKBMMib BM i?2 bKTH2 7Q` r?B+? r2 QMHv ?p2 T?QiQK2i`B+ `2/b?B7ibX
:HtB2b r2`2 b2T`i2/ #v ivT2 Ubi`@7Q`KBM; p2`bmb [mB2b+2MiV #b2/ QM i?2B`
`2bi@7`K2 l@o M/ o@C +QHQm`bX 6Q` 2+? ;Htv BM i?2 T?QiQK2i`B+ bKTH2 r2
2biBKi2/ i?2 T`Q##BHBiv i?i Bi Bb T`i Q7 i?2 +Hmbi2` #b2/ QM Bib ivT2- bi2H@
H` Kbb M/ +Hmbi2`+2Mi`B+ /BbiM+2X h?Bb `2bmHi2/ BM biiBbiB+HHv +QKTH2i2
bKTH2 Q7 +Hmbi2` K2K#2`b iQ K2bm`2 i?2 aJ6 7`QKX
b `272`2M+2 }2H/ aJ6 r2 mb2/ lHi`oAah- r?B+? Bb M2r LA_ bm`p2v
i?i Qp2`HTb rBi? *PaJPa- `2bmHiBM; BM jy #M/ T?QiQK2i`B+ +Qp2`;2 Qp2`
RXek b[m`2 /2;`22bX MHQ;QmbHv iQ :*Gaa- bQm`+2b r2`2 b2H2+i2/ 7`QK i?2
Eb @#M/- M/ ;HtB2b r2`2 b2T`i2/ #2ir22M i?2 bi`@7Q`KBM; M/ [mB2b+2Mi
ivT2 mbBM; i?2 `2bi@7`K2 loC ~mt2bX h?Bb H2/ iQ K2bm`2K2Mi Q7 i?2 aJ6
7Q` }2H/ ;HtB2b i 0.85 < z < 1.20 i?i Bb +QKTH2i2 /QrM iQ bi2HH` Kbb2b
Q7 1010 J" X
lM/2` i?2 bbmKTiBQM Q7 bBM;H2 a+?2+?i2` 7mM+iBQM }i- r2 7QmM/ i?i i?2
b?T2 Q7 i?2 aJ6 7Q` bi`@7Q`KBM; ;HtB2b Bb bBKBH` #2ir22M i?2 +Hmbi2` M/
}2H/ 2MpB`QMK2Mi- M/ i?i i?2 +QK#BMiBQM Q7 #2bi@}iiBM; a+?2+?i2` T`K2@
i2`b α M/ M ∗ ;`22 iQ Rσ #2ir22M i?2 +Hmbi2` M/ }2H/X 6m`i?2`KQ`2- 7Q` i?2
bKTH2b Q7 [mB2b+2Mi ;HtB2b r2 Q#iBM bBKBH` `2bmHiX h?2 b?T2 Q7 i?2 aJ6
7Q` [mB2b+2Mi ;HtB2b Bb bBKBH` #2ir22M i?2 +Hmbi2` M/ }2H/ i J" > 1010 J" X
h?2 b?T2 Q7 i?2 aJ6 7Q` i?2 iQiH ;Htv TQTmHiBQM Bb bB;MB}+MiHv /Bz2`2Mi
#2ir22M i?2 +Hmbi2` M/ }2H/X h?Bb Bb +mb2/ #v /Bz2`2Mi 7`+iBQM Q7 [mB2b@
+2Mi ;HtB2b BM #Qi? 2MpB`QMK2MibX q2 }M/ i?i i?2`2 Bb `2HiBp2 /2}+Bi Q7
;HtB2b rBi? HQr bi2HH` Kbb2b BM i?2 +Hmbi2` +QKT`2/ iQ i?2 }2H/X >Qr2p2`-
kXeX alJJ_u L. *PL*GlaAPLa
jN
r?2M r2 MQ`KHBb2 i?2 aJ6 #v i?2 iQiH KQmMi Q7 Kii2` BM 2+? `2bT2+iBp2
T`i Q7 i?2 lMBp2`b2- r2 }M/ i?i i?2`2 Bb bi`QM; 2t+2bb Q7 ;HtB2b Qp2` i?2
2MiB`2 bi2HH` Kbb `M;2 r2 T`Q#2X h?Bb BM/B+i2b i?i i?2 +Hmbi2` 2MpB`QM@
K2Mi Kmbi ?p2 #22M bm#biMiBHHv KQ`2 2{+B2Mi BM i`Mb7Q`KBM; Kbb BMiQ
bi`b +QKT`2/ iQ i?2 }2H/X LQi2 i?i i?Bb /Q2b MQi BKTHv i?i }2H/ ;HtB2b
`2 H2bb 2{+B2Mi- #mi `i?2` Bi Bb i?2 +QMb2[m2M+2 Q7 i?2 7+i i?i pQB/b +QMiBM
/`F Kii2`- #mi `2HiBp2Hv 72r bi`bX
h?2 bBKBH`Biv BM i?2 b?T2 Q7 i?2 [mB2b+2Mi M/ bi`@7Q`KBM; aJ6 #2@
ir22M i?2 +Hmbi2` M/ i?2 }2H/ BM/B+i2b i?i- B7 /Bz2`2Mi T`Q+2bb2b `2 iQ #2
`2bTQMbB#H2 7Q` i?2 [m2M+?BM; Q7 bi` 7Q`KiBQM BM /Bz2`2Mi 2MpB`QMK2Mib- i?2b2
T`Q+2bb2b ?p2 iQ rQ`F BM bm+? rv i?i i?2 b?T2b Q7 i?2 [mB2b+2Mi M/ bi`@
7Q`KBM; aJ6 `2 bBKBH` BM i?2b2 /Bz2`2Mi 2MpB`QMK2Mib i z = 1X h?Bb TQb2b
+?HH2M;2 iQ MHviB+H KQ/2Hb i?i ii2KTi iQ 2tTHBM i?2 #mBH/@mT Q7 i?2
[mB2b+2Mi TQTmHiBQM #v +QK#BMiBQM Q7 Kbb [m2M+?BM; M/ 2MpB`QMK2Mi
[m2M+?BM;X bBKTH2 KQ/2H bm;;2bib i?i 45+4
−3 W Q7 i?2 bi`@7Q`KBM; ;HtB2b
r?B+? MQ`KHHv rQmH/ #2 7Q`KBM; bi`b BM i?2 }2H/- rQmH/ #2 [m2M+?2/ #v i?2
+Hmbi2`X Hi?Qm;? i?2 T?vbB+H T`Q+2bb2b i?i +mb2 ;HtB2b iQ [m2M+? 2MpB@
`QMK2MiHHv `2 MQi v2i +QKTH2i2Hv mM/2`biQQ/- Bi Bb +H2` i?i T`Q+2bb HBF2
2MpB`QMK2MiH [m2M+?BM; i z ∼ 1 Bb BKTQ`iMiX
q2 i?MF :`2;Q`v _m/MB+F- J`BDM 6`Mt M/ aBKQM2 q2BMKMM 7Q` /Bb+mb@
bBQMb M/ ?2HT7mH bm;;2biBQMb 7Q` i?Bb bim/vX 6m`i?2` r2 i?MF C2M@*?`H2b
*mBHHM/`2 7Q` T`QpB/BM; BM7Q`KiBQM QM i?2 J2;*K KTHB}2` /`B7i T`Q#H2KM/ JB+?2H "HQ;? 7Q` ;2M2`H 722/#+F QM i?2 TT2` /`7iX
_X6XCX pM /2` "m`; M/ >X >Q2Fbi` +FMQrH2/;2 bmTTQ`i 7`QK i?2 L2i?2`@
HM/b P`;MBbiBQM 7Q` a+B2MiB+ _2b2`+? ;`Mi MmK#2` ejNXy9kX3R9X *X GB/KM
Bb i?2 `2+BTB2Mi Q7 M mbi`HBM _2b2`+? *QmM+BH 6mim`2 62HHQrb?BT UT`Q;`K
MmK#2` 6hyNNkk8NVX >X >BH/2#`M/i Bb bmTTQ`i2/ #v i?2 J`B2 *m`B2 AP6
k8kdey- *Ah LiBQMH 62HHQrb?BT- M/ i?2 .6: ;`Mi >B R9N8fk@RX _X.X
;`i27mHHv +FMQrH2/;2b i?2 bmTTQ`i T`QpB/2/ #v i?2 "aG *2Mi2` 7Q` b@
i`QT?vbB+b M/ bbQ+Bi2/ h2+?MQHQ;B2b U*hV- M/ #v 6PL.1*uh ;`Mi
LX RRjy8k3X
"b2/ QM Q#b2`piBQMb Q#iBM2/ i i?2 :2KBMB P#b2`piQ`v- r?B+? Bb QT@
2`i2/ #v i?2 bbQ+BiBQM Q7 lMBp2`bBiB2b 7Q` _2b2`+? BM bi`QMQKv- AM+XmM/2` +QQT2`iBp2 ;`22K2Mi rBi? i?2 La6 QM #2?H7 Q7 i?2 :2KBMB T`i@
M2`b?BT, i?2 LiBQMH a+B2M+2 6QmM/iBQM UlMBi2/ aii2bV- i?2 LiBQMH _2@
b2`+? *QmM+BH U*M/V- *PLA*uh U*?BH2V- i?2 mbi`HBM _2b2`+? *QmM+BH
Umbi`HBV- JBMBbiû`BQ / *BāM+B- h2+MQHQ;B 2 AMQpϽQ U"`xBHV M/ JBMBb@
i2`BQ /2 *B2M+B- h2+MQHQ;ő 2 AMMQp+BƦM S`Q/m+iBp U`;2MiBMVX "b2/ QM
Q#b2`piBQMb Q#iBM2/ rBi? J2;S`BK2fJ2;*K- DQBMi T`QD2+i Q7 *6>h
M/ *1f.SLA- i i?2 *M/@6`M+2@>rBB h2H2b+QT2 U*6>hV r?B+?
9y
*>Sh1_ kX h>1 1LoA_PLJ1LhG .1S1L.1L*1 P6 h>1
ah1GG_ Jaa 6lL*hAPL h z ∼ 1
Bb QT2`i2/ #v i?2 LiBQMH _2b2`+? *QmM+BH UL_*V Q7 *M/- i?2 AMbiB@
imi2 LiBQMH /2b a+B2M+2b /2 HǶlMBp2`b Q7 i?2 *2Mi`2 LiBQMH /2 H _2+?2`+?2
a+B2MiB}[m2 Q7 6`M+2- M/ i?2 lMBp2`bBiv Q7 >rBBX "b2/ QM Q#b2`piBQMb
Q#iBM2/ rBi? qA_*K- DQBMi T`QD2+i Q7 *6>h- hBrM- EQ`2- *M/6`M+2- M/ i?2 *M/@6`M+2@>rBB h2H2b+QT2 U*6>hV r?B+? Bb QT2`i2/
#v i?2 LiBQMH _2b2`+? *QmM+BH UL_*V Q7 *M/- i?2 AMbiBimi2 LiBQMH
/2b a+B2M+2b /2 HǶlMBp2`b Q7 i?2 *2Mi`2 LiBQMH /2 H _2+?2`+?2 a+B2MiB}[m2
Q7 6`M+2- M/ i?2 lMBp2`bBiv Q7 >rBBX h?Bb rQ`F Bb #b2/ BM T`i QM Q#b2`@
piBQMb K/2 rBi? i?2 aTBix2` aT+2 h2H2b+QT2- r?B+? Bb QT2`i2/ #v i?2 C2i
S`QTmHbBQM G#Q`iQ`v- *HB7Q`MB AMbiBimi2 Q7 h2+?MQHQ;v mM/2` +QMi`+i
rBi? LaX amTTQ`i 7Q` i?Bb rQ`F rb T`QpB/2/ #v La i?`Qm;? M r`/
Bbbm2/ #v CSGf*Hi2+?X h?Bb TT2` BM+Hm/2b /i ;i?2`2/ rBi? i?2 eX8 K2i2`
J;2HHM h2H2b+QT2b HQ+i2/ i Gb *KTMb P#b2`piQ`v- *?BH2X h?Bb rQ`F
Bb #b2/ QM Q#b2`piBQMb Q#iBM2/ i i?2 *hAP "HM+Q 9@K i2H2b+QT2b- r?B+?
`2 QT2`i2/ #v i?2 bbQ+BiBQM Q7 lMBp2`bBiB2b 7Q` _2b2`+? BM bi`QMQKv AM+X
Ul_V- mM/2` +QQT2`iBp2 ;`22K2Mi rBi? i?2 La6 b T`i Q7 i?2 LiBQMH
PTiB+H bi`QMQKv P#b2`piQ`B2b ULPPVX "b2/ QM Q#b2`piBQMb i?i r2`2
+``B2/ Qmi mbBM; i?2 o2`v G`;2 h2H2b+QT2 i i?2 1aP S`MH P#b2`piQ`vX
"b2/ QM /i T`Q/m+ib 7`QK Q#b2`piBQMb K/2 rBi? 1aP h2H2b+QT2b i i?2
G aBHH S`MH P#b2`piQ`B2b mM/2` 1aP T`Q;`KK2 A. RdNX@kyy8 M/ QM
/i T`Q/m+ib T`Q/m+2/ #v h1_SAs M/ i?2 *K#`B/;2 bi`QMQKv am`p2v
lMBi QM #2?H7 Q7 i?2 lHi`oAah +QMbQ`iBmKX
h?Bb TT2M/Bt Bb K2Mi iQ ;Bp2 KQ`2 2H#Q`i2 /2b+`BTiBQM Q7 i?2 /i `2/m+@
iBQM bi2Tb Ua2+iX kXXRV M/ BM T`iB+mH` i?2 T`Q+2/m`2 7Q` ?QKQ;2MBbBM; i?2
Sa6 M/ K2bm`BM; +QHQm`b mbBM; :mbbBM r2B;?i2/ T2`im`2b Ua2+iX kXXkVX
"2+mb2 r2 +QK#BM2 T?QiQK2i`B+ /i Qp2` rB/2 `M;2 Q7 rp2H2M;i?b M/
7Q` +Hmbi2`b i?i `2 #Qi? BM i?2 LQ`i?2`M M/ aQmi?2`M bFv- r2 M2+2bb`BHv
?p2 iQ +QK#BM2 /i 7`QK /Bz2`2Mi i2H2b+QT2b M/fQ` BMbi`mK2MibX
h?2 biM/`/ `2/m+iBQM bi2Tb BM+Hm/2 #Bb M/ ~i}2H/ +Q``2+iBQMbX Hi?Qm;?
i?2 BK;2b ?p2 #22M ~i}2H/2/ U2X;X #v Elixir 7Q` i?2 J2;*K /iV iQ vB2H/
mMB7Q`K x2`QTQBMi 7Q` i?2 bQm`+2 ~mt2b- i?2`2 `2 biBHH `2bB/mH #+F;`QmM/
Tii2`Mb /m2 iQ b+ii2`2/ HB;?i- 7`BM;2 `2bB/mHb- M/ KTHB}2` /`B7i U*mBHHM/`2T`Bpi2 +QKKmMB+iBQMVX h?2b2 Tii2`Mb `2 `2bQM#Hv bi#H2 Qp2` iBK2- M/
bBM+2 KQbi 2tTQbm`2b BM ;Bp2M }Hi2` ?p2 #22M iF2M +QMb2+miBp2Hv QM i?2
bK2 MB;?i- r2 +M bm#i`+i i?2b2 #+F;`QmM/ 2z2+ibX q2 /Q i?Bb #v mbBM;
kXX .h S_P*1aaAL: L. *hGP:l1 *_1hAPL
9R
i?2 /Bi?2`2/ Tii2`M Q7 Q#b2`piBQMb iQ /Bz2`2MiBi2 bB;MHb i?i `2 QM }t2/
TQbBiBQM QM i?2 ++/ ``v 7`QK bFv@#QmM/ bB;MHbX
hQ `2KQp2 +QbKB+ `vb 7`QK ++/ BK;2b QM2 mbmHHv +QKT`2b /Bz2`2Mi
7`K2b Q7 i?2 bK2 T`i Q7 i?2 bFvX >Qr2p2`- bBM+2 r2 QMHv ?p2 72r /22T
2tTQbm`2b BM bQK2 Q7 i?2 }Hi2`b- i?2 MmK#2` Q7 Qp2`HTTBM; 7`K2b Q7 Qm` /i
b2i Bb MQi Hrvb bm{+B2Mi iQ #2 #H2 iQ B/2MiB7v HH +QbKB+ `vbX h?2`27Q`2 r2
`2KQp2 +QbKB+ `vb #v mbBM; i?2 GTH+BM *QbKB+ _v A/2MiB}+iBQM K2i?Q/
UpM .QFFmK kyyRV- r?B+? rQ`Fb QM BM/BpB/mH BK;2bX q2 QTiBKBb2 i?2 T@
`K2i2`b BM i?2 b2imT Q7 i?2 +Q/2 bm+? i?i r2 KBMBKBb2 i?2 KQmMi Q7 7Hb2
TQbBiBp2b U#`B;?i bi`bV M/ 7Hb2 M2;iBp2bX q2 /Q i?Bb #v i2biBM; i?2 +Q/2 QM
`M;2 Q7 BK;2b rBi? /Bz2`2Mi b22BM;X h?2 QMHv T`K2i2` i?i ?b bB;MB7@
B+Mi BM~m2M+2 QM i?2 7`+iBQM Q7 7Hb2 TQbBiBp2b M/ 7Hb2 M2;iBp2b Bb objlimr?B+? r2 iF2 iQ #2 jXyX
q2 Q#iBM bi`QK2i`B+ M/ `2HiBp2 T?QiQK2i`B+ bQHmiBQMb 7Q` 2+? +?BT
mbBM; a*JS U"2`iBM kyyeV- r?2`2 r2 mb2 HH 2tTQbm`2b BM ;Bp2M }Hi2` 7Q` HH
+Hmbi2`b i QM+2 iQ 2z2+iBp2Hv BM+`2b2 i?2 bQm`+2 /2MbBiv- M/ Q#iBM bi#H2
bQHmiBQMbX b `272`2M+2 +iHQ;m2 r2 mb2 a.aa@._d /i- Q` i?2 laLP@"
+iHQ;m2 r?2M2p2` +Hmbi2` 7HHb QmibB/2 i?2 a.aa 7QQiT`BMiX h?Bb H2/b iQ
+QMbBbi2Mi bi`QK2i`B+ bQHmiBQMb #2ir22M i?2 /Bz2`2Mi }Hi2`b rBi? M BMi2`MH
b+ii2` Q7 #Qmi 0.05$$ X
"2+mb2 i?2 b?T2 M/ bBx2 Q7 i?2 TQBMi bT`2/ 7mM+iBQM USa6V `2 /Bz2`2Mi
#2ir22M 2tTQbm`2b M/ }Hi2`b- Bi Bb MQM@i`BpBH iQ K2bm`2 ++m`i2 +QHQm`b Q7
;HtvX h?2 bBKTH2bi TT`Q+? rQmH/ #2 iQ iF2 i?2 `iBQ Q7 i?2 iQiH ~mt Q7
;Htv BM /Bz2`2Mi #M/b- #mi i?Bb `2[mB`2b p2`v H`;2 T?QiQK2i`B+ T2`im`2b,
7Q` #+F;`QmM/@HBKBi2/ Q#b2`piBQMb i?2b2 `2 p2`v MQBbvX
>Qr2p2`- `2HB#H2 +QHQm` K2bm`2K2Mi 7Q` i?2 Tm`TQb2 Q7 T?QiQK2i`B+
`2/b?B7i /2i2`KBMiBQM +M HbQ #2 K/2 #v iFBM; i?2 `iBQ Q7 T2`im`2 ~mt2b
BM /Bz2`2Mi #M/b- T`QpB/2/ i?2b2 T2`im`2b `2T`2b2Mi i?2 bK2 BMi`BMbB+ T`i
Q7 i?2 ;HtvX q2 ?p2 7QHHQr2/ i?Bb TT`Q+? ?2`2- #b2/ QM KQ/B}+iBQM Q7
i?2 :mbbBM@T2`im`2@M/@Sa6 U:SV T?QiQK2i`v K2i?Q/ UEmBDF2M kyy3VX
h?2 }`bi bi2T Bb iQ +QMpQHp2 2+? BK;2 rBi? bmBi#H2 TQbBiBQM@/2T2M/2Mi
F2`M2H i?i KQ/B}2b Bib Sa6 BMiQ mMB7Q`K bBx2- +B`+mH` M/ :mbbBMX h?Bb
F2`M2H +M #2 +QMbi`m+i2/ mbBM; i?2 b?T2H2i U_27`2;B2` kyyjc EmBDF2M kyyeV
7Q`KHBbK- b rb /QM2 BM i?2 HQ+H TT`Q+? /2b+`B#2/ BM >BH/2#`M/i 2i HX
UkyRkV- rBi? QM2 KQ/B}+iBQM, ?2`2 r2 HHQr i?2 `2bmHiBM; Sa6 bBx2 7Q` 2+?
BK;2 iQ #2 /Bz2`2MiX aT2+B}+HHv- 7Q` 2+? }Hi2` M/ }2H/ r2 +?QQb2 i?2 bBx2
Q7 i?2 `2bmHiBM; Sa6 iQ #2 bHB;?iHv H`;2` U+X RyWV i?M i?2 K2/BM ;mbbBM
`/Bmb Q7 HH #`B;?i bi`b BM i?2 BK;2bX hQ Q#iBM bi#H2 Sa6 BM i?2 bi+F2/
BK;2b 7Q` 2+? }Hi2` r2 :mbbBMBb2 i?2 Sa6 Q7 i?2 BM/BpB/mH bi`QK2i`B+HHv
+Q``2+i2/ 2tTQbm`2b #27Q`2 bi+FBM;X
9k
*>Sh1_ kX h>1 1LoA_PLJ1LhG .1S1L.1L*1 P6 h>1
ah1GG_ Jaa 6lL*hAPL h z ∼ 1
6QHHQrBM; EmBDF2M Ukyy3V r2 i?2M K2bm`2 ~mt2b BM i?2 7QHHQrBM; rvX
AMbi2/ Q7 mbBM; 7mM+iBQM r?2`2 i?2 r2B;?i Bb 2Bi?2` y Q` R- b Bb i?2 +b2 7Q`
`2;mH` T2`im`2 T?QiQK2i`v K2bm`2/ rBi? iQT@?i r2B;?iBM; 7mM+iBQM U2X;X
#v `mMMBM; a1ti`+iQ` BM /mH BK;2 KQ/2V- r2 mb2 bKQQi? r2B;?i 7mM+iBQM
i?i KF2b mb2 Q7 i?2 7+i i?i i?2 afL 7Q` 2+? TBt2H /2+`2b2b rv 7`QK i?2
T2F TBt2HX q?2M i?2 Sa6 BM 2+? }Hi2` 7QHHQrb :mbbBM T`Q}H2- i?2 +?QB+2
iQ T2`7Q`K T?QiQK2i`v mbBM; :mbbBM r2B;?i 7mM+iBQM Bb +QKTmiiBQMHHv
+QMp2MB2Mi- b r2 b?Qr M2tiX
EmBDF2M Ukyy3V /2}M2b i?2 Ǵ:mbbBM@T2`im`2@M/@Sa6Ǵ ~mt Fq b i?2
:mbbBM r2B;?i2/ ~mt bQm`+2 rQmH/ ?p2 B7 Bi r2`2 Q#b2`p2/ rBi? :mbbBM
Sa6 rBi? i?2 bK2 rB/i? q b i?2 r2B;?i 7mM+iBQMX >2M+2
Fq ≡
#
/` 2
−r 2 /2q 2
#
2−(`−` ) /2q
/` S(` )
,
2πq 2
$
$
$ 2
2
UkXjV
r?2`2 S Bb i?2 BMi`BMbB+ HB;?i /Bbi`B#miBQM Q7 i?2 bQm`+2 UBX2X #27Q`2 bK2`BM;
rBi? i?2 Sa6V M/ q Bb i?2 b+H2 `/Bmb Q7 i?2 r2B;?i 7mM+iBQMX Ai Bb bi`B;?i@
7Q`r`/ iQ bBKTHB7v 1[X kXj iQ
#
2
2
1
Fq = /` S(`) 2−r /4q ,
UkX9V
2
r?B+? b?Qrb i?i Fq Bb :mbbBM@T2`im`2 T?QiQK2i`B+ K2bm`2K2Mi Q7 i?2
BMi`BMbB+ ;HtvX
7i2` ;mbbBMBbBM; i?2 BK;2b- S ?b H`2/v #22M +QMpQHp2/ rBi? :mb@
bBM i?i ?b +QMbiMi /BbT2`bBQM gP SF 7Q` 2+? bi+F2/ BK;2X h?2 ~mt
/Bbi`B#miBQM QM i?2 ++/ Bb i?2`27Q`2
#
2
−(`−`$ )2 /2 gP
SF
$
$ 2
I(`) = /` S(` )
.
UkX8V
2π gP2 SF
MHviB+HHv r2 ?p2 M B/2MiB+H 2tT`2bbBQM 7Q` Fq
#
$ 2
2
2
q2
Fq = /`$ I(`$ ) 2
2−(`−` ) /2(2q −gP SF ) ,
2
2q − gP SF
UkXeV
r?B+? i?mb b?Qrb i?i i?2 bK2 BMi`BMbB+ T2`im`2 ~mt Fq +M #2 K2bm`2/
7`QK BK;2b rBi? `M;2 Q7 :mbbBM Sa6 bBx2bX h?2`27Q`2- 7`QK Qm` Sa6@
;mbbBMBb2/ BK;2b- r2 +M K2bm`2 +QHQm`b Q7 i?2 bK2 BMi`BMbB+ T`i Q7 i?2
;Htv B7 r2 mb2 :mbbBM r2B;?i 7mM+iBQMb iQ K2bm`2 ~mt2bX LQi2 i?i Bi Bb
MQ HQM;2` M2+2bb`v i?i i?2 bi+Fb Q7 i?2 /Bz2`2Mi }Hi2`b ?p2 Sa6 rBi? i?2
bK2 :mbbBM 6q>J- b HQM; b i?2 r2B;?i 7mM+iBQM Bb /Ti2/ ++Q`/BM;Hv
7Q` 2+? }Hi2`X
LK2
aT_*a@yyj9
aT_*a@yyj8
aT_*a@yyje
aT_*a@ykR8
aT_*a@Ry9d
aT_*a@Ry8R
aT_*a@ReRj
aT_*a@ReRe
aT_*a@Rej9
aT_*a@Rej3
uHBK
(K;" )
kjXR#
k9X9#
kkXN#
k9X3
k8X8
k8Xe
k8X8
k8XR
k8Xe
k8X9
gHBK
(K;" )
k8Xj#
k8X9#
k8XR#
k8XR#
k8Xd
k8X3
keXy
k8Xd
keXR
k8XN
rHBK
(K;" )
k9X9#
k9XN#
k9X9#
k9Xd#
k8Xy
k8Xk
k8X9
k8XR
k8Xe
k8X9
iHBK
(K;" )
k9Xj#
k9Xj#
kjXd#
k9X9#
k9Xd
k8Xy
k9Xd
k9X3
k8XR
k8XR
zHBK
(K;" )
kjXN+
kjXe+
kjX8+
kjXd
kjX3
k9Xy
k9Xy
kjX8
k9X9
k9Xk
CHBK
(K;" )
kkX82
k9XR7
kkXd2
kkX32
kjXR/
kjXk/
kjXR/
kjXj/
kjXd/
kjX9/
Eb,HBK
(K;" )
kkXk2
kjX97
kRX82
kkXy2
kkXj/
kkX9/
kkXd/
kkXd/
kjXR/
kkX3/
j.eµKHBK
(K;" )
kRX9;
kkX3;
kRXk;
kRXj;
kRXe;
kRXd;
kkXd;
kkXe;
kjXk;
kjXy;
J2;*K- *M/@6`M+2@>rBB h2H2b+QT2 U*6>hV
#
AJ*a- J;2HHM h2H2b+QT2
+
JPaA*@AA- "HM+Q h2H2b+QT2- *2``Q hQHQHQ AMi2`@K2`B+M P#b2`piQ`v U*hAPV
/
qA_*K- *M/@6`M+2@>rBB h2H2b+QT2 U*6>hV
2
AaSA- "HM+Q h2H2b+QT2- *2``Q hQHQHQ AMi2`@K2`B+M P#b2`piQ`v U*hAPV
7
>qE@A- o2`v G`;2 h2H2b+QT2 UoGhV lh9
;
A_*- aTBix2` aT+2 h2H2b+QT2
9.8µKHBK
(K;" )
kRXk;
kkXj;
kRXR;
kRXR;
kRXj;
kRXj;
kkXe;
kkX9;
kjXk;
kjXR;
8.3µKHBK
(K;" )
RNXd;
kyX3;
RNXN;
RNX8;
RNXd;
RNX3;
kRXk;
kRXk;
kRXe;
kRXj;
3.yµKHBK
(K;" )
RNXe;
kyX9;
RNXe;
RNX9;
RNXd;
RNXd;
kyXN;
kyXN;
kRXj;
kRXj;
kXX .h S_P*1aaAL: L. *hGP:l1 *_1hAPL
h#H2 kX8, h?2 :*Gaa T?QiQK2i`B+ /i b2iX h?2 BMbi`mK2Mib mb2/ 7Q` i?2 /Bz2`2Mi +Hmbi2`b M/ }Hi2`b `2 BM/B+i2/X h?2 HBKBiBM;
K;MBim/2b `2TQ`i2/ `2 K2/BM 8@σ ~mt K2bm`2K2Mi HBKBib 7Q` TQBMi bQm`+2b K2bm`2/ rBi? :mbbBM r2B;?i 7mM+iBQMX
9j
99
*>Sh1_ kX h>1 1LoA_PLJ1LhG .1S1L.1L*1 P6 h>1
ah1GG_ Jaa 6lL*hAPL h z ∼ 1
q2 /Dmbi q iQ 2Mbm`2 i?2 T2`im`2 `Qm;?Hv Ki+?2b 2+? ;HtvǶb bBx2iQ QTiBKBb2 i?2 afLX q2 #b2 Qm` +?QB+2 7Q` q QM i?2 a1ti`+iQ` T`K2i2`
6Glsn_.Ala K2bm`2/ BM i?2 Eb @#M/ BK;2- bm+? i?i q = 0.85·6Glsn@
_.AlaX h?2 7+iQ` Q7 yX38 Bb +?Qb2M iQ QTiBKBb2 i?2 afL Q7 bQm`+2 rBi?
+B`+mH` :mbbBM Sa6@T`Q}H2X 6m`i?2` r2 KF2 bm`2 i?i q Bb +?Qb2M bm+?
i?i q > gP SF BM HH }Hi2`bX
h?Bb K2i?Q/ Bb TTHB2/ iQ K2bm`2 ~mt2b BM i?2 u− Eb @#M/b- #mi bBM+2 i?2
A_* /i bmz2` 7`QK Km+? H`;2` Sa6 r2 rQ`F BM irQ bi;2 T`Q+2bb iQ
BM+Q`TQ`i2 i?2 A_* ~mt2b BM rv i?i `2/m+2b i?2 T`Q#H2Kb 7`QK +QM7mbBQMX
q2 +QMbi`m+i k@bi;2 KmHiB@+QHQm` +iHQ;m2 r?2`2 r2 KmHiBTHv i?2 A_* ~mt
K2bm`2/ BM i?2 #B;;2` T2`im`2 rBi? i?2 7`+iBQMH /Bz2`2M+2 Q7 i?2 Eb @#M/
~mt K2bm`2/ BM i?2 bKHH M/ #B;;2` T2`im`2X h?Bb rv r2 2z2+iBp2Hv +Q``2+i
i?2 A_* ~mt 7Q` #H2M/BM; rBi? M2`#v Q#D2+ib #v bbmKBM; i?2b2 M2B;?#Qm`b
?p2 i?2 bK2 UEb @A_*V +QHQm` b i?2 bQm`+2X 6Q` +QMiKBMiBM; ;HtB2b
i?Bb Bb Q7i2M i?2 +b2X hQ p2`B7v i?i Mv `2bB/mH #H2M/BM; BM i?2 A_* #M/b
/Q2b MQi z2+i Qm` `2bmHib- r2 `2T2i2/ i?2 MHvbBb r?BH2 2t+Hm/BM; i?2 A_*
/i BM HH a1. }ibX q2 }M/ MQ #Bb BM i?2 bi2HH` Kbb 2biBKi2b- M/ 2p2M
7Q` i?2 HQr2bi Kbb2b UJ" = 1010 J" V- 68W Q7 i?2 2biBKi2/ bi2HH` Kbb2b
/Bz2` #v H2bb i?M yXy8 /2t 7`QK Qm` }/m+BH MHvbBbX
q2 +HB#`i2 i?2 T?QiQK2i`B+ x2`QTQBMib QM +iHQ;m2 #bBb #v KFBM;
mb2 Q7 i?2 mMBp2`bHBiv Q7 i?2 bi2HH` HQ+mb U>B;? 2i HX kyyNVX q2 mb2 bi2HH`
/i 7`QK *Qp2v 2i HX UkyydV- +QMiBMBM; eyy-yyy TQBMi bQm`+2b b2H2+i2/ 7`QK
i?2 a.aa M/ kJaa bm`p2vbX "v TTHvBM; HBM2` +QHQm` i2`Kb r2 +QKT`2
i?2b2 +QHQm`b iQ bi`b K2bm`2/ rBi? i?2 }Hi2` b2ib BM i?2 i2H2b+QT2 r2 mb2/X
LQi2 i?i i?2b2 /i `2 2bT2+BHHv 7pQm`#H2 iQ +HB#`i2 i?2 x2`QTQBMib mbBM;
i?2 bi2HH` HQ+mb bBM+2 i?2 KQmMi Q7 ;H+iB+ /mbi Bb p2`v HQr BM i?2b2 }2H/bX
q2 /Ti i?2 x2`QTQBMib Q7 i?2 ugriz CEb }Hi2`b iQ #`BM; i?2 +QHQm`b Q7 bi`b
BM Qm` /i BM HBM2 rBi? i?2 `272`2M+2 +iHQ;m2X *Q``2+iBQMb `2 ivTB+HHv QM
i?2 Q`/2` Q7 yXy8 K;MBim/2bX hQ ++QmMi 7Q` mM+2`iBMiB2b BM i?2 #bQHmi2
x2`QTQBMi Q7 A_*- r2 BM+Hm/2/ RyW bvbi2KiB+ 2``Q` iQ i?2 A_* ~mt2bX
7i2` ;mbbBMBbiBQM- i?2 #+F;`QmM/ MQBb2 BM i?2 BK;2b Bb +Q``2Hi2/
#2ir22M TBt2HbX h?2`27Q`2 r2 2biBKi2 i?2 2``Q`b QM i?2 ~mt K2bm`2K2Mib
BM i?2 bi+Fb Q7 2+? }Hi2` #v K2bm`BM; i?2 ~m+imiBQMb BM i?2 ~mt pHm2b
K2bm`2/ 7`QK T2`im`2b i?i `2 `M/QKHv TH+2/ QM i?2 BK;2bX q2 iF2
++QmMi Q7 i?2 MQM@mMB7Q`K 2tTQbm`2 iBK2 Qp2` i?2 BK;2 bi+FbX h#H2 kX8
b?Qrb M Qp2`pB2r Q7 i?2 K2/BM 8@σ ~mt K2bm`2K2Mib 7Q` TQBMi bQm`+2b BM
2+? }Hi2` M/ 2+? +Hmbi2`X
h?MFb iQ i?2 `2HiBp2Hv rB/2 `2b i?i r2`2 Q#b2`p2/ iQ Q#iBM i?2 :*Gaa
KmHiB@+QHQm` +iHQ;m2b U15$ × 15$ +2Mi`2/ QM i?2 +Hmbi2`b BM i?2 LQ`i?2`M bFv-
kX"X 6A1G. aJ6 J1al_1J1Lha 6_PJ :*Gaa
98
6B;m`2 kXRR, h?2 lHi`oAah UK;2MiV p2`bmb :*Gaa U#H+FV }2H/ K2bm`2K2MibX G27i
TM2H, i?2 iQiH ;Htv TQTmHiBQM BM #Qi? }2H/bX JB//H2 TM2H, i?2 aJ6 7Q` i?2 bm#b2i Q7
bi`@7Q`KBM; ;HtB2bX _B;?i TM2H, i?2 bm#b2i Q7 [mB2b+2Mi ;HtB2bX 1``Q` #`b b?Qr i?2
68W +QM}/2M+2 `2;BQMb 7Q` SQBbbQM 2``Q` #`bX h?2 ;`2v +m`p2b b?Qr i?2 Ry +QMi`B#miBQMb
iQ i?2 }2H/ aJ6 `QmM/ i?2 :*Gaa +Hmbi2`b- r?B+? /Bz2` #2+mb2 Q7 +QbKB+ p`BM+2 /m2
iQ i?2 bKHH pQHmK2b T`Q#2/ BM i?2b2 BM/BpB/mH }2H/bX HbQ i?2 }2H/b +QMi`B#mi2 QMHv /QrM
iQ T`iB+mH` Kbb `2bT2+iBM; i?2 p`vBM; /2Ti?b Q7 i?2 :*Gaa }2H/bX "QiiQK TM2Hb,
i?2 7`+iBQMH /Bz2`2M+2b #2ir22M i?2 irQ }2H/ K2bm`2K2Mib- ;Bp2M #v :*Gaa−lHi`oAah
lHi`oAah
iQ;2i?2` rBi? i?2 2biBKi2/ 2``Q`bX
M/ 10$ × 10$ 7Q` i?2 +Hmbi2`b BM i?2 aQmi?2`M bFvV- i?2b2 /i +M HbQ #2 mb2/
iQ bim/v ;HtB2b QmibB/2 i?2 +Hmbi2`b M/ ?2M+2 iQ K2bm`2 i?2 aJ6 Q7 i?2
;2M2`H }2H/X AM i?Bb TT2M/Bt r2 K2bm`2 i?2 }2H/ aJ6 7`QK :*Gaa BM i?2
`2/b?B7i `M;2 0.85 < z < 1.20 M/ +QKT`2 i?Bb iQ i?2 }2H/ aJ6 K2bm`2/
7`QK lHi`oAahX
aBM+2 i?2 lHi`oAah bKTH2 Bb #b2/ QM `2HiBp2Hv /22T U+QKT`2/ iQ
:*GaaV jy@#M/ T?QiQK2i`B+ +iHQ;m2- Bi Bb +QKTH2i2 BM i?2 Kbb `M;2
UJ" > 1010 J" V i i?Bb `2/b?B7i `M;2X +QKT`BbQM #2ir22M :*Gaa M/
lHi`oAah Kv `2p2H TQbbB#H2 bvbi2KiB+ /Bz2`2M+2b BM i?2 bi2HH` Kbb +i@
HQ;m2b- M/ Mv `2bB/mH BM+QKTH2i2M2bb BM :*GaaX
hQ KBMBKBb2 i?2 +QMiKBMiBQM #v +Hmbi2` ;HtB2b BM i?2 bKTH2- r2 mb2 +QMb2`piBp2 b2H2+iBQM Q7 }2H/ ;HtB2b BM :*GaaX ;Htv Bb +QMbB/2`2/ b
T`i Q7 i?2 }2H/ r?2M Bi Bb b2T`i2/ 7`QK i?2 +Hmbi2` +2Mi`2 #v KQ`2 i?M i?2
M;mH` /BbiM+2 i?i +Q``2bTQM/b iQ RX8 JT+ i i?2 `2/b?B7i Q7 i?2 +Hmbi2`X
6m`i?2`KQ`2 r2 `2[mB`2 }2H/ ;Htv iQ ?p2 T?QiQK2i`B+ `2/b?B7i |zT?Qi −
z+Hmbi2` | > 0.05X 7i2` iFBM; ++QmMi Q7 i?2 `2b KbF2/ #v #`B;?i bi`bi?Bb `2bmHib BM iQiH T`Q#2/ pQHmK2 Q7 i?2 }2H/ i?i Bb ∼ 6 iBK2b bKHH2`
9e
*>Sh1_ kX h>1 1LoA_PLJ1LhG .1S1L.1L*1 P6 h>1
ah1GG_ Jaa 6lL*hAPL h z ∼ 1
BM :*Gaa +QKT`2/ iQ lHi`oAahX aBM+2 i?2 Ry :*Gaa TQBMiBM;b ?p2
/Bz2`2Mi /2Ti?b- r2 ?p2 iQ iF2 ++QmMi Q7 i?2 2biBKi2/ Kbb@+QKTH2i2M2bb
Q7 i?2 /2i2+iBQM #M/bX h?Bb Bb K2bm`2/ bBKBH`Hv b a2+iX kXjXk- #mi mbBM; `2/b?B7i HBKBi Q7 RXky BM 2+? }2H/ UBMbi2/ Q7 i?2 BM/BpB/mH +Hmbi2` `2/b?B7ibVX
h?Bb rv r2 +Q``2+i 7Q` JHK[mBbi #Bb BM bBKBH` rv b BM i?2 1/VKt
r2B;?iBM; K2i?Q/X
6B;X kXRR b?Qrb +QKT`BbQM Q7 i?2 }2H/ aJ6 K2bm`2/ BM i?2 :*Gaa
U#H+FV M/ lHi`oAah UK;2MiV bm`p2vbX h?2 +m`p2b `2 MQ`KHBb2/ rBi?
`2bT2+i iQ i?2 iQiH pQHmK2 bm#i2M/2/ #v i?2b2 bm`p2vbX h?2 ;`2v +m`p2b b?Qr
i?2 +QMi`B#miBQMb iQ i?2 }2H/ aJ6 Q7 i?2 Ry BM/BpB/mH :*Gaa }2H/bX h?2b2
+QMi`B#miBQMb /Bz2` #2ir22M i?2 TQBMiBM;b #2+mb2 i?2B` /2Ti?b `2 /Bz2`2MiM/ HbQ i?2 `2 bm``QmM/BM; i?2 +Hmbi2` i?i Bb T`i Q7 i?2 }2H/ /Bz2`bX h?2
/Bz2`2M+2b BM i?2 ;`2v +m`p2b `2 7m`i?2` +mb2/ #v +QbKB+ p`BM+2X h?2
}2H/ BM i?2 aT_*a@Ry9d BK;2 7Q` 2tKTH2 Bb bB;MB}+MiHv Qp2`/2Mb2 BM i?2
`2/b?B7i #BM 0.85 < z < 1.20X LQi2 ?Qr2p2` i?i- r?2M i?2b2 Ry BM/2T2M/2Mi
bB;?i@HBM2b Q7 :*Gaa `2 +QK#BM2/- i?2 mM+2`iBMiv /m2 iQ +QbKB+ p`BM+2
Bb ;`2iHv `2/m+2/ UaQK2`pBHH2 2i HX kyy9VX
h?2`2 Bb ;2M2`HHv ;QQ/ ;`22K2Mi #2ir22M i?2 }2H/ aJ6 K2bm`2K2Mib
7`QK :*Gaa M/ lHi`oAah- 2bT2+BHHv i i?2 ?B;?@Kbb 2M/X h?Bb BM@
/B+i2b i?i i?2`2 `2 MQ bm#biMiBH bvbi2KiB+ /Bz2`2M+2b #2ir22M i?2 irQ
+iHQ;m2b i?Bb bim/v Bb #b2/ QMX i i?2 HQr@Kbb 2M/ Q7 i?2 aJ6 i?2`2 `2
bQK2 bvbi2KiB+ /Bz2`2M+2b BM #Qi? i?2 bi`@7Q`KBM; M/ [mB2b+2Mi TQTmH@
iBQM- BM+`2bBM; iQ b2p2`H ∼ 10W BM i?2 HQr2bi Kbb #BMbX AM a2+iX kX9XR r2
2tTHBM2/ i?i r2 +Q``2+i2/ i?2 :*Gaa +Hmbi2` aJ6 /i #v i?2b2 +QKTH2i2@
M2bb +Q``2+iBQM 7+iQ`bX h?i rv r2 +M MQi QMHv +QKT`2 i?2 +Hmbi2` M/
}2H/ [mHBiiBp2Hv- #mi ?p2 KQ`2 `2HBbiB+ pB2r QM i?2 #bQHmi2 a+?2+?i2` T@
`K2i2`bX LQi2 i?i i?Bb //BiBQMH +QKTH2i2M2bb +Q``2+iBQM /Q2b MQi +?M;2
Mv Q7 i?2 [mHBiiBp2 bii2K2Mib BM i?Bb TT2`- MQ` z2+ib i?2 +QM+HmbBQMb Q7
i?Bb TT2` BM Mv rvX
*?Ti2`
j
h?2 S?b2 aT+2 M/ ai2HH`
SQTmHiBQMb Q7 *Hmbi2` :HtB2b
i z ∼ R
q2 BMp2biB;i2 i?2 p2HQ+Biv pbX TQbBiBQM T?b2 bT+2 Q7 z ∼ R +Hmbi2` ;HtB2b
mbBM; b2i Q7 9k9 bT2+i`Qb+QTB+ `2/b?B7ib BM N +Hmbi2`b /`rM 7`QK i?2 :*Gaa
bm`p2vX .BpB/BM; i?2 ;Htv TQTmHiBQM BMiQ i?`22 +i2;Q`B2b, [mB2b+2Mi- bi`@
7Q`KBM;- M/ TQbibi`#m`bi- r2 }M/ i?i i?2b2 TQTmHiBQMb ?p2 /BbiBM+i /Bb@
i`B#miBQMb BM T?b2 bT+2X JQbi bi`BFBM; `2 i?2 TQbibi`#m`bi ;HtB2b- r?B+?
`2 +QKKQMHv 7QmM/ i bKHH +Hmbi2`+2Mi`B+ `/BB rBi? ?B;? +Hmbi2`+2Mi`B+ p2@
HQ+BiB2b- M/ TT2` iQ i`+2 +Q?2`2Mi dz`BM;Ǵ BM T?b2 bT+2X lbBM; b2p2`H
xQQK bBKmHiBQMb Q7 +Hmbi2`b r2 b?Qr i?i i?2 +Q?2`2Mi /Bbi`B#miBQM Q7 i?2
TQbibi`#m`bib +M #2 `2bQM#Hv r2HH@`2T`Q/m+2/ mbBM; bBKTH2 [m2M+?BM;
b+2M`BQX aT2+B}+HHv- i?2 T?b2 bT+2 Bb #2bi `2T`Q/m+2/ B7 bi2HHBi2 [m2M+?BM;
Q++m`b QM `TB/ iBK2b+H2 UyXR < τQ < yX8 :v`V 7i2` ;HtB2b KF2 i?2B`
}`bi Tbb;2 Q7 _ ∼ yX8_200 - T`Q+2bb i?i iF2b iQiH iBK2 Q7 ∼ R :v` 7i2`
}`bi BM7HHX h?2 TQbibi`#m`bi T?b2 bT+2 Bb MQi r2HH@`2T`Q/m+2/ mbBM; HQM;
[m2M+?BM; iBK2b+H2b UτQ > yX8V- Q` #v [m2M+?BM; ;HtB2b i H`;2` `/BB U_ ∼
_200 VX q2 +QKT`2 i?Bb [m2M+?BM; iBK2b+H2 iQ i?2 iBK2b+H2 BKTHB2/ #v i?2
bi2HH` TQTmHiBQMb Q7 i?2 TQbibi`#m`bi ;HtB2b M/ }M/ i?i i?2 TQbibi`#m`bi
bT2+i` `2 r2HH@}i #v `TB/ [m2M+?BM; UτQ 4 yX9+0.3
−0.4 :v`V Q7 ivTB+H bi`@
7Q`KBM; ;HtvX h?2 bBKBH`Biv #2ir22M i?2 [m2M+?BM; iBK2b+H2b /2`Bp2/ 7`QK
i?2b2 BM/2T2M/2Mi BM/B+iQ`b Bb bi`QM; +QMbBbi2M+v +?2+F Q7 i?2 [m2M+?BM;
KQ/2HX :Bp2M i?i i?2 KQ/2H BKTHB2b bi2HHBi2 [m2M+?BM; Bb `TB/- M/ Q++m`b
r2HH rBi?BM _200 - i?Bb rQmH/ bm;;2bi i?i `K@T`2bbm`2 bi`BTTBM; Q7 2Bi?2` i?2
?Qi Q` +QH/ ;b +QKTQM2Mi Q7 ;HtB2b `2 i?2 KQbi THmbB#H2 +M/B/i2b 7Q`
i?2 T?vbB+H K2+?MBbKX h?2 ?B;? +QH/ ;b +QMbmKTiBQM `i2b i z ∼ R KF2
9d
Bi /B{+mHi iQ /2i2`KBM2 B7 ?Qi Q` +QH/ ;b bi`BTTBM; Bb /QKBMMic ?Qr2p2`- K2@
bm`2K2Mib Q7 i?2 `2/b?B7i 2pQHmiBQM Q7 i?2 bi2HHBi2 [m2M+?BM; iBK2b+H2 M/
HQ+iBQM Kv #2 +T#H2 Q7 /BbiBM;mBb?BM; #2ir22M i?2 irQX
/K JmxxBM- _2K+Q 6XCX pM /2` "m`;- a2M GX J+:22- JB+?2H "HQ;?- J`BDM
6`Mt- >2MF >Q2Fbi`- JB+?2H CX >m/bQM- HHBbQM LQ#H2- .M aX h`Mm- h`+v q2##:BHHBM qBHbQM- >X EX *X u22
h?2 bi`QT?vbB+H CQm`MH- bm#KBii2/
93
jXRX ALh_P.l*hAPL
9N
Ai Bb r2HH FMQrM i?i ;HtB2b BM ?B;?@/2MbBiv 2MpB`QMK2Mib bm+? b ;Htv
;`QmTb M/ +Hmbi2`b UBX2X- bi2HHBi2 ;HtB2bV 2t?B#Bi ?B;?2` 7`+iBQM Q7 [mB2b@
+2Mi ;HtB2b i }t2/ bi2HH` Kbb i?M KQ`2 BbQHi2/ dz}2H/Ǵ ;HtB2b UBX2X+2Mi`H ;HtB2bVX h?Bb Bb i`m2 #Qi? BM i?2 HQ+H mMBp2`b2 U2X;X- "H/`v 2i HX
kyyec pM /2M "Qb+? 2i HX kyy3c S2M; 2i HX kyRyc q2ix2H 2i HX kyRkc _b@
Kmbb2M 2i HX kyRkc >BM2b 2i HX kyRjV- M/ i z ∼ R U2X;X- Si2H 2i HX kyyNc
*QQT2` 2i HX kyRyc aQ#`H 2i HX kyRRc JmxxBM 2i HX kyRkc _B+?QQ` M@
/`2QM kyRkc pM /2` "m`; 2i HX kyRjc JQF 2i HX kyRjc qQQ 2i HX kyRjc LM@
iBb 2i HX kyRjc EQpÍ 2i HX kyR9VX q?BH2 i?2 +Q``2HiBQM #2ir22M ;Htv
[mB2b+2M+2 M/ 2MpB`QMK2Mi Bb r2HH@2bi#HBb?2/- M/ ?2m`BbiB+ KQ/2Hb i?i +M
2tTHBM i?2 [m2M+?BM; `i2b M/ iBK2b+H2b 2tBbi U2X;X- S2M; 2i HX kyRyc q2i@
x2H 2i HX kyRkV- i T`2b2Mi i?2`2 Bb HBiiH2 /B`2+i Q#b2`piBQMH 2pB/2M+2 HBMFBM;
i?2 bi2HHBi2 [m2M+?BM; K2+?MBbK iQ bT2+B}+ T?vbB+H T`Q+2bb i?i Q++m`b BM
+Hmbi2`bf;`QmTb bm+? b `K@T`2bbm`2 bi`BTTBM; Q7 +QH/ ;b U2X;X- :mMM :Qii
RNdkV Q` ?Qi ;b U2X;- dzbi`M;mHiBQMǴ- G`bQM 2i HX RN3yc "HQ;? 2i HX RNNNVK2`;2`b- Q` ?`bbK2Mi U2X;X- JQQ`2 2i HX RNNeVX PM2 rv iQ KF2 7m`i?2`
T`Q;`2bb BM B/2MiB7vBM; i?2 /QKBMMi bi2HHBi2 [m2M+?BM; K2+?MBbK rBHH #2
iQ #2ii2` +QMbi`BM #Qi? i?2 iBK2b+H2 Qp2` r?B+? [m2M+?BM; Q++m`b- M/ Bib
HQ+iBQM rBi?BM i?2 +Hmbi2`f;`QmT U2X;X- h`2m 2i HX kyyjc JQ`M 2i HX kyydVX
a2KB@MHviB+ KQ/2Hb `2 T?vbB+HHv KQiBpi2/ M/ `2+2Mi rQ`Fb ?p2 `@
;m2/ i?i BM Q`/2` iQ T`QT2`Hv `2T`Q/m+2 i?2 7`+iBQM Q7 [mB2b+2Mi ;HtB2b b 7mM+iBQM Q7 +Hmbi2`+2Mi`B+ `/Bmb- HQM; [m2M+?BM; iBK2b+H2b- Q7 Q`/2` j @ d :v``2 M2+2bb`v U2X;X- q2BMKMM 2i HX kyRyc J+:22 2i HX kyRRc .2 Gm+B 2i HX
kyRkVX hF2M i 7+2 pHm2- i?2b2 HQM; iBK2b+H2b `2 /B{+mHi iQ `2+QM+BH2 rBi?
Q#b2`piBQMb- r?2`2 r2F /2T2M/2M+2 Q7 i?2 bT2+B}+ bi` 7Q`KiBQM `i2b
Uaa6_bV Q7 bi`@7Q`KBM; ;HtB2b QM 2MpB`QMK2Mi Bb 7QmM/ U2X;X- EmzKMM
2i HX kyy9c S2M; 2i HX kyRyc omH+MB 2i HX kyRyc JmxxBM 2i HX kyRkc q2ix2H
2i HX kyRjVX AM/22/- i?2 Q#b2`piBQMb bm;;2bi `TB/ [m2M+?BM; iBK2b+H2 U2X;XJmxxBM 2i HX kyRkc q2ix2H 2i HX kyRjc JQF 2i HX kyRj- Hi?Qm;? b22 h`Mm
2i HX kyRk 7Q` 2pB/2M+2 Q7 HQM;2` iBK2b+H2bV- M/ i?Bb ?vTQi?2bBb Bb bmTTQ`i2/
#v M #mM/M+2 Q7 TQbibi`#m`bi ;HtB2b 7QmM/ BM +Hmbi2`b i ?B;?2` `2/b?B7ib
U2X;X- SQ;;BMiB 2i HX kyy9c h`M 2i HX kyydc SQ;;BMiB 2i HX kyyNc "HQ;?
2i HX kyRRc JmxxBM 2i HX kyRkc JQF 2i HX kyRjc qm 2i HX kyRjVX AMi2`2bi@
BM;Hv- ?v/`Q/vMKB+H bBKmHiBQMb T`2/B+i Km+? 7bi2` [m2M+?BM; iBK2b+H2b
i?M b2KB@MHviB+ KQ/2Hb U2X;X- J+*`i?v 2i HX kyy3c "?û 2i HX kyRjc *2M
kyR9V- M/ bBKBH` iQ i?2 Q#b2`piBQMb- i?2v /Q MQi b22 i?2 bi`QM; /2T2M/2M+2
Q7 aa6_ QM 2MpB`QMK2MiX Ai ?b #22M `;m2/ #v q2ix2H 2i HX UkyRjV i?i QM2
rv iQ `2+QM+BH2 i?2 HQM; [m2M+?BM; iBK2b+H2b `2[mB`2/ #v b2KB@MHviB+ KQ/@
2Hb rBi? i?2 b?Q`i [m2M+?BM; iBK2b+H2b `2[mB`2/ #v Q#b2`piBQMb Bb iQ ?p2 dz/2Hv2/@i?2M@`TB/Ǵ [m2M+?BM;- r?2`2 ;HtB2b 2tT2`B2M+2 ∼ k Ĝ 9 :v` /2Hv
7i2` BM7HH BMiQ +Hmbi2` r?2`2 i?2v #2?p2 b MQ`KH bi`@7Q`KBM; ;HtB2b
*>Sh1_ jX h>1 S>a1 aS*1 L. ah1GG_ SPSlGhAPLa P6
8y
*Glah1_ :GsA1a h z ∼ R
#27Q`2 [m2M+?BM; BM < R :v`X
q?BH2 bQK2 T`Q;`2bb iQr`/b /2}MBM; i?2 iBK2b+H2 Q7 bi2HHBi2 [m2M+?BM;
Bb #2BM; K/2- i?2`2 `2 biBHH 72r Q#b2`piBQMH +QMbi`BMib QM r?2`2 rBi?BM i?2
+Hmbi2`f;`QmT i?2 T`Q+2bb #2;BMb- M/ i?Bb Bb F2v BM7Q`KiBQM 7Q` B/2MiB7vBM;
i?2 T?vbB+H T`Q+2bb2b BMpQHp2/ U2X;X- h`2m 2i HX kyyjVX Pm` T`2pBQmb rQ`F QM
z ∼ R +Hmbi2`b b?Qr2/ i?i TQbibi`#m`bib `2 KQ`2 +QKKQM BM i?2 +Hmbi2`
+Q`2 i?M BM i?2 QmibFB`ib UJmxxBM 2i HX kyRkVc ?Qr2p2`- KQbi T`2pBQmb bim/B2b
bBKTHv +QKT`2/ i?2 TQbibi`#m`bi 7`+iBQM #2ir22M +Hmbi2` M/ }2H/X #2ii2`
rv Q7 B/2MiB7vBM; TQTmHiBQMb rBi?BM i?2 +Hmbi2` Bb iQ mb2 i?2 p2HQ+Biv pbX
TQbBiBQM T?b2 bT+2 Q7 +Hmbi2`b U2X;X- "BpBMQ 2i HX kyykc J?DM 2i HX kyRRc
>BM2b 2i HX kyRjc PKM 2i HX kyRjVX _2+2MiHv LQ#H2 2i HX UkyRjV T2`7Q`K2/
bm+? M MHvbBb QM i?2 KQbi KbbBp2 +Hmbi2` BM i?2 :*Gaa bKTH2- M/
b?Qr2/ i?i i?Bb +QK#BM2/ bT+2 Bb KQ`2 2z2+iBp2 rv Q7 B/2MiB7vBM; bm#@
TQTmHiBQMb rBi?BM i?2 +Hmbi2` i?M bBKTHv mbBM; +Hmbi2`+2Mi`B+ `/BmbX AM
T`iB+mH`- i?2v b?Qr2/ i?i r?BH2 T`QT2`iB2b bm+? b aa6_ M/ .n U9yyyV b?Qr
HBiiH2 /2T2M/2M+2 QM +Hmbi2`+2Mi`B+ `/Bmb- QM+2 ;HtB2b `2 b2T`i2/ BM T?b2
bT+2 i?2`2 Bb /2T2M/2M+2 Q7 i?Qb2 T`QT2`iB2b b 7mM+iBQM Q7 2MpB`QMK2MiX
AM i?Bb TT2` r2 +QMiBMm2 i?2 T?b2 bT+2 MHvbBb TT`Q+? Q7 LQ#H2 2i HX
UkyRjV mbBM; i?2 7mHH :*Gaa bKTH2 M/ 2tKBM2 i?2 HQ+iBQM Q7 +Hmbi2`
;HtB2b i z ∼ R BM T?b2 bT+2X AM T`iB+mH`- r2 7Q+mb QM i?2 TQbibi`#m`bi
TQTmHiBQM BM Q`/2` iQ i`v M/ B/2MiB7v i?2 bi2HHBi2 [m2M+?BM; iBK2b+H2 M/
HQ+iBQM i z ∼ RX h?`Qm;?Qmi i?2 TT2` r2 bbmK2 +QbKQHQ;v rBi? >0 4
dy FK b−1 JT+−1 M/ Ωm 4 yXj- ΩΛ 4 yXdX
Pm` MHvbBb Bb #b2/ QM bT2+i`Qb+QTB+ bKTH2 Q7 9k9 +Hmbi2` ;HtB2b BM N
+Hmbi2`b i z ∼ R 7`QK i?2 :*Gaa bm`p2v Ub22 JmxxBM 2i HX kyRkVX h?2
:*Gaa +Hmbi2`b r2`2 b2H2+i2/ 7`QK i?2 9k /2;2 aT_*a bm`p2v UJmxxBM
2i HX kyyNc qBHbQM 2i HX kyyNV mbBM; M QTiB+HfA_ /TiiBQM Q7 i?2 `2/@
b2[m2M+2 K2i?Q/ U:H//2`b u22 kyyyV i?i Bb /Bb+mbb2/ BM JmxxBM 2i HX
Ukyy3VX h?2 +Hmbi2`b ?p2 ?HQ Kbb2b #2ir22M J200 ∼ URXy @ kyXyV × Ry14 J"
UpM /2` "m`; 2i HX kyR9- :X qBHbQM 2i HX- BM T`2T`iBQMV r?B+? ?p2 #22M
BM72``2/ 7`QK i?2 +Hmbi2` HBM2@Q7@bB;?i p2HQ+Biv /BbT2`bBQM Uσv VX
q2 +HbbB7v 2+? ;Htv BM i?2 bT2+i`Qb+QTB+ bKTH2 b 2Bi?2` bi`@7Q`KBM;[mB2b+2Mi- Q` TQbibi`#m`biR mbBM; i?2 (PAA) 2KBbbBQM HBM2 M/ .n U9yyyV b
/B;MQbiB+bX ai`@7Q`KBM; ;HtB2b `2 +HbbB}2/ b i?Qb2 ;HtB2b rBi? /2i2+i2/
(PAA) 2KBbbBQM- r?2`2 i?2 /2i2+iBQM HBKBi Bb ∼ R @ j³ 2[mBpH2Mi rB/i? U1qVR
AM i?Bb TT2`- 7QHHQrBM; +QMp2MiBQM- r2 `272` iQ i?2b2 ;HtB2b b ǴTQbibi`#m`bibǴX AM
7+i- r2 rBHH b?Qr Hi2` i?i i?2b2 ;HtB2b `2 r2HH@}i #v `TB/Hv@i`mM+i2/ bi`@7Q`KiBQM
rBi? MQ b2+QM/`v Ǵ#m`biǴX h?2v +QmH/ HbQ #2 +QMbB/2`2/ b dz`2+2MiHv [m2M+?2/Ǵ ;HtB2b#mi r2 F22T i?2 TQbibi`#m`bi /2bB;MiBQM 7Q` +QMbBbi2M+v rBi? T`2pBQmb rQ`FX
jXjX :GsA1a AL h>1 *Glah1_ S>a1 aS*1
8R
/2T2M/BM; QM bB;MH@iQ@MQBb2X ZmB2b+2Mi ;HtB2b `2 /2}M2/ b i?Qb2 rBi?Qmi
/2i2+i2/ (PAA) 2KBbbBQMX aBKBH` iQ JmxxBM 2i HX UkyRkV- TQbibi`#m`bi ;HtB2b
`2 /2}M2/ b i?2 bm#b2i Q7 [mB2b+2Mi ;HtB2b i?i ?p2 .n U9yyyV < RX98
UBX2X- i?Qb2 i?i `2 [mB2b+2Mi #mi ?p2 vQmM; bi2HH` TQTmHiBQMbVX h?Bb Bb
bQK2r?i /Bz2`2Mi i?M i?2 KQ`2 ivTB+H 1qU>δ V > j Ĝ 8³ /2}MBiBQM mb2/
7Q` EY ;HtB2b BM KMv bim/B2b U2X;X- .`2bbH2` 2i HX RNNNc "HQ;? 2i HX RNNNc
SQ;;BMiB 2i HX kyyNVc ?Qr2p2`- b /Bb+mbb2/ BM JmxxBM 2i HX UkyRkV- >δ Bb r2F HBM2 M/ Bb /B{+mHi iQ K2bm`2 +QMbBbi2MiHv BM HH bT2+i` i z ∼ R- M/ r2F .n U9yyyV b2`p2b b ;QQ/ T`Qtv 7Q` bi`QM; >δ BM ;HtB2b rBi?Qmi (PAA)
2KBbbBQMX h?2 p2`;2 bi+F2/ bT2+i`mK Q7 Qm` TQbibi`#m`bi /2}MBiBQM /Q2b
?p2 1qU>δ V > 8³ UJmxxBM 2i HX kyRk- b22 HbQ § 8V- M/ bi`QM; "HK2`
HBM2b- bQ QM p2`;2 Qm` b2H2+iBQM Q7 TQbibi`#m`bib Bb +QKT`#H2 iQ i?2 EY
b2H2+iBQM +`Bi2`BX
q2 MQi2 i?i i?2 TQbibi`#mbi +HbbB}+iBQM Kv MQi #2 RyyW +QKTH2i2
7Q` HH ;HtB2b rBi? bi`QM;Hv i`mM+i2/ bi` 7Q`KiBQMX PM2 TQTmHiBQM i?i
rQmH/ #2 KBbb2/ `2 QH/ ;HtB2b i?i 2tT2`B2M+2/ `2+2Mi `2Dmp2MiBQM Q7 bi`
7Q`KiBQM M/ i?2M bm#b2[m2Mi i`mM+iBQM Q7 i?i bi` 7Q`KiBQMX A7 i?2 iQiH
bi2HH` Kbb 7Q`K2/ BM i?i 2p2Mi rb KQ/2bi- i?2v rBHH ?p2 .n U9yyyV > RX98
M/ `2KBM2/ +HbbB}2/ b [mB2b+2MiX Ai Bb mM+H2` B7 bm+? TQTmHiBQM 2tBbib
BM +Hmbi2`b i z ∼ Rc ?Qr2p2`- B7 bQ- i?2M Bi rQmH/ #2 #b2Mi 7`QK i?2 +m``2Mi
bKTH2X
AM i?2 H27i TM2H Q7 6B;m`2 jXR r2 THQi i?2 p2HQ+Biv pbX T`QD2+i2/ +Hmbi2`+2Mi`B+
`/Bmb T?b2 bT+2 U?2`27i2` `272``2/ iQ bBKTHv b dzT?b2 bT+2ǴV 7Q` HH N
+Hmbi2`bX h?2 +Hmbi2`b `2 +QK#BM2/ #v MQ`KHBxBM; 2+? `2HiBp2 iQ Bib σv M/
_200 Ub22 pM /2` "m`; 2i HX kyR9- h#H2 RVX
6B;m`2 jXR b?Qrb i?i i?2`2 Bb b2;`2;iBQM BM T?b2 bT+2 #2ir22M [mB@
2b+2Mi ;HtB2b U`2/ i`BM;H2bV M/ bi`@7Q`KBM; ;HtB2b U#Hm2 i`BM;H2bVX ZmB@
2b+2Mi ;HtB2b `2 ivTB+HHv 7QmM/ i bKHH2` +Hmbi2`+2Mi`B+ `/BB- M/ HQr2`
+Hmbi2`+2Mi`B+ p2HQ+BiB2bc r?2`2b i?2 bi`@7Q`KBM; TQTmHiBQM Bb KQ`2 2ti2M/2/
BM #Qi? TQbBiBQM M/ p2HQ+BivX bBKBH` b2;`2;iBQM #2ir22M i?2b2 ivT2b BM
T?b2 bT+2 ?b HbQ #22M b22M BM HQr2`@`2/b?B7i +Hmbi2` bKTH2b U2X;X- *`H#2`;
2i HX RNNd+c "BpBMQ 2i HX kyykVX q?i Bb bm`T`BbBM; #Qmi 6B;m`2 jXR Bb i?2
T?b2 bT+2 HQ+iBQM Q7 i?2 TQbibi`#m`bi ;HtB2b U;`22M bi`b rBi? +B`+H2bVX
aBKBH` iQ i?2 [mB2b+2Mi ;HtB2b- i?2b2 i2M/ iQ HB2 i bKHH2` +Hmbi2`+2Mi`B+
`/BBc ?Qr2p2`- i?2v ivTB+HHv ?p2 ?B;?2` p2HQ+BiB2bX JQbi bi`BFBM;Hv- i?2b2
;HtB2b b22K iQ pQB/ i?2 dz+Q`2Ǵ `2;BQM BM T?b2 bT+2- r?2`2 i?2 KDQ`Biv
Q7 i?2 [mB2b+2Mi ;HtB2b `2 HQ+i2/X AM/22/- i?2v TT2` iQ 7Q`K `Qm;?Hv +Q?2`2Mi dz`BM;Ǵ bi`m+im`2 `QmM/ i?2 +Q`2 BM T?b2 bT+2- Hi?Qm;? bQK2 Q7
i?2 TQTmHiBQM /Q2b 2ti2M/ b 7` Qmi b _ ∼ _200 X
*>Sh1_ jX h>1 S>a1 aS*1 L. ah1GG_ SPSlGhAPLa P6
8k
*Glah1_ :GsA1a h z ∼ R
6B;m`2 jXR, G27i TM2H, h?2 p2HQ+Biv pbX +Hmbi2`+2Mi`B+ `/Bmb T?b2 bT+2 Q7 ;HtB2b BM
i?2 N :*Gaa +Hmbi2`bX h?2 p2HQ+BiB2b `2 BM mMBib `2HiBp2 iQ i?2 BM/BpB/mH +Hmbi2` p2HQ+Biv
/BbT2`bBQMb M/ i?2 `/BB `2 `2HiBp2 iQ i?2 TQbBiBQM Q7 i?2 #`B;?i2bi +Hmbi2` ;Htv b+H2/
#v i?2 _200 Q7 i?2 +Hmbi2`X h?2 b?/2/ `2;BQMb `2 `#Bi``BHv /2}M2/ #mi `2 BM/B+iBp2 Q7
BM+`2bBM; iBK2 bBM+2 BM7HH Ub22 i2tiVX ZmB2b+2Mi ;HtB2b U`2/ i`BM;H2bV- bi` 7Q`KBM; ;HtB2b
U#Hm2 i`BM;H2bV M/ TQbibi`#m`bi ;HtB2b U;`22M bi`bV HH Q++mTv /BbiBM+i HQ+iBQMb BM T?b2
bT+2X _B;?i TM2Hb, h?2 `iBQ Q7 [mB2b+2Mi M/ TQbibi`#m`bi ;HtB2b +QKT`2/ iQ bi`@
7Q`KBM; ;HtB2b b2T`i2/ BMiQ i?2 i?`22 `/BH #BMb K`F2/ #v i?2 /Qii2/ HBM2b UiQT TM2HVM/ i?2 i?`22 T?b2 bT+2 #BMb K`F2/ #v i?2 b?/2/ `2;BQMb U#QiiQK TM2HVX h?2 2``Q` #`b
`2 Rσ SQBbbQM 2``Q`bX SQbibi`#m`bi ;HtB2b `2 /Bbi`B#mi2/ 7B`Hv mMB7Q`KHv BM i?2 +Hmbi2` #v
`/Bmb UiQT TM2HV- rBi? T2F BM i?2 KB//H2 #BMc ?Qr2p2`- BM T?b2 bT+2 i?2v `2 KQbi
T`2pH2Mi BM i?2 KB//H2 #BM M/ +QKTH2i2Hv #b2Mi BM i?2 BMM2` #BM U#QiiQK TM2HVX
h?2 T?b2 bT+2 b2;`2;iBQM Bb BHHmbi`i2/ BM i?2 iQT `B;?i TM2H Q7 6B;@
m`2 jXR- r?2`2 r2 THQi i?2 MmK#2` Q7 [mB2b+2Mi M/ TQbibi`#m`bi ;HtB2b
`2HiBp2 iQ i?2 MmK#2` Q7 bi`@7Q`KBM; ;HtB2b BM i?`22 `/BH #BMb U/Qii2/
HBM2b BM i?2 H27i TM2HV- M/ i?2 #QiiQK `B;?i TM2H- r?2`2 r2 THQi i?2b2 `@
iBQb BM i?`22 T?b2 bT+2 #BMb Ub?/2/ `BM;@b?T2/ `2;BQMb BM i?2 H27i TM2HVX
h?2 b?/2/ `2;BQMb BM 6B;m`2 jXR ?p2 #22M `#Bi``BHv /2}M2/ iQ 2M?M+2 i?2
+QMi`bi Q7 i?2 TQbibi`#m`bib BM T?b2 bT+2c ?Qr2p2`- i?2v `2 bBKBH` iQ i?2
p`B#H2@bHQT2 dz+?2p`QMbǴ i?i ?p2 #22M b?QrM iQ +Q``2Hi2 rBi? i?2 BM7HH ?Bb@
iQ`B2b Q7 ;HtB2b BM L@#Q/v bBKmHiBQMb Ub22 2X;X- J?DM 2i HX kyRRc h`Mm
2i HX kyRkc PKM 2i HX kyRjVX qBi?BM i?2 KBM `2;BQM Q7 T?b2 bT+2 i?2v `2
HbQ bBKBH` iQ i?2 dzi`mKT2iǴ@b?T2/ +m`p2b Q7 +QMbiMi `f_200 × pfσv i?i
?p2 #22M b?QrM iQ +Q``2Hi2 rBi? BM7HH iBK2b #v LQ#H2 2i HX UkyRjV #b2/ QM
bBKmHi2/ ++`2iBQM ?BbiQ`B2b 7`QK >BM2b 2i HX UkyRkVX h?2`27Q`2- r?BH2 i?2
T`2+Bb2 /2}MBiBQM Q7 i?2 T?b2 bT+2 `2;BQMb Bb `#Bi``v UBX2X- `BM;b- +?2p`QMbQ` +m`p2bV- HH i?`22 `2 [mBi2 bBKBH` M/ +Q``2Hi2 rBi? iBK2 bBM+2 BM7HH BMiQ
i?2 +Hmbi2`- KFBM; i?2K T?vbB+HHv@KQiBpi2/ /2K`+iBQMbX
h?2 `B;?i TM2Hb Q7 6B;m`2 jXR b?Qr i?i i?2 i`2M/ 7Q` i?2 7`+iBQM Q7
jX9X aAJlGh1. *Glah1_ S>a1 aS*1
8j
[mB2b+2Mi ;HtB2b iQ BM+`2b2 iQr`/b i?2 BMM2` #BM Bb `Qm;?Hv i?2 bK2 BM #Qi?
i?2 T?b2 bT+2 M/ `/BH #BMbX AM `/BH #BMb- i?2 7`+iBQM Q7 TQbibi`#m`bi
;HtB2b ?b T2F BM i?2 KB//H2 #BMc ?Qr2p2`- BM T?b2 bT+2 #BMb i?2`2 `2 MQ
TQbibi`#m`bib BM i?2 +Q`2 `2;BQM- M/ i?2 KDQ`Biv `2 +QM}M2/ iQ i?2 KB//H2
T?b2 bT+2 #BM- rBi? KMv #2BM; i HQr `/BB M/ ?B;? p2HQ+BiB2bX
AM Q`/2` iQ i2bi B7 i?2 i?`22 TQTmHiBQMb ?p2 /Bbi`B#miBQMb BM T?b2 bT+2
i?i `2 /Bz2`2Mi- M/ i?i i?2 /Bz2`2M+2 Bb biiBbiB+HHv bB;MB}+Mi- r2 T2`7Q`K
k /BK2MbBQMH EQHKQ;Q`Qp@aKB`MQp i2bi Q7 i?2 /Bbi`B#miBQM U?2`27i2` i?2
dzk.@EaǴ i2biVX *QKT`BM; i?2 k /BK2MbBQMH /Bbi`B#miBQM Q7 TQbibi`#mbib
iQ i?2 [mB2b+2Mi M/ bi`@7Q`KBM; ;HtB2b r2 }M/ S@pHm2b Q7 yXyj3- M/
yXyyN- `2bT2+iBp2HvX q2 i?2`27Q`2 `2D2+i i?2 MmHH ?vTQi?2bBb i?i i?2v `2 HBF2Hv
iQ #2 /`rM 7`QK i?2 bK2 /Bbi`B#miBQM i ∼ kσ M/ jσ - `2bT2+iBp2HvX h?Bb
/2KQMbi`i2b i?i i?2 TQbibi`#m`bib ?p2 /Bbi`B#miBQM i?i Bb /BbiBM+iBp2
+QKT`2/ iQ i?2 Qi?2` ;Htv ivT2b BM T?b2 bT+2X
h?2 +Q?2`2Mi /Bbi`B#miBQM Q7 i?2 TQbibi`#m`bi ;HtB2b BM T?b2 bT+2 bm;;2bib
i?i Bi Kv #2 TQbbB#H2 iQ mb2 i?2B` /Bbi`B#miBQM iQ +QMbi`BM i?2 HQ+iBQM M/
iBK2b+H2 Q7 bi2HHBi2 [m2M+?BM;X AM i?Bb b2+iBQM r2 mb2 b2i Q7 /`F@Kii2`@
QMHv xQQK bBKmHiBQMb Q7 +Hmbi2`b iQ i2bi B7 i?2 T?b2@bT+2 /Bbi`B#miBQM Q7 i?2
TQbibi`#m`bib +M #2 /2b+`B#2/ mbBM; bBKTH2 [m2M+?BM; KQ/2HX
Pm` TT`Q+? Bb iQ bbmK2 i?i bi2HHBi2 [m2M+?BM; Kv #2;BM i T`iB+@
mH` +Hmbi2`+2Mi`B+ `/BmbX q2 i?2M 7QHHQr i?2 2pQHmiBQM Q7 +Hmbi2` bm#?HQb BM
T?b2 bT+2 7i2` i?2v KF2 i?2B` }`bi +`QbbBM; Q7 i?i `/Bmb iQ i2bi B7 i bQK2
iBK2 bi2T U?2`27i2` T V Hi2` i?2v `2b2K#H2 i?2 T?b2 bT+2 Q7 i?2 Q#b2`p2/
TQbibi`#m`bi ;HtB2bX A7 bQ- i?Bb iBK2bi2T rQmH/ #2 BM/B+iBp2 Q7 i?2 bi2HHBi2
[m2M+?BM; iBK2b+H2 U?2`27i2` τQ VX 6Q` i?Bb bBKTH2 2tT2`BK2Mi r2 mb2 i?`22
TQbbB#H2 +Hmbi2`+2Mi`B+ `/BB r?2`2 [m2M+?BM; +QmH/ #2;BM, i?2 }`bi iBK2 bm#@
?HQ Tbb2b _ = yXk8- yX8- M/ RXy _200 X h?2b2 `/BB `Qm;?Hv +Q``2bTQM/ iQ
}`bi Tbb;2 Q7 i?2 +Hmbi2` +Q`2- }`bi Tbb;2 Q7 i?2 /2Mb2 BMi`@+Hmbi2` K2/BmK
UA*JV- M/ }`bi Tbb;2 Q7 i?2 pB`BH `/BmbX q2 7QHHQr i?2 ;HtB2b BM iBK2
bi2Tb Q7 ∆T 4 yXk :v` mT iQ RXR :v` 7i2` +`QbbBM; i?2 [m2M+?BM; HQ+iBQMX
h?Bb iBK2 Bb TT`QtBKi2Hv i?2 HQM;2bi iBK2 i?i r2 +M 2tT2+i iQ /2i2+i i?2
TQbibi`#m`bi bB;Mim`2 BM ;HtB2b U2X;X- "HQ;? 2i HX RNNNc SQ;;BMiB 2i HX
RNNNVX
q2 bi`2bb i?i r?BH2 i?2b2 KQ/2Hb `2 #b2/ QM +QbKQHQ;B+H bBKmHiBQMb
M/ i?2`27Q`2 i?2 Q`#Bib M/ BM7HH `i2b Kv #2 +Q``2+i- i?2v `2 2ti`2K2Hv
bBKTHB}2/ iQv KQ/2Hb 7Q` i?2 bi2HHBi2 [m2M+?BM; T`Q+2bbX h?2 bi2HHBi2 [m2M+?@
BM; T`Q+2bb Bb HKQbi +2`iBMHv KQ`2 +QKTH2t- HBF2Hv rBi? KmHiBTH2 iBK2b+H2bHQ+iBQMb- M/ 2p2M /2T2M/2M+2 QM ;Htv T`QT2`iB2b bm+? b bi2HH` Kbbc
HH Q7 r?B+? Bb M2;H2+i2/ BM i?2 +m``2Mi MHvbBbX 6m`i?2`KQ`2- bQK2 Q7 i?2
*>Sh1_ jX h>1 S>a1 aS*1 L. ah1GG_ SPSlGhAPLa P6
89
*Glah1_ :GsA1a h z ∼ R
-0.1 Gyr > T > 0.1 Gyr
R = 1.0 R200
2
0
-2
0.1 Gyr > T > 0.3 Gyr
2
0
-2
2
0
V /σcluster
0.3 Gyr > T > 0.5 Gyr
R = 0.25 R200
-2
2
Δ
0.5 Gyr > T > 0.7 Gyr
0.7 Gyr > T > 0.9 Gyr
0.9 Gyr > T > 1.1 Gyr
R = 0.5 R200
0
-2
2
0
-2
2
0
-2
0.0
0.5
1.0
1.5
0.0
0.5
1.0
1.5
0.0
0.5
1.0
1.5
Projected Radius [R/R200]
6B;m`2 jXk, h?2 p2`;2 T`QD2+i2/ T?b2 bT+2 Q7 bm#?HQb BM i?2 +QK#BM2/ /`F@Kii2`@QMHv
L@#Q/v xQQK bBKmHiBQMb Q7 7Qm` +Hmbi2`b BM /Bz2`2Mi iBK2 bi2TbX h?2 #H+F TQBMib b?Qr HH
bm#?HQb M/ i?2 `2/ bi`b BM i?2 i?`22 +QHmKMb 7QHHQr bm#?HQb 7i2` i?2v ?p2 K/2 i?2B`
}`bi +`QbbBM; Q7 _ 4 RXy- yX8- M/ yXk8 _200 X 1+? `Qr Bb iBK2bi2T Q7 yXk :v` 7i2` }`bi
+`QbbBM; Q7 i?i `/BmbX aBKBH` iQ i?2 Q#b2`p2/ TQbibi`#m`bib U6B;m`2 jXRV- `BM; bi`m+im`2
+M #2 b22M BM i?2 bm#?HQb 7Q` i?2 b?Q`i2bi iBK2bi2Tb Uh < yX8 :v`V 7i2` bm#?HQb ?p2
+`Qbb2/ i?2 bKHH2` `/BB U_ < yX8_200 VX h?Bb bm;;2bib i?i i?2 [m2M+?BM; iBK2b+H2 7Q` i?2
TQbibi`#m`bib Bb HBF2Hv iQ #2 b?Q`i- M/ Q++m` BM i?2 BMM2` T`i Q7 i?2 +Hmbi2`X
jX9X aAJlGh1. *Glah1_ S>a1 aS*1
88
TQbibi`#m`bib 7QmM/ i H`;2` `/BB `2 HKQbi +2`iBMHv 7HHBM; BM iQ i?2 +Hmb@
i2` H`2/v [m2M+?2/ BM i?2 }2H/- M/ r2 ?p2 MQi ii2KTi2/ iQ ++QmMi 7Q`
dzT`2@[m2M+?2/Ǵ ;HtB2bX h?2 ;QH Q7 i?Bb KQ/2HBM; Bb MQi iQ KF2 +QKT`2@
?2MbBp2 /2b+`BTiBp2 KQ/2H Q7 T?b2 bT+2 M/ [m2M+?BM;- #mi bBKTHv iQ i2bi B7
i?2 +Q?2`2Mi /Bbi`B#miBQM Q7 i?2 TQbibi`#m`bi ;HtB2b BM T?b2 bT+2 +M #2
`2T`Q/m+2/ i HH- M/ B7 bQ- r?i Bi Kv BKTHv 7Q` i?2 HQ+iBQM M/ iBK2b+H2
7Q` bi2HHBi2 [m2M+?BM;X
6Q` i?2 KQ/2Hb r2 mb2 b2i Q7 L@#Q/v xQQK bBKmHiBQMb Q7 7Qm` +Hmbi2`b i?i
r2`2 }`bi T`2b2Mi2/ BM h`Mm 2i HX UkyRkVX q2 `272` i?2 `2/2` iQ i?i TT2`
7Q` /2iBH2/ /2b+`BTiBQM Q7 i?2 bBKmHiBQMbX AM #`B27- i?2 +Hmbi2`b r2`2 b2H2+i2/
7Q` `2@bBKmHiBQM 7`QK H`;2` HQr@`2bQHmiBQM bBKmHiBQM +Qp2`BM; 8Rkh−1 JT+3 X
1+? `2@bBKmHiBQM ?b RkX8 KBHHBQM T`iB+H2b rBi? Kbb Q7 eXRe × Ry8 J" - M/
`2bQHp2b JBHFv@qv@HBF2 ?HQb rBi? ∼ Ryyy T`iB+H2b M/ J;2HHMB+@*HQm/@HBF2
?HQb rBi? ∼ jy T`iB+H2bX h?2 bBKmHi2/ +Hmbi2`b ?p2 pB`BH Kbb2b Q7 Jvir
∼ yXN Ĝ RX3 × Ry15 J" i z = 0- M/ i?2`27Q`2 `2 +QKT`#H2 iQ KbbBp2
+Hmbi2`b bm+? b *QKX h?2B` Kbb2b `2 7+iQ` Q7 72r bKHH2` i z ∼ RKFBM; i?2K M 2t+2HH2Mi Ki+? BM ?HQ Kbb iQ i?2 :*Gaa +Hmbi2`bX
AM Q`/2` iQ KF2 7B` +QKT`BbQM #2ir22M i?2 T?b2 bT+2 Q7 i?2 KQ/2Hb
M/ i?2 Q#b2`piBQMb- +Q``2+iBQM 7Q` i?2 BM+QKTH2i2M2bb Q7 i?2 bT2+i`Qb+QTB+
bKTH2 Kmbi #2 TTHB2/X h?2 :*Gaa bKTH2 ?b ?B;? bT2+i`Qb+QTB+ +QK@
TH2i2M2bb Qp2`HHc ?Qr2p2`- i?2`2 Bb biBHH bT2+i`Qb+QTB+ i`;2iBM; #Bb- rBi?
;HtB2b M2` i?2 +Q`2 #2BM; i`;2i2/ KQ`2 7`2[m2MiHv- M/ KQ`2 KbbBp2 ;Ht@
B2b HbQ #2BM; i`;2i2/ KQ`2 7`2[m2MiHv Ub22 6B;m`2 9 Q7 JmxxBM 2i HX kyRk- 7Q`
i?2 bT2+i`Qb+QTB+ +QKTH2i2M2bb +Q``2+iBQMbVX _i?2` i?M +Q``2+i i?2 Q#b2`@
piBQMb 7Q` +QKTH2i2M2bb- r2 ?p2 K/2 i?2 bBKmHiBQMb dzBM+QKTH2i2Ǵ BM i?2
bK2 rv b i?2 Q#b2`piBQMb- bQ b iQ Ki+? i?2 Q#b2`p2/ T?b2 bT+2X 6Q`
bBKTHB+Biv- i?2 bi2HH` Kbb BM i?2 bBKmHiBQMb ?b #22M bbB;M2/ #v bbmKBM;
mMB7Q`K bi2HH`@Kbb@iQ@?HQ@Kbb `iBQ Q7 yXR M/ i?2 ?HQ Kbb Bb i?2 Kbb
Q7 i?2 bm#?HQ #27Q`2 Bi Bb ++`2i2/X
AM 6B;m`2 jXk r2 THQi i?2 T`QD2+i2/ T?b2 bT+2 Q7 HH ;HtB2b U#H+F TQBMibVb r2HH b i?Qb2 ;HtB2b i?i }`bi +`Qbb2/ i?2 i?`22 [m2M+?BM; `/BB Ui?2 i?`22
+QHmKMb Q7 6B;m`2 jXkV i T 4 y U`2/ bi`bV M/ 7QHHQr i?2B` 2pQHmiBQM i?`Qm;?
p`BQmb iBK2 bi2TbX q2 rQ`F BM T`QD2+i2/ T?b2 bT+2 bQ iQ Ki+? i?2 Q#b2`p@
iBQMH /iX :2M2`HHv bT2FBM;- i?2 K`F2/ ;HtB2b BM 6B;m`2 jXk 7QHHQr bBK@
BH` Q`#BiH ?BbiQ`B2bX JQbi `2 7HHBM; /B`2+iHv BMiQ i?2 +Hmbi2`- HBF2Hv #2+mb2
i?2v `2 ++`2i2/ i?`Qm;? }HK2Mib BM i?Bb 2`Hv bi;2 Q7 +Hmbi2` 7Q`KiBQMX
PM+2 i?2v Tbb i?2 +?Qb2M `/Bmb i?2v +QMiBMm2 iQ TB+F mT p2HQ+Biv M/ KF2
+HQb2 Tbb;2 Q7 i?2 +Hmbi2` +Q`2 UBX2X- }`bi T2`B+2Mi2`VX b rQmH/ #2 2tT2+i2/i?2 Tbb;2 Q7 i?2 +Hmbi2` +Q`2 ?TT2Mb 2`HB2` 7Q` bm#?HQb i?i r2 K`F i
bKHH2` +Hmbi2`+2Mi`B+ `/BB U∼ yXR :v` 7i2` +`QbbBM; yXk8_200 M/ ∼ yX9 :v`
7i2` +`QbbBM; _200 VX .m`BM; i?2B` }`bi +Q`2 Tbb;2 i?2v i2M/ iQ #2 7QmM/ i
?B;? T`QD2+i2/ p2HQ+BiB2b- M/ bKHH +Hmbi2`+2Mi`B+ `/BBX "2+mb2 Q7 i?Bb i?2v
`2 MQi 7QmM/ BM i?2 +2Mi`H dz+Q`2Ǵ `2;BQM Q7 i?2 +Hmbi2` T?b2 bT+2 i HQr
*>Sh1_ jX h>1 S>a1 aS*1 L. ah1GG_ SPSlGhAPLa P6
8e
*Glah1_ :GsA1a h z ∼ R
p2HQ+BiB2b M/ bKHH +Hmbi2`+2Mi`B+ `/BB r?2`2 KMv Q7 i?2 KbbBp2 [mB2b+2Mi
;HtB2b `2bB/2 BM i?2 Q#b2`piBQMb U2X;X- 6B;m`2 jXRVX PM+2 i?2v KF2 ?B;?
p2HQ+Biv +`QbbBM; Q7 i?2 +Q`2 i?2v i2M/ iQ #+FbTHb? Qmi iQ H`;2` `/BB- b
7` Qmi b _ ∼ _200 X 7i2` MQi?2` ∼ yX8 :v` i?2v #2;BM iQ 7HH #+F BM M/
TT2` iQ #2 Km+? KQ`2 KBt2/ BM T?b2 bT+2 rBi? i?2 `2bi Q7 i?2 TQTmH@
iBQMX AM T`iB+mH`- bQK2 ;HtB2b KM;2 iQ T2M2i`i2 BMiQ i?2 HQr@p2HQ+BivbKHH@`/Bmb +Q`2 `2;BQM BM T?b2 bT+2X
q2 KF2 [mMiBiiBp2 +QKT`BbQM #2ir22M i?2 `2/ bi`b BM i?2 R3 TM2Hb
Q7 6B;m`2 jXk rBi? i?2 TQbibi`#m`bib BM 6B;m`2 jXR mbBM; i?2 k.@Ea i2biX HH
#mi 7Qm` Q7 i?2 bMTb?Qib ?p2 S < yXy8 M/ ?2M+2 r2 +M `2D2+i i?2 MmHH
?vTQi?2bBb i?i i?2v `2 /`rM 7`QK i?2 bK2 /Bbi`B#miBQM i ∼ kσ X h?2 7Qm`
`/BBfiBK2b+H2b i?i ?p2 S > yXy8 M/ `2 i?2`27Q`2 +QMbBbi2Mi rBi? #2BM;
/`rM 7`QK i?2 bK2 /Bbi`B#miBQM b i?2 TQbibi`#m`bib `2 7Q` _ 4 yX8_200
i T 4 yXy M/ yX9- M/ 7Q` _ 4 _200 i T 4 yXk M/ yX9X AM #Qi? +b2b b?Q`i iBK2b+H2 Bb 7pQ`2/- M/ [m2M+?BM; QmibB/2 i?2 +Hmbi2` +Q`2 Bb 7pQ`2/X
AMi2`2biBM;Hv- i?2`2 Bb MQ HQM; iBK2bi2T 7`QK Mv `/Bmb r?2`2 i?2 /Bbi`B#miBQM
Q7 bm#?HQb `2b2K#H2b i?2 TQbibi`#m`bi /Bbi`B#miBQMX h?Bb TT2`b iQ `mH2
Qmi i?2 TQbbB#BHBiv Q7 HQM; [m2M+?BM; iBK2b UτQ > yX8 :v`V MQ Kii2` r?i
i?2 [m2M+?BM; `/BmbX h?Bb Kv ?p2 #22M 2tT2+i2/- b i?2 TQbibi`#m`bi
/Bbi`B#miBQM TT2`b +Q?2`2Mi- M/ +Q?2`2Mi bi`m+im`2b rBHH #2+QK2 KBt2/ M/
2p2MimHHv rb?2/ Qmi BM T?b2 bT+2 QM i?2 Q`/2` Q7 /vMKB+H iBK2X
6Q`KHHv- i?2 [m2M+?BM; `/BB M/ iBK2b+H2b HBbi2/ #Qp2 `2 i?2 KQbi
`2T`2b2MiiBp2 Q7 i?2 Qp2`HH /Bbi`B#miBQM Q7 TQbibi`#m`bib- r?B+? 2ti2M/b Qmi
iQ H`;2` `/BBc ?Qr2p2`- 7`QK 2tKBMiBQM Q7 6B;m`2 jXk Bi TT2`b i?i i?2
[m2M+?BM; i _ 4 _200 TM2Hb /Q MQi `2T`Q/m+2 i?2 BMM2` `BM; bi`m+im`2 Q7 i?2
TQbibi`#m`bib T`iB+mH`Hv r2HHX h?2v `2 HBF2Hv biiBbiB+HHv ++2Ti#H2 /Bbi`B@
#miBQMb #2+mb2 i?2v ;2i i?2 Qp2`HH `/BH /Bbi`B#miBQM `2bQM#Hv +Q``2+i- MQi
i?2 `BM; bi`m+im`2X b /Bb+mbb2/ 2`HB2`- bQK2 Q7 i?2 TQbibi`#m`bi TQTmHiBQM
i H`;2` `/Bmb Bb HBF2Hv iQ ?p2 #22M ++`2i2/ 7`QK i?2 }2H/ dzT`2@[m2M+?2/ǴX
h?2 TQbibi`#m`bi 7`+iBQM BM i?2 }2H/ i i?Bb `2/b?B7i Bb ∼ R Ĝ jW- UuM 2i HX
kyyNc JmxxBM 2i HX kyRkV- r?B+? 7Q` ∼ 9yy +Hmbi2` K2K#2`b BKTHB2b KtBKmK
Q7 9 @ Rk ;HtB2b Kv #2 BM7HHBM; H`2/v [m2M+?2/X h?Bb MmK#2` Bb Q7 Q`/2`
i?2 iQiH MmK#2` Q7 TQbibi`#m`bib b22M i _ > yX8 _200 Ub22 6B;m`2 jXRVX A7
i?2 TQbibi`#m`bib `2 H`;2` +Hmbi2`+2Mi`B+ `/BB `2 T`2@[m2M+?2/- i?2M Bi Kv
#2 i?i i?2 BMM2` `BM; Q7 TQbibi`#m`bib Bb i?2 T`BK`BHv bB;Mim`2 Q7 bi2HHBi2
[m2M+?BM;- M/ Bb i?2 /Bbi`B#miBQM i?i b?QmH/ #2 Ki+?2/ BM i?2 bBKmHiBQMX
:Bp2M i?Bb- r2 mb2/ i?2 k.@Ea i2bi iQ /2i2`KBM2 BM r?B+? iBK2bi2Tb i?2
/Bbi`B#miBQM Q7 bm#?HQb Bb +QMbBbi2Mi rBi? i?2 /Bbi`B#miBQM Q7 i?2 TQbibi`#m`bi
TQTmHiBQM mbBM; QMHv bm#?HQb M/ ;HtB2b i _ < yX8_200 - r?2`2 i?2 `BM;
bi`m+im`2 Bb bi`QM;2biX h?2b2 `2bmHib `2 [mBi2 /Bz2`2Mi 7`QK i?2 Qp2`HH k.@Ea
i2biX h?2 irQ iBK2bi2Tb 7Q` _ 4 _200 i?i r2`2 7pQ`2/ #v i?2 7mHH k.@Ea i2bi
?p2 Km+? bKHH2` S pHm2b r?2M QMHv ;HtB2b i _ < yX8_200 `2 +QMbB/2`2/
US 4 yXye M/ yXy8V- M/ `2 `2D2+i2/ i i?2 ∼ kσ H2p2HX h?2 QMHv iBK2bi2Tb i?i
jX9X aAJlGh1. *Glah1_ S>a1 aS*1
8d
R = 0.50
0.1 Gyr < T < 0.5 Gyr
0
Δ
V /σcluster
2
-2
0.0
0.5
1.0
1.5
Projected Radius [R/R200]
6B;m`2 jXj, h?2 T?b2 bT+2 Q7 i?2 bBKmHiBQMb rBi? i?2 bK2 T?b2 bT+2 +QMiQm`b b BM
6B;m`2 jXRX :`22M bi`b b?Qr ;HtB2b i?i }`bi +`Qbb2/ _ 4 yX8_200 rBi?BM i?2 Hbi yXR < T <
yX8 :v`X h?Bb Bb i?2 QMHv [m2M+?BM; iBK2b+H2 M/ HQ+iBQM i?i Tbb2b k.@Ea i2bi 7Q` #Qi?
BM i?2 BMM2` M/ Qmi2` `2;BQMb M/ i?2`27Q`2 ?p2 /Bbi`B#miBQM i?i Bb +QMbBbi2Mi rBi? ?pBM;
#22M /`rM 7`QK i?2 TQbibi`#m`bi /Bbi`B#miBQM BM 6B;m`2 jXR
`2 +QMbBbi2Mi rBi? i?2 Q#b2`piBQMb `2 7Q` [m2M+?BM; i _ 4 yX8_200 i T 4
yXR- yXj- M/ yX8- M/ 7Q` _ 4 yXk8_200 i T 4 yXRX h?2 bi`QM; `BM; bi`m+im`2
7`QK i?2b2 TM2Hb +M HbQ #2 b22M [mBi2 +H2`Hv #v 2v2 BM 6B;m`2 jXkX h?2
`2bQM bQK2 Q7 i?2b2 `2 MQi 7Q`KHHv i?2 ;QQ/ /2b+`BTiBQMb Q7 i?2 /i BM i?2
7mHH k.@Ea i2bi Bb bBKTHv #2+mb2 i?2v 7BH iQ `2T`Q/m+2 i?2 72r TQbibi`#m`bi
;HtB2b i H`;2` `/BB i?i `2 b22M BM i?2 Q#b2`piBQMbX h?2`27Q`2- i?Bb Kv
+imHHv KF2 i?2b2 i?2 KQbi HBF2Hv +M/B/i2b 7Q` i?2 HQ+iBQM M/ iBK2b+H2
Q7 i?2 /QKBMMi bi2HHBi2 [m2M+?BM; T`Q+2bb- 2p2M i?Qm;? b2p2`H Q7 i?2K 7BH
iQ `2T`Q/m+2 i?2 7mHH T?b2 bT+2 /Bbi`B#miBQM Q7 T?b2 bT+2X
A;MQ`BM; i?Bb TQbbB#BHBiv 7Q` i?2 KQK2Mi- M/ ii2KTiBM; Ki+? #Qi? i?2
BMM2` `BM; M/ i?2 Qp2`HH /Bbi`B#miBQM Q7 i?2 TQbibi`#m`bib rBi? bBM;H2 KQ/2Hr2 +QK#BM2/ 72r Q7 i?2 iBK2b+H2b iQ T`Q/m+2 i?2 #2bi@TQbbB#H2 /2b+`BTiBQM
Q7 i?2 Q#b2`piBQMbX h?Bb Bb b?QrM BM 6B;m`2 jXj r?2`2 r2 THQi i?2 /Bbi`B#miBQM
Q7 ;HtB2b [m2M+?2/ i _ 4 yX8_200 QM iBK2b+H2 Q7 yXR < T < yX8X k.@Ea i2bi TTHB2/ iQ i?i /ib2i T`QpB/2b pHm2b Q7 S 4 yXj83 M/ yXR38 7Q`
HH ;HtB2b- M/ ;HtB2b i _ < yX8_200 - `2bT2+iBp2Hv- M/ ?2M+2 Bb i?2 QMHv
KQ/2H i?i ?b ++2Ti#H2 S@pHm2b 7Q` #Qi? i?2 Qp2`HH /Bbi`B#miBQM M/ i?2
*>Sh1_ jX h>1 S>a1 aS*1 L. ah1GG_ SPSlGhAPLa P6
83
*Glah1_ :GsA1a h z ∼ R
BMM2` `BM; bi`m+im`2X q2 i?2`27Q`2 /QTi Bi b Qm` #2bi Qp2`HH KQ/2H 7Q` i?2
HQ+iBQM M/ iBK2b+H2 Q7 bi2HHBi2 [m2M+?BM;X
h?2 T?b2 bT+2 KQ/2HBM; bm;;2bib i?i bi2HHBi2 [m2M+?BM; Q++m`b QM iBK2b+H2
Q7 `Qm;?Hv yXR :v` < τQ < yX8 :v` 7i2` ;HtB2b KF2 i?2B` }`bi Tbb;2 Q7 _
∼ yX8_200 X h?2 bBKmHiBQMb BKTHv i?i i?2 K2/BM iBK2 Bi iF2b 7Q` M ++`2i2/
;Htv iQ i`p2H 7`QK kXy_200 iQ yX8_200 Bb ∼ yXd ± yXk :v`- r?2`2 i?2 mM+2`@
iBMiv Bb i?2 Rσ `Kb /BbT2`bBQM BM BM7HH iBK2bX h?Bb b+2M`BQ Bb [mHBiiBp2Hv
bBKBH` iQ i?2 dz/2Hv2/@i?2M@`TB/Ǵ [m2M+?BM; KQ/2H T`QTQb2/ #v q2ix2H 2i HX
UkyRjV- r?2`2 i?2 [m2M+?BM; iBK2 TT2`b iQ #2 `Qm;?Hv bBKBH`- #mi i?2 /2Hv
iBK2 Kv #2 7+iQ` Q7 ∼ k Ĝ 9 7bi2` i z ∼ RX q2 MQi2 i?i i?Bb +QKT`@
BbQM Q7 /2Hv iBK2 Bb [mHBiiBp2- #2+mb2 Qm` /2Hv iBK2 Bb BM72``2/ bBM+2 }`bi
Tbb;2 Q7 kXy_200 - r?2`2b i?2 q2ix2H 2i HX UkyRjV /2Hv iBK2 Bb K2bm`2/
b i?2 iBK2 bBM+2 ;Htv Bb B/2MiB}2/ b bm#?HQ Q7 T`2Mi ?HQ BM M
L@#Q/v bBKmHiBQM mbBM; 7`B2M/b@Q7@7`B2M/b HBMFBM;X Ai Bb i?2`27Q`2 MQi BKK2@
/Bi2Hv +H2` ?Qr i?2b2 irQ /2}MBiBQMb `2 `2Hi2/X Hi?Qm;? [mHBiiBp2- Bi Bb
mMHBF2Hv i?i i?2 HQM;2` 2M/ Q7 i?2 /2Hv iBK2 T`QTQb2/ #v q2ix2H 2i HX UkyRjV
U2X;X- j Ĝ 9 :v`V +QmH/ #2 bmTTQ`i2/ #v i?2 /i i z ∼ R 7Q` irQ `2bQMbX
6B`biHv- #2+mb2 i?2 bBKmHiBQMb b?Qr i?i HKQbi HH bm#?HQb rQmH/ ?p2 H@
`2/v K/2 Tbb;2 Q7 _ 4 yX8_200 M/ ?2M+2 b?QmH/ #2 [m2M+?2/ #b2/ QM
Qm` KQ/2H- M/ b2+QM/Hv- #2+mb2 i?Bb HQM; /2Hv iBK2 Bb TT`Q+?BM; i?2 ;2
Q7 i?2 mMBp2`b2 i z = R U∼ e :v`V r?B+? rQmH/ `2[mB`2 +Hmbi2`b iQ 7Q`K i
p2`v ?B;? `2/b?B7i Ux > jVX
A7 i?2 iBK2b+H2b BM Qm` T?b2 bT+2 KQ/2H `2 +Q``2+i- i?2v TH+2 +QM@
bi`BMib QM i?2 ;2b Q7 i?2 bi2HH` TQTmHiBQMb Q7 #Qi? i?2 TQbibi`#m`bi ;Ht@
B2b M/ i?2B` bi`@7Q`KBM; T`Q;2MBiQ`bX SQbibi`#m`bi ;HtB2b b?QmH/ ?p2 bi`
7Q`KiBQM ?BbiQ`B2b i?i `2 +QMbBbi2Mi rBi? i?Bb `TB/ [m2M+?BM; iBK2b+H2M/ +Hmbi2` bi`@7Q`KBM; ;HtB2b b?QmH/ #2 i H2bi QH/ 2MQm;? i?i i?2v ?p2
?/ iBK2 iQ KB;`i2 7`QK i?2 +Hmbi2` QmibFB`ib iQ _ 4 yX8_200 r?BH2 KBMiBM;
+iBp2 bi` 7Q`KiBQMX
AM Q`/2` iQ i2bi i?2 +QMbBbi2M+v Q7 i?2 T?b2 bT+2 KQ/2H M/ i?2 bi2HH`
TQTmHiBQMb Q7 i?2 ;HtB2b- r2 }i i?2 bT2+i` Q7 #Qi? i?2 bi`@7Q`KBM; ;HtB2b
M/ i?2 TQbibi`#m`bib- rBi? i?2 bbmKTiBQM i?i i?2 +Hmbi2` bi` 7Q`KBM;
;HtB2b `2 i?2 T`Q;2MBiQ` TQTmHiBQM Q7 i?2 TQbibi`#m`bi TQTmHiBQMX Pm`
K2i?Q/QHQ;v Bb b 7QHHQrb, r2 }i i?2 ;2 Q7 i?2 bi`@7Q`KBM; ;HtB2b iQ /2}M2
i?2 BMBiBH ;2 Q7 i?2 TQbibi`#m`bi ;HtB2b QM+2 [m2M+?BM; #2;M- /2}M2/ b
t1 X q2 i?2M }i i?2 TQbibi`#m`bi bT2+i`mK bi`iBM; 7`QK i?Bb ;2 M/ }i 7Q` irQ
T`K2i2`b- τQ - i?2 iBK2b+H2 Qp2` r?B+? [m2M+?BM; Q++m``2/- M/ t2 - i?2 ;2
Q7 i?2 ;Htv bBM+2 Bi rb 7mHHv [m2M+?2/X h?Bb }/m+BH bi`@7Q`KiBQM ?BbiQ`v
Ua6>V Bb BHHmbi`i2/ BM i?2 #QiiQK H27i TM2H Q7 6B;m`2 jX9- M/ Bb- ;BM-
jX8X a1. 6AhhAL: P6 SPahah_"l_ah :GsA1a
8N
6B;m`2 jX9, hQT TM2H, J2M bi+F2/ bT2+i`mK Q7 bi`@7Q`KBM; U#Hm2V M/ TQbibi`#m`bi
U;`22MV ;HtB2b BM i?2 :*Gaa +Hmbi2`b rBi? T`QKBM2Mi #bQ`TiBQM 72im`2b H#2HH2/X h?2
Qp2`HB/ #H+F bT2+i` b?Qr i?2 #2bi@}i "`mxmH *?`HQi UkyyjV bT2+i`mK 7Q` i?2b2 ivT2b
bbmKBM; i?2 bi`@7Q`KiBQM ?BbiQ`v BM i?2 HQr2` H27i TM2HX h?2 KQbi +QMbi`BMBM; 72im`2 BM
i?2 bi`@7Q`KBM; bT2+i`mK Bb i?2 *H+BmK E HBM2- r?B+? BKTHB2b i?2 TQTmHiBQM Bb bQK2r?i
2pQHp2/X h?2 KQbi +QMbi`BMBM; 72im`2b BM i?2 TQbibi`#m`bi bT2+i`mK `2 *H+BmK E M/ i?2
:@#M/ r?B+? HbQ BKTHv KQ`2 2pQHp2/ TQTmHiBQM- #mi HbQ i?2 /22T >δ #bQ`TiBQM r?B+?
BKTHB2b `2+2Mi 2M/ iQ i?2 bi`@7Q`KiBQMX "QiiQK H27i TM2H, h?2 #2bi@}i bi` 7Q`KiBQM
?BbiQ`v bbmKBM; i?2 TQbibi`#m`bi ;HtB2b `2 /2b+2M/Mib Q7 i?2 bi`@7Q`KBM; ;HtB2b M/
mM/2`;Q [m2M+?BM; T`Q+2bbX "QiiQK `B;?i TM2H, *QM}/2M+2 BMi2`pHb QM i?2 [m2M+?BM;
iBK2b+H2 UτQ V M/ iBK2 bBM+2 bi` 7Q`KiBQM 2M/2/ Ut2 VX h?2b2 iBK2b+H2b `2 +QMbBbi2Mi rBi?
i?Qb2 /2`Bp2/ 7`QK i?2 T?b2 bT+2 MHvbBbX
*>Sh1_ jX h>1 S>a1 aS*1 L. ah1GG_ SPSlGhAPLa P6
ey
*Glah1_ :GsA1a h z ∼ R
b+?2KiB+HHv bBKBH` iQ i?2 dz/2Hv2/@i?2M@`TB/Ǵ a6> T`QTQb2/ #v Uq2ix2H
2i HX kyRj- b22 i?2B` 6B;m`2 RkV
q2 #2;BM #v bi+FBM; i?2 bT2+i` Q7 HH bi`@7Q`KBM; ;HtB2b U/2iBHb Q7
i?2 bi+FBM; T`Q+2bb `2 /Bb+mbb2/ BM JmxxBM 2i HX kyRkV- rBi? M //BiBQMH
+mi `2[mB`BM; i?i .n U9yyyV < RX98X h?2`2 `2 `2HiBp2Hv 72r bi`@7Q`KBM;
;HtB2b rBi? .n U9yyyV > RX98c ?Qr2p2`- ;Bp2M i?i i?Bb +mi Bb `2[mB`2K2Mi
7Q` i?2 TQbibi`#m`bi b2H2+iBQM- Bi Bb BKTQbbB#H2 i?i bi` 7Q`KBM; ;HtB2b rBi?
.n U9yyyV > RX98 +M #2 i?2 T`Q;2MBiQ`b Q7 i?2 TQbibi`#m`bi TQTmHiBQMX h?2
iQT TM2H Q7 6B;m`2 jX9 b?Qrb i?2 K2M bi+F2/ bT2+i`mK Q7 i?2 bi`@7Q`KBM;
;HtB2b rBi? T`QKBM2Mi #bQ`TiBQM 72im`2b H#2HH2/X
hQ }i i?2 bT2+i`mK r2 2KTHQv i?2 ?B;?@`2bQHmiBQM KQ/2Hb 7`QK "`mxmH *?`HQi UkyyjV bbmKBM; bQH` K2iHHB+Biv- *Hx2iiB 2i HX UkyyyV /mbi Hr Uv
4 y Ĝ 9V- M/ *?#`B2` UkyyjV AJ6X q2 /2;`/2 i?2 bT2+i`H `2bQHmiBQM Q7
i?2 KQ/2Hb iQ Ki+? i?i Q7 i?2 /i r?B+? Bb Rd³ BM i?2 Q#b2`p2/ 7`K2- M/
+Q``2bTQM/b iQ ∼ N³ `2bi@7`K2VX q2 bbmK2 /2+HBMBM; a6> #b2/ QM i?2
/2+HBM2 Q7 i?2 ;HQ#H bi`@7Q`KiBQM `i2 Ua6_V 7`QK z = j iQ z = y +QKTBH2/
#v "Qmr2Mb 2i HX UkyRkVX q2 HbQ i`B2/ a6> rBi? +QMbiMi a6_c ?Qr2p2`i?Bb +QMiBMm2/ ?B;? H2p2H Q7 bi` 7Q`KiBQM +MMQi `2T`Q/m+2 i?2 bi`2M;i? Q7
i?2 *H+BmK E #bQ`TiBQM HBM2 BM i?2 bi`@7Q`KBM; ;HtB2b 2p2M i QH/ ;2b M/
i?2`27Q`2 bQK2 7Q`K Q7 /2+HBMBM; a6> Bb `2[mB`2/X h?2 "`mxmH *?`HQi
UkyyjV KQ/2Hb /Q MQi +QMiBM 2KBbbBQM HBM2b- bQ i?2 (PAA) 2KBbbBQM HBM2 Bb MQi
}i #v i?2 KQ/2HX
h?2 #H+F bQHB/ HBM2 BM 6B;m`2 jX9 b?Qrb i?2 #2bi@}i KQ/2H iQ i?2 bi`@
7Q`KBM; TQTmHiBQM r?B+? ?b iBK2 bBM+2 bi`@7Q`KiBQM #2;M Q7 i1 4 kXj+0.5
−0.1
:v`X h?Bb BKTHB2b Kbb@r2B;?i2/ ;2 Q7 i?2 bi2HH` TQTmHiBQM Q7 RX8+0.2
−0.1 :v`X
h?2 bi`QM;2bi +QMbi`BMi QM i?2 ;2 +QK2b 7`QK i?2 `2HiBp2Hv bi`QM; *H+BmK
E HBM2- r?B+? +MMQi #2 `2T`Q/m+2/ #v p2`v vQmM; bi2HH` TQTmHiBQMX h?Bb
BMi2`K2/Bi2@;2 TQTmHiBQM Bb QH/ 2MQm;? i?i Bi rQmH/ #2 +QMiBMmQmbHv 7Q`K@
BM; bi`b Qp2` i?2 BM7HH iBK2 7`QK _ 4 kXy_200 iQ _ 4 yX8_200 - M/ i?2`27Q`2
Bb +QMbBbi2Mi rBi? i?2 /2Hv iBK2 BKTHB2/ #v i?2 bBKmHiBQMX
hQ }i i?2 TQbibi`#m`bi TQTmHiBQM- r2 +`2i2 b2i Q7 M2r KQ/2H ;`B/b
rBi? i?2 bK2 `M;2 Q7 ;2b M/ /mbi 2tiBM+iBQMb b i?2 /2+HBMBM; a6> Q7 i?2
bi`@7Q`KBM; ;HtB2bX q2 i?2M // HBM2` [m2M+?BM; Q7 bi` 7Q`KiBQM i t1
4 kXj :v`- M/ +`2i2 RR M2r ;`B/b rBi? τQ `M;BM; 7`QK y @ RXy :v` BM bi2Tb
Q7 yXR :v`- r?2`2 τQ Bb i?2 iBK2 #2ir22M r?2M bi` 7Q`KiBQM bi`ib iQ /2+HBM2
M/ a6_ 4 y Ub22 6B;m`2 jX9VX q2 i?2M }i i?2 TQbibi`#mbi bT2+i`mK iQ 2+?
Q7 i?2b2 ;`B/b M/ }i 7Q` i2 Ui?2 iBK2 bBM+2 a6_ 4 yV M/ v X q2 i?2M }M/
i?2 KBMBKmK χ2 +`Qbb i?2 RR ;`B/b r?B+? ;Bp2b mb #2bi }i τQ - i2 - M/ v X
h?2 #2bi }i KQ/2H 7Q` i?2 a6> Q7 i?2 TQbibi`#m`bib Ui1 4 kXj+0.5
−0.1 :v`- τQ
+0.4
4 yX9+0.3
:v`i
4
yXR
:v`V
Bb
THQii2/
BM
6B;m`2
jX9
b
i?2
#H+F KQ/2H
2
−0.4
−0.1
QM iQT Q7 i?2 ;`22M bT2+i`mKX h?2 #2bi }i `2T`Q/m+2b i?2 HBM2 bi`2M;i?b Q7
i?2 *H+BmK E HBM2- i?2 :@#M/- M/ >δ BKT`2bbBp2Hv r2HHX h?Bb Bb `2K`F@
#H2 BM i?2 b2Mb2 i?i *H+BmK E M/ i?2 :@#M/ `2 ivTB+H Q7 QH/2` bi2HH`
jXeX .Aa*laaAPL
eR
TQTmHiBQMb- r?2`2b bi`QM; >δ Bb 7`QK `2+2MiHv@[m2M+?2/ ;HtB2bX Ai rQmH/
#2 /B{+mHi iQ `2T`Q/m+2 bm+? bT2+i`mK rBi? Mv 7Q`K Q7 a6> Qi?2` i?M
i?i BM 6B;m`2 jX9X
_2K`F#Hv- i?2 BKTHB2/ a6>- τQ - M/ #2bi@}i ;2b Q7 i?2 bi2HH` TQT@
mHiBQMb BM72``2/ 7`QK i?2 bT2+i`H }iiBM; `2 +QMbBbi2Mi rBi? i?2 iBK2b+H2b
BKTHB2/ #v i?2 T?b2 bT+2 KQ/2HBM;X Ai Bb TQbbB#H2 i?i i?2 a6> M/ ;2b
+QmH/ #2 }i #v rB/2` `M;2 Q7 KQ/2Hb r?B+? r2 ?p2 MQi 2tTHQ`2/ BM 2t@
?mbiBp2 /2iBHc ?Qr2p2`- i?2 +QMbBbi2M+v #2ir22M i?2 irQ rBi? #bB+ KQ/2H@
BM; Bb 2M+Qm`;BM;X Ai Bb T`iB+mH`Hv 2M+Qm`;BM; +QMbB/2`BM; i?i i?2 bi2HH`
TQTmHiBQM K2bm`2K2Mib Q7 i?2 bi2HHBi2 [m2M+?BM; iBK2b+H2 `2 +QKTH2i2Hv
BM/2T2M/2Mi Q7 i?2 p2HQ+BiB2b M/ TQbBiBQMb Q7 i?2 ;HtB2b rBi?BM i?2 +Hmbi2`X
h?2 Qp2`HH TB+im`2 Q7 bi2HHBi2 [m2M+?BM; i?i `Bb2b 7`QK i?2 KQ/2HBM; Bb
i?i bi`@7Q`KBM; ;HtB2b i z ∼ R `2 MQi BKK2/Bi2Hv [m2M+?2/ QM+2 i?2v
`2 ++`2i2/ #v +Hmbi2`f;`QmTX AMbi2/- i?2v 2pQHp2 b MQ`KH bi`@7Q`KBM;
;HtB2b b i?2v 7HH BMiQ i?2 +2Mi`H `2;BQMb Q7 i?2 +Hmbi2`X "b2/ QM i?2 L@
#Q/v bBKmHiBQM- Bi iF2b ∼ yXd :v` 7Q` ;Htv iQ }`bi +`Qbb _ ∼ yX8_200 - M/
i?Bb Bb r?2`2 bi2HHBi2 [m2M+?BM; #2;BMbX PM+2 i?2 bi2HHBi2 [m2M+?BM; T`Q+2bb
bi`ib- Bi T`Q+22/b QM b?Q`i iBK2b+H2 yXR < τQ < yX8 :v`X JQ`2Qp2`- MQi
QMHv Bb i?2 [m2M+?BM; iBK2b+H2 b?Q`i- #mi KQbi Q7 i?2 Q#b2`p2/ TQbibi`#m`bib
`2 +QMbBbi2Mi rBi? ?pBM; i?2B` bi` 7Q`KiBQM 7mHHv 2M/2/ QMHv `2+2MiHvX h?Bb
Q#b2`piBQM Q7 KQbi TQbibi`#m`bib ?pBM; #22M `2+2MiHv [m2M+?2/ Bb MQi b2H2+iBQM 2z2+i- b Qm` b2H2+iBQM +`Bi2`B 7Q` i?2 TQbibi`#m`bib Q7 .n U9yyyV <
RX98 M/ (PAA) < j³ +QmH/ b2H2+i ;HtB2b b QH/ b ∼ RXy @ RX8 :v`- /2T2M/BM;
QM i?2 τQ X
h?Bb b+2M`BQ M/ i?2 BM72``2/ iBK2b+H2b `2 `2K`F#Hv bBKBH` iQ i?i
T`2b2Mi2/ #v aKBi? 2i HX UkyRy#V 7Q` i?2 *QK +Hmbi2`X h?2v 7QmM/ i?i ;Ht@
B2b rBi? bvKK2i`B+ lo KQ`T?QHQ;B2b r2`2 +QM+2Mi`i2/ rBi?BM i?2 +2Mi`H 8yy
FT+ UBX2X- _ ∼ yXk8 _200 V Q7 i?2 *QK +Hmbi2`X qBi? MmK2`B+H KQ/2HBM; i?2v
b?Qr2/ i?i i?Bb TQTmHiBQM +QmH/ #2 2tTHBM2/ B7 i?2v r2`2 [m2M+?2/ i _ ∼
R JT+ UBX2X- _ ∼ yX8 _200 V M/ i?2v r2`2 pB2r#H2 7Q` ∼ yX8 :v` 7i2` [m2M+?@
BM; #2;MX h?Bb [m2M+?BM; HQ+iBQM M/ iBK2b+H2 `2 M2`Hv B/2MiB+H iQ i?i
/2`Bp2/ 7`QK i?2 T?b2 bT+2 MHvbBb i z ∼ RX
Pm` BM72``2/ iBK2b+H2 Bb HbQ +QMbBbi2Mi rBi? i?2 [m2M+?BM; iBK2b+H2 i
z ∼ R T`QTQb2/ #v JQF 2i HX UkyRjV #b2/ QM i?2B` MHvbBb Q7 i?2 7`+iBQM Q7
`2/- #Hm2- M/ dz;`22MǴ ;HtB2b BM ;`QmTbX h?2v b?Qr2/ i?i BM Q`/2` iQ T`QT@
2`Hv `2T`Q/m+2 i?2 7`+iBQMb Q7 i?2b2 ;Htv ivT2b- /2Hv iBK2b #27Q`2 [m2M+?BM;
#2;BMb Q7 < k :v` r2`2 `2[mB`2/ HQM; rBi? τQ < R :v`X Pm` [m2M+?BM;
iBK2b+H2 Bb HbQ bBKBH` iQ i?2 [m2M+?BM; iBK2b+H2 T`QTQb2/ #v q2ix2H 2i HX
*>Sh1_ jX h>1 S>a1 aS*1 L. ah1GG_ SPSlGhAPLa P6
ek
*Glah1_ :GsA1a h z ∼ R
UkyRjV i z = y UτQ 4 yXk Ĝ yX3 :v`Vc ?Qr2p2`- Bi TT2`b i?i i?2 /2Hv iBK2
#27Q`2 [m2M+?BM; Kv #2 7+iQ` Q7 k Ĝ 9 HQM;2` i z = yX
PM2 TQi2MiBH Bbbm2 rBi? i?2 T`QTQb2/ b+2M`BQ 7Q` bi2HHBi2 [m2M+?BM; Bb
i?i r2 ?p2 T`2@b2H2+i2/ QMHv TQbibi`#m`bi ;HtB2b b Qm` i`+2` Q7 i?2
[m2M+?2/f [m2M+?BM; TQTmHiBQMX A7 i?2`2 `2 ;HtB2b i?i [m2M+? QM p2`v
HQM; iBK2b+H2b- i?2v rBHH ?p2 #22M QKBii2/ 7`QK i?Bb MHvbBbX q?BH2 r2 +M@
MQi 7Q`KHHv `mH2 i?Bb Qmi- r2 MQi2 i?i bB;MB}+Mi MmK#2` Q7 bim/B2b ?p2
b?QrM i?i i?2 aa6_ Q7 bi`@7Q`KBM; ;HtB2b ?b HBiiH2 /2T2M/2M+2 QM +Hmb@
i2`+2Mi`B+ `/Bmb i #Qi? ?B;? M/ HQr `2/b?B7i U2X;X- Si2H 2i HX kyyNc omH+MB
2i HX kyRyc JmxxBM 2i HX kyRkc q2ix2H 2i HX kyRjVX Hi?Qm;? i?Bb /Q2b MQi `mH2
Qmi bQK2 TQTmHiBQM Q7 bHQr [m2M+?BM; bi2HHBi2 ;HtB2b- Bi bi`QM;Hv bm;;2bib
i?i bHQr [m2M+?BM; +MMQi #2 i?2 /QKBMMi ivT2 Q7 [m2M+?BM; 7Q` bi2HHBi2bX
Ai Bb `2K`F#H2 i?i i?2 [m2M+?BM; iBK2b+H2b /2i2`KBM2/ 7`QK 7Qm` BM/2@
T2M/2Mi K2i?Q/b UaKBi? 2i HX kyRy#c q2ix2H 2i HX kyRjc JQF 2i HX kyRj- M/
i?2 +m``2Mi T?b2 bT+2 MHvbBbV `2 +QMbBbi2MiX h?2 T?b2 bT+2 +QMbi`BMib
`2 T`iB+mH`Hv mb27mH #2+mb2 i?2v HbQ T`QpB/2 M //BiBQMH +QMbi`BMi QM
r?2`2 rBi?BM i?2 +Hmbi2`f;`QmT i?2 bi2HHBi2 [m2M+?BM; #2;BMbX qBi? #Qi? M
BM72``2/ HQ+iBQM M/ iBK2b+H2- r2 +M ii2KTi iQ BM72` i?2 T?vbB+H T`Q+2bb
i?i Kv #2 `2bTQMbB#H2X
q2 }`bi +QMbB/2` i?2 HQ+iBQM rBi?BM i?2 +Hmbi2` r?2`2 [m2M+?BM; #2;BMbX
b /2`Bp2/ #v h`2m 2i HX UkyyjV M/ JQ`M 2i HX UkyydV- [m2M+?BM; 7`QK K2`;@
2`b Q` ?B;?@bT22/ ;Htv BMi2`+iBQMb Udz?`bbK2MiǴV Q++m`b T`272`2MiBHHv i
_ > _200 - r?B+? Bb BM+QMbBbi2Mi rBi? Qm` /2`Bp2/ [m2M+?BM; `/BmbX GBF2rBb2iB/H T`Q+2bb2b bm+? b ?HQ bi`BTTBM; Q` /Bb`mTiBQM Q++m` +HQb2 iQ i?2 +Hmbi2`
+Q`2 U_ < yXk8 _200 V- M/ HbQ b22K BM+QMbBbi2Mi rBi? Qm` /i- r?2`2 i?2
BKTHB2/ [m2M+?BM; `/Bmb Bb _ ∼ yX8_200 X >Qi ?HQ ;b bi`BTTBM; Udzbi`M;m@
HiBQMǴV M/ +QH/ ;b bi`BTTBM; Udz`K@T`2bbm`2ǴV `2 KQbi 2z2+iBp2 r?2`2 i?2
A*J Bb /2Mb2- i `Qm;?Hv _ < kXy_200 M/ _ < yX8_200 - `2bT2+iBp2Hv U2X;X"?û 2i HX kyRjVX "b2/ QM i?2 HQ+iBQM r?2`2 r2 2tT2+i [m2M+?BM; iQ Q++m`i?2b2 TT2` iQ #2 i?2 #2bi +M/B/i2b 7Q` i?2 T?vbB+H T`Q+2bbX
A7 i?2 iBK2b+H2 7Q` [m2M+?BM; Bb +QMbB/2`2/ i 7+2 pHm2- Bi rQmH/ bm;@
;2bi i?i +QKTH2i2 `2KQpH Q7 i?2 ;Htv +QH/ ;b pB `K@T`2bbm`2 bi`BTTBM;
rBHH #2 M2+2bb`v iQ [m2M+? ;HtB2b bQ `TB/HvX >Qr2p2`- *`BHHB qHi2`
UkyRjV ?p2 +QKTBH2/ i?2 Hi2bi K2bm`2K2Mib Q7 ;b 7`+iBQMb UBX2X- 7gas 4
Jgas fUJgas YJstar VV Q7 ;HtB2b i z ∼ R M/ i?2b2 `2 Q7 Q`/2` yXjX Pm`
K2bm`2K2Mib Q7 i?2 aa6_b Q7 ;HtB2b BM i?2 :*Gaa bKTH2 Ub22 JmxxBM
2i HX kyRkV b?Qr i?i ;HtB2b rBi? bi2HH` Kbb2b Q7 72r iBK2b Ry10 J" Ui?2
ivTB+H bi2HH` Kbb Q7 i?2 TQbibi`#m`bi ;HtB2bV ?p2 GQ;Uaa6_bV ∼ @3X3r?B+? BKTHB2b i?i B7 i?2v r2`2 +mi Qz 7`QK i?2B` ?Qi ;b bmTTHv +QKTH2i2Hvi?2v rQmH/ +QMbmK2 i?2B` +QH/ ;b BM ∼ yX8 :v`X h?Bb Bb +QMbBbi2Mi rBi? i?2
HQM; 2M/ Q7 [m2M+?BM; iBK2b+H2 i?i r2 /2`Bp2c M/ i?2`27Q`2 Bi K2Mb i?i
r2 +MMQi 7Q`KHHv `mH2 Qmi ?Qi ;b bi`BTTBM; b THmbB#H2 K2+?MBbK 7Q`
[m2M+?BM; i?2 TQbibi`#m`bib BM i?2 +Hmbi2`X
jXdX alJJ_u L. PlhGPPE
ej
Ai Bb HbQ rQ`i? +QMbB/2`BM; i?i i?2 +QH/ ;b +QMbmKTiBQM iBK2b+H2b i2M/
iQ 2pQHp2 iQ HQM;2` pHm2b i HQr2` `2/b?B7iX h?Bb Bb bBKTHv #2+mb2 aa6_b
/2+HBM2 7bi2` i?M 7gas rBi? /2+`2bBM; `2/b?B7i U2X;X- *`BHHB qHi2` kyRjVX
h?Bb 2pQHmiBQM Q7 i?2 +QH/ ;b +QMbmKTiBQM iBK2b+H2 Bb 7B`Hv r2F U2pQHpBM;
7`QK ∼ yX8 :v` i z ∼ R- iQ ∼ R :v` i z ∼ yVc ?Qr2p2`- Bi Bb TQi2MiBHHv
K2bm`#H2X A7 +QH/ ;b bi`BTTBM; UBX2X- `K@T`2bbm`2V Bb i?2 /QKBMMi bi2HHBi2
[m2M+?BM; T`Q+2bb- r2 KB;?i 2tT2+i i?i i?2 bi2HHBi2 [m2M+?BM; iBK2b+H2 Kv
MQi 2pQHp2 rBi? `2/b?B7iX >Qr2p2`- B7 ?Qi ;b bi`BTTBM; /QKBMi2b i?2M i?2 2pQ@
HmiBQM Q7 i?2 +QH/ ;b +QMbmKTiBQM iBK2b+H2 rQmH/ bm;;2bi i?i i?2 bi2HHBi2
[m2M+?BM; iBK2b+H2 Kv HbQ 2pQHp2 iQ HQM;2` pHm2b i HQr2` `2/b?B7iX h?2`2@
7Q`2- K2bm`BM; i?2 `2/b?B7i 2pQHmiBQM Q7 i?2 bi2HHBi2 [m2M+?BM; iBK2b+H2 Kv
#2 mb27mH TT`Q+? 7Q` B/2MiB7vBM; r?2i?2` ?Qi Q` +QH/ ;b bi`BTTBM; Bb i?2
/QKBMMi T?vbB+H T`Q+2bb 7Q` bi2HHBi2 [m2M+?BM;X AMi2`2biBM;Hv- HQr2` `2/b?B7i
bim/B2b bm+? b q2ix2H 2i HX UkyRjV b22K iQ bm;;2bi bHB;?iHv HQM;2` [m2M+?BM;
iBK2b+H2b UτQ 4 yXk Ĝ yX3 :v`V- Hi?Qm;? i?Bb ?b bB;MB}+Mi Qp2`HT rBi? i?2
iBK2b+H2 /2`Bp2/ i z ∼ R UτQ 4 yXR Ĝ yX8 :v`VX A7 i?Bb +QmH/ #2 b?QrM iQ #2
biiBbiB+HHv bB;MB}+Mi- i?2M Bi rQmH/ BKTHv i?i ?Qi ;b bi`BTTBM; Bb HBF2Hv i?2
KQbi BKTQ`iMi bi2HHBi2 [m2M+?BM; T`Q+2bbX >Qr2p2`- ;Bp2M i?2 H`;2 mM+2`@
iBMiB2b i T`2b2Mi i?Bb +H2`Hv `2[mB`2b KQ`2 /2iBH2/ BMp2biB;iBQMX Ai rQmH/
HbQ #2M2}i 7`QK +QKT`BbQM Q7 iBK2b+H2b K2bm`2/ mbBM; bBKBH` i2+?MB[m2b
iQ pQB/ bvbi2KiB+ 2``Q`bX
AM i?Bb TT2` r2 ?p2 b?QrM i?i i?2 TQTmHiBQM Q7 TQbibi`#m`bi ;HtB2b BM
+Hmbi2`b i z ∼ R ?b /Bbi`B#miBQM BM T?b2 bT+2 i?i Bb /BbiBM+iBp2 7`QK #Qi?
i?2 [mB2b+2Mi M/ bi`@7Q`KBM; +Hmbi2` ;Htv TQTmHiBQMbX lbBM; b2i Q7 /`F@
Kii2`@QMHv xQQK bBKmHiBQMb Q7 +Hmbi2`b r2 b?Qr2/ i?i i?Bb /Bbi`B#miBQM +M
#2 `2+Qp2`2/ B7 ;HtB2b [m2M+? QM `TB/ iBK2b+H2 UyXR < τQ < yX8 :v`V 7i2`
}`bi Tbb;2 Q7 _ ∼ yX8_200 X h?2 bBKmHiBQMb HbQ b?Qr i?i HQM;2` [m2M+?BM;
iBK2b+H2b UτQ > yX8 :v`V- Q` [m2M+?BM; i _ ∼ _200 T`QpB/2 TQQ` /2b+`BTiBQMb
Q7 i?2 TQbibi`#m`bi T?b2 bT+2 /Bbi`B#miBQMX 6BiiBM; Q7 i?2 bi+F2/ bT2+i` Q7
i?2 bi`@7Q`KBM; M/ TQbibi`#m`bi ;HtB2b b?Qrb i?i i?2 a6>- τQ - M/ ;2b
Q7 i?2B` bi2HH` TQTmHiBQMb `2 +QMbBbi2Mi rBi? i?2 iBK2b+H2b /2`Bp2/ 7`QK i?2
T?b2 bT+2 MHvbBb- M/ i?2 bBKBH`Biv #2ir22M i?2b2 BM/2T2M/2Mi BM/B+iQ`b
T`QpB/2b i?2 bi`QM;2bi +QMbBbi2M+v +?2+F Q7 i?2 Qp2`HH KQ/2HX
h?2 /2`Bp2/ [m2M+?BM; HQ+iBQM M/ iBK2b+H2 bm;;2bi i?i ;b bi`BTTBM;
T`Q+2bb2b `2 KQbi HBF2Hv `2bTQMbB#H2 7Q` [m2M+?BM; i?2 bi2HHBi2 TQTmHiBQMc
?Qr2p2`- i?2 +m``2Mi +QMbi`BMib `2 MQi bi`QM; 2MQm;? iQ /BbiBM;mBb? #2ir22M
?Qi Q` +QH/ ;b bi`BTTBM; b i?2 /QKBMMi [m2M+?BM; K2+?MBbKX J2bm`2K2Mi
Q7 i?2 2pQHmiBQM Q7 i?2 [m2M+?BM; iBK2b+H2 M/ TQbbB#Hv i?2 HQ+iBQM +QmH/ #2
2ti`2K2Hv pHm#H2 7Q` /2i2`KBMBM; i?2 /QKBMMi T?vbB+H T`Q+2bbX *Hmbi2`
*>Sh1_ jX h>1 S>a1 aS*1 L. ah1GG_ SPSlGhAPLa P6
e9
*Glah1_ :GsA1a h z ∼ R
bKTH2b rBi? ?B;?@[mHBiv bT2+i`Qb+QTB+ /i 2tBbi i HQr2` `2/b?B7i- M/ bQ
i?Bb Bb i`+i#H2 T`Q#H2K 7Q` i?2 7mim`2X
M //BiBQMH +QM+HmbBQM Q7 i?Bb rQ`F Bb i?i i?2 TT`Q+? Q7 mbBM; T?b2
bT+2 M/ bBKmHiBQMb iQ +QMbi`BM i?2 HQ+iBQM M/ iBK2b+H2 Q7 bi2HHBi2 [m2M+?@
BM; b22Kb iQ #2 T`QKBbBM; M2r rv 7Q`r`/ QM i?Bb T`Q#H2K Ub22 HbQ LQ#H2
2i HX kyRjVX q2 MQi2 i?i #2ii2` +QMbi`BMib i z ∼ R mbBM; i?Bb TT`Q+?
+QmH/ #2 K/2 rBi? H`;2` bKTH2b Q7 bT2+i`Qb+QTB+ +Hmbi2` K2K#2`bX h?2
`2bmHib Q7 KQbi Q7 i?2 k.@Ea i2bib BM i?Bb rQ`F T`QpB/2 +QMbi`BMib QM i?2
iBK2b+H2b i i?2 ∼ kσ H2p2H- rBi? i?2 HBKBiiBQM #2BM; i?2 iQiH MmK#2` Q7
TQbibi`#m`bib BM i?2 bKTH2 UQMHv k3 ;HtB2b Qmi Q7 9k9 +Hmbi2` K2K#2`bVX
AM+`2bBM; i?2 MmK#2` Q7 bT2+i` Q7 TQbibi`#m`bib #v 7+iQ` Q7 72r rQmH/
HHQr +QMbi`BMib i ∼ jσ H2p2H Q` #2ii2`- r?B+? rQmH/ #2 mb27mH 7Q` 7m`i?2`
`2}MBM; i?2 [m2M+?BM; KQ/2HX HbQ- KQ`2 /2iBH2/ KQ/2HBM; Q7 i?2 BM7HHBM;
T`Q+2bb i?i BM+Hm/2b i`+FBM; b2H7@[m2M+?BM; Q7 i?2 BM7HHBM; }2H/ TQTmHiBQM
rQmH/ #2 mb27mH 7Q` mM/2`biM/BM; i?2 TQTmHiBQM Q7 TQbibi`#m`bib `2 H`;2`
`/BB M/ TmiiBM; iB;?i2` +QMbi`BMib QM i?2 [m2M+?BM; iBK2b+H2X h?Bb rBHH #2
//`2bb2/ BM 7mim`2 TT2`bX
q2 +FMQrH2/;2 i?2 rQ`F Q7 *?`Bb SQr2` M/ "`/ E`M2 BM /2p2HQTBM; i?2
L@#Q/v bBKmHiBQMb mb2/ BM i?Bb MHvbBbX J M/ J6 +FMQrH2/;2 bmTTQ`i
7`QK M LqP aTBMQx ;`MiX _6Cp/" M/ >> +FMQrH2/;2 bmTTQ`i 7`QK
i?2 L2i?2`HM/b P`;MBbiBQM 7Q` a+B2MiB+ _2b2`+? ;`Mi MmK#2` ejNXy9kX3R9X
JG" +FMQrH2/;2b bmTTQ`i 7`QK M La1_* .Bb+Qp2`v :`Mi- M/ 7`QK LPo
M/ LqP pBbBiQ` ;`Mib i?i bmTTQ`i2/ ?Bb b##iB+H i G2B/2M P#b2`piQ`vr?2`2 i?Bb rQ`F rb +QKTH2i2/X JC> +FMQrH2/;2b bmTTQ`i 7`QK M La1_*
.Bb+Qp2`v :`MiX
*?Ti2`
9
*2Mbmb Q7 ai2HH` Jbb BM Ry
JbbBp2 >HQ2b i z ∼ 1 7`QK
i?2 :*Gaa am`p2v
q2 bim/v i?2 bi2HH` Kbb +QMi2Mi Q7 KbbBp2 ?HQ2b BM i?2 `2/b?B7i `M;2 0.86 <
z < 1.34- #v K2bm`BM; URV i?2 bi2HH` Kbb BM i?2 +2Mi`H ;Htv p2`bmb iQiH
/vMKB+H ?HQ Kbb- UkV i?2 iQiH bi2HH` Kbb UBM+Hm/BM; bi2HHBi2bV p2`bmb
iQiH ?HQ Kbb- M/ UjV i?2 `/BH bi2HH` Kbb M/ MmK#2` /2MbBiv T`Q}H2b
7Q` i?2 2Mb2K#H2 ?HQX q2 mb2 Eb @#M/ b2H2+i2/ +iHQ;m2 7Q` i?2 Ry +Hmbi2`b
BM i?2 :2KBMB *Hmbi2` bi`QT?vbB+b aT2+i`Qb+QTB+ am`p2v U:*GaaV- rBi?
T?QiQK2i`B+ `2/b?B7ib M/ bi2HH` Kbb2b K2bm`2/ 7`QK RR@#M/ a1. }iiBM;X
*QK#BMBM; i?2 T?QiQK2i`B+ +iHQ;m2b rBi? i?2 /22T bT2+i`Qb+QTB+ +QKTQM2Mi
Q7 :*Gaa- r2 +Q``2+i i?2 +Hmbi2` ;Htv bKTH2 7Q` BMi2`HQT2`bX q2 HbQ
T2`7Q`K /vMKB+H MHvbBb Q7 i?2 +Hmbi2` ;HtB2b iQ 2biBKi2 i?2 ?HQ Kbb
M200 7Q` 2+? +Hmbi2` #b2/ QM K2bm`2K2Mi Q7 Bib p2HQ+Biv /BbT2`bBQMX URV q2
}M/ i?i i?2 +2Mi`H ;Htv bi2HH` Kbb 7`+iBQM /2+`2b2b rBi? iQiH ?HQ Kbb
M/ i?i i?Bb Bb BM `2bQM#H2- [mMiBiiBp2 ;`22K2Mi rBi? K2bm`2K2Mib 7`QK
#mM/M+2 Ki+?BM; bim/B2b i z ∼ 1X UkV h?2 iQiH bi2HH` Kbb 7`+iBQMb Q7
i?2b2 bvbi2Kb /2+`2b2 rBi? ?HQ Kbb- BM/B+iBM; i?i HQr2` Kbb bvbi2Kb `2
KQ`2 2{+B2Mi i i`Mb7Q`KBM; #`vQMb BMiQ bi`bX q2 }M/ i?2 iQiH bi2HH` Kbb
iQ #2 ;QQ/ T`Qtv 7Q` iQiH ?HQ Kbb- rBi? bKHH BMi`BMbB+ b+ii2`X q?2M
r2 +QKT`2 i?2b2 `2bmHib 7`QK :*Gaa rBi? HBi2`im`2 K2bm`2K2Mib- r2 }M/
i?i i?2 bi2HH` Kbb 7`+iBQM i }t2/ ?HQ Kbb b?Qrb MQ bB;MB}+Mi 2pQHmiBQM
BM i?2 `M;2 0 < z < 1X UjV q2 K2bm`2 `2HiBp2Hv ?B;? L6q +QM+2Mi`iBQM
T`K2i2` +; ∼ 7 7Q` i?2 bi2HH` Kbb /Bbi`B#miBQM BM i?2b2 +Hmbi2`b- M/ /2#i2
TQbbB#H2 b+2M`BQ 7Q` 2tTHBMBM; i?2 2pQHmiBQM Q7 i?2 bi2HH` Kbb /Bbi`B#miBQM
e8
7`QK i?2 :*Gaa bKTH2 iQ i?2B` HBF2Hv /2b+2M/Mib i HQr2` `2/b?B7iX h?2
bi2HH` Kbb K2bm`2K2Mib BM i?2 z ∼ 1 ?HQ2b T`QpB/2/ #v :*Gaa Tmib
+QMbi`BMib QM i?2 bi2HH` Kbb bb2K#Hv ?BbiQ`v Q7 +Hmbi2`b Q#b2`p2/ BM i?2
HQ+H lMBp2`b2X bBKTH2 KQ/2H b?Qrb i?i i?2 bi2HH` Kbb +QMi2Mi Q7 :*Gaa
+M 2pQHp2 BM ivTB+H /Bbi`B#miBQMb Q#b2`p2/ i HQr2` `2/b?B7ib B7 i?2 +Hmbi2`b
T`BK`BHv ++`2i2 bi2HH` Kbb QMiQ i?2 QmibFB`ibX
_2K+Q 6XCX pM /2` "m`;- /K JmxxBM- >2MF >Q2Fbi`- :BHHBM qBHbQM- *?`Bb
GB/KM- >XEX*X u22
bi`QMQKv bi`QT?vbB+b- oQHmK2 8eR- dN UkyR9V
ee
9XRX ALh_P.l*hAPL
ed
PM2 Q7 i?2 KBM Q#D2+iBp2b BM i?2 }2H/ Q7 2ti`;H+iB+ bi`QMQKv Bb iQ mM@
/2`biM/ i?2 +QMM2+iBQM #2ir22M ;HtB2b M/ i?2 /Bbi`B#miBQM Q7 i?2 mM/2`@
HvBM; /`F Kii2`X h?2 ;`Qri? Q7 /`F Kii2` bi`m+im`2b ?b #22M bim/B2/ BM
H`;2 L@#Q/v bBKmHiBQMb U2X;X aT`BM;2H 2i HX kyy8c "QvHM@EQH+?BM 2i HX kyyNc
Lp``Q 2i HX kyRyVX 6`QK i?2b2 bBKmHiBQMb- i?2 /2MbBiv T`Q}H2b Q7 +QHHTb2/
bi`m+im`2b ?p2 #22M 7QmM/ iQ #2 r2HH `2T`2b2Mi2/ #v L6q@T`Q}H2b ULp``Q
2i HX RNNdVX h?2b2 T`Q}H2b `2 /2b+`B#2/ #v irQ T`K2i2`b, i?2 ?HQ Kbb
M/ i?2 ?HQ +QM+2Mi`iBQM T`K2i2`X h?2 /2T2M/2M+2 Q7 i?2 +QM+2Mi`iBQM
T`K2i2` c QM i?2 ?HQ Kbb- 7Q`KiBQM iBK2 M/ `2/b?B7i ?b #22M bim/B2/
rBi? L@#Q/v bBKmHiBQMb U2X;X q2+?bH2` 2i HX kyykc L2iQ 2i HX kyydc .mzv
2i HX kyy3c :Q 2i HX kyy3VX h?2b2 ?p2 b?QrM i?i c- 7Q` i?2 /`F Kii2`- Bb
?B;?2` 7Q` HQr2` Kbb ?HQ2b- ?B;?2` 7Q` ?HQ2b i?i +QHHTb2 2`Hv- M/ ?B;?2`
7Q` ?HQ2b i HQr2` `2/b?B7iX
>Qr #`vQMb z2+i i?2 /Bbi`B#miBQM Q7 i?2 /`F Kii2` Bb biBHH mM/2` /2#i2
U.QH; 2i HX kyyNc pM .H2M 2i HX kyRRc L2rKM 2i HX kyRjVX "`vQMb BM
i?2 ;b T?b2 +M +QQH M/ 7Q`K bi`b i i?2 #QiiQK Q7 i?2 TQi2MiBH r2HHb BM
i?2 /`F Kii2` Ubm#@V?HQ2bX h?2 2{+B2M+v rBi? r?B+? i?Bb ?TT2Mb /2T2M/b
QM i?2 T`QT2`iB2b Q7 i?2 ?HQ Ub22 2X;X E`pibQp "Q`;MB kyRkc SHM2HH2b 2i HX
kyRjVX hQ +QMbi`BM i?2 T?vbB+b #2?BM/ i?2b2 T`Q+2bb2b- i?2`2 `2 MmK#2` Q7
F2v Q#b2`p#H2b i?i +M #2 2tTHQBi2/X AM i?Bb TT2` r2 +QM+2Mi`i2 QM i?`22
Q7 i?2b2- r?B+? r2 BMi`Q/m+2 BM im`M #2HQr- M/ K2bm`2 i z ∼ 1 7Q` bKTH2
Q7 i2M +Hmbi2` bBx2/ ?HQ2bX
6B`bi- iQ +QMbi`BM i?2 #mBH/ mT Q7 bi2HH` Kbb BM +2Mi`H ;HtB2b- r2 K2@
bm`2 i?2 bi2HH` Kbb T`2b2Mi BM i?2 +2Mi`H ;HtB2b Q7 :*Gaa M/ +QKT`2
Bi iQ /B`2+i K2bm`2K2Mib Q7 i?2B` iQiH ?HQ Kbb2bX "2?`QQxB 2i HX UkyRjV
2biBKi2 i?2 bi2HH` Kbb BM +2Mi`H ;HtB2b p2`bmb iQiH ?HQ Kbb Qp2` `M;2
Q7 `2/b?B7ib M/ ?HQ Kbb2b BM biiBbiB+H rv mbBM; i?2 #mM/M+2 Ki+?BM;
i2+?MB[m2X AM i?Bb i2+?MB[m2 Q#b2`p#H2b- bm+? b i?2 bi2HH` Kbb 7mM+iBQM M/
+QbKB+ bi` 7Q`KiBQM ?BbiQ`v- `2 +QK#BM2/ rBi? K2`;2` i`22b 7`QK /`F Ki@
i2` bBKmHiBQMb iQ T`QpB/2 +QMbi`BMib QM i?2 T`Q+2bb2b i?i #mBH/ mT i?2 bi2HH`
Kbb BM +2Mi`H ;HtB2bX h?2 bi2HH` +QMi2Mi Q7 +2Mi`H ;HtB2b- Q` #`B;?i2bi
+Hmbi2` ;HtB2b U"*:bV BM i?2 +b2 Q7 +Hmbi2`b- +M ;`Qr #v bi` 7Q`KiBQM
BM i?2 ;Htv Bib2H7 Q` #v K2`;BM; rBi? Qi?2` ;HtB2bX :Bp2M i?2 bB;MB}+Mi
;`Qri? Q7 bi2HH` Kbb BM "*:b b 7mM+iBQM Q7 `2/b?B7i UGBM JQ?` kyy9c
GB/KM 2i HX kyRkV- i?Bb #mBH/@mT Bb HBF2Hv iQ Q++m` i?`Qm;? KBMHv /`v K2`;@
2`bX >Qr2p2`- i?2 Kbb bb2K#Hv ?b #22M b?QrM UGB/KM 2i HX kyRkV iQ
BM+`2b2 KQ`2 bHQrHv i?M Bb 2tT2+i2/ 7`QK b2KB@MHviB+ KQ/2Hb U.2 Gm+B "HBxQi kyydV- #mi BM ;QQ/ ;`22K2Mi rBi? KQ`2 `2+2Mi bBKmHiBQMb UGTQ`i2
2i HX kyRjVX aBM+2 i?2 KBM ?HQ HbQ ++`2i2b Kii2` r?BH2 i?2 +2Mi`H ;Htv
Bb #mBH/BM; mT Bib bi2HH` +QMi2Mi- bim/B2b ?p2 7Q+mbb2/ QM i?2 `2HiBQMb?BT #2@
ir22M i?Qb2 T`Q+2bb2bX h?2 "2?`QQxB 2i HX UkyRjV 2biBKi2b i z = 1.0 +Qp2` *>Sh1_ 9X *1Lala P6 ah1GG_ Jaa AL Ry JaaAo1 >GP1a
e3
h z ∼ 1 6_PJ h>1 :*Gaa al_o1u
`M;2 Q7 ?HQ Kbb2b 7`QK 1011.3 < Mh /J" < 1014.2 - M/ `2 +QMbBbi2Mi rBi?
T`2/B+iBQMb 7`QK Qi?2` #mM/M+2 Ki+?BM; MHvb2b U2X;X JQbi2` 2i HX kyRykyRjVX AM ;2M2`H i?2 ?B;?2bi +2Mi`H bi2HH` Kbb 7`+iBQM Bb 7QmM/ BM ?HQ2b Q7
`QmM/ 1012 J" X "v +QK#BMBM; /B`2+i K2bm`2K2Mib Q7 iQiH Kbb M/ bi2HH`
Kbb BM i?2 bK2 ?HQ2b- r2 i2bi i?2 `2bmHib 7`QK #mM/M+2 Ki+?BM; bim/B2b
i z ∼ 1X
a2+QM/- F2v K2bm`2K2Mi 7Q` mM/2`biM/BM; i?2 BMi2`THv #2ir22M i?2
;`Qri? Q7 H`;2 b+H2 bi`m+im`2 M/ i?2 7Q`KiBQM M/ ++`2iBQM Q7 ;HtB2b Bb
iQ +QKT`2 i?2 iQiH bi2HH` Kbb b 7mM+iBQM Q7 ?HQ KbbX 6Q` bKTH2
Q7 ;`QmTb b2H2+i2/ i 0.1 < z < 1.0 7`QK *PaJPa- :BQ/BMB 2i HX UkyyNV
b?Qr i?i i?2B` bi2HH` Kbb 7`+iBQM Bb /2+`2bBM; 7mM+iBQM Q7 ?HQ KbbX
aBKBH` `2bmHib `2 7QmM/ #v :QMxH2x 2i HX Ukyyd- kyRjV- M/`2QM UkyRyV
M/ >BHiQM 2i HX UkyRjV 7Q` bKTH2b Q7 +Hmbi2`b `QmM/ z = 0.1- z < 0.1
M/ z = 0.5- `2bT2+iBp2HvX :Bp2M i?i i?2 KQbi KbbBp2 ?HQ2b `2 2tT2+i2/
iQ ;`Qr #v ++`2iBM; HQr2` Kbb bvbi2Kb- r?B+? ?p2 ?B;?2` bi2HH` Kbb
7`+iBQM- QM2 rQmH/ MBp2Hv 2tT2+i i?2 bi2HH` Kbb 7`+iBQM Q7 KbbBp2 ?HQ2b iQ
;`Qr rBi? +QbKB+ iBK2- 2p2M BM i?2 #b2M+2 Q7 BM bBim bi`@7Q`KiBQM T`Q+2bb2bX
*QMb2[m2MiHv- K2bm`2K2Mib QM i?2 bi2HH` Kbb 7`+iBQM BM i?2b2 ?HQ2b `2
mb2/ iQ +QMbi`BM i?2 T`Q;2MBiQ` TQTmHiBQM i?i 7Q`K i?2 #mBH/BM; #HQ+Fb Q7
i?2b2 ?HQ2b U"HQ;? 2i HX kyy3c J+:22 2i HX kyyNVX .m2 iQ i?2 KDQ` +p2ib
BM +QKT`BM; K2bm`2K2Mib 7`QK /Bz2`2Mi bim/B2b rBi? BM?QKQ;2M2Qmb /i
M/ /Bz2`2Mi MHvb2b- i?2 `2HiBQM Bib2H7 Bb ?`/ iQ +QMbi`BM Q#b2`piBQMHHv
UG2mi?m/ 2i HX kyRkc "m/xvMbFB 2i HX kyRjVX aQ 7` HBiiH2 2pQHmiBQM rBi?
`2/b?B7i ?b #22M 7QmM/ U:BQ/BMB 2i HX kyyNc GBM 2i HX kyRkVX
h?B`/- i?2 bTiBH /Bbi`B#miBQM Q7 i?2 bi2HH` Kbb +QKTQM2Mi Q7 bi2HHBi2b
rBi?BM i?2 KBM ?HQ Bb BMiBKi2Hv `2Hi2/ iQ ++`2iBQM T`Q+2bb2b- M/ 2p2Mim@
HHv i?2 ;`Qri? Q7 i?2 +2Mi`H ;HtvX q?BH2 i?2 bm#@?HQ2b BM Tm`2 ;`pBi@
iBQMH L@#Q/v bBKmHiBQMb ;2i /2bi`Qv2/ #v iB/H /Bb`mTiBQMb- i?2 ;HtB2b i?i
?p2 7Q`K2/ BMbB/2 Q7 i?2K `2 KQ`2 `2bBbiBp2 iQ i?Qb2 7Q`+2b U2X;X "m/xvM@
bFB 2i HX kyRkVX h?2 LA_ HmKBMQbBiv M/ MmK#2` /2MbBiv T`Q}H2b `2 7QmM/
iQ #2 /2b+`B#2/ #v L6q T`Q}H2b 7Q` ;`QmT@bBx2/ ?HQ2b U2X;X :BQ/BMB 2i HX
kyyNc hH 2i HX kyRjV- M/ +Hmbi2`b U2X;X *`H#2`; 2i HX RNNd#c GBM 2i HX kyy9c
JmxxBM 2i HX kyydVX "m/xvMbFB 2i HX UkyRkV K2bm`2/ i?2 `/BH /Bbi`B#miBQM
Q7 ;HtB2b 7`QK i?2 a.aa `QmM/ GmKBMQmb _2/ :HtB2b BM `2/b?B7i `M;2
0.15 < z < 0.4- M/ 7QmM/ i?i i?Bb /Bbi`B#miBQM Bb HbQ r2HH /2b+`B#2/ #v
M L6q T`Q}H2X >Qr2p2`- i?2v 7QmM/ i?i i?2 +QM+2Mi`iBQM T`K2i2` c Bb
HQr2` 7Q` i?2 ;HtB2b i?M 7Q` i?2 mM/2`HvBM; /`F Kii2`X h?2v 7QmM/ i?i
i?2 +QM+2Mi`iBQM Bb BM/2T2M/2Mi Q7 Kbb- #mi i?i i?2`2 Bb ?BMi Q7 KBH/
/2T2M/2M+2 Q7 i?2 bi2HH` Kbb +QM+2Mi`iBQM QM `2/b?B7iX +QKT`BbQM Q7 i?2
`/BH bi2HH` Kbb /2MbBiv /Bbi`B#miBQM Q7 +Hmbi2`b Qp2` `M;2 Q7 `2/b?B7ibHBMFBM; ?B;?@z bvbi2Kb iQ i?2B` HBF2Hv /2b+2M/Mib- vB2H/b BMbB;?ib BM i?2 2pQ@
HmiBQM Q7 i?2 ;Htv /Bbi`B#miBQMX AM i?Bb bim/v r2 rBHH 2ti2M/ i?2 `2/b?B7i
#b2HBM2 Q7 i?2b2 +QKT`BbQMb iQr`/b z = 1X
9XkX :*Gaa .h LGuaAa
eN
q2 T2`7Q`K i?2 7Q`2K2MiBQM2/ F2v K2bm`2K2Mib BM M mM2tTHQ`2/ +QK@
#BMiBQM Q7 `2/b?B7i M/ ?HQ Kbb `M;2 mbBM; i?2 :*Gaa bm`p2v- r?B+?
+QMiBMb /22T RR@#M/ T?QiQK2i`v M/ bT2+i`Qb+QTv 7Q` Ry `B+? +Hmbi2`b i
0.86 < z < 1.34X h?Bb TT2` #mBH/b 7m`i?2` QM i?2 `2bmHib T`2b2Mi2/ BM b2p2`H
TT2`b QM i?2 :*Gaa bKTH2X JmxxBM 2i HX UkyRk- ?2`27i2` JRkV T`2b2Mi
i?2 bT2+i`Qb+QTB+ bKTH2- r?B+? Bb +`BiB+H BM i?Bb bim/v iQ +Q``2+i i?2 T?QiQ@
K2i`B+HHv b2H2+i2/ ;HtB2b #v +Hmbi2` K2K#2`b?BTX pM /2` "m`; 2i HX UkyRj?2`27i2` p/"RjV K2bm`2 i?2 bi2HH` Kbb2b Q7 i?2 ;HtB2b BM i?2 bKTH2 M/
T`2b2Mi i?2B` bi2HH` Kbb 7mM+iBQM UaJ6VX q2 rBHH mb2 i?2 bi2HH` Kbb2b 2biB@
Ki2/ BM i?Bb rQ`F 7Q` i?2 +m``2Mi bim/vX GB/KM 2i HX UkyRkV B/2MiB}2b M/
bim/B2b i?2 "*:b Q7 :*Gaa +Hmbi2`b b T`i Q7 i?2B` MHvbBb QM i?2 +2Mi`H
;Htv bi2HH` Kbb ;`Qri?X h?2 iQiH :*Gaa ?HQ Kbb2b `2 2biBKi2/
#b2/ QM i?2 p2HQ+Biv /BbT2`bBQMb 2biBKi2/ BM qBHbQM 2i HX UBM T`2TXVX hQ
/2b+`B#2 i?2 Kbb2b Q7 i?2 +Hmbi2`b- r2 rBHH mb2 R200 M/ M200 - r?B+? `2 /2@
}M2/ b i?2 `/Bmb i r?B+? i?2 K2M BMi2`BQ` /2MbBiv Bb kyy iBK2b i?2 +`BiB+H
/2MbBiv Q7 i?2 lMBp2`b2- M/ i?2 Kbb 2M+HQb2/ rBi?BM i?Bb `/Bmb- `2bT2+iBp2HvX
h?2 bi`m+im`2 Q7 i?Bb TT2` Bb b 7QHHQrbX AM a2+iX 9Xk r2 T`2b2Mi i?2
:*Gaa +Hmbi2` bKTH2- i?2 pBH#H2 T?QiQK2i`B+ M/ bT2+i`Qb+QTB+ /i- M/
;Bp2 i?2 `2bmHib 7`QK /vMKB+H MHvbBb iQ 2biBKi2 i?2 iQiH ?HQ Kbb2bX
q2 HbQ b?Qr ?Qr r2 Q#iBM T?QiQK2i`B+ `2/b?B7ib M/ bi2HH` Kbb 2biBKi2b
#v bmKK`BxBM; i?2 MHvbBb 7`QK p/"RjX q2 7m`i?2` b?Qr ?Qr i?2 bT2+@
i`Qb+QTB+ /i `2 mb2/ iQ +Q``2+i i?2 7mHH T?QiQK2i`B+ +iHQ;m2 7Q` +Hmbi2`
K2K#2`b?BTX AM a2+iX 9Xj r2 +QKT`2 i?2 bi2HH` Kbb BM i?2 +2Mi`H ;HtB2b
rBi? i?2B` ?HQ Kbb2bX AM a2+iX 9X9 r2 T`2b2Mi `2bmHib QM i?2 iQiH bi2HH` Kbb
p2`bmb ?HQ Kbb `2HiBQM Q7 i?2 +Hmbi2`bX AM a2+iX 9X8 r2 b?Qr ?Qr i?2 ;HtB2b
`2 /Bbi`B#mi2/ `/BHHv M/ +QKT`2 i?Bb iQ i?2 2tT2+i2/ /`F Kii2` T`Q}H2b
7Q` i?2b2 bvbi2KbX 6m`i?2`- r2 /Bb+mbb TQbbB#H2 2pQHmiBQM`v KQ/2H iQ +QM@
M2+i i?2 z ∼ 1 K2bm`2K2Mib iQ i?2B` HBF2Hv /2b+2M/Mib i HQr2` `2/b?B7iX AM
2+? b2+iBQM r2 +QKT`2 i?2 `2bmHib rBi? i?2 HBi2`im`2 M/ /Bb+mbb ?Qr i?2v
`2 z2+i2/ #v TQbbB#H2 bvbi2KiB+bX q2 bmKK`Bb2 M/ +QM+Hm/2 BM a2+iX 9XeX
HH K;MBim/2b r2 [mQi2 `2 BM i?2 " K;MBim/2b bvbi2K M/ r2 /QTi
Λ*.J +QbKQHQ;v rBi? ΩK = 0.3- ΩΛ = 0.7 M/ >y = dy FK b−R JT+−R X
6Q` bi2HH` Kbb 2biBKi2b r2 bbmK2 i?2 AMBiBH Jbb 6mM+iBQM UAJ6V 7`QK
*?#`B2` UkyyjVX
h?2 :*Gaa +Hmbi2` bKTH2 +QMbBbib Q7 Ry `B+? +Hmbi2`b BM i?2 `2/b?B7i `M;2
0.86 < z < 1.34 b2H2+i2/ rBi? i?2 `2/@b2[m2M+2 b2H2+iBQM K2i?Q/ U:H//2`b
u22 kyyyV mbBM; i?2 z $ − 3.6µK +QHQm` 7`QK i?2 9k b[m`2 /2;`22 aT_*a
bm`p2v UJmxxBM 2i HX kyyNc qBHbQM 2i HX kyyNVX h?2b2 Ry +Hmbi2`b- r?B+? `2
KQM;bi i?2 `B+?2bi i z ∼ 1 BM i?Bb bm`p2v `2- `2 /2b+`B#2/ BM JRk- M/ +M
*>Sh1_ 9X *1Lala P6 ah1GG_ Jaa AL Ry JaaAo1 >GP1a
dy
h z ∼ 1 6_PJ h>1 :*Gaa al_o1u
h#H2 9XR, h?2 Ry :*Gaa +Hmbi2`b b2H2+i2/ 7`QK aT_*a i?i 7Q`K i?2 #bBb Q7 i?Bb bim/vrBi? i?2B` /vMKB+H T`QT2`iB2bX
LK2
zbT2+
aT_*a@yyj9
aT_*a@yyj8
aT_*a@yyje
aT_*a@ykR8
aT_*a@Ry9d
aT_*a@Ry8R
aT_*a@ReRj
aT_*a@ReRe
aT_*a@Rej9
aT_*a@Rej3
yX3ed
RXjj8
yX3eN
RXyy9
yXN8e
RXyj8
yX3dR
RXR8e
RXRdd
RXRNe
_#
Ckyyy
yy,j9,9kXye
yy,j8,9NXdy
yy,je,98Xyj
yk,R8,k9Xyy
Ry,9d,jjX9j
Ry,8R,RRXkR
Re,Rj,R9Xej
Re,Re,9RXjk
Re,j9,j3Xkk
Re,j3,8RXe9
.1*#
Ckyyy
@9j,yd,8jX9R
@9j,Rk,k9Xky
@99,Ry,9NXNR
@yj,9j,jkXR8
8d,9R,RjXjy
83,R3,yjXRd
8e,9N,kNXN8
88,98,RkX99
9y,ky,83Xje
9y,j3,9kXNR
σv+
[FK/b]
700+90
−150
780+80
−120
750+80
−90
640+120
−130
660+70
−120
500+40
−100
+100
1350−100
680+80
−110
790+60
−110
480+50
−100
/
M200
(1014 J! )
2.4+1.0
−1.2
2.5+0.9
−1.0
2.9+1.0
−0.9
1.7+1.1
−0.8
1.9+0.7
−0.9
0.8+0.2
−0.4
+4.0
16.9−3.5
1.9+0.7
−0.8
2.9+0.7
−1.0
0.6+0.2
−0.3
/
R200
(JT+)
0.9+0.1
−0.2
0.8+0.1
−0.1
1.0+0.1
−0.1
0.8+0.2
−0.2
0.8+0.1
−0.2
0.6+0.1
−0.1
1.8+0.1
−0.1
0.8+0.1
−0.1
0.9+0.1
−0.1
0.5+0.1
−0.1
aT2+@z
J2K#2`b
98
ky
9d
93
jR
j9
Nk
9e
8y
99
6Q` 7mHH MK2b r2 `272` iQ JmxxBM 2i HX UkyRkVX
#
*QQ`/BMi2b Q7 i?2 "*:b- b B/2MiB}2/ #v GB/KM 2i HX UkyRkVX
+
o2HQ+Biv /BbT2`bBQMb 2biBKi2/ #v qBHbQM 2i HX- BM T`2TX
/
.vMKB+H T`QT2`iB2b 2biBKi2/ mbBM; i?2 `2HiBQM #2ir22M σv M/ M200
7`QK 1p``/ 2i HX Ukyy3VX
#2 +QMbB/2`2/ b 7B` `2T`2b2MiiBQM Q7 A_@b2H2+i2/ `B+? +Hmbi2`b rBi?BM i?Bb
`2/b?B7i `M;2X Ai Bb Hrvb [m2biBQM ?Qr `2T`2b2MiiBp2 +Hmbi2` bKTH2 Bb
Q7 i?2 7mHH /Bbi`B#miBQM Q7 KbbBp2 ?HQ2b- b Bi Bb BKTQbbB#H2 iQ b2H2+i bKTH2
#b2/ QM ?HQ KbbX 1+? b2H2+iBQM K2i?Q/ ?b TQi2MiBH #Bb2b- r?2i?2` Bi
Bb s@`v b2H2+i2/- aw@b2H2+i2/ Q` ;Htv@b2H2+i2/X >Qr2p2`- 2bT2+BHHv i i?2
?B;?@Kbb 2M/ Q7 i?2 /Bbi`B#miBQM- i?2b2 b2H2+iBQM K2i?Q/b `2 mMHBF2Hv iQ +mb2
bB;MB}+Mi #Bb2b BM 7pQm` Q7 T`iB+mH` ivT2b Q7 ;Htv +Hmbi2`bX aT2+B}+HHvb 2X;X "HF2bH22 2i HX UkyyjV M/ JmHHBb 2i HX Ukyy8V b?Qr- s@`v M/ aw@
b2H2+i2/ +Hmbi2`b HbQ b?Qr bB;MB}+Mi Qp2`@/2MbBiB2b Q7 `2/@b2[m2M+2 ;HtB2bX
q2 rBHH /Bb+mbb TQbbB#H2 b2H2+iBQM #Bb 7m`i?2` BM a2+iX 9X8XRX M Qp2`pB2r Q7
i?2 :*Gaa bKTH2 Bb ;Bp2M BM h#H2 9XRX
h?2 "*:b Q7 i?2b2 +Hmbi2`b ?p2 #22M B/2MiB}2/ M/ bim/B2/ BM GB/KM
2i HX UkyRkVX AM ;2M2`H i?2 B/2MiB}+iBQM Q7 i?2 "*:b Bb bi`B;?i7Q`r`/#2BM; i?2 #`B;?i2bi +Hmbi2` K2K#2` BM i?2 Eb @#M/- M/ r2 rBHH mb2 i?2 bK2
B/2MiB}+iBQM b /QM2 BM GB/KM 2i HX UkyRkVX AM i?2 +b2b Q7 aT_*a@Ry8R
M/ aT_*a@Rej9- GB/KM 2i HX UkyRkV 7QmM/ i?i i?2 "*:b `2 Qz@b2i 7`QK
i?2 TT`QtBKi2 +Hmbi2` +2Mi`2 #v #Qmi k8yFT+ UT`QD2+i2/VX
h?2 T?QiQK2i`B+ /i b2i +QMbBbib Q7 BK;BM; BM ugriz CEb M/ 9 A_*
+?MM2Hb 7Q` 2+? +Hmbi2`X 6Q` /2iBHb QM i?2 /i `2/m+iBQM- M/ /2b+`BTiBQM
Q7 i?2 +iHQ;m2- r2 `272` iQ p/"RjX AM bmKK`v- i?2 +iHQ;m2b +QMiBM Q#@
9XkX :*Gaa .h LGuaAa
dR
D2+ib /2i2+i2/ BM i?2 Eb @#M/- rBi? :mbbBM@r2B;?i2/ T2`im`2 ~mt2b BM RR
}Hi2`b iQ +QMbi`BM i?2 a1.b Q7 i?2 Q#D2+ib- M/ iQ b2T`i2 bi`b 7`QK ;HtB2b
#v +QK#BMBM; i?2B` u − C M/ C − E +QHQm`bX h?2 /2Ti? Q7 i?2 BK;2b- M/
i?2`27Q`2 i?2 +QKTH2i2M2bb Q7 i?2 +iHQ;m2b- /Bz2`b bHB;?iHv 7`QK +Hmbi2` iQ
+Hmbi2`X h?2 K2/BM T?QiQK2i`B+ +QKTH2i2M2bb HBKBi U3yWV- BM i2`Kb Q7 bi2HH`
Kbb- Bb 1010.16 J" 7Q` i?2 Ry +Hmbi2`b BM i?2 :*Gaa bKTH2X
1+? +Hmbi2` ?b bm#biMiBH bT2+i`Qb+QTB+ +Qp2`;2 T`QpB/2/ #v i?2 :JPa
BMbi`mK2Mib QM :2KBMB LQ`i? M/ :2KBMB aQmi?X h?2 i`;2ib 7Q` bT2+i`Qb+QTB+
7QHHQr@mT r2`2 T`BQ`BiBx2/ #v i?2B` 3.6µK ~mt M/ i?2B` T`QD2+i2/ +Hmbi2`@
+2Mi`B+ /BbiM+2- b 2tTHBM2/ BM JRkX h?2 K2K#2`b?BT Q7 i?2 KbbBp2 ;HtB2b
i?i +QMbiBimi2 KQbi Q7 i?2 bi2HH` Kbb BM i?2 +Hmbi2`b `2 i?mb +QM}`K2/
bT2+i`Qb+QTB+HHvX aBM+2 i?2 i`;2iBM; +QKTH2i2M2bb Bb r2HH mM/2`biQQ/- r2
+M mb2 i?2 bm#@bKTH2 7Q` r?B+? r2 ?p2 bT2+i` iQ biiBbiB+HHv +Q``2+i i?2
7mHH +iHQ;m2 7Q` +Hmbi2` K2K#2`b?BTX >Qr i?Bb Bb /QM2 Bb QmiHBM2/ BM p/"Rj
Ua2+iX jX9V- M/ 2tTM/2/ QM BM a2+iX 9XkXjX
lbBM; i?2 bKTH2 Q7 bT2+i`Qb+QTB+HHv B/2MiB}2/ +Hmbi2` ;HtB2b- iQiHHBM; 98d
K2K#2`b 7Q` Ry +Hmbi2`b- r2 T2`7Q`K /vMKB+H MHvbBb iQ 2biBKi2 Kbb2b
7Q` 2+? +Hmbi2`X 6`QK i?2 HBM2@Q7@bB;?i p2HQ+Biv /Bbi`B#miBQMb- r?B+? b?Qr T@
T`QtBKi2Hv :mbbBM T`Q}H2b- i?2 p2HQ+Biv /BbT2`bBQMb `2 K2bm`2/ UqBHbQM
2i HX- BM T`2TXV mbBM; biM/`/ K2i?Q/b bm+? b i?2 b?B7iBM; ;TT2` M/ i?2
#B@r2B;?i 2biBKiQ` U"22`b 2i HX RNNyc :B``/B 2i HX RNNjc 6// 2i HX RNNeVb22 h#H2 9XRX aBM+2 r2 /Q MQi K2bm`2 i?2 p2HQ+Biv /BbT2`bBQM 7`QK /`F Ki@
i2` T`iB+H2b #mi 7`QK bm#?HQ2b UQ` ;HtB2bV- b2p2`H /vMKB+H 2z2+ib `2M/2`
i?Bb M BKT2`72+i i`+2` Q7 i?2 ;`pBiiBQMH TQi2MiBH U2X;X a`Q 2i HX kyRjVX AM
M ii2KTi iQ iF2 ++QmMi Q7 i?2b2 #Bb2b Ur?B+? HbQ /2T2M/ QM i?2 bT2+i`Q@
b+QTB+ i`;2i b2H2+iBQMV- p`BQmb b+HBM;b #2ir22M i?2 p2HQ+Biv /BbT2`bBQM M/
?HQ Kbb UM200 V ?p2 #22M T`QTQb2/ BM i?2 HBi2`im`2 U2X;X *`H#2`; 2i HX
RNNdc 1p``/ 2i HX kyy3c JmM`B 2i HX kyRjVX h?2b2 `2 Q7 i?2 7Q`K
σ1. = R.
$
h(z) M200
1015 J"
%α
FK b−R ,
U9XRV
r?2`2 R. M/ α `2 T`K2i2`b i?i `2 /Bz2`2Mi 7Q` 2+? bim/v U6B;X 9XRVX
AM Q`/2` iQ /2i2`KBM2 r?B+? b+HBM; `2HiBQM ;Bp2b i?2 #2bi ?HQ Kbb 2biB@
Ki2 7Q` i?2 K2bm`2/ p2HQ+Biv /BbT2`bBQMb BM :*Gaa- r2 +QMbB/2` bKTH2
Q7 +Hmbi2`b r?B+? r2`2 Q`B;BMHHv bim/B2/ b T`i Q7 i?2 *M/BM L2irQ`F 7Q`
P#b2`piBQMH *QbKQHQ;v U*LP*- u22 2i HX RNNeVX r2F@H2MbBM; bim/v ?b
#22M T2`7Q`K2/ 7Q` i?2b2 bvbi2Kb- r?B+? T`QpB/2b 7Q` BM/2T2M/2Mi Kbb 2b@
iBKi2b U>Q2Fbi` kyydc >Q2Fbi` 2i HX kyRk- `2pBb2/ BM >Q2Fbi` 2i HX- BM
T`2TXVX 6Q` Rj Q7 i?2 +Hmbi2`b BM i?Bb bKTH2- p2HQ+Biv /BbT2`bBQMb ?p2 #22M
*>Sh1_ 9X *1Lala P6 ah1GG_ Jaa AL Ry JaaAo1 >GP1a
dk
h z ∼ 1 6_PJ h>1 :*Gaa al_o1u
K2bm`2/ 7`QK bT2+i`Qb+QTB+ i`;2ib i?i r2`2 +?Qb2M BM bBKBH` rv b
i?2 i`;2ib b2H2+i2/ BM i?2 :*Gaa bKTH2 U"Q`;MB 2i HX RNNNc :B``/B J2xx2iiB kyyRVX 6B;X 9XR +QKT`2b i?2 r2F@H2MbBM; Kbb2b UM200 V iQ i?2 HBM2@
Q7@bB;?i +Hmbi2` p2HQ+Biv /BbT2`bBQMbX q2 }i HBM2` `2HiBQM BM i?Bb HQ;`Bi?KB+
THM2- r?BH2 }tBM; i?2 bHQT2 iQ α = 13 - M/ HHQr 7Q` i?2 T`2b2M+2 Q7 BMi`BM@
bB+ b+ii2` BM i?2 }iX h?2 #H+F HBM2 b?Qrb i?2 #2bi@}iiBM; b+HBM; `2HiBQM
ey
−R
iQ i?2 /i TQBMib UR. = Ndk+
V- M/ r2 }M/ bB;MB}+Mi KQmMi
−8k FK b
Q7 BMi`BMbB+ b+ii2` `QmM/ i?Bb `2HiBQM UHQ;(σσv |h(z)·M200 ) = 0.07+0.03
−0.02 /2tVX
h?2 #2bi@}iiBM; b+HBM; `2HiBQM Bb
p2`v bBKBH` iQ i?2 `2HiBQM bm;;2bi2/
#v 1p``/ 2i HX Ukyy3VX hQ 2biBKi2
?HQ Kbb2b Q7 i?2 :*Gaa +Hmbi2`br2 rBHH i?2`27Q`2 mb2 i?2 1p``/ 2i HX
Ukyy3V b+HBM; `2HiBQMX h?Bb `2HiBQM
rb HbQ mb2/ #v `2+2Mi /vMKB@
+H bim/v QM i?2 *h +Hmbi2` bK@
TH2 UaB7ƦM 2i HX kyRjV- r?B+? bBK@
THB}2b +QKT`BbQM rBi? i?2 `2bmHib
7`QK i?Bb bKTH2 U2X;X >BHiQM 2i HX
kyRjV BM i?2 `2bi Q7 i?Bb TT2`X oHm2b 6B;m`2 9XR, J2bm`2/ p2HQ+Biv /BbT2`bBQM p2`@
Q7 M200 M/ R200 `2 b?QrM BM h@ bmb ?HQ Kbb Uh(z) · M200 VX .i TQBMib `2
#H2 9XRX aiiBbiB+H mM+2`iBMiB2b `2 K2bm`2K2Mib QM i?2 *LP* bKTH2X G2MbBM;
;Bp2M UT`QT;i2/ 7`QK mM+2`iBMiB2b Kbb2b `2 7`QK >Q2Fbi` 2i HX UkyRkV Ur?B+?
`2 `2pBb2/ BM ?Q2Fbi` 2i HX- BM T`2TXV- r?2`2b
QM i?2 p2HQ+Biv /BbT2`bBQMV- #mi MQi2 p2HQ+Biv /BbT2`bBQMb `2 Q#iBM2/ 7`QK "Q`;MB
i?i i?2`2 Bb HbQ bB;MB}+Mi bvb@ 2i HX URNNNV M/ :B``/B J2xx2iiB UkyyRVX
i2KiB+ mM+2`iBMiv U∼ 20WV- +Q`@ Hi?Qm;? i?2`2 Bb bm#biMiBH KQmMi Q7 BM@
`2bTQM/BM; iQ i?2 +?QB+2 Q7 b+HBM; i`BMbB+ b+ii2` U;`2v `2;BQM BM/B+i2b ±R@σ BM@
`2HiBQM- M/ BM/B+i2/ #v i?2 bm#@ i`BMbB+ b+ii2` `QmM/ i?2 `2HiBQMV- i?2 #2bi }i
biMiBH KQmMi Q7 BMi`BMbB+ b+ii2`X iQ i?2b2 /i U#H+F HBM2V Bb p2`v +HQb2 iQ i?2
LQi2 i?i i?2 R200 pHm2b ?p2 1p``/ 2i HX Ukyy3V b+HBM; `2HiBQM U`2/VX
bKHH2` 7`+iBQMH mM+2`iBMiv- bBM+2
1/3
R200 ∝ M200 X
q2 2biBKi2 T?QiQK2i`B+ `2/b?B7ib 7Q` HH ;HtB2b BM i?2 Eb @#M/ b2H2+i2/
+iHQ;m2 mbBM; i?2 1wu +Q/2 U"`KK2` 2i HX kyy3VX AM p/"Rj r2 bb2bb2/
i?2 T2`7Q`KM+2 #v +QKT`BM; i?2 T?QiQ@z 2biBKi2b iQ bT2+@z K2bm`2K2Mib
7Q` i?2 ;HtB2b i?i ?p2 #22M Q#b2`p2/ bT2+i`Qb+QTB+HHvX q2 7QmM/ b+ii2`
∆z
Q7 σz = 0.036 BM 1+z
- M2;HB;B#H2 #Bb M/ 72r2` i?M 8W QmiHB2`bX
7i2` }tBM; i?2 `2/b?B7i 7Q` 2+? Q#D2+i i Bib bT2+@z - Q` i?2 T?QiQ@z r?2M
bT2+@z Bb MQi pBH#H2- r2 2biBKi2 bi2HH` Kbb2b mbBM; 6ah UE`B2F 2i HX
kyyNVX h?2 bi2HH` TQTmHiBQM HB#``B2b 7`QK "`mxmH *?`HQi UkyyjV `2 mb2/
9XkX :*Gaa .h LGuaAa
dj
iQ Q#iBM i?2 KQ/2H a1. i?i ;Bp2b i?2 #2bi }i iQ i?2 T?QiQK2i`B+ /iX q2
mb2 T`K2i2`BxiBQM Q7 i?2 bi` 7Q`KiBQM ?BbiQ`v b SF R ∝ e−t/τ - r?2`2
i?2 iBK2@b+H2 τ Bb HHQr2/ iQ `M;2 #2ir22M Ry Jv` M/ Ry :v`X q2 HbQ
bbmK2 *?#`B2` UkyyjV AJ6- bQH` K2iHHB+Biv- M/ i?2 *Hx2iiB 2i HX UkyyyV
/mbi HrX 6Q` 2biBKi2b QM i?2 bi2HH`@Kbb +QKTH2i2M2bb Q7 i?2 +iHQ;m2br2 `272` iQ p/"RjX hQ TT`QtBKi2 i?2 biiBbiB+H mM+2`iBMiv QM 2+? bi2H@
H` Kbb K2bm`2K2Mi- r2 T2`7Q`K Ryy JQMi2@*`HQ bBKmHiBQMb BM r?B+? r2
T2`im`# i?2 T?QiQK2i`B+ T2`im`2 ~mt K2bm`2K2Mib rBi?BM i?2B` 2biBKi2/
2``Q`bX 1+? `2HBbiBQM Q7 i?2 +iHQ;m2 ;Bp2b bHB;?iHv /Bz2`2Mi a1. }i- M/
i?2`27Q`2 i?2 Kbb@iQ@HB;?i `iBQ UM" /LV Bb /Bz2`2MiX q2 i`MbHi2 i?2 Q#@
iBM2/ b+ii2` BM M" /L BMiQ M TT`QtBKi2 mM+2`iBMiv QM i?2 bi2HH` Kbb7i2` BM+Hm/BM; mM+2`iBMiB2b QM i?2 bT2+i`H i2KTHi2b i?2Kb2Hp2bX q2 }M/
ivTB+H mM+2`iBMiB2b QM M" /L Q7 yXkR /2t i M" ∼ 1010 J" - M/ yXRj /2t i
M" ∼ 1011 J" X
6B;X 9Xk b?Qrb i?2 /Bbi`B#miBQM Q7 iQ@
iH bi2HH` Kbb +QMiBM2/ BM ;Ht@
B2b rBi? ;Bp2M bi2HH` KbbX h?2
#2bi@}iiBM; a+?2+?i2` 7mM+iBQM iQ i?2
iQiH ;Htv TQTmHiBQM 7`QK p/"Rj
Bb HbQ b?QrMX h?2 TQBMib rBi? 2`@
`Q` #`b `2 i?2 K2bm`2K2Mib Q7 i?2
aJ6 T`2b2Mi2/ i?2`2- M/ `2 BMi2@
;`i2/ Kbb2b Qp2` i?2 aJ6 BM 2+?
& MKt
#BM- BX2X
Φ(M ) · M · dM MKBM
6B;m`2 9Xk, aQHB/ HBM2, i?2 /Bbi`B#miBQM Q7 iQiH
r?2`2 Φ(M ) `2T`2b2Mib i?2 MmK@ bi2HH` Kbb +QMiBM2/ BM ;HtB2b rBi? ;Bp2M
#2` /2MbBiv Q7 ;HtB2b b 7mM+iBQM bi2HH` KbbX h?2 TQBMib rBi? 2``Q` #`b `2
Q7 bi2HH` KbbX qBi? i?2 +?`+@ i?2 K2bm`2K2Mib Q7 i?2 aJ6 T`2b2Mi2/ BM pM
i2`BbiB+ Kbb Q7 i?2 a+?2+?i2` 7mM+@ /2` "m`; 2i HX UkyRjV- #mi BMi2;`i2/ Qp2` i?2
iBQM `QmM/ M" = 1011 J" - ;HtB2b Kbb #BMbX .Qii2/ HBM2, i?2 bT2+i`Qb+QTB+ +QK@
`QmM/ i?Bb Kbb +QMi`B#mi2 KQbi iQ TH2i2M2bb 7Q` ;HtB2b rBi? T`QD2+i2/ /BbiM+2b
7`QK i?2 "*: H2bb i?M R X 6Q` i?2 ;Ht@
i?2 iQiH bi2HH` Kbb Q7 i?2 +Hmbi2`X B2b i?i +QMbiBimi2 KQbi Q7200
i?2 bi2HH` Kbb BM
6Q` i?2 ;HtB2b rBi? bi2HH` Kbb2b i?2 +Hmbi2`b- i?2 bT2+i`Qb+QTB+ +QKTH2i2M2bb Bb
`QmM/ M" = 1011 J" - i?2 +QK@ ?B;? U! 50WVX
TH2i2M2bb Bb ?B;? U≥ 50WVX 6Q` K2@
bm`2K2Mib rBi?BM R500 i?2 +QKTH2i2M2bb Bb 2p2M ?B;?2`X 6Q` i?i `2bQM- i?2
K2bm`2K2Mib Q7 i?2 iQiH bi2HH` Kbb Q7 i?2 +Hmbi2`b `2 #b2/ KQbiHv QM
bT2+i`Qb+QTB+ `2/b?B7ib- M/ `2 `Q#mbi rBi? `2bT2+i iQ ?Qr r2 +Q``2+i i?2
T?QiQK2i`B+ bKTH2 7Q` +QKTH2i2M2bbX
q2 mb2 i?2 HBKBi2/ MmK#2` Q7 ;HtB2b BM i?2 }2H/b i?i ?p2 #22M i`;2i2/
bT2+i`Qb+QTB+HHv iQ 2biBKi2 i?2 T`Q##BHBiv i?i ;Htv Bb T`i Q7 i?2 +Hmbi2`
*>Sh1_ 9X *1Lala P6 ah1GG_ Jaa AL Ry JaaAo1 >GP1a
d9
h z ∼ 1 6_PJ h>1 :*Gaa al_o1u
7Q` i?2 Q#D2+ib i?i /Q MQi ?p2 K2bm`2/ bT2+i`Qb+QTB+ `2/b?B7iX 6Q` Q#D2+ib
rBi? bi2HH` Kbb2b 2t+22/BM; ∼ 1010 J" i?i r2`2 i`;2i2/- i?2 bm++2bb `i2 Q7
Q#iBMBM; `2HB#H2 bT2+@z Bb ?B;?2` i?M NyW UJRkVX :Bp2M i?i i?2 i`;2iBM;
T`BQ`BiBxiBQM Bb FMQrM UJRkV- r2 +M +Q``2+i i?2 T?QiQK2i`B+HHv b2H2+i2/
bKTH2 7Q` +Hmbi2` K2K#2`b?BT mbBM; i?2 bm#@bKTH2 Q7 bT2+i`Qb+QTB+ i`;2ibX
hQ /Q i?Bb r2 iF2 bBKBH` TT`Q+? b QmiHBM2/ BM p/"Rj Ua2+iX jX9V- #mi
rBi? 72r /TiiBQMbX
h?2 `/BH /BbiM+2 Q7 2+?
;Htv Bb `2b+H2/ iQ mMBib Q7 R200 BMbi2/ Q7 T?vbB+H /BbiM+2X h?2M
r2 K2bm`2 7Q` i?2 +Hmbi2` 2Mb2K@
#H2- BM #BMb Q7 `/BH /BbiM+2 M/
bi2HH` Kbb- i?2 7`+iBQM Q7 +Q``2+iHv
B/2MiB}2/ +Hmbi2` ;HtB2b #b2/ QM
i?2B` T?QiQ@z X *QKT`BM; i?Bb MmK@
#2` iQ i?2 iQiH MmK#2` Q7 bT2+@z b2@
H2+i2/ +Hmbi2` K2K#2`b BM i?Bb #BM- r2
Q#iBM K2K#2`b?BT +Q``2+iBQM 7+@
6B;m`2 9Xj, *Q``2+iBQM 7+iQ`b b 7mM+iBQM
Q7 `/Bmb- b+H2/ #v R200 - 7Q` i?2 +Hmbi2` 2M@ iQ`b i?i `2 mb2/ iQ +Q``2+i i?2
b2K#H2X 1``Q` #`b `2T`2b2Mi mM+2`iBMiB2b 2biB@ T?QiQK2i`B+HHv b2H2+i2/ MmK#2`b 7Q`
Ki2/ 7`QK JQMi2@*`HQ bBKmHiBQMbX 6m`i?2` K2K#2`b?BTX h?2 +Q``2+iBQM 7+iQ`b
rv 7`QK i?2 T`QD2+i2/ +2Mi`2b- i?2 +Q``2+iBQM b 7mM+iBQM Q7 `/BH /BbiM+2 `2
7+iQ`b ;Q /QrM #2+mb2 ;HtB2b `2 BM+`2b@ b?QrM BM 6B;X 9XjX h?2 K2K#2`b?BT
BM;Hv KQ`2 HBF2Hv iQ #2 T`i Q7 i?2 }2H/X
+Q``2+iBQM 7+iQ`b `2 /2+`2bBM;
7mM+iBQM Q7 /BbiM+2- bBM+2 i?2 +Hmb@
i2`b `2 H2bb Qp2`/2Mb2 7m`i?2` rv 7`QK i?2B` +Hmbi2` +2Mi`2X h?2 #Hm2 U`2/V
TQBMib `2T`2b2Mi i?2 TQTmHiBQM Q7 bi`@7Q`KBM; U[mB2b+2MiV ;HtB2bX 6Q` i?2
+Q``2+iBQM 7+iQ`b b 7mM+iBQM Q7 bi2HH` Kbb r2 `272` iQ p/"Rj U6B;X 9VX
hQ 7m`i?2` BKT`Qp2 i?2 2biBKi2b QM i?2 iQiH bi2HH` Kbb bbQ+Bi2/ rBi?
2+? +Hmbi2`- r2 2biBKi2 i?2 +QMiKBMiBQM #v }2H/ ;HtB2b 7Q` 2+? BM/BpB/mH
+Hmbi2`X h?Bb KBMQ` +Q``2+iBQM iQ i?2 T?QiQ@z b2H2+i2/ bKTH2 7Q` 2+? +Hmbi2`
Bb /m2 iQ +QbKB+ p`BM+2- bHB;?i /Bz2`2M+2b BM T?QiQK2i`B+ `2/b?B7i [mHBiv
#2ir22M i?2 }2H/b- M/ HbQ i?2 /2T2M/2M+2 Q7 M;mH` bBx2 bbQ+Bi2/ rBi?
R200 QM i?2 +Hmbi2` Kbb M/ `2/b?B7iX hQ 2biBKi2 i?Bb Qp2`/2MbBiv T`K2i2`
r2 RV TTHv i?2 +Q``2+iBQM 7+iQ`b i?i r2 mb2 QM i?2 T?QiQK2i`B+ bKTH2 U2X;X
6B;X 9Xj M/ p/"Rj U6B;X 9VV QM HH bT2+i`Qb+QTB+HHv i`;2ii2/ ;HtB2b- i?2M kV
mb2 i?Bb iQ 2biBKi2 i?2 MmK#2` Q7 +Hmbi2` K2K#2`b BM i?Bb bKTH2- M/ jV /BpB/2
i?2 +imH MmK#2` Q7 bT2+i`Qb+QTB+ +Hmbi2` K2K#2`b #v i?2 2biBKi2/ MmK#2`
Q7 +Hmbi2` K2K#2`b iQ ;Bp2 i?2 +Q``2+iBQM 7+iQ`X h?Bb +Hmbi2` Qp2`/2MbBiv
T`K2i2` Bb #v +QMbi`m+iBQM `QmM/ RXy M/ `M;2b 7`QK yX3e iQ RXkk 7Q` i?2
+Hmbi2`b BM Qm` bKTH2X
9XjX *1Lh_G ah1GG_ Jaa o1_ala >GP Jaa
d8
AM 6B;X 9X9 r2 b?Qr i?2 bi2HH` Kbb Q7 i?2 +2Mi`H ;Htv b 7mM+iBQM Q7 /v@
MKB+H ?HQ KbbX ai2HH` Kbb2b `2 K2bm`2/ #b2/ QM M" /LǶb 2biBKi2/
rBi? 6ah- KmHiBTHB2/ rBi? i?2 iQiH ~mt BM i?2 Eb @#M/X aBM+2 #`B;?i2bi +Hmb@
i2` ;HtB2b U"*:bV ;2M2`HHv ?p2 2ti2M/2/ HB;?i T`Q}H2b- i?2B` ~mt K2bm`2/
rBi? a1ti`+iQ` BM E`QM 2HHBTiB+H T2`im`2b Bb mM/2`@2biBKi2/X hQ ++QmMi
7Q` i?2 iQiH ~mt Q7 i?2 "*:b BM i?2 Eb @#M/- r2 mb2 :G6Ah iQ }i aû`bB+
T`Q}H2b iQ i?2b2 ;HtB2bX q2 KF2 bm`2 i?i r2 +`27mHHv KbF Mv M2`#v
bi2HHBi2 ;HtB2b M/ T2`7Q`K Ry /Bz2`2Mi }ib r?2`2 r2 +QMpQHp2 i?2 T`Q}H2b
rBi? /Bz2`2Mi bi`b iQ TT`QtBKi2 mM+2`iBMiB2b /m2 iQ i?2 Sa6X q2 +QKT`2
i?2 BMi2;`i2/ ~mt BM i?2b2 aû`bB+ T`Q}H2b rBi? i?2 a1ti`+iQ` K;MBim/2b BM
h#H2 9XkX h?2 pHm2b b?Qr i?2 K2/BM pHm2b M/ i?2 KtBKmK M/ KBMBKmK
pHm2b 7Q` i?2 Ry /Bz2`2Mi :G6Ah `mMb- 7i2` `2D2+iBM; i?2 ?B;?2bi M/ HQr2bi
pHm2X h?2 /Bz2`2M+2 #2ir22M i?2 :G6Ah M/ a1ti`+iQ` K2bm`2K2Mib Bb
ivTB+HHv #Qmi yXk K;- M/ /2T2M/b KBMHv QM i?2 b?T2 Q7 i?2 T`Q}H2- r?B+?
Bb /2b+`B#2/ #v i?2 aû`bB+ T`K2i2` nX hQ Q#iBM i?2 iQiH bi2HH` Kbb2b Q7
i?2 +2Mi`H ;HtB2b r2 KmHiBTHv i?2 iQiH ~mt BM i?2 Eb @#M/ rBi? i?2 M" /L
2biBKi2/ mbBM; 6ah- M/ BM+Hm/2 #Qi? i?2 ~mt@2``Q` M/ i?2 2``Q` QM M" /L
Ur?B+? Bb i?2 /QKBMMi bQm`+2 Q7 mM+2`iBMivVX
h#H2 9Xk, Eb @#M/ K;MBim/2b 7Q` i?2 "*:b B/2MiB}2/ BM GB/KM 2i HX UkyRkV 7Q` i?2
:*Gaa +Hmbi2`bX h?2 Hbi +QHmKM ;Bp2b i?2 bi2HH` Kbb2b +Q``2bTQM/BM; iQ i?2 :G6Ah
iQiH BMi2;`i2/ K;MBim/2- M/ i?2 2``Q`b HbQ BM+Hm/2 i?2 biiBbiB+H mM+2`iBMiv QM M! /LX
LK2
aT_*a@yyj9
aT_*a@yyj8
aT_*a@yyje
aT_*a@ykR8
aT_*a@Ry9d
aT_*a@Ry8R
aT_*a@ReRj
aT_*a@ReRe
aT_*a@Rej9
aT_*a@Rej3
J:nlhP
[K;" ]
16.59 ± 0.01
17.27 ± 0.01
16.40 ± 0.01
17.05 ± 0.01
17.29 ± 0.01
17.11 ± 0.02
15.67 ± 0.01
17.01 ± 0.01
17.41 ± 0.01
17.71 ± 0.02
:G6Ah
[K;" ]
16.51+0.04
−0.03
17.06+0.01
−0.01
16.10+0.01
−0.04
16.86+0.02
−0.02
17.03+0.01
−0.03
16.73+0.03
−0.04
15.50+0.00
−0.01
16.96+0.01
−0.02
17.42+0.01
−0.01
17.43+0.01
−0.01
:G6Ah
aû`bB+ @ n
3.68+0.36
−0.37
3.77+0.13
−0.13
3.82+0.30
−0.37
3.02+0.14
−0.13
4.35+0.22
−0.41
6.87+0.97
−0.93
3.25+0.10
−0.15
3.03+0.18
−0.15
0.83+0.01
−0.01
5.23+0.12
−0.12
M",BCG
[1011 J" ]
3.56+0.36
−0.54
4.61+0.97
−0.60
6.92+0.30
−1.25
3.36+0.47
−0.94
2.42+0.29
−0.58
4.49+0.15
−0.72
10.91+0.44
−2.40
3.24+0.26
−0.13
1.89+0.23
−0.21
2.36+0.47
−0.40
*QMbB/2`BM; i?2 :*Gaa /i BM 6B;X 9X9- r2 }M/ KBH/ 2pB/2M+2 7Q` +Q``2HiBQM #2ir22M i?2 "*: bi2HH` Kbb M/ ?HQ Kbb- rBi? aT2`KM
*>Sh1_ 9X *1Lala P6 ah1GG_ Jaa AL Ry JaaAo1 >GP1a
de
h z ∼ 1 6_PJ h>1 :*Gaa al_o1u
`MF +Q2{+B2Mi ρ = 0.49X h?2 7`+iBQM Q7 Kbb +QMiBM2/ BM bi2HH` 7Q`K BM i?2
"*: Bb TT`QtBKi2Hv yXyyR Q7 i?2 ?HQ KbbX
"2?`QQxB 2i HX UkyRyV M/ "2?`QQxB 2i HX UkyRjV 2biBKi2/ i?2 bi2HH` Kbb
p2`bmb pB`BH ?HQ Kbb `2HiBQM Qp2` `M;2 Q7 `2/b?B7ib M/ ?HQ Kbb2b mbBM;
i?2 #mM/M+2 Ki+?BM; i2+?MB[m2X i i?2 ?B;? Kbb 2M/ r2 KF2 +QKT`@
BbQM #2ir22M i?2B` 2biBKi2b M/ Qm` Q#b2`piBQMb- r?B+? `2 #b2/ QM /B`2+i
K2bm`2K2Mib Q7 i?2 iQiH ?HQ Kbb2b M/ bi2HH` Kbb2b Q7 +2Mi`Hb BM i?2
bK2 bvbi2KbX q2 KmHiBTHv i?2 "2?`QQxB ?HQ Kbb2b #v 7+iQ` RXRR iQ +@
+QmMi 7Q` i?2 /Bz2`2M+2 #2ir22M i?2B` pB`BH ?HQ Kbb2b M/ M200 U"`vM LQ`KM RNN3VX q2 b?Qr i?2 "2?`QQxB 2i HX UkyRyV U"2?`QQxB 2i HX UkyRjVV
T`2/B+iBQM 7Q` z = 1 #v i?2 HB;?i U/`FV b?/2/ `2 BM 6B;X 9X9X Hi?Qm;? i?2
HHQr2/ `2b `2 H`;2 #2+mb2 Q7 BM+Hm/BM; biiBbiB+H M/ bvbi2KiB+ mM+2`@
iBMiB2b- i?2 `2bmHib 7`QK "2?`QQxB 2i HX UkyRyV b22K iQ #2 BM #2ii2` ;`22K2Mi
rBi? i?2 :*Gaa /i i?M i?2 `2bmHib 7`QK "2?`QQxB 2i HX UkyRjVX q?i Bb
/Bz2`2Mi BM #Qi? #m/M+2 Ki+?BM; bim/B2b Bb i?2 bT2+B}+ i`2iK2Mi Q7 BMi`@
+Hmbi2` HB;?i UA*GV BM "2?`QQxB 2i HX UkyRjVX q?2M ;Htv K2`;2` Q++m`b BM
i?Bb M2r KQ/2H- i?2 bi`b bbQ+Bi2/ rBi? i?2 bi2HHBi2 ;Htv Kv 2Bi?2` #2
/2TQbBi2/ QMiQ i?2 +2Mi`H ;Htv Q` #2 2D2+i2/ BMiQ i?2 A*GX aBM+2 "2?`QQxB
2i HX UkyRjV 2biBKi2 i?2 A*G iQ #2 Q7 bB;MB}+Mi +QMi`B#miBQM iQ i?2 iQiH
bi2HH` Kbb i z = 1- i?Bb Bb TQi2MiBHHv `2Hi2/ iQ M mM/2`@T`2/B+iBQM Q7 i?2
bi2HH` Kbb BM i?2 +2Mi`H ;HtB2bX
hQ BM+`2b2 i?2 /vMKB+ `M;2 BM i2`Kb Q7 +Hmbi2` ?HQ Kbb- BM Q`/2` iQ
+QMbi`BM i?2 TQr2`@Hr bHQT2 Q7 i?Bb `2HiBQM- r2 +QKT`2 Qm` `2bmHib iQ i?Qb2
7`QK >BHiQM 2i HX UkyRjV- r?B+? r2`2 Q#iBM2/ 7`QK bKTH2 Q7 *h aw@
b2H2+i2/ +Hmbi2`bX hQ #2 #H2 iQ +QKT`2 i?2 `2bmHib /B`2+iHv- r2 `2/m+2 i?2
bi2HH` Kbb2b 2biBKi2/ 7`QK >BHiQM 2i HX UkyRjV #v yXk9 /2t iQ ++QmMi 7Q`
/Bz2`2M+2b BM i?2 /QTi2/ AJ6X LQi2 i?i >BHiQM 2i HX UkyRjV /B/ MQi }i i?2
a1. Q7 i?2 "*: rBi? KQ/2H iQ +QMbi`BM M" /L- #mi `i?2` bbmK2/ bBM;H2
#m`bi bi2HH` TQTmHiBQM i?i ?b 7Q`KiBQM `2/b?B7i z7 = 3X 6Q` i?2 Tm`TQb2
Q7 2biBKiBM; "*: bi2HH` Kbb2b i?2 /Bz2`2M+2 #2ir22M i?2b2 TT`Q+?2b Bb
bKHH U<yXR /2tV- #2+mb2 i?2 "*:b +QMiBM `2HiBp2Hv QH/ bi2HH` TQTmHiBQMbX
h?2 M200 K2bm`2K2Mib 7Q` i?Bb +Hmbi2` bKTH2 `2 iF2M 7`QK aB7ƦM 2i HX
UkyRjVX 6B;X 9X9 b?Qrb +H2` `2HiBQM #2ir22M i?2 "*: bi2HH` Kbb M/ iQiH
?HQ Kbb 7`QK :*Gaa M/ >BHiQM 2i HX UkyRjVX
q?2M r2 }i bHQT2 iQ i?2 +QK#BM2/ b2i Q7 /i TQBMib- r2 ?p2 iQ ++QmMi
7Q` BMi`BMbB+ b+ii2` BM i?2 `2HiBQM iQ 2Mbm`2 i?i r2 /Q MQi ;Bp2 iQQ Km+?
r2B;?i iQ T`2+Bb2 K2bm`2K2Mib i?i `2 7` Qz i?2 K2M `2HiBQMX q2 7QHHQr
i?2 TT`Q+? QmiHBM2/ BM >Q2Fbi` 2i HX UkyRRV iQ T2`7Q`K i?`22 T`K2i2` }i
iQ i?2b2 /i TQBMibX "2bB/2b i?2 T`K2i2`b /2b+`B#BM; i?2 TQr2`@Hr `2HiBQMi?2 BMi`BMbB+ b+ii2` Bb bbmK2/ iQ #2 /2b+`B#2/ #v HQ;@MQ`KH /Bbi`B#miBQM7Q` r?B+? r2 }i i?2 /BbT2`bBQM σ X h?2 BMi`BMbB+ b+ii2` Bb #2bi /2b+`B#2/ #v
HQ;(σMBCG |M200 ) = 0.12+0.03
−0.02 /2t- M/ i?2 #2bi@}iiBM; `2HiBQM Bb HQ;(MBCG ) =
(11.66 ± 0.03) + 0.42+0.06
−0.07 · [HQ;(M200 ) − 14.5]X h?Bb `2HiBQM Bb THQii2/ BM
9X9X hPhG ah1GG_ Jaa o1_ala >GP Jaa
dd
6B;X 9X9 M/ BM/B+i2b i?i i?2 "*: bi2HH` Kbb 7`+iBQM Bb HQr2` 7Q` ?B;?2`
Kbb ?HQ2bX h?2 }i b?Qrb i?i i?2`2 Bb bB;MB}+Mi KQmMi Q7 BMi`BMbB+ b+ii2`
BM i?2 `2HiBQM #2ir22M +2Mi`H ;Htv bi2HH` Kbb M/ ?HQ Kbb- r?B+? Bb
+QMbBbi2Mi rBi? i?2 }M/BM; Q7 2X;X G2mi?m/ 2i HX UkyRk#VX
LQi2 i?i Qm` /i /Q MQi HHQr 7Q` K2bm`2K2Mib Q7 i?2 BMi`+Hmbi2` HB;?i
UA*GV- M/ i?2`27Q`2 i?2 +QMi`B#miBQM Q7 BMi`+Hmbi2` bi`b iQ i?2 +2Mi`H bi2HH`
Kbb Bb M2;H2+i2/X 6Q`KHHv i?2 K2bm`2/ pHm2b `2 i?2`27Q`2 HQr2` HBKBib#mi "m`F2 2i HX UkyRkV b?Qr i?i i?2 +QMi`B#miBQM Q7 BMi`+Hmbi2` bi`b iQ i?2
iQiH bi2HH` Kbb i z ∼ 1 Bb 2tT2+i2/ iQ #2 bB;MB}+MiHv bKHH2` i?M i
HQr2` `2/b?B7ibX AM +QMi`bi- "2?`QQxB 2i HX UkyRjV bm;;2bi TB+im`2 BM r?B+?
bB;MB}+Mi 7`+iBQM Q7 i?2 A*G ?b H`2/v #22M 7Q`K2/ i z ∼ 1X h?2`2 Bb?Qr2p2`- bHB;?i i2MbBQM #2ir22M i?2B` biiBbiB+H bim/v M/ Qm` Q#b2`piBQMb Q7
i?2 bi2HH` Kbb BM i?2 +2Mi`H ;Htv Ur?B+? Bb `2Hi2/ iQ i?2 #mBH/@mT Q7 i?2
A*G +QKTQM2MiV BM 6B;X 9X9X
GB/KM 2i HX UkyRkV K2bm`2 i?2 "*: bi2HH` Kbb p2`bmb ?HQ Kbb 7Q`
bKTH2 Q7 Rey "*:b BM i?2 `2/b?B7i BMi2`pH 0.03 < z < 1.63X "2bB/2b i?2
/Bz2`2Mi `2/b?B7i `M;2 i?2v bim/v- i?2B` MHvbBb Bb bHB;?iHv /Bz2`2Mi 7`QK Qm`bX
GB/KM 2i HX UkyRkV +QMbi`BM i?2 M" /L Q7 i?2 "*:b rBi? C@- M/ Eb @#M/
/i M/ /Q MQi mb2 :G6Ah iQ T`Q#2 i?2 2ti2M/2/ HB;?i T`Q}H2b Q7 i?2 "*:bX
1.6±0.2
h?2 bHQT2 }ii2/ #v GB/KM 2i HX UkyRkV Bb M200 ∝ M"*:
X h?2 `2+BT`Q+H
Q7 i?Bb Bb +QMbBbi2Mi rBi? Qm` bHQT2 iQ rBi?BM k@σ X
q2 KF2 +QKT`BbQM #2ir22M i?2 ?HQ Kbb2b M/ i?2 iQiH bi2HH` Kbb
BM i?2 ?HQ- BM+Hm/BM; i?2 bi2HHBi2bX q2 rBHH T2`7Q`K HH K2bm`2K2Mib #Qi?
rBi?BM R200 M/ rBi?BM R500 iQ T`QpB/2 `272`2M+2 M/ 7+BHBii2 i?2 +QKT`@
BbQM rBi? HBi2`im`2 K2bm`2K2MibX q?2M M2+2bb`v- r2 rBHH +QMp2`i #2ir22M
R200 M/ R500 #v TTHvBM; i?2 +QM+2Mi`iBQM T`K2i2` 2biBKi2/ 7`QK .mzv
2i HX Ukyy3VX 6Q` i?2 Kbb M/ `2/b?B7i `M;2 Q7 i?2 :*Gaa +Hmbi2`b- .mzv
2i HX Ukyy3V }M/ ivTB+H +QM+2Mi`iBQM Q7 c = 2.7- r?B+? Bb +QMbBbi2Mi rBi?
bi+F2/ r2F@H2MbBM; K2bm`2K2Mi Q7 +Hmbi2`b i z ∼ 1 Ua2`2MQ *QpQM2
kyRjVX *Q``2bTQM/BM; iQ i?Bb +QM+2Mi`iBQM T`K2i2`- r2 rBHH mb2 i?2 `2H@
iBQMb?BTb R500 = 0.632 · R200 M/ M500 = 0.631 · M200 X
6Q` 2+? +Hmbi2` r2 bmK i?2 bi2HH` Kbb +QMiBM2/ BM ;HtB2b rBi? bT2+@
i`Qb+QTB+ `2/b?B7i +QMbBbi2Mi rBi? i?2 +Hmbi2` i?i 2t+22/ i?2 Kbb +QKTH2i2M2bb
HBKBi Q7 i?2 +Hmbi2`X h?2 Eb @#M/ ~mt HBKBib r2`2 bBKmHi2/ 7Q` 2+? +Hmbi2`M/ +Q``2bTQM/BM; bi2HH` Kbb +QKTH2i2M2bb HBKBib r2`2 2biBKi2/ M/ T`2@
b2Mi2/ BM p/"Rj Uh#H2 RVX hQ i?Bb r2 // i?2 T?QiQ@z b2H2+i2/ bQm`+2b i?i
r2 +Q``2+i 7Q` +Hmbi2` K2K#2`b?BT mbBM; i?2 K2i?Q/ 2tTHBM2/ BM a2+iX 9XkXjT`QpB/2/ i?i i?2B` T`QD2+i2/ `/BB 7`QK i?2 "*: `2 H2bb i?M R200 UQ` R500 VX
aBM+2 i?2 Qp2`/2MbBiv Q7 i?2 +Hmbi2` rBi? `2bT2+i iQ i?2 }2H/ Bb /Bz2`2Mi 7Q`
*>Sh1_ 9X *1Lala P6 ah1GG_ Jaa AL Ry JaaAo1 >GP1a
d3
h z ∼ 1 6_PJ h>1 :*Gaa al_o1u
6B;m`2 9X9, "*: bi2HH` Kbb p2`bmb iQiH ?HQ KbbX "H+F /Qib b?Qr HBM2b Q7 +QMbiMi
bi2HH` Kbb 7`+iBQMb Q7 yXyyyR- yXyyR M/ yXyRX ! +$ @bB;Mb b?Qr i?2 `2bmHib 7`QK >BHiQM 2i HX
UkyRjVX h?2 `2HiBQM Bb i?2 #2bi }i iQ i?2 +QK#BM2/ /i b2i Q7 >BHiQM 2i HX UkyRjV M/ i?2
+m``2Mi bim/vX 1biBKi2b 7`QK "2?`QQxB 2i HX UkyRyV M/ "2?`QQxB 2i HX UkyRjV `2 BM/B+i2/
#v i?2 b?/2/ `2;BQMbX
2+? +Hmbi2`- b 2tTHBM2/ BM a2+iX 9XkXj- r2 +Q``2+i i?2 iQiH bi2HH` Kbb Q7 i?2
T?QiQK2i`B+ bKTH2 rBi? i?2 +Hmbi2` Qp2`/2MbBiv T`K2i2` 7Q` 2+? +Hmbi2`X
h?2 bi2HH` Kbb Bb MQr K2bm`2/ rBi?BM T`QD2+i2/ `/Bmb Q7 R200 UQ`
R500 V- #mi iQ 2biBKi2 i?2 bi2HH` Kbb 7`+iBQM M/ #2 #H2 iQ +QKT`2 iQ
`2bmHib BM i?2 HBi2`im`2 r2 ?p2 iQ /2T`QD2+i i?2 bi2HH` Kbb QMiQ bT?2`2
rBi? `/Bmb r200 UQ` r500 V- bBM+2 i?2 ?HQ Kbb M200 UQ` M500 V Bb /2}M2/ BM i?i
rvX bbmKBM; +QM+2Mi`iBQM T`K2i2` c = 2.7 M/ BMi2;`iBM; i?2 L6q
T`Q}H2 HQM; i?2 HBM2 Q7 bB;?i- r2 }M/ i?i d9W Q7 i?2 Kbb BM i?2 +vHBM/2`
HbQ HB2b rBi?BM i?2 bT?2`2 rBi? `/Bmb R200 UM/ eNW r?2M r2 KF2 i?Bb
+QKT`BbQM 7Q` R500 VX q2 i?2`27Q`2 KmHiBTHv i?2 bi2HH` Kbb 2biBKi2b #v 7+iQ` yXd9 UyXeN 7Q` R500 VX
aBM+2 bQ 7` r2 QMHv +QMbB/2`2/ ;HtB2b rBi? bi2HH` Kbb2b 2t+22/BM; i?2
Kbb +QKTH2i2M2bb HBKBib- r2 ?p2 iQ 2biBKi2 i?2 bi2HH` Kbb +QMiBM2/ BM
HQr2` Kbb ;HtB2bX q2 K2bm`2/ i?2 a+?2+?i2` T`K2i2`b Q7 i?2 aJ6 BM
p/"Rj- M/ Hi?Qm;? i?2b2 T`K2i2`b r2`2 +QMbi`BM2/ #v ;HtB2b rBi? bi2HH`
Kbb2b 2t+22/BM; 1010 J" - r2 mb2 i?2 BMi2;`H Q7 i?Bb a+?2+?i2` 7mM+iBQM 7Q`
Kbb2b #2HQr i?2 bi2HH` Kbb +QKTH2i2M2bb HBKBib iQ +Q``2+i 7Q` i?2b2 HQr2`
Kbb ;HtB2bX 6B;X 9Xk b?Qrb i?i i?2 iQiH bi2HH` Kbb +QMiBM2/ BM HQr@
Kbb ;HtB2b Bb bKHHX h?2 T2`+2Mi;2 #v r?B+? r2 +Q``2+i i?2 bi2HH` Kbb
9X9X hPhG ah1GG_ Jaa o1_ala >GP Jaa
dN
/2T2M/b QM i?2 bi2HH` Kbb +QKTH2i2M2bb M/ `M;2b 7`QK 4W 7Q` aT_*a@
yyj8 iQ 25W 7Q` aT_*a@yyjeX :Bp2M i?2 bBx2 Q7 i?2b2 +Q``2+iBQMb 7+iQ`b- i?2v
/Q MQi ?p2 bB;MB}+Mi 2z2+i QM i?2 `2bmHib- 2bT2+BHHv #2+mb2 i?2 /2Ti? BM
i2`Kb Q7 bi2HH` Kbb Bb BM/2T2M/2Mi Q7 i?2 `2/b?B7i Q` ?HQ Kbb Q7 i?2 +Hmbi2`bX
hQiH bi2HH` Kbb2b `2 HBbi2/ BM h#H2 9XjX
AM 6B;X 9X8 r2 b?Qr i?2 iQiH bi2HH` Kbb p2`bmb iQiH ?HQ Kbb +QKT`2/
rBi?BM R200 M/ R500 UH27i M/ `B;?i TM2Hb- `2bT2+iBp2HvV 7Q` i?2 :*Gaa
bvbi2KbX 1``Q` #`b BM i?2 p2`iB+H /B`2+iBQM BM+Hm/2 biiBbiB+H mM+2`iBMiB2b
QM BM/BpB/mH bi2HH` Kbb K2bm`2K2Mib- M/ mM+2`iBMiB2b QM i?2 2biBKi2/
T`Q##BHBiB2b i?i T?QiQK2i`B+HHv b2H2+i2/ ;Htv Bb T`i Q7 i?2 +Hmbi2`X h?2
Hii2` mM+2`iBMiv- r?B+? /QKBMi2b- BM+Hm/2b i?2 2``Q` QM i?2 Qp2`/2MbBiv T@
`K2i2` 7Q` 2+? +Hmbi2`X h?2 :*Gaa /i b?Qr +H2` +Q``2HiBQM- rBi?
bT2`KM +Q2{+B2Mi ρ = 0.65 UrBi?BM R200 V- M/ ρ = 0.62 UrBi?BM R500 VX
q2 }i TQr2`@Hr `2HiBQM iQ i?2 :*Gaa /i TQBMib- rBi? i?2 KQmMi
Q7 BMi`BMbB+ b+ii2` b 7`22 T`K2i2`- M/ /2b+`B#2/ #v HQ;@MQ`KH /Bbi`B@
#miBQM rBi? b+ii2` σ X q2 }M/ i?2 7QHHQrBM; #2bi@}iiBM; T`K2i2`b 7Q` i?2
+QKT`BbQM rBi?BM R200 c HQ;(σM200,! |M200 ) = 0.08+0.04
−0.05 /2t- M/ i?2 `2HiBQM
HQ;(M200," ) = (12.44 ± 0.04) + (0.59 ± 0.10) · [HQ;(M200 ) − 14.5]X q?2M r2 T2`@
7Q`K i?2 }i iQ i?2 /i rBi?BM R500 r2 }M/c HQ;(σM500,! |M500 ) = 0.11+0.05
−0.04 /2tM/ i?2 `2HiBQM HQ;(M500," ) = (12.44+0.05
)
+
(0.62
±
0.12)
·
[
HQ;
(M
500 ) − 14.5]X
−0.06
"Qi? `2HiBQMb `2 b?QrM BM 6B;X 9X8X h?2 bHQT2 Q7 i?2 `2HiBQM Bb +QMbBbi2Mi
rBi? i?2 bHQT2 7QmM/ #v GBM 2i HX UkyRkV- r?Q K2bm`2/ Bi iQ #2 0.71 ± 0.04
7Q` bKTH2 Q7 `2/b?B7i z < 0.6 +Hmbi2`bX h?2 bKHH KQmMi Q7 BMi`BMbB+ b+ii2`
BM i?2 `2HiBQM #2ir22M iQiH bi2HH` Kbb M/ ?HQ Kbb BM/B+i2b i?i bi2H@
H` Kbb Bb ;QQ/ T`Qtv 7Q` iQiH ?HQ Kbb UH#2Bi rBi? H`;2 K2bm`2K2Mi
mM+2`iBMiB2b QM BM/BpB/mH +Hmbi2`bV- b rb HbQ bm;;2bi2/ #v M/`2QM UkyRkVX
6Q` e s@`v b2H2+i2/ ;Htv +Hmbi2`b i z ∼ 1- "m`F2 2i HX UkyRkV b?Qr i?i
i?2 +QMi`B#miBQM Q7 i?2 A*G iQ i?2 iQiH C@#M/ ~mt rBi?BM R500 Bb #Qmi R@9WX
aBM+2 i?Bb +QMi`B#miBQM Bb Km+? U7+iQ` ∼k@9V bKHH2` i?M i?2 +QMi`B#miBQM Q7
i?2 A*G i HQr@z - Qm` K2bm`2K2Mib b?QmH/ #2 +HQb2 iQ i?2 +imH Kbb BM
bi`bX
:Bp2M i?i i?Bb iB;?i `2HiBQM #2ir22M iQiH bi2HH` Kbb M/ ?HQ Kbb
H`2/v 2tBbib i z ∼ 1- M/ i?i i?2 bi2HH` Kbb 7`+iBQM Bb /2+`2bBM; rBi?
BM+`2bBM; ?HQ Kbb- QM2 rQmH/ MBp2Hv 2tT2+i i?2 bi2HH` Kbb 7`+iBQM Q7
i?2b2 KbbBp2 ?HQ2b iQ BM+`2b2 iQr`/b HQr2` `2/b?B7ibX h?i Bb #2+mb2 i?2
HBF2Hv bvbi2Kb i?i rBHH #2 +QMbmK2/ #v i?2b2 ?HQ2b `2 i?Qb2 rBi? ?B;?
bi2HH` Kbb 7`+iBQM UJ+:22 2i HX kyyNVX AM i?Bb bBKTH2 TB+im`2 i?2 bi2HH`
Kbb 7`+iBQM rQmH/ BM+`2b2- 2p2M BM i?2 #b2M+2 Q7 BM@bBim bi` 7Q`KiBQMX
:Bp2M i?Bb MBp2 2tT2+iiBQM- Bi Bb i?2`27Q`2 BMi2`2biBM; iQ KF2 +QKT`BbQM
Q7 i?2 bi2HH` Kbb +QMi2Mi Q7 ?HQ2b i HQr2` `2/b?B7ibX
*>Sh1_ 9X *1Lala P6 ah1GG_ Jaa AL Ry JaaAo1 >GP1a
3y
h z ∼ 1 6_PJ h>1 :*Gaa al_o1u
h#H2 9Xj, hQiH bi2HH` Kbb2b T`QD2+i2/ QMiQ bT?2`2b rBi? `/BB R200 M/ R500 7Q` i?2
:*Gaa +Hmbi2`bX
LK2
aT_*a@yyj9
aT_*a@yyj8
aT_*a@yyje
aT_*a@ykR8
aT_*a@Ry9d
aT_*a@Ry8R
aT_*a@ReRj
aT_*a@ReRe
aT_*a@Rej9
aT_*a@Rej3
M200,"
12
[10 J" ]
2.40+0.16
−0.15
1.89+0.22
−0.20
3.30+0.16
−0.15
2.86+0.25
−0.23
1.45+0.15
−0.13
1.00+0.07
−0.07
7.35+0.60
−0.55
3.29+0.20
−0.19
1.88+0.13
−0.12
1.13+0.14
−0.13
M500,"
12
[10 J" ]
2.10+0.14
−0.14
1.50+0.18
−0.16
2.74+0.14
−0.13
1.55+0.15
−0.14
0.94+0.09
−0.08
0.60+0.06
−0.06
5.68+0.42
−0.39
2.75+0.16
−0.15
1.38+0.11
−0.10
0.92+0.13
−0.11
M500," (3.6µK)
[1012 J" ]
@
5.43+2.92
−1.90
@
@
@
@
18.72+9.65
−6.37
7.14+2.19
−1.68
3.37+2.58
−1.46
2.33+1.56
−0.93
hFBM; i?2 #+F;`QmM/ bm#i`+i2/ ~mt BM A_* jXeµK M/ bbmKBM;
i?2 bK2 M" /L 7Q` 2p2`v ;Htv BM 2+? +Hmbi2`- #b2/ QM bBM;H2 #m`bi
bi2HH` TQTmHiBQM rBi? τ = 0.1 :v` 7Q`K2/ i z7 = 3X
q2 +QKT`2 Qm` K2bm`2K2Mib iQ Qi?2`b BM i?2 HBi2`im`2 UKQbiHv T2`7Q`K2/
i HQr@z V 7Q` R500 - bBM+2 i?Bb `/Bmb rb mb2/ #v KQbi bim/B2b i?i 2biBKi2 i?2
?HQ Kbb2b rBi? s@`v /iX >Qr2p2`- i?2`2 `2 b2p2`H BKTQ`iMi +p2ib iQ
KF2 #27Q`2 r2 +M KF2 7B` +QKT`BbQMX h?2 /QTi2/ M" /L Bb KDQ`
bvbi2KiB+ mM+2`iBMiv BM Mv bim/v M/ /2T2M/b QM i?2 bbmK2/ AJ6 /m2
iQ /Bz2`2M+2b BM i?2 +QMi`B#miBQM Q7 HQr Kbb bi`b iQ i?2 iQiH KbbX q2
i`Mb7Q`K i?2 `2bmHib 7`QK Qi?2` bim/B2b iQ i?2 *?#`B2` AJ6 #v bm#i`+i@
BM; yXk9 /2t BM Kbb 7Q` aHT2i2` AJ6- Q` //BM; yXy9 /2t iQ i?2 Kbb 7Q`
E`QmT AJ6X h?2 M" /L /2T2M/b QM ;Htv ivT2- #mi /m2 iQ i?2 H+F Q7
KmHiB@rp2H2M;i? T?QiQK2i`v- Bi Bb Q7i2M bbmK2/ i?i HH +Hmbi2` ;HtB2b `2
+QKTQb2/ Q7 i?2 bK2 bi2HH` TQTmHiBQMX A7 QM2 bbmK2b M QH/ bi2HH` TQT@
mHiBQM UM/ i?2`27Q`2 ?B;? M" /LV- i?2 Kbb Q7 i?2 Hi2@ivT2 ;HtB2b UM/
i?mb i?2 +Hmbi2` b r?QH2V Bb Qp2`@2biBKi2/X am+? M 2z2+i rBHH #2 KQ`2 T`Q@
MQmM+2/ i ?B;?2` `2/b?B7i #2+mb2 Q7 i?2 ?B;?2` MmK#2` /2MbBiv Q7 Hi2@ivT2
;HtB2b BM ?B;?@z +Hmbi2`b UJRk- p/"RjVX q2 rBHH TQBMi Qmi TQbbB#H2 Bbbm2b 7Q`
2+? Q7 i?2 +QKT`BbQM bKTH2b #2HQrX
M Q#pBQmb bim/v iQ +QKT`2 Qm` `2bmHib iQ Bb #b2/ QM M aw@b2H2+i2/
+Hmbi2` bKTH2 7`QK i?2 *h- rBi? `2/b?B7i `M;2 Qp2`HTTBM; rBi? :*Gaa
M/ K2/BM `2/b?B7i Q7 z = 0.50 U>BHiQM 2i HX kyRjVX +QKTHB+iBQM Bb i?i
9X9X hPhG ah1GG_ Jaa o1_ala >GP Jaa
3R
6B;m`2 9X8, hQiH bi2HH` Kbb p2`bmb ?HQ Kbb rBi?BM bT?2`2 rBi? `/Bmb R200 M/ R500
UH27i M/ `B;?i TM2Hb- `2bT2+iBp2HvVX 1``Q` #`b `2T`2b2Mi mM+2`iBMiB2b QM BM/BpB/mH Kbb
K2bm`2K2Mib M/ mM+2`iBMiB2b QM i?2 K2K#2`b?BT +Q``2+iBQM 7Q` ;HtB2b r2 /Q MQi ?p2
bT2+i` 7Q`X .Qii2/ HBM2b b?Qr HQ+iBQMb rBi? +QMbiMi bi2HH` Kbb 7`+iBQMbX h?2 HBi2`im`2
K2bm`2K2Mib U`B;?i TM2HV `2 K2bm`2/ Qp2` `M;2 Q7 `2/b?B7ib- M/ `2 #b2/ QM /Bz2`2Mi
MHvb2bX q?2M TQbbB#H2- i?2 /i TQBMib `2 +Q``2+i2/ 7Q` /Bz2`2M+2b BM AJ6 M/ M! /LǶbb 2tTHBM2/ BM i?2 i2tiX
>BHiQM 2i HX UkyRjV 2biBKi2/ +Hmbi2` bi2HH` Kbb2b #b2/ QM i?2 iQiH A_*
jXeµK ~mt K2bm`2/ 7i2` biiBbiB+H #+F;`QmM/ bm#i`+iBQMX AMbi2/ Q7
}iiBM; M" /L 7Q` 2+? ;Htv #b2/ QM a1. KQ/2HHBM;- i?2v bbmK2 bi2HH`
TQTmHiBQM i?i Bb 7Q`K2/ i z7 = 3- 7QHHQrBM; τ = 0.1 :v` bBM;H2 #m`bi
KQ/2H M/ i?2 "`mxmH *?`HQi UkyyjV bi2HH` TQTmHiBQM bvMi?2bBb KQ/2HX
hQ 2biBKi2 i?2 2z2+ib Q7 i?2b2 bbmKTiBQMb M/ b22 B7 i?Bb +`2i2b #Bb- r2
7QHHQr i?2 K2i?Q/ /2b+`B#2/ #v >BHiQM 2i HX UkyRjV iQ Q#iBM i?2 #+F;`QmM/
bm#i`+i2/ A_* jXeµK ~mt rBi?BM R500 7Q` i?2 8 :*Gaa +Hmbi2`b 7Q` r?B+?
r2 ?p2 /22T A_* /i Up/"RjV- M/ 2biBKi2 i?2 iQiH bi2HH` Kbb #b2/ QM
i?2 /2b+`B#2/ bi2HH` TQTmHiBQMX h#H2 9Xj +QKT`2b i?2b2 2biBKi2b rBi? i?2
iQiH bi2HH` Kbb BM i?2 +Hmbi2`b Q#iBM2/ #v i?2 7mHH a1. }iiBM; MHvbBbX h?2
TT`Q+? rBi? }t2/ M" /L Qp2`@2biBKi2b i?2 bi2HH` Kbb BM HH +Hmbi2`b #v i
H2bi 7+iQ` Q7 k- M/ i?Bb /Bz2`2M+2 b22Kb iQ #2 H`;2bi 7Q` i?2 ?B;?2bi `2/b?B7i
+Hmbi2`X h?Bb Bb +QMbBbi2Mi rBi? i?2 MQiBQM i?i i?2 #Hm2 7`+iBQM- M/ i?2`27Q`2
i?2 7`+iBQM Q7 ;HtB2b rBi? `2HiBp2Hv HQr M" /L- BM+`2b2b rBi? `2/b?B7i U+7X
"mi+?2` P2KH2` RNd3VX Ai Bb HbQ TQbbB#H2 i?i i?2 bi2HH` TQTmHiBQM bbmK2/
#v >BHiQM 2i HX UkyRjV ?b 7Q`KiBQM `2/b?B7i Uz7 = 3V i?i Bb iQQ ?B;?X 7i2`
+Q``2+iBM; i?2 bi2HH` Kbb2b 7`QK >BHiQM 2i HX UkyRjV iQ *?#`B2` AJ6r2 /BpB/2 i?2K #v M //BiBQMH 7+iQ` Q7 k b M TT`QtBKi2 +Q``2+iBQM 7Q`
i?2 M" /L 2tTHBM2/ #Qp2X h?2b2 /i TQBMib `2 Qp2`THQii2/ BM 6B;X 9X8
U`B;?i TM2H- !@bvK#QHbV- M/ HB2 `QmM/ i?2 `2HiBQM i?i Bb i?2 #2bi }i iQ i?2
*>Sh1_ 9X *1Lala P6 ah1GG_ Jaa AL Ry JaaAo1 >GP1a
3k
h z ∼ 1 6_PJ h>1 :*Gaa al_o1u
:*Gaa /iX LQi2 i?i bBM+2 r2 mb2/ i?2 `2/@b2[m2M+2 b2H2+i2/ :*Gaa
bKTH2 iQ K2bm`2 i?Bb #Bb- i?2 `2H #Bb KB;?i #2 2p2M H`;2` B7 i?2 aw@b2H2+i2/
bKTH2 +QMiBMb HQr2` 7`+iBQM Q7 [mB2b+2Mi ;HtB2bX
hQ bim/v TQbbB#H2 2pQHmiBQM BM i?2 bi2HH` Kbb +QMi2Mi Q7 +Hmbi2`b r2
+QMbB/2` G;M€ 2i HX UkyRjV- r?Q K2bm`2 i?2 bi2HH` Kbb +QMi2Mi BM bKTH2
Q7 z < 0.3 +Hmbi2`bX 1biBKi2b 7Q` M500 `2 Q#iBM2/ 7`QK s@`v Q#b2`piBQMbX
hQ K2bm`2 i?2 iQiH bi2HH` Kbb 7`QK i?2 pBH#H2 a.aa /i- i?2 ;Htv
TQTmHiBQM Bb b2T`i2/ #2ir22M 2`Hv@ivT2 M/ Hi2@ivT2 ;HtB2b mbBM; i?2
Uu − iV +QHQm`X 1tTHQBiBM; i?2 M" /L 7`QK EmzKMM 2i HX UkyyjV BM i?2
i@#M/ 7Q` i?2b2 ;Htv ivT2b- G;M€ 2i HX UkyRjV 2biBKi2 bi2HH` Kbb2bX
aBM+2 i?2 EmzKMM 2i HX UkyyjV M" /LǶb `2 #b2/ QM i?2 E`QmT AJ6r2 bm#i`+i yXy9 /2t iQ +QKT`2 i?2B` `2bmHib iQ Qm`b- M/ Qp2`THQi i?2K BM
6B;X 9X8 U`B;?i TM2H- ♦@bvK#QHbVX
MQi?2` M2`#v +Hmbi2` bKTH2 Bb i?2 QM2 bim/B2/ #v :QMxH2x 2i HX UkyydVr?B+? Bb BM i?2 `M;2 0.03 < z < 0.13- M/ i?2b2 K2bm`2K2Mib `2 `2pBb2/
BM :QMxH2x 2i HX UkyRjVX AM i?2b2 bim/B2b- bBM;H2 M" /L rb mb2/ 7Q` 2+?
;Htv- B``2bT2+iBp2 Q7 i?2B` ivT2X 6`QK /vMKB+H MHvbBb Q7 i?2 al_PL
T`QD2+i- i?2v 2biBKi2 i?2 p2`;2 M" /L BM i?2 i@#M/- r?B+? i?2v 7QmM/ iQ
#2 HQr2` i?M i?2 M" /L #b2/ QM M bbmK2/ aHT2i2` AJ6X q2 +Q``2+i i?2B`
M" /L iQ *?#`B2` AJ6 #v bm#i`+iBM; yXRk /2t- M/ Qp2`THQi i?2 TQBMib
7`QK :QMxH2x 2i HX UkyRjV BM 6B;X 9X8 U`B;?i TM2H- ×@bvK#QHbVX h?2 bi2HH`
Kbb 7`+iBQMb i?2v }M/ `2 BM TT`QtBKi2 ;`22K2Mi rBi? i?2 bi2HH` Kbb
7`+iBQMb Q7 i?2 :*Gaa +Hmbi2`b- Hi?Qm;? i?2v }M/ bQK2r?i b?HHQr2`
bHQT2 Q7 0.52 ± 0.04 r?2M i?2v }i `2HiBQM iQ QMHv i?2B` /i b2iX :Bp2M i?i
i?2 7`+iBQM Q7 `2/ UrBi? H`;2 M" /LV ;HtB2b /2T2M/b QM ?HQ Kbb- Bi Bb
TQbbB#H2 i?i i?Bb bHQT2 Bb #Bb2/ /m2 iQ i?2 bbmKTiBQM Q7 bBM;H2 M" /L 7Q`
i?2 bKTH2X
hQ BM+`2b2 i?2 /vMKB+ `M;2 Q7 i?2 +QKT`BbQM bKTH2b- r2 KF2 +QKT`BbQM iQ i?2 K2bm`2K2Mib 7`QK "m/xvMbFB 2i HX UkyRjV- r?Q K2bm`2/
i?2 bi2HH` Kbb 7`+iBQM +`Qbb rB/2 `M;2 Q7 Kbb2b BM i?2 ;`QmT M/ +Hmbi2`
`2;BK2 7`QK i?2 a.aaX h?2B` bi+F2/ K2bm`2K2Mi Q7 Qp2` ky-yyy QTiB+HHv
b2H2+i2/ bvbi2Kb i 0.15 < z < 0.4 Bb b?QrM #v i?2 b?/2/ `2;BQM BM 6B;X 9X8X
aBM+2 i?2B` MHvbBb Bb p2`v bBKBH` iQ Qm`- r2 /Q MQi ?p2 iQ +Q``2+i i?2B`
K2bm`2K2Mib 7Q` /Bz2`2M+2b BM 2X;X M" /LX "Qi? i?2 MQ`KHBbiBQM M/ i?2B`
bHQT2 Q7 0.89±0.14 `2 +QMbBbi2Mi rBi? i?2 `2HiBQM r2 }M/ 7Q` :*GaaX q?2M
i?2v bi+F Q`B;BMH a.aa BK;2b iQ K2bm`2 i?2 +QMi`B#miBQM 7`QK i?2 A*G iQ
i?2 bi2HH` Kbb BM i?2B` bKTH2- i?2v }M/ bHQT2 i?i Bb 2p2M bi22T2`X
q2 MQi2 i?i i?2`2 `2 +p2ib i?i `Bb2 r?2M +QKT`BM; /Bz2`2Mi +Hmbi2`
bKTH2b- b rb HbQ TQBMi2/ Qmi #v b2p2`H Qi?2` bim/B2b U2X;X G2mi?m/
2i HX kyRkc "m/xvMbFB 2i HX kyRjVX S2`7Q`KBM; i?2 MHvbBb /2b+`B#2/ #v
>BHiQM 2i HX UkyRjV QM i?2 :*Gaa /i b?Qrb i?i i?2`2 Bb #Bb BM i?2
iQiH bi2HH` Kbb r?2M bBM;H2 M" /L Bb bbmK2/ 7Q` HH +Hmbi2` ;HtB2b2bT2+BHHv i ?B;?@z X h?Bb #Bb BM i?2 bi2HH` Kbb +M #2 H`;2` i?M i?2
9X8X _.AG ah1GG_ .1LaAhu .Aah_A"lhAPL
3j
2pQHmiBQM 2tT2+i2/ BM i?2 `2/b?B7i `M;2 0 < z < 1X h?Bb b?Qrb i?i Bi Bb
BKTQ`iMi iQ MHvb2 i?2 7mHH a1. Q7 2+? ;Htv iQ 2biBKi2 Bib bi2HH` KbbX
h?MFb iQ i?2 bT2+i`Qb+QTB+ +Qp2`;2 Q7 i?2 :*Gaa bKTH2- r?B+? Bb KQ`2
i?M 8yW +QKTH2i2 rBi?BM R200 7Q` i?2 ;HtB2b i?i /QKBMi2 i?2 iQiH bi2HH`
Kbb +QMi2Mi- K2K#2`b?BT bbB;MK2Mi Bb `2HiBp2Hv bi`B;?i@7Q`r`/X AM Qi?2`
MHvb2b- r?2`2 biiBbiB+H #+F;`QmM/ bm#i`+iBQM Bb T2`7Q`K2/- i?Bb +M
#2 KDQ` mM+2`iBMiv 7Q` BM/BpB/mH bvbi2KbX q2 ii2KTi2/ iQ +Q``2+i 7Q`
/Bz2`2M+2b BM i?2 MHvb2b #2ir22M HBi2`im`2 bim/B2b iQ #2 #H2 iQ +QKT`2 i?2
iQiH bi2HH` Kbb 7`+iBQMb #2ir22M /Bz2`2Mi 2TQ+?bX qBi?BM i?2 mM+2`iBMiB2b
i?2`2 b22Kb iQ #2 ;QQ/ ;`22K2Mi #2ir22M i?2 bim/B2b Qp2` i?Bb `2/b?B7i
`M;2- b?QrBM; i?i i?2`2 Bb MQ bB;MB}+Mi 2pQHmiBQM BM i?2 bi2HH` Kbb 7`+iBQM
i }t2/ ?HQ Kbb BM i?2 `2/b?B7i `M;2 0 < z < 1X hQ iB;?i2M i?2 +QMbi`BMib
QM TQbbB#H2 2pQHmiBQM Q7 i?Bb `2HiBQM- H`;2 M/ KQ`2 ?QKQ;2M2Qmb /ib2i
M/ MHvbBb `2 `2[mB`2/X
J2bm`2K2Mib Q7 i?2 2pQHmiBQM Q7 i?2 bTiBH ;Htv MmK#2` /2MbBiv M/ bi2HH`
Kbb /2MbBiv /Bbi`B#miBQMb `2 F2v iQ mM/2`biM/ ?Qr bi2HH` Kbb ++`2i2b
QMiQ KbbBp2 ?HQ2bX q2 T2`7Q`K i?2b2 K2bm`2K2Mib BM :*Gaa #v /BpB/BM;
i?2 bKTH2 BM `/BH #BMbX q2 /Q i?Bb #v bi+FBM; i?2 +Hmbi2` 2Mb2K#H2 i i?2
HQ+iBQM Q7 i?2 "*:b- M/ b+HBM; i?2 +Hmbi2`b #v i?2B` `2bT2+iBp2 R200 X q2
K2bm`2 i?2 `2 BM 2+? #BM #v KbFBM; i?2 HQ+iBQMb QM i?2 BK;2b i?i `2
+QMiKBMi2/ #v #`B;?i bi`bX HbQ- bBM+2 r2 /Q MQi iF2 i?2 bi2HH` Kbb Q7 i?2
"*:b BMiQ ++QmMi BM i?Bb bim/v- r2 KbF i?2 HQ+iBQM Q7 i?2 +2Mi`H ;HtB2b
bBM+2 i?Bb HQ+iBQM /Q2b MQi HHQr 7Q` i?2 /2i2+iBQM Q7 ivTB+H +Hmbi2` K2K#2`bX
h?2 MmK#2` /2MbBiv /Bbi`B#miBQM Bb b?QrM BM 6B;X 9Xe- r?2`2 BM 2+? `/BH
#BM i?2 MmK#2` Q7 bT2+@z B/2MiB}2/ +Hmbi2` K2K#2`b M/ i?2 K2K#2`b?BT@
+Q``2+i2/ T?QiQ@z K2K#2`b rBi? bi2HH` Kbb2b 2t+22/BM; 1010.2 M" `2 +QK@
#BM2/X 1``Q`b QM 2+? TQBMi `2 +QK#BMiBQM Q7 SQBbbQM bKTHBM; 2``Q`b- M/
2``Q`b T`QT;i2/ 7`QK i?2 K2K#2`b?BT +Q``2+iBQM r?B+? r2 2biBKi2/ 7`QK b2`B2b Q7 JQMi2@*`HQ bBKmHiBQMbX q2 mb2/ i?2 `2@r2B;?i2/ TQbBiBQM iQ THQi
i?2 /i TQBMib BM i?2 ?Q`BxQMiH /B`2+iBQMX h?2 ! +$ @bB;Mb b?Qr i?2 BMM2`KQbi
TQBMi BM+Hm/BM; i?2 "*:bX h?2 #QiiQK TM2H Q7 6B;X 9Xe b?Qrb i?2 bT2+i`Q@
b+QTB+ i`;2iBM; +QKTH2i2M2bb b 7mM+iBQM Q7 `/BH /BbiM+2- r?B+? b?Qrb
i?i @b /2bB;M2/@ i?2 +QKTH2i2M2bb Bb ?B;?2` 7Q` Q#D2+ib M2` i?2 T`QD2+i2/
+Hmbi2` +2Mi`2bX 6m`i?2` rv 7`QK i?2 +Hmbi2` +2Mi`2- i?2 2``Q`b i?i `Bb2
7`QK K2K#2`b?BT 2biBKi2b `2 /QKBMMiX
h?2 `/BH /Bbi`B#miBQM Q7 bi2HH` Kbb BM i?2 2Mb2K#H2 +Hmbi2` Bb b?QrM
BM 6B;X 9XdX "2bB/2b SQBbbQM +QmMiBM; 2``Q`b M/ 2``Q`b i?i `Bb2 7`QK +Hmb@
i2` K2K#2`b?BT +Q``2+iBQMb- i?2 2``Q` #`b BM+Hm/2 bi2HH` Kbb K2bm`2K2Mi
2``Q`b QM BM/BpB/mH ;HtB2bX *QKT`2/ iQ i?2 MmK#2` /2MbBiv T`Q}H2- i?2
*>Sh1_ 9X *1Lala P6 ah1GG_ Jaa AL Ry JaaAo1 >GP1a
39
h z ∼ 1 6_PJ h>1 :*Gaa al_o1u
6B;m`2 9Xe, h?2 MmK#2` /2MbBiv Q7 ;HtB2b rBi? bi2HH` Kbb2b > 1010.2 J! BM i?2 Ry
:*Gaa +Hmbi2`b b 7mM+iBQM Q7 `/BH /BbiM+2X h?2 iQiH ;Htv TQTmHiBQM U#H+FV Bb
b2T`i2/ #2ir22M bi`@7Q`KBM; U#Hm2V M/ [mB2b+2Mi U`2/V ;HtB2bX h?B+F TQBMib b?Qr i?2
K2K#2`b?BT@+Q``2+i2/ MmK#2` /2MbBiv- r?2`2 i?2 2``Q` #`b `2T`2b2Mi i?2 mM+2`iBMiB2b i?i
`Bb2 7`QK K2K#2`b?BT +Q``2+iBQMX h?2 TQBMib `2 }ii2/ #v T`QD2+i2/ L6q 7mM+iBQMb UHBM2bVrBi? /Bz2`2Mi +QM+2Mi`iBQM T`K2i2`bX h?2 HQr2` TM2H b?Qrb i?2 7`+iBQM Q7 ;HtB2b BM
2+? #BM rBi? bT2+i`Qb+QTB+ `2/b?B7iX
6B;m`2 9Xd, h?2 bi2HH` Kbb /2MbBiv /Bbi`B#miBQM BM ;HtB2b rBi? bi2HH` Kbb2b > 1010.2 J!
Q7 i?2 +QKTQbBi2 +Hmbi2` b 7mM+iBQM Q7 `/BH /BbiM+2X *QKT`BM; i?2b2 /Bbi`B#miBQMb iQ
i?Qb2 b?QrM BM 6B;X 9Xe- r2 }M/ i?i i?2 bi2HH` Kbb /Bbi`B#miBQMb `2 T2F2/ KQ`2 bi`QM;Hv
i?M i?2 MmK#2` /2MbBiv /Bbi`B#miBQMX h?i Bb M BM/B+iBQM 7Q` Kbb b2;`2;iBQM Q7 [mB2b+2Mi
;HtB2b BM i?2b2 bvbi2KbX h?2 HQr2` TM2H b?Qrb i?2 7`+iBQM Q7 bi2HH` Kbb BM ;HtB2b rBi?
bT2+i`Qb+QTB+ `2/b?B7iX
9X8X _.AG ah1GG_ .1LaAhu .Aah_A"lhAPL
38
bT2+i`Qb+QTB+ i`;2iBM; +QKTH2i2M2bb Bb ?B;?2` /m2 iQ i?2 b2H2+iBQM Q7 bT2+i`Q@
b+QTB+ i`;2ib #v i?2B` jXeµK ~mtX
h#H2 9X9, "2bi@}iiBM; L6q T`K2i2`b iQ i?2 `/BH /2MbBiv /Bbi`B#miBQMbX _2/m+2/ χ2
pHm2b `2 ;Bp2M URk /2;`22b Q7 7`22/QKVX
ΣJ,HH
ΣM,HH
ΣJ,[mB2b+2Mi
ΣM,[mB2b+2Mi
ΣJ,bi`−7Q`KBM;
ΣM,bi`−7Q`KBM;
cL6q
7.12+1.53
−0.99
5.14+0.54
−0.63
9.46+2.02
−1.62
7.12+0.81
−0.90
2.35+0.90
−0.72
1.63+0.54
−0.36
χ2 /d.o.f.
yXN9
yX39
RXyd
yXNk
yXje
yXdj
q2 }i T`QD2+i2/ L6q ULp``Q 2i HX RNNdV T`Q}H2b iQ i?2 /i TQBMib2t+Hm/BM; i?2 "*:b- iQ #2 #H2 iQ BMi2`T`2i i?2 `2bmHib BM i?2 +QMi2ti Q7 i?2
L6q +QM+2Mi`iBQM T`K2i2`X lbBM; χ2 KBMBKBxiBQM- iFBM; ++QmMi Q7 i?2
k. MMmHmb@b?T2/ #BMb- r2 }M/ i?2 #2bi }iiBM; 7mM+iBQMb- r?B+? ;Bp2 ;QQ/
`2T`2b2MiiBQMb Q7 i?2 /i Ub22 i?2 `2/m+2/ χ2 pHm2b BM h#H2 9X9VX q2 ;Bp2
i?2 #2bi@}iiBM; +QM+2Mi`iBQM T`K2i2`b M/ i?2B` K`;BMHBx2/ 2``Q`b BM i?2
i#H2 7Q` #Qi? i?2 MmK#2` /2MbBiv M/ i?2 bi2HH` Kbb /2MbBiv T`Q}H2bX h?2
#2bi@}iiBM; T`Q}H2b `2 b?QrM BM i?2 +Q``2bTQM/BM; };m`2bX
6`QK #Qi? i?2 MmK#2` /2MbBiv M/ i?2 bi2HH` Kbb /2MbBiv T`Q}H2b r2
}M/ i?i i?2 [mB2b+2Mi ;Htv TQTmHiBQM Bb +QM+2Mi`i2/ KQ`2 bi`QM;Hv i?M
i?2 bi`@7Q`KBM; TQTmHiBQM- r?B+? Bb +QMbBbi2Mi rBi? i?2 pB2r i?i i?2 bi`@
7Q`KBM; TQTmHiBQM Bb ++`2i2/ KQ`2 `2+2MiHv #v i?2 +Hmbi2` U7Q` K2bm`2K2Mi
i HQr@z - +7X "BpBMQ 2i HX kyykVX
q2 HbQ }M/ i?i i?2 bi2HH`@Kbb /Bbi`B#miBQM Q7 [mB2b+2Mi ;HtB2b Bb +QM@
+2Mi`i2/ KQ`2 bi`QM;Hv i?M i?2B` MmK#2` /2MbBiv T`Q}H2- r?B+? Bb M BM/B+@
iBQM i?i KQ`2 KbbBp2 ;HtB2b `2 bBimi2/ +HQb2` iQr`/b i?2 +Hmbi2` +2Mi`2b
i?M HQr2` Kbb ;HtB2bX h?Bb Bb HBF2Hv +mb2/ #v /vMKB+H 7`B+iBQM Q7 i?2
+Hmbi2` K2K#2`b- r?B+? Bb KQ`2 2{+B2Mi 7Q` KbbBp2 ;HtB2bX LQi2 i?i i?Bb
2z2+i Bb Q#b2`p2/ rBi?Qmi iFBM; ++QmMi Q7 i?2 "*:bX
q2 K2bm`2/ i?2 ;Htv +QM+2Mi`iBQM T`K2i2`b BM i?2 2Mb2K#H2 :*Gaa
+Hmbi2`- M/ Bi Kv #2 i?i bm#b2i Q7 i?2b2 bvbi2Kb Bb /`BpBM; i?2 +QM+2M@
i`iBQM iQ i?Bb `2HiBp2Hv ?B;? pHm2X hQ BMp2biB;i2 i?Bb r2 T2`7Q`K /Bz2`2Mi
bi+Fb mbBM; bm#b2ib Q7 i?2 :*Gaa bKTH2X q2 b2T`i2 i?2 bKTH2 BM j
*>Sh1_ 9X *1Lala P6 ah1GG_ Jaa AL Ry JaaAo1 >GP1a
3e
h z ∼ 1 6_PJ h>1 :*Gaa al_o1u
#BMb- M/ iQ KF2 bm`2 i?2 biiBbiB+b BM 2+? #BM `2 bm{+B2MiHv ?B;?- r2 `MF
Q`/2` i?2 +Hmbi2`b #v iQiH bi2HH` Kbb M/ }HH i?2 #BMb #v e- j- M/ R +Hmb@
i2`UbV- `2bT2+iBp2HvX q2 }M/ i?i i?2 #2bi@}iiBM; bi2HH` Kbb +QM+2Mi`iBQMb
7Q` i?2b2 j 2Mb2K#H2b `2 BM i?2 `M;2 6.0 < c < 9.0- M/ ;`22 iQ rBi?BM 2σ
Q7 i?2B` K2bm`2K2Mi 2``Q`bX h?Bb bm;;2bib i?i i?2 bi2HH` Kbb BM 2+? Q7 i?2
:*Gaa +Hmbi2`b Bb HBF2Hv iQ #2 /Bbi`B#mi2/ rBi? +QM+2Mi`iBQM T`K2i2`
`QmM/ c ∼ 7X
h?Bb ?B;? +QM+2Mi`iBQM T`K2i2` 7Q` i?2 bi2HH` Kii2` bm;;2bi i?i i?2
bi2HH` Kbb Bb +QM+2Mi`i2/ KQ`2 bi`QM;Hv i?M i?2 /`F Kii2` Bb 2tT2+i2/
iQ #2X 6Q` i?2 :*Gaa ?HQ2b .mzv 2i HX Ukyy3V 2biBKi2b +QM+2Mi`iBQM
T`K2i2` `QmM/ c = 2.7 7`QK bBKmHiBQMb i?i QMHv +QMiBM /`F Kii2`X
Hi?Qm;? i?Bb pHm2 Bb i?2 K2/BM pHm2 7Q` KbbBp2 ?HQ2b i z = 1- i?2 /Bbi`B@
#miBQM Q7 +QM+2Mi`iBQMb Bb 7QmM/ iQ #2 /Bbi`B#mi2/ #v HQ;@MQ`KH /Bbi`B#miBQM
rBi? b+ii2` σ(HQ;(c)) = 0.15X Ai Bb TQbbB#H2 i?i i?2 `2/@b2[m2M+2 b2H2+@
iBQM K2i?Q/ Bb #Bb2/ iQr`/b bvbi2Kb rBi? ?B;?Hv +QM+2Mi`i2/ `2/@b2[m2M+2
;HtB2bX >Qr2p2`- ;Bp2M i?2 H`;2 /Bz2`2M+2 BM +QM+2Mi`iBQM #2ir22M i?2 bi2H@
H` Kbb M/ /`F Kii2`- M/ i?2 `2HiBp2Hv bKHH b+ii2` BM i?2 /Bbi`B#miBQMbBi Bb mMHBF2Hv i?i i?Bb /Bz2`2M+2 Bb K2`2Hv M 2z2+i Q7 i?2 b2H2+iBQM K2i?Q/X
LQi2 i?i Bi Bb TQbbB#H2 i?i i?2 BM+HmbBQM Q7 #`vQMB+ T?vbB+b BM bBKmHiBQMb
rBHH Hi2` i?2 /`F Kii2` /Bbi`B#miBQM- b `2+2Mi bim/B2b ?p2 bm;;2bi2/ U2X;X
pM .H2M 2i HX kyRRVX h?Bb KB;?i #`BM; i?2 /`F Kii2` M/ bi2HH` Kbb
+QM+2Mi`iBQMb #2ii2` BM ;`22K2MiX q2 +?2+F2/ i?i i?2 `2bmHib b?QrM BM
6B;X 9X8 `2 QMHv K`;BMHHv z2+i2/ B7 r2 +?M;2 i?2 +QM+2Mi`iBQM iQ c = 7X
h?2 +QKTQbBi2 +Hmbi2` bKTH2 Bb Q#iBM2/ 7i2` bi+FBM; i?2 BM/BpB/mH +Hmb@
i2`b QM i?2 HQ+iBQMb Q7 i?2B` "*:bX AM bQK2 +b2b i?2 B/2MiB}+iBQM Q7 i?2 "*:
Bb K#B;mQmbX 6Q` aT_*a@Ry8R M/ aT_*a@Rej9 i?2 B/2MiB}2/ "*:b `2
b2T`i2/ #v ∼ 250FT+ 7`QK i?2 TT`QtBKi2 T`QD2+i2/ +Hmbi2` +2Mi`2bX q2
i2bi r?i i?2 2z2+i Q7 TQbbB#H2 KBb@+2Mi`BM; Bb QM i?2 +QM+2Mi`iBQM Q7 i?2 K2@
bm`2/ `/BH /2MbBiv T`Q}H2bX q2 }M/ i?i- B7 i?2 BMi`BMbB+ +Hmbi2` T`Q}H2b `2
/2b+`B#2/ #v c = 10 L6q T`Q}H2- M/ Ry +Hmbi2`b `2 bi+F2/ rBi? KBb@
+2Mi`BM; bKTH2/ 7`QK :mbbBM /Bbi`B#miBQM rBi? σ = 0.1r200 - i?2 K2bm`2/
+QM+2Mi`iBQM rQmH/ #2 c = 7X Mv KBbHB;MK2Mi rBi? i?2 Ǵi`m2Ǵ +Hmbi2` +2M@
i`2 rQmH/ `2bmHi BM +QM+2Mi`iBQM i?i Bb #Bb2/ HQrX :Bp2M i?2b2 i2bib- Bi Bb
HBF2Hv i?i i?2 bi2HH` Kbb Bb +QM+2Mi`i2/ 2p2M KQ`2 bi`QM;Hv i?M BM/B+i2/
#v i?2 L6q }ib iQ i?2 +Hmbi2` 2Mb2K#H2X
6`QK MmK2`B+H bBKmHiBQMb Uq2+?bH2` 2i HX kyykV r2 FMQr i?i KbbBp2
?HQ2b `2 HBF2Hv iQ ;`Qr #v 7+iQ` Q7 ∼ 2.5 #2ir22M z = 1.0 M/ z = 0.3X
h?Bb bm;;2bib i?i i?2 :*Gaa +Hmbi2` bKTH2- rBi? ivTB+H ?HQ Kbb2b Q7
Jkyy $ 2 × 1014 - Bb i?2 HBF2Hv T`Q;2MBiQ` TQTmHiBQM Q7 i?2 +Hmbi2`b Q#b2`p2/ BM
i?2 *LP* bm`p2v Uu22 2i HX RNNec *`H#2`; 2i HX RNNeV- r?B+? ?p2 ivTB+H
9X8X _.AG ah1GG_ .1LaAhu .Aah_A"lhAPL
3d
?HQ Kbb2b Q7 Jkyy $ 7 × 1014 X h?2 +QM+2Mi`iBQM Q7 i?2 mM/2`HvBM; /`F
Kii2` /Bbi`B#miBQM Bb 2tT2+i2/ iQ BM+`2b2 #v ∼ 10W BM i?Bb `2/b?B7i BMi2`pH
U.mzv 2i HX kyy3VX JmxxBM 2i HX UkyydV K2bm`2/ i?2 E@#M/ HmKBMQbBiv M/
MmK#2` /2MbBiv T`Q}H2b 7Q` R8 Q7 i?2 *LP*R +Hmbi2`b- M/ b?Qr2/ i?i i?2
E@#M/ HmKBMQbBiv /Bbi`B#miBQM Bb r2HH /2b+`B#2/ #v T`QD2+i2/ L6q T`Q}H2
rBi? +QM+2Mi`iBQM T`K2i2` c = 4.28 ± 0.57X Hi?Qm;? i?2 HmKBMQbBiv BM i?2
E@#M/ Bb ;QQ/ T`Qtv 7Q` i?2 bi2HH` Kbb- i?2 Kbb@iQ@HB;?i `iBQ BM i?Bb }Hi2`
/2T2M/b QM ;Htv ivT2X aBM+2 r2 }M/ /Bz2`2Mi /Bbi`B#miBQM Q7 bi2HH` Kbb
BM [mB2b+2Mi M/ bi`@7Q`KBM; ;HtB2b U6B;X 9XdV- i?Bb bm;;2bib i?i i?2 E@#M/
HmKBMQbBiv T`Q}H2 /Bz2`b 7`QK i?2 bi2HH` Kbb /2MbBiv T`Q}H2X AM/22/- B7 r2
b+H2 i?2 bi`@7Q`KBM; ;HtB2b BM :*Gaa #v 7+iQ` Q7 k iQ ++QmMi 7Q` i?2
`Qm;? /Bz2`2M+2 BM M" /L- r2 K2bm`2 HmKBMQbBiv T`Q}H2 rBi? +QM+2Mi`@
iBQM c < 6X Hi?Qm;? i?2 /Bz2`2M+2 #2ir22M :*Gaa M/ *LP*R Bb i?mb MQi
b 2ti`2K2- i?2b2 `2bmHib bm;;2bi i?i i?2 /`F Kii2` M/ bi2HH` Kbb /2MbBiv
/Bbi`B#miBQMb 2pQHp2 BM /BbiBM+i rvbX h?Bb Bb HbQ bm;;2bi2/ #v "m/xvMbFB 2i HX
UkyRkV- r?Q #b2/ i?2B` bim/v QM bKTH2 Q7 ;`QmTb M/ +Hmbi2`b BM i?2 `2/b?B7i
`M;2 0.15 < z < 0.4 7`QK i?2 a.aaX 6Q` i?Bb bKTH2 "m/xvMbFB 2i HX UkyRkV
7QmM/ i?i i?2 +QM+2Mi`iBQM Q7 i?2 MmK#2` /2MbBiv T`Q}H2 Bb HQr2` i?M i?2
/`F Kii2` T`2/B+iBQMX h?2`2 `2 b2p2`H +p2ib- M/ TQbbB#H2 2tTHMiBQMb
7Q` i?2 Q#b2`p2/ 2pQHmiBQM Q7 i?2 bi2HH` Kbb /Bbi`B#miBQMX
6B`bi- bBM+2 r2 /Q MQi iF2 ++QmMi Q7 i?2 bi2HH` Kbb T`2b2Mi BM i?2 +2M@
i`H ;HtB2b r?2M }iiBM; L6q T`Q}H2b- ++`2iBQM Q7 ;HtB2b QMiQ i?2 +2Mi`H
;Htv KB;?i +?M;2 i?2 /Bbi`B#miBQM Q7 bi2HH` Kbb BM bi2HHBi2b- M/ i?2`27Q`2
i?2 +QM+2Mi`iBQM T`K2i2`- Qp2` iBK2X J2`;2`b THv /QKBMMi `QH2 BM i?2
#mBH/@mT Q7 bi2HH` Kbb BM "*:b UGB/KM 2i HX kyRjc "m`F2 *QHHBMb kyRjVX
JbbBp2 ;HtB2b i?i `2 +HQb2 iQ i?2 +2Mi`2 `2 2tT2+i2/ iQ K2`;2 rBi? i?2
"*: QM `2HiBp2Hv b?Q`i iBK2b+H2 U"BH/72HH 2i HX kyRkc GB/KM 2i HX kyRjVi?2`2#v `2M/2`BM; i?2 "*: M BM+`2bBM;Hv biiBbiB+HHv /Bz2`2Mi TQTmHiBQM
+QKT`2/ iQ +Hmbi2` bi2HHBi2 ;HtB2bX M BM/B+iQ` 7Q` i?Bb T`Q+2bb Bb M BM@
+`2b2 BM i?2 HmKBMQbBiv ;T #2ir22M i?2 "*: M/ i?2 b2+QM/ #`B;?i2bi +Hmbi2`
;Htv U2X;X aKBi? 2i HX kyRyVX >Qr2p2`- ;Bp2M i?2 b?HHQr bHQT2 Q7 i?2 +2M@
i`H bi2HH`@?HQ Kbb `2HiBQM Ua2+iX 9XjV- "*:b `2 2tT2+i2/ iQ ;`Qr QMHv #v
7+iQ` Q7 RX8 BM i?2 `2/b?B7i `M;2 1.0 > z > 0.3 Ub22 HbQ GB/KM 2i HX
UkyRkVVX A7 i?2 bmTTHv Q7 i?Bb bi2HH` Kbb ;`Qri? Bb Q#iBM2/ 7`QK ;HtB2b
M2` i?2 +2Mi`2- i?2 +QM+2Mi`iBQM T`K2i2` Q7 i?2 bi2HHBi2 ;Htv TQTmHiBQM
rQmH/ ;Q /QrMX
q2 T2`7Q`K bBKTH2 bBKmHiBQM BM r?B+? r2 `2/m+2 i?2 bi2HH` Kbb BM
bi2HHBi2 ;HtB2b rBi?BM 0.5 · R200 BM ++Q`/M+2 rBi? "*: ;`Qri? Q7 7+iQ`
Q7 RX8- M/ i?Bb b?Qrb i?i i?Bb Bb MQi bm{+B2Mi iQ 2tTHBM i?2 /`KiB+ /2+`2b2
BM i?2 +QM+2Mi`iBQM T`K2i2` Uc /2+`2b2b 7`QK dXy iQ eXyVX L2p2`i?2H2bb- Bi Bb
TQbbB#H2 i?i i?2 #mBH/@mT Q7 i?2 A*G +QKTQM2Mi iQr`/b HQr2` `2/b?B7i THvb
`QH2 BM HQr2`BM; i?2 +QM+2Mi`iBQM T`K2i2` Q7 bi2HH` Kbb BM bi2HHBi2bX
a2+QM/- b +Hmbi2`b ;2i H`;2`- i?2 /vMKB+H 7`B+iBQM iBK2b+H2 Q7 ;Htv
*>Sh1_ 9X *1Lala P6 ah1GG_ Jaa AL Ry JaaAo1 >GP1a
33
h z ∼ 1 6_PJ h>1 :*Gaa al_o1u
rBi? ;Bp2M Kbb BM+`2b2b- bQ i?i Bi iF2b HQM;2` 7Q` ;HtB2b iQ bBMF iQ
i?2 +2Mi`2 Q7 i?2 TQi2MiBH r2HHX h?Bb Bb HbQ ?BMi2/ i r?2M r2 +QKT`2 i?2
`2HiBQM #2ir22M +2Mi`H bi2HH` M/ ?HQ Kbb Ua2+iX 9XjV- M/ #2ir22M iQiH
bi2HH` Kbb M/ ?HQ Kbb Ua2+iX 9X9VX :Bp2M i?i i?2 Hii2` bHQT2 Bb bi22T2`i?2 7`+iBQM Q7 bi2HH` Kbb BM bi2HHBi2 ;HtB2b Bb ?B;?2` BM KQ`2 KbbBp2 ?HQ2bX
Ai Bb TQbbB#H2 i?i ;HtB2b i?i `2 ++`2i2/ QMiQ i?2 +Hmbi2` i Hi2` iBK2
`2 bBimi2/ +HQb2` iQ i?2 QmibFB`ib Q7 i?2 +Hmbi2`b /m2 iQ i?2 bK2 T`Q+2bb- M/
i?mb `2 H2bb +QM+2Mi`i2/ i?M i?2 TQTmHiBQM i?i rb ++`2i2/ 2`HB2`X
q2 T2`7Q`K bBKTH2 i2bi BM r?B+? r2 BM+`2b2 i?2 Kbb Q7 i?2 2Mb2K#H2
+Hmbi2` #v 7+iQ` kX8 #v //BM; bi2HH` Kbb i?i Bb /Bbi`B#mi2/ 7QHHQrBM;
M L6q /Bbi`B#miBQM rBi? ;Bp2M +QM+2Mi`iBQMX A7 r2 p`v i?2 +QM+2Mi`iBQM
T`K2i2` Q7 i?2 TQTmHiBQM i?i r2 //- r2 }M/ i?i- BM Q`/2` iQ 2M/ mT rBi? +QM+2Mi`iBQM Q7 c = 4.0 #v z = 0.3 UBX2X- bBKBH` iQ i?2 +QM+2Mi`iBQM K2bm`2/
BM *LP*V- r2 ?p2 iQ // bi2HHBi2b rBi? +QM+2Mi`iBQM T`K2i2` Q7 c = 2.8
iQ i?2 bi2HH` Kbb /2MbBiv /Bbi`B#miBQM Q#b2`p2/ BM :*GaaX h?Bb b+2M`BQ
+QmH/ TQi2MiBHHv 2tTHBM i?2 /Bz2`2M+2 rBi? i?2 `2bmHib 7`QK "m/xvMbFB 2i HX
UkyRkV- r?Q }M/ i?i i HQr@z i?2 bi2HH` Kbb Bb +QM+2Mi`i2/ KQ`2 bi`QM;Hv
i?M i?2 /`F Kii2`- M/ bm;;2bib i?i i?2 bi2HH` Kbb +QMi2Mi KQbiHv ;`Qrb
#v ++`2iBM; bi2HH` Kbb QMiQ i?2 +Hmbi2` QmibFB`ibX
AM i?Bb TT2` r2 T`QpB/2 i?`22 F2v K2bm`2K2Mib +QM+2`MBM; i?2 bi2HH` +QMi2Mi
BM Ry +Hmbi2`b i z ∼ 1 7`QK i?2 :*Gaa bm`p2vX :*Gaa #2M2}ib 7`QK RR
#M/ T?QiQK2i`B+ +Qp2`;2 M/ /22T bT2+i`Qb+QTB+ +Qp2`;2 iQ T`QpB/2 7mHH
+2Mbmb Q7 bi2HH` Kbb BM +Hmbi2` K2K#2`b /QrM iQ #Qmi M" = 1010.2 J" X
*QK#BMBM; i?2b2 Q#b2`piBQMb rBi? K2bm`2K2Mib i HQr2` `2/b?B7ib r2 ?QT2
iQ T`QpB/2 +QMbi`BMib QM i?2 rv #`vQMb +QQH M/ 7Q`K bi`b BM ;HtB2b BM
?B;? /2MbBiv 2MpB`QMK2MibX
AM a2+iX 9Xj r2 T`2b2Mi2/ +QKT`BbQM Q7 i?2 +2Mi`H bi2HH` Kbb rBi? iQiH
?HQ Kbb- M/ 7QmM/ +Q``2HiBQM i?i bm;;2bib i?i i?2 7`+iBQM Q7 Kbb BM
i?2 +2Mi`H ;Htv Bb /2+`2bBM; 7mM+iBQM Q7 ?HQ Kbb- M/ #Qmi yXyyR 7Q`
i?2 Kbb `M;2 T`Q#2/ #v :*GaaX q2 +QM}`K2/ i?2 i`2M/ T`2/B+i2/ mbBM;
#mM/M+2 Ki+?BM; i2+?MB[m2b- #Qi? BM [mHBiiBp2 b [mMiBiiBp2 b2Mb2X
a2+iX 9X9 b?Qr2/ +QKT`BbQM Q7 i?2 iQiH bi2HH` Kbb2b UBM+Hm/BM; bi2H@
HBi2bV rBi? i?2 /vMKB+H ?HQ Kbb2b- #Qi? rBi?BM R200 M/ R500 X q2 7QmM/
i?i i?2 iQiH bi2HH` Kbb BM+`2b2b rBi? ?HQ Kbb- M/ i?i i?2 7`+iBQM Bb
`QmM/ yXyR 7Q` Qm` bKTH2 M/ TT2`b iQ /2+`2b2 iQr`/b ?B;?2` ?HQ Kbb2bX
+QKT`BbQM Q7 i?Bb `2HiBQM rBi? bKTH2b i Qi?2` `2/b?B7ib +M vB2H/ BMbB;?ib
QM i?2 rv i?2b2 bvbi2Kb ++`2i2 i?2B` bi2HH` Kbb- #mi Bb /B{+mHi /m2 iQ BM@
?QKQ;2M2Qmb bKTH2 b2H2+iBQMb M/ MHvb2bX 1bT2+BHHv BM++m`i2 2biBKi2b
QM i?2 bi2HH` Kbb@iQ@HB;?i `iBQ `2 bQm`+2 Q7 +QM7mbBQMX 7i2` +Q``2+iBM;
9XeX alJJ_u L. *PL*GlaAPLa
3N
i?2 `272`2M+2 bim/B2b 7Q` /Bz2`2M+2b BM i?2B` MHvb2b- r2 7QmM/ MQ bB;MB}+Mi
2pQHmiBQM rBi? `2/b?B7i BM i?2 bi2HH` Kbb 7`+iBQM i }t2/ ?HQ KbbX
AM a2+iX 9X8 r2 bim/B2/ i?2 `/BH MmK#2` /2MbBiv M/ bi2HH` Kbb /2M@
bBiv T`Q}H2b Q7 ;HtB2b BM i?2 bKTH2- M/ 7QmM/ i?i i?2b2 `2 `2T`2b2Mi2/
#v T`QD2+i2/ L6q T`Q}H2bX h?2 bi2HH` Kbb /2MbBiv /Bbi`B#miBQM Bb +QM+2M@
i`i2/ KQ`2 bi`QM;Hv i?M i?2 ;Htv MmK#2` /2MbBiv /Bbi`B#miBQM- r?B+? b?Qrb
i?i KQ`2 KbbBp2 ;HtB2b `2 bBimi2/ +HQb2` iQ i?2 +Hmbi2` +Q`2b UBX2X Kbb
b2;`2;iBQMVX h?2 bi2HH` Kbb /2MbBiv T`Q}H2 ?b M L6q +QM+2Mi`iBQM T@
`K2i2` Uc = 7V i?i Bb bB;MB}+MiHv ?B;?2` i?M i?2 /`F Kii2` /Bbi`B#miBQM
Bb 2tT2+i2/ iQ #2 Uc = 2.7V 7`QK MmK2`B+H bBKmHiBQMbX *QKT`BbQM Q7 i?2
+QM+2Mi`iBQM T`K2i2` rBi? i?2 *LP*R bm`p2v i z = 0.3 bm;;2bib i?i i?2
bi2HH` Kbb +QM+2Mi`iBQM b?QmH/ /2+`2b2 iQr`/b HQr2` `2/b?B7iX bBKTH2
bBKmHiBQM b?Qr2/ i?i bi2HH` Kbb ;`Qri? Q7 i?2 "*: HQM2 Bb MQi 2MQm;?
iQ 2tTHBM i?2 2pQHmiBQM #2ir22M :*Gaa M/ *LP*R- M/ i?i i?2 +Hmbi2`b
`2 HBF2Hv iQ ++`2i2 KQ`2 bi2HH` Kbb QM i?2 +Hmbi2` QmibFB`ib b i?2v ;`Qr #v
7+iQ` Q7 kX8 BM iQiH Kbb 7`QK z = 1 iQ z = 0.3X HbQ i?2 #mBH/@mT Q7 i?2
A*G +M THv `QH2 BM i?2 Q#b2`p2/ 2pQHmiBQMX
q2 MQi2 i?i +QKT`BbQMb Q7 Qm` `2bmHib rBi? Qi?2` bim/B2b `2 +QKTHB+i2/
/m2 iQ BM?QKQ;2M2Qmb bKTH2b M/ /Bz2`2Mi MHvb2bX AM Q`/2` iQ /`r }`K
+QM+HmbBQMb `2;`/BM; i?2 2pQHmiBQM Q7 i?2 #`vQMB+ +QMi2Mi- M/ BM T`iB+mH`
bi2HH` Kbb- Q#b2`piBQMH /i M22/ iQ #2 ?QKQ;2MBx2/X q2 ?p2 HbQ b22M
i?i i?2 bbmKTiBQM Q7 bBM;H2 bi2HH` Kbb@iQ@HB;?i `iBQ Bb BM/2[mi2 iQ
K2bm`2 i?2 iQiH bi2HH` Kbb +QMi2Mi Q7 ;Htv +Hmbi2`bX _i?2`- QM2 b?QmH/
}i i?2 7mHH aT2+i`H 1M2`;v .Bbi`B#miBQMb Ua1.bV iQ 2biBKi2 i?2 bi2HH` Kbb2b
7Q` BM/BpB/mH ;HtB2bX JQ`2Qp2`- bBM+2 i?2 ;HtB2b rBi? ?B;? Kbb@iQ@HB;?i
`iBQ `2 ;2M2`HHv KQ`2 +QM+2Mi`i2/ BM i?2 +Hmbi2` +Q`2b- K2bm`2K2Mib Q7
i?2 E@#M/ HmKBMQbBiv T`Q}H2 M/ bi2HH` Kbb /2MbBiv T`Q}H2 b?QmH/ MQi #2
iF2M b 2[mBpH2Mi K2bm`2K2MibX h?MFb iQ i?2 /pM+2 Q7 H`;2 QTiB+H M/
M2`@BM7``2/ BK;BM; 7+BHBiB2b Qp2` i?2 Tbi /2+/2b- i?2b2 KmHiB@rp2H2M;i?
/i `2 `2HiBp2Hv 2bv iQ Q#iBM- bQ i?i r2 rBHH bQQM 2tT2+i iQ #2 #H2 iQ
+QKT`2 +QMbBbi2Mi bi2HH` Kbb K2bm`2K2Mib rBi? 7mHH a1. }iiBM; Qp2` H`;2 `2/b?B7i #b2HBM2X
q2 i?MF J`+2HHQ *++BiQ- .2MMBb Cmbi- _Q# *`BM- Mi?QMv :QMxH2xJB+?2H "HQ;? M/ ApQ G##û 7Q` pHm#H2 /Bb+mbbBQMb i?i BKT`Qp2/ i?2 [mH@
Biv Q7 i?Bb rQ`FX
_X6XCX pM /2` "m`; M/ >X >Q2Fbi` +FMQrH2/;2 bmTTQ`i 7`QK i?2 L2i?2`@
HM/b P`;MBbiBQM 7Q` a+B2MiB+ _2b2`+? ;`Mi MmK#2` ejNXy9kX3R9X *X GB/KM
Bb i?2 `2+BTB2Mi Q7 M mbi`HBM _2b2`+? *QmM+BH 6mim`2 62HHQrb?BT UT`Q;`K
MmK#2` 6hyNNkk8NVX
*?Ti2`
8
h?2 /Bbi`B#miBQM Q7 bi2HH` Kbb
BM ;Htv +Hmbi2`b i z ∼ 0.15
q2 bim/v i?2 `/BH ;Htv M/ bi2HH` Kbb /2MbBiv /Bbi`B#miBQMb BM bKTH2
Q7 Ry ;Htv +Hmbi2`b i 0.07 < z < 0.26 b2H2+i2/ 7`QK irQ bm`p2vbc i?2
JmHiB@1TQ+? L2`#v *Hmbi2` am`p2v UJ1L2*aV M/ i?2 *M/BM *Hmbi2`
*QKT`BbQM S`QD2+i U***SVX .22T ugri@#M/ BK;BM; Bb mb2/ iQ 2biBKi2
T?QiQK2i`B+ `2/b?B7ib M/ bi2HH` Kbb2b- M/ i?2M biiBbiB+HHv bm#i`+i 7Q`2@M/ #+F;`QmM/ bQm`+2b mbBM; /i 7`QK i?2 *PaJPa bm`p2vX h?Bb T`Q+2/m`2
T2`7Q`Kb r2HH- ;Bp2M i?i B/2MiB+H `2bmHib `2 Q#iBM2/ 7Q` i?2 2Mb2K#H2 +Hmbi2`
#v +QMbB/2`BM; i?2 ∼ 3000 bT2+i`Qb+QTB+HHv +QM}`K2/ K2K#2` ;HtB2b r?B+?
KF2 mT i?2 #mHF Q7 i?2 bi2HH` KbbX q2 }M/ i?i i?2 `/BH /Bbi`B#miBQM
Q7 bi2HH` Kbb Bb r2HH@/2b+`B#2/ #v M L6q /Bbi`B#miBQM rBi? +QM+2Mi`iBQMb
BM i?2 `M;2 0.8 < c < 5.6- M/ M 2Mb2K#H2 p2`;2/ pHm2 Q7 c = 1.92 ±
0.19 UR@σ biiBbiB+HVX q2 2biBKi2 M BMi`BMbB+ b+ii2` Q7 σc,BMi = 0.70+0.33
−0.22
UQ` σHQ;Ry c,BMi = 0.25 ± 0.05 /2tV- r?B+? Bb HBF2Hv +mb2/ #v +QK#BMiBQM
Q7 +2Mi`QB/BM; mM+2`iBMiB2b- `M;2 Q7 /Bz2`2Mi ?HQ bb2K#Hv ?BbiQ`B2b- M/
/Bz2`2Mi Q`B2MiiBQMb QM i?2 bFvX
h?2 ?HQ Kbb2b- r?B+? `M;2 7`QK 4.8 × 1014 J" iQ 2.3 × 1015 J" UM200c VKi+? i?2 TT`QtBKi2 /2b+2M/2Mi TQTmHiBQM Q7 i?2 :*Gaa +Hmbi2` bKTH2
i z ∼ 1- 7Q` r?B+? bi2HH` Kbb +QM+2Mi`iBQM Q7 c = 7.12+1.53
−0.99 rb 2biBKi2/X
+QKT`BbQM Q7 i?2b2 `2bmHib b?Qrb i?i i?2 bTiBH /Bbi`B#miBQM Q7 bi2HH`
Kbb 2pQHp2b bm#biMiBHHv iQr`/b HQr@z - i`2M/ i?i Bb QTTQbBi2 iQ r?i Bb
7QmM/ 7Q` i?2 /`F@Kii2` /Bbi`B#miBQM BM L@#Q/v bBKmHiBQMbX q2 +QKT`2 i?2
bi2HH` Kbb /2MbBiv /Bbi`B#miBQMb i z ∼ 1 M/ z ∼ 0.15 BM i?2 bK2 T?vbB+H
mMBib- b?QrBM; i?i i?2 bi2HH` Kbb /2MbBiv BM i?2 +Hmbi2` +Q`2b U_IyXk JT+V
/2+`2b2b bBM+2 z ∼ 1X h?Bb Kv #2 `2Hi2/ iQ i?2 #mBH/@mT Q7 i?2 A*GY"*:
+QKTQM2Mi Qp2` +QbKB+ iBK2X q2 HbQ }M/ i?i i?2 +Hmbi2`b i z ∼ 1 ?p2
NR
iQ ;`Qr BM bi2HH` Kbb i H`;2` `/BB iQ Ki+? i?2 /2b+2M/2Mi TQTmHiBQMX
*QKT`BbQMb rBi? bBKmHiBQMb ?p2 i?2 TQi2MiBH iQ T`QpB/2 +QMbi`BMib QM i?2
bi2HH` Kbb +QMi2Mi Q7 ?HQ2b 7HHBM; BMiQ i?2b2 +Hmbi2`b- M/ i?2 /vMKB+H
7`B+iBQM iBK2@b+H2 i?i Bb TTHB2/ BM b2KB@MHviB+ KQ/2HbX
_2K+Q 6XCX pM /2` "m`;- >2MF >Q2Fbi`- /K JmxxBM- *`BbiƦ#H aB7ƦM- a2M J+:22JB+?2H "HQ;?
AM T`2T`iBQM
Nk
8XRX ALh_P.l*hAPL
Nj
F2v QT2M [m2biBQM BM i?2 }2H/ Q7 2ti`;H+iB+ bi`QMQKv iQ/v Bb iQ mM/2`@
biM/ ?Qr ;HtB2b 7Q`K BM Qm` /`F@Kii2` /QKBMi2/ lMBp2`b2 U2X;X :mQ 2i HX
kyRyVX hQ H2`M #Qmi i?2 #`vQMB+ T?vbB+b i?i ;Qp2`M +QKTH2t T`Q+2bb2b bm+?
b i?2 +QQHBM; Q7 ;b- 7Q`KiBQM Q7 bi`b M/ b2p2`H 722/#+F KQ/2b- KQ/2Hb
M22/ iQ #2 iBHQ`2/ iQ Ki+? i?2 Q#b2`piBQMbX P#b2`piBQMH T`Q#2b bm+? b
i?2 HmKBMQbBiv 7mM+iBQM M/ bi2HH` Kbb 7mM+iBQM U2X;X "2HH 2i HX kyyjc Sû`2x@
:QMx€H2x 2i HX kyy3c AH#2`i 2i HX kyRyc JmxxBM 2i HX kyRjV ?p2 #22M mb2/
b 7mM/K2MiH Q#b2`p#H2b iQ +QMbi`BM T?vbB+H KQ/2Hb U2X;X >2M`B[m2b 2i HX
kyRkc q2BMKMM 2i HX kyRkV- Q` i2bi `2bmHib 7`QK ?v/`Q/vMKB+H bBKmHiBQMb
U2X;X a+?v2 2i HX kyRyc *2M kyR9VX :HtB2b `2 MQi `M/QKHv /Bbi`B#mi2/
BM bT+2- M/ T`QT2`iB2b bm+? b i?2 bi`@7Q`KiBQM `i2 Ua6_V- KQ`T?QHQ;vbi2HH` Kbb- M/ K2iHHB+Biv Q7 ;HtB2b `2 /2T2M/2Mi QM i?2B` 2MpB`QMK2Mi
U.`2bbH2` RN3yc EmzKMM 2i HX kyy9c "H/`v 2i HX kyyec JmxxBM 2i HX kyRkc
qQQ 2i HX kyRjc pM /2` "m`; 2i HX kyRjVX *2Mi`H ;HtB2b M/ bi2HHBi2
;HtB2b- i?2 Hii2` Q7 r?B+? `2 ivTB+HHv HQr2` Kbb ;HtB2b i?i `2 T`i Q7
i?2 bK2 ?HQ- 2pQHp2 BM /Bz2`2Mi rvb M/ `2 i?mb bim/B2/ b2T`i2Hv US2M;
2i HX kyRy- kyRkc EMQ#2H 2i HX kyRjVX
h?2 Q#b2`p2/ #mM/M+2 M/ bTiBH /Bbi`B#miBQM Q7 bi2HHBi2 ;HtB2b T`Q@
pB/2 7m`i?2` +QMbi`BMib QM ;Htv 7Q`KiBQM KQ/2HbX +QKT`BbQM #2ir22M
i?2 Qmi+QK2b Q7 MmK2`B+H L@#Q/v bBKmHiBQMb M/ Q#b2`piBQMb ?b `2p2H2/
T`Q#H2K FMQrM b i?2 ǶKBbbBM; bi2HHBi2b T`Q#H2KǶ UEHvTBM 2i HX RNNNc "mH@
HQ+F kyRyVX h?2 MmK#2` Q7 bi2HHBi2 ;HtB2b BM i?2 HQ+H ;`QmT Bb bB;MB}+MiHv
HQr2` i?M T`2/B+i2/ #v i?2 Λ*.J KQ/2HX TQbbB#H2 BMi2`T`2iiBQM Q7 i?Bb
Bb i?2 BM2{+B2MiHv Q7 HQr@Kbb ?HQ2b BM 7Q`KBM; bi`b- TQbbB#Hv /m2 iQ bmT2`@
MQp 722/#+F U17bii?BQm kyyyc .HH o2++?B a+?v2 kyy3V- bi2HH` rBM/bM/ i?2 T`2b2M+2 Q7 T?QiQ@BQMBxBM; #+F;`QmM/ U"2MbQM 2i HX kyykVX Ai Kv
HbQ ?BMi i 7mM/K2MiH T`Q#H2K rBi? Qm` }/m+BH Λ*.J KQ/2H- bm+? i?i
bBKmHi2/ ?HQ2b ?p2 KQ`2 bm#bi`m+im`2 UBX2X bm#@?HQ2bV i?M ?HQ2b BM i?2
+imH lMBp2`b2 U"QvHM@EQH+?BM 2i HX kyRRVX
:Bp2M i?2 UM2`HvV b2H7@bBKBH` T`QT2`iB2b Q7 /`F Kii2` ?HQ2b- r2 +M
i2bi i?2 Λ*.J KQ/2H #v bim/vBM; KQ`2 KbbBp2 ?HQ2b bm+? b ;Htv ;`QmTb
M/ +Hmbi2`bX am#@?HQ2b BM i?2b2 bvbi2Kb `2 +Q``2bTQM/BM;Hv KQ`2 KbbBp2r?B+? KF2b i?2K KQ`2 2{+B2Mi i 7Q`KBM; bi`b- M/ i?mb 2bB2` iQ B/2MiB7v
i?`Qm;? Q#b2`piBQMbX >Qr2p2`- QM i?2 i?2Q`v bB/2 i?Bb +QKT`BbQM HbQ ?b
HBKBiiBQMbX JQbi bim/B2b `2 #b2/ QM H`;2 L@#Q/v bBKmHiBQMb UaT`BM;2H
2i HX kyy8V- M/ /`F Kii2` ?HQ2b 7HHBM; BMiQ H`;2` ?HQ2b 2tT2`B2M+2 iB/H
7Q`+2b H2/BM; iQ i?2 bi`BTTBM; Q7 i?2B` +QMbiBim2Mi T`iB+H2b U:?B;M 2i HX
kyyyc "BMM2v h`2KBM2 kyy3V- HbQ b22 Li`DM 2i HX UkyykVc :BHHBb 2i HX
UkyRjV 7Q` M Q#b2`piBQMH bim/vX b bm#@?HQ 7HHb BMiQ i?2 KBM ?HQ- Bi
rBHH +QMiBMmQmbHv HQb2 Kbb i?`Qm;? i?2 T`Q+2bb Q7 iB/H bi`BTTBM;- M/ Bi Kv
2p2MimHHv 7HH #2HQr i?2 Kbb `2bQHmiBQM Q7 i?2 bBKmHiBQMX h?2 bm#@?HQ Bb
*>Sh1_ 8X h>1 .Aah_A"lhAPL P6 ah1GG_ Jaa AL :Gsu
N9
*Glah1_a h z ∼ 0.15
i?2M MQ HQM;2` B/2MiB}2/ b bm+?- Bib Kbb Bb /2TQbBi2/ QM i?2 +2Mi`H ;Htv
Q` /BbT2`b2/ #2ir22M i?2 ;HtB2b- M/ Bib Q`#Bi Bb MQ HQM;2` /2}M2/X 6Q` i?Bb
`2bQM- i?2 `/BH /Bbi`B#miBQM Q7 bm#@?HQ2b Bb H2bb +QM+2Mi`i2/ i?M i?2 /`F
Kii2` BM L@#Q/v bBKmHiBQMb UL;B E`pibQp kyy8VX q?BH2 i?2 bm#@?HQ2b
BM i?2b2 /BbbBTiBQMH2bb bBKmHiBQMb `2 2p2MimHHv /2bi`Qv2/- i?2 ;HtB2b i?i
?p2 7Q`K2/ BMbB/2 Q7 i?2K `2 2tT2+i2/ iQ #2 KQ`2 `2bBbiBp2 iQ iB/H 7Q`+2bX
AM b2KB@MHviB+ KQ/2Hb Q7 ;Htv 7Q`KiBQM- r?B+? `2 #b2/ QM K2`;2` i`22b
7`QK i?2b2 bBKmHiBQMb- i?2 KQ`2 +QM+2Mi`i2/ #`vQMB+ T`ib Q7 ;HtB2b `2
7QHHQr2/ MHviB+HHv 7i2` i?2 bm#@?HQ Bb /BbT2`b2/ U"Qr2` 2i HX kyyec .2
Gm+B "HBxQi kyydVX /vMKB+H 7`B+iBQM iBK2@b+H2 Bb ;2M2`HHv TTHB2/r?B+? /2i2`KBM2b r?2M i?2 ;Htv Bb /2TQbBi2/ QMiQ i?2 +2Mi`H ;Htv- M/
?Qr i?2 BMi`@+Hmbi2` HB;?i Bb #mBH/BM; mT U*QMiBMB 2i HX kyRjVX J2bm`2K2Mib
Q7 i?2 ;`Qri? Q7 #`B;?i2bi +Hmbi2` ;HtB2b U"*:bV UGBM JQ?` kyy9c GB/KM
2i HX kyRk- kyRjV M/ i?2 BMi`+Hmbi2` HB;?i UA*GV U:QMxH2x 2i HX kyRjV +M
#2 mb2/ iQ +QMbi`BM i?Bb iBK2@b+H2- b i?2 #mBH/@mT Q7 i?2b2 +QKTQM2Mib `2
/B`2+iHv `2Hi2/ iQ i?2 BM@7HH Q7 bi2HHBi2 ;HtB2bX
h?2 `/BH MmK#2` M/ bi2HH` Kbb /2MbBiv /Bbi`B#miBQM Q7 bi2HHBi2 ;HtB2b
/B`2+iHv T`Q#2 i?2 #mM/M+2 Q7 bm#@?HQ2b- M/ +M HbQ #2 mb2/ iQ +QMbi`BM
i?2 /vMKB+H 7`B+iBQM iBK2@b+H2X h?2b2 /Bbi`B#miBQMb `2 Q#b2`p2/ iQ #2 r2HH
/2b+`B#2/ #v L6q ULp``Q 2i HX RNNdV T`Q}H2b 7Q` ;`QmT@bBx2/ ?HQ2b M/
+Hmbi2`b 7`QK i?2 HQ+H lMBp2`b2 iQ z ∼ 1 U*`H#2`; 2i HX RNNdc GBM 2i HX
kyy9c JmxxBM 2i HX kyydc :BQ/BMB 2i HX kyyNc "m/xvMbFB 2i HX kyRkc pM /2`
"m`; 2i HX kyR9VX 1+? Q#b2`piBQMH bim/v ?Qr2p2` Bb #b2/ QM /Bz2`2Mi
/i b2i M/ MHvbBb- M/ T`2b2Mib `2bmHib BM /Bz2`2Mi 7Q`KX GBM 2i HX Ukyy9V
M/ "m/xvMbFB 2i HX UkyRkV bim/v i?2 MmK#2` /2MbBiv Q7 ;HtB2b- #mi /m2 iQ
K2`;2`b M/ BMi2`+iBQMb #2ir22M ;HtB2b- i?2 MmK#2` /2MbBiv /Bbi`B#miBQM
Q7 ;HtB2b +M #2 /Bz2`2Mi 7Q` ;HtB2b rBi? /Bz2`2Mi HmKBMQbBiB2b Q` bi2HH`
Kbb2bX h?2B` `2bmHib `2 i?2`27Q`2 /2T2M/2Mi QM i?2 /2Ti? Q7 i?2B` /i b2iX
:BQ/BMB 2i HX UkyyNV K2bm`2 i?2 MmK#2` /2MbBiv /Bbi`B#miBQM Q7 ;2M2`HHv HQr2`
Kbb bvbi2Kb 7`QK i?2 *PaJPa }2H/X *`H#2`; 2i HX URNNdV M/ JmxxBM
2i HX UkyydV K2bm`2 i?2 HmKBMQbBiv /2MbBiv /Bbi`B#miBQM BM i?2 r@#M/ M/
E@#M/- `2bT2+iBp2Hv- 7Q` i?2 *LP*R Uu22 2i HX RNNeV +Hmbi2` bKTH2X h?2
/pMi;2 Q7 i?Bb K2bm`2K2Mi Bb i?i- T`QpB/2/ i?2 K2bm`2K2Mib 2ti2M/
bB;MB}+MiHv #2HQr i?2 +?`+i2`BbiB+ HmKBMQbBiv L∗ - Bi Bb HKQbi BMb2MbBiBp2 iQ
i?2 T`2+Bb2 HmKBMQbBiv +miX h?i Bb #2+mb2 i?2 iQiH HmKBMQbBiv BM 2+? `/BH
#BM Bb /QKBMi2/ #v ;HtB2b `QmM/ L∗ X >Qr2p2`- 2bT2+BHHv BM i?2 r@#M/ Bi
Bb MQi bi`B;?i7Q`r`/ iQ `2Hi2 i?2 HmKBMQbBiv /Bbi`B#miBQM iQ bi2HH` Kbb
/Bbi`B#miBQM /m2 iQ /Bz2`2M+2b BM Kbb@iQ@HB;?i@`iBQ #2ir22M /Bz2`2Mi ;Htv
ivT2b- M/ #2+mb2 i?2 /Bbi`B#miBQMb Q7 i?2b2 ivT2b p`v bTiBHHvX AM+QMbBb@
i2M+B2b #2ir22M HH i?2b2 bim/B2b T`2p2Mi mb 7`QK /`rBM; }`K +QM+HmbBQMb QM
+QKT`BbQMb #2ir22M i?2KX
h?2 MmK#2` /2MbBiv U/QrM iQ ;HtB2b rBi? bi2HH` Kbb 1010.2 J" V M/
bi2HH` Kbb /2MbBiv /Bbi`B#miBQM Q7 ;HtB2b BM i?2 :*Gaa +Hmbi2` bKTH2 i
8XkX .h Po1_oA1q S_P*1aaAL:
N8
z ∼ 1 ?p2 #22M K2bm`2/ #v pM /2` "m`; 2i HX UkyR9- ?2`27i2` p/"R9VX
h?2v }M/ i?i #Qi? /Bbi`B#miBQMb `2 bB;MB}+MiHv KQ`2 +QM+2Mi`i2/ i?M
i?2 bBKmHi2/ /Bbi`B#miBQM Q7 /`F Kii2` BM L@#Q/v bBKmHiBQMb- M/ HbQ
KQ`2 +QM+2Mi`i2/ i?M bi+F2/ r2F@H2MbBM; K2bm`2K2Mi Q7 z ∼ 1 +Hmbi2`b
Ua2`2MQ *QpQM2 kyRjVX h?2 QMHv HQ+H K2bm`2K2Mi i?Bb bim/v +QmH/ +QK@
T`2 iQ Bb i?2 E@#M/ HmKBMQbBiv /Bbi`B#miBQM K2bm`2/ #v JmxxBM 2i HX UkyydV
7Q` i?2 *LP*R +Hmbi2`b- r?B+? `2 TT`QtBKi2 /2b+2M/Mib Q7 i?2 :*Gaa
+Hmbi2` #v ?HQ Kbb U2biBKi2/ ;Bp2M i?2 2pQHmiBQM Q7 ?HQ2b BM L@#Q/v bBK@
mHiBQMbVX HbQ i?2 E@#M/ HmKBMQbBiv Bb ;QQ/ T`Q#2 Q7 i?2 bi2HH` Kbb Q7
;HtB2b U"2HH /2 CQM; kyyRV- 2bT2+BHHv BM i?2 HQ+H lMBp2`b2 r?2`2 i?2 +Hmb@
i2`b `2 /QKBMi2/ #v ;HtB2b rBi? QH/ bi2HH` TQTmHiBQMbX h?2 +QKT`BbQM
bm;;2bib i?i i?2 bi2HH` Kbb /2MbBiv /Bbi`B#miBQM 2pQHp2b bB;MB}+MiHv bBM+2
z ∼ 1- M/ i?i i?2 /Bbi`B#miBQM #2+QK2b H2bb +QM+2Mi`i2/ Qp2` +QbKB+ iBK2X
AM i?Bb TT2` r2 T`2b2Mi K2bm`2K2Mi Q7 i?2 `/BH ;Htv MmK#2` /2MbBiv
M/ bi2HH` Kbb /2MbBiv 7`QK bKTH2 Q7 TT`QtBKi2 /2b+2M/Mib Q7 i?2
:*Gaa bKTH2- #mi i HQr2` `2/b?B7i Q7 0.07 < z < 0.26X q2 K2bm`2
i?2b2 BM rv i?i Bb b +QMbBbi2Mi b TQbbB#H2 rBi? i?2 :*Gaa K2bm`2K2MiX
AM i?2 /Bb+mbbBQM T`2b2Mi2/ BM p/"R9 r2 bm;;2bi i?i i?2 ;`Qri? Q7 i?2 A*G
Q` i?2 ++`2iBQM Q7 ;HtB2b QMiQ i?2 QmibFB`ib Q7 i?2 +Hmbi2` +QmH/ 2tTHBM i?2
bB;MB}+Mi 2pQHmiBQM #2ir22M i?2 K2bm`2K2Mib BM :*Gaa M/ *LP*RX AM
i?Bb TT2` r2 `2pBbBi i?Bb /Bb+mbbBQM #v HbQ BM+Hm/BM; i?2 M2r K2bm`2K2Mib
i z ∼ 0.15X
h?2 bi`m+im`2 Q7 i?Bb TT2` Bb b 7QHHQrbX AM a2+iX 8Xk r2 ;Bp2 M Qp2`pB2r
Q7 i?2 +Hmbi2` bKTH2- i?2 pBH#H2 bT2+i`Qb+QTB+ /i b2i M/ i?2 T?QiQK2i`B+
+iHQ;m2b #b2/ QM ugri@#M/ T?QiQK2i`vX a2+iBQM 8Xj T`2b2Mib i?2 K2bm`2@
K2Mi Q7 i?2 `/BH /2MbBiv T`Q}H2b- #b2/ QM irQ BM/2T2M/2Mi MHvb2b i?i
r2 rBHH +QKT`2 7Q` `Q#mbiM2bb i2bibX h?2 `2bmHib `2 T`2b2Mi2/ BM a2+iX 8X9M/ Tmi BMiQ +QMi2ti ;BMbi HQr@z HBi2`im`2 K2bm`2K2MibX AM a2+iX 8X8 r2
/Bb+mbb i?2 Q#b2`p2/ 2pQHmiBQM M/ bm;;2bi TQbbB#H2 b+2M`BQb iQ 2tTHBM i?2
/Bz2`2M+2b #2ir22M z ∼ 1 M/ i?2 HQ+H bim/vX q2 bmKK`Bb2 M/ +QM+Hm/2 BM
a2+iX 8XeX
HH K;MBim/2b r2 [mQi2 `2 BM i?2 " K;MBim/2b bvbi2K UmMH2bb 2tTHB+@
BiHv K2MiBQM2/ Qi?2`rBb2V M/ r2 /QTi Λ*.J +QbKQHQ;v rBi? ΩK = 0.3ΩΛ = 0.7 M/ >y = dy FK b−R JT+−R X 6Q` bi2HH` Kbb 2biBKi2b r2 bbmK2
i?2 AMBiBH Jbb 6mM+iBQM UAJ6V 7`QK *?#`B2` UkyyjVX
h?2 bKTH2 r2 bim/v Bb /`rM 7`QK irQ H`;2 s@`v b2H2+i2/ +Hmbi2` bm`p2vbi?2 JmHiB@1TQ+? L2`#v *Hmbi2` am`p2v UJ1L2*aV M/ i?2 *M/BM *Hmbi2`
*QKT`BbQM S`QD2+i U***SVX bm#biMiBH MmK#2` Q7 bT2+i`Qb+QTB+ `2/b?B7ib
BM i?2b2 +Hmbi2` }2H/b `2 pBH#H2 7`QK i?2 HBi2`im`2- bT2+B}+HHv i?2 *M@
*>Sh1_ 8X h>1 .Aah_A"lhAPL P6 ah1GG_ Jaa AL :Gsu
Ne
*Glah1_a h z ∼ 0.15
/BM L2irQ`F 7Q` P#b2`piBQMH *QbKQHQ;v am`p2v U*LP*c u22 2i HX RNNeVi?2 aHQM .B;BiH aFv am`p2v .i _2H2b2 Ry Ua.aa ._Ryc ?M 2i HX kyRjVM/ i?2 >2+iQbT2+ *Hmbi2` am`p2v U>2*ac _BM2b 2i HX kyRjVX q2 b2`+?2/
i?2 LafAS* 1ti`;H+iB+ .i#b2 UL1.VR iQ Q#iBM //BiBQMH bT2+@
i`Qb+QTB+ BM7Q`KiBQM 7Q` ;HtB2b i?i ?p2 MQi #22M i`;2i2/ #v i?2b2 bm`p2vbX
AM //BiBQM iQ i?2 /2i2`KBMiBQM Q7 +Hmbi2` K2K#2`b?BT i?2b2 `2/b?B7ib H@
HQr mb iQ 2biBKi2 /vMKB+H Kbb2bX q2 `272` iQ aB7ƦM 2i HX UBM T`2TXV 7Q`
/2iBHbX AM bmKK`v- +Hmbi2` K2K#2`b?BT M/ p2HQ+Biv /BbT2`bBQMb `2 /2i2`@
KBM2/ mbBM; i?2 biM/`/ b?B7iBM; ;TT2` TT`Q+? U6// 2i HX RNNeV- b22
HbQ aB7ƦM 2i HX UkyRjVX hQ `2Hi2 i?2 p2HQ+Biv /BbT2`bBQM σv iQ 2biBKi2b Q7
R200 - i?2 `/Bmb i r?B+? i?2 K2M BMi2`BQ` /2MbBiv Bb kyy iBK2b i?2 +`BiB+H
/2MbBiv Uρ+`Bi V- M/ M200 - i?2 Kbb +QMiBM2/ rBi?BM R200 - i?2 1p``/ 2i HX
Ukyy3V b+HBM; `2HiBQM Bb mb2/X a22 p/"R9 Ua2+iX kXRV 7Q` i?2 TTHB+iBQM Q7
i?Bb b+HBM; `2HiBQM iQ i?2 :*Gaa +Hmbi2` bKTH2X
h?Bb Bb TBHQi bim/v Q7 Ry +Hmbi2`b r?B+? r2`2 /`rM 7`QK i?Qb2 J1@
L2*a M/ ***S +Hmbi2`b i?i r2`2 Q#b2`p2/ rBi? J2;*K Ub QTTQb2/
iQ i?2 QH/2` *6>RkF +K2`V BM i?2 g @ M/ r@#M/b M/ ?p2 //BiBQMH u@
M/ i@#M/ T?QiQK2i`v iQ HHQr 7Q` +H2M2` +Hmbi2` ;Htv b2H2+iBQMX h?2
Ry +Hmbi2`b `2 HBbi2/ BM h#H2 8XR- M/ r2`2 b2H2+i2/ 7`QK i?2 H`;2` bKTH2
7QHHQrBM; b2p2`H +`Bi2`BX 6B`biHv- i?2v ?p2 ?B;? /vMKB+H Kbb2b iQ 2Mbm`2
i?i i?2v `2 bB;MB}+MiHv Qp2`@/2Mb2 +QKT`2/ iQ i?2 }2H/- r?B+? rBHH H2/ iQ
+H2M #+F;`QmM/ bm#i`+iBQMX a2+QM/Hv- i?2v ?p2 H`;2 MmK#2` Q7 bT2+@
i`Qb+QTB+ K2K#2`b iQ i2bi i?2 T?QiQK2i`B+ #+F;`QmM/ bm#i`+iBQM K2i?Q/ #v
QMHv +QMbB/2`BM; i?2 bT2+i`Qb+QTB+HHv +QM}`K2/ +Hmbi2` K2K#2`bX h?B`/Hv- r2
T`BQ`BiBx2 }2H/b rBi? HQr KQmMib Q7 :H+iB+ /mbi 7Q` +H2M2` T?QiQK2i`B+
+HB#`iBQM #v 2tTHQBiBM; i?2 bi2HH` HQ+mbX M/ }MHHv- BM Q`/2` iQ MQi mM/2`@
2biBKi2 i?2 +QM+2Mi`iBQM Q7 i?2 bi2HH` Kbb /Bbi`B#miBQM- r2 2t+Hm/2 FMQrM
KDQ` K2`;2`b bm+? b #2HH 8ky UJ?/pB 2i HX kyydc *HQr2 2i HX kyRkVX
6B;m`2 8XR bm;;2bib i?i i?Bb Bb UrBi?BM 7+iQ` Q7 ∼ 2V i?2 Kbb `2;BK2
Q7 i?2 HBF2Hv /2b+2M/Mib 7`QK :*Gaa BM i?2 HQ+H lMBp2`b2X *m`p2b BM i?Bb
};m`2 +QMM2+i ?HQ2b b2H2+i2/ 7`QK i?2 JBHH2MMBmK bBKmHiBQM UaT`BM;2H 2i HX
kyy8V i }t2/ +QKQpBM; MmK#2` /2MbBiv- M/ `2 i?mb TT`QtBKi2 ;`Qri?
+m`p2bX q2 HbQ b?Qr i?i i?2 *LP*R +Hmbi2` bKTH2- bim/B2/ #v JmxxBM
2i HX UkyydV- Bb QM i?Bb TT`QtBKi2 2pQHmiBQM`v b2[m2M+2- M/ r2 rBHH HbQ
+QKT`2 Qm` `2bmHib iQ i?2B`b BM i?Bb TT2`X
1+? Q7 i?2b2 +Hmbi2`b Bb +Qp2`2/ #v /22T T?QiQK2i`B+ /i iF2M i?`Qm;?
i?2 g @- M/ r@}Hi2`b mbBM; J2;*K KQmMi2/ i i?2 *M/@6`M+2@>rBB
h2H2b+QT2 U*6>hV- r?B+? Bb je **. BK;BM; ``v +Qp2`BM; 7mHH R×R
R
?iiT,ffM2/XBT+X+Hi2+?X2/mf
8XkX .h Po1_oA1q S_P*1aaAL:
Nd
h#H2 8XR, h?2 Ry #2HH +Hmbi2`b b2H2+i2/ 7`QK J1L2*a M/ ***S i?i 7Q`K i?2 #bBb Q7
i?Bb bim/v- rBi? i?2B` /vMKB+H T`QT2`iB2bX
LK2
zbT2+
e88
Ryjj
Rye3
R3j8
RNR9
kykN
kyeN
kRRR
kR9k
kkeR
yXRkd
yXRkk
yXRjN
yXk8k
yXRed
yXyd3
yXRR9
yXkk3
yXyNy
yXkke
_
Ckyyy
y3,k8,kNXyk
Ry,jR,99XjR
Ry,9y,99X9e
R9,yR,ykXy9
R9,k8,8eXeN
R8,Ry,8eXRk
R8,k9,y3X99
R8,jN,9yX99
R8,83,kyXy3
Rd,kk,kdXRe
.1*
Ckyyy
9d,y3,yyXRy
j8,yk,k3XdR
jN,8d,RRX9R
yk,8k,9kXNe
jd,9N,yyXRk
y8,99,9yX3R
kN,8k,89X8N
j9,k8,kdX93
kd,R9,yRXRR
jk,yd,8dXje
σv#
[FK/b]
934 ± 67
761 ± 85
1054 ± 138
1324 ± 104
962 ± 83
1103 ± 64
1026 ± 76
964 ± 72
1105 ± 37
976 ± 197
#
M200
(1014 J! )
8.7 ± 1.9
4.8 ± 1.6
12.4 ± 4.8
23.2 ± 5.5
9.4 ± 2.4
14.6 ± 2.5
11.6 ± 2.6
9.1 ± 2.0
14.6 ± 1.5
9.5 ± 5.7
#
R200
(JT+)
1.9 ± 0.1
1.5 ± 0.2
2.1 ± 0.3
2.5 ± 0.2
1.9 ± 0.2
2.3 ± 0.1
2.1 ± 0.2
1.9 ± 0.1
2.3 ± 0.1
1.9 ± 0.4
*QQ`/BMi2b Q7 i?2 "*:bX
#
.vMKB+H T`QT2`iB2b 2biBKi2/ #v aB7ƦM 2i HX UBM T`2TXVX
aT2+@z
hQiH UJ2K#2`bV
8N9 Ujy9V
9Ne URdRV
ekR URj9V
eNy UkdjV
dyy Uke9V
3yy UjR8V
3kR Uj9dV
d3y Uk9jV
R3eN URyeRV
e99 UkR9V
b[m`2 /2;`22X h?2 /i `2 T`2@T`Q+2bb2/ mbBM; i?2 1HBtB` TBT2HBM2 UJ;MB2`
*mBHHM/`2 kyy9VX 6Q` J1L2*a- T?QiQK2i`B+ /i BM i?2 irQ #M/b ?p2
#22M iF2M 7Q` i?2b2 +Hmbi2`b- rBi? bB;MB}+Mi /Bi?2` Tii2`M- M/ +/2M+2 Q7
b2p2`H r22Fb iQ HHQr 7Q` i?2 /2i2+iBQM Q7 ivT2 A bmT2`MQp2 BM i?2b2 +Hmbi2`bX
.i 7Q` ***S ?p2 #22M iF2M +QMb2+miBp2Hv mM/2` i?2 #2bi b22BM; +QM/BiBQMb
iQ 7+BHBii2 r2F@H2MbBM; K2bm`2K2MibX 6Q` i?2 +Hmbi2` #2HH e88 r2 7m`i?2`
`2i`B2p2/ `+?BpH J2;*K /i BM i?2 u@- M/ i@#M/bX
h?2 TT`Q+? r2 iF2 iQ T`Q+2bb i?2b2 /i 7m`i?2` Bb H`;2Hv HB/ Qmi
BM pM /2` "m`; 2i HX UkyRj- ?2`27i2` p/"Rj- TT2M/Bt V- M/ H2/b iQ
/22T BK;2 bi+Fb iQ K2bm`2 ++m`i2 M/ T`2+Bb2 +QHQm`b 7Q` i?2 Tm`TQb2 Q7
2biBKiBM; T?QiQK2i`B+ `2/b?B7ib M/ bi2HH` Kbb2bX q2 ?QKQ;2MBb2 i?2 Sa6
Q7 2+? 2tTQbm`2 #27Q`2 bi+FBM;- b QTTQb2/ iQ ?QKQ;2MBbBM; i?2 bi+FX h?2
7Q`K2` TT`Q+? H2/b iQ }MH /22T BK;2 rBi? +H2M2` Sa6- 2bT2+BHHv
;Bp2M i?i i?2 J1L2*a /i ?p2 #22M iF2M mM/2` p`vBM; +QM/BiBQMb M/
rBi? bm#biMiBH /Bi?2`bX h?2 bTiBHHv /2T2M/2Mi +QMpQHmiBQM F2`M2H ?b #22M
+?Qb2M bm+? i?i i?2 Sa6 BM i?2 }MH bi+F ?b i?2 b?T2 Q7 +B`+mH` :mbbBMX
"v TTHvBM; :mbbBM r2B;?i 7mM+iBQM 7Q` T2`im`2 ~mt2b r2 i?2M QTiBKBb2
+QHQm` K2bm`2K2Mib BM i2`Kb Q7 afL Ub22 p/"Rj UTT2M/Bt Vc EmBDF2M kyy3VX
:Bp2M i?2 H`;2 MmK#2` M/ i?2 `M;2 BM BK;2 [mHBiv Q7 i?2 Uk KBMmi2
/22TV J2;*K 2tTQbm`2b 7Q` i?2 J1L2*a +Hmbi2`b- r2 bi+F QMHv i?2 ky
2tTQbm`2b rBi? i?2 #2bi BK;2 [mHBiv UAZ- 6q>J Q7 i?2 b22BM; /BbFV 7Q`
2+? +Hmbi2` M/ }Hi2`X A7 i?2`2 `2 KQ`2 i?M ky 2tTQbm`2b rBi? AZIyX3Ǵ- r2
+QK#BM2 HH 2tTQbm`2b i?i biBb7v i?Bb HBKBiX
*>Sh1_ 8X h>1 .Aah_A"lhAPL P6 ah1GG_ Jaa AL :Gsu
N3
*Glah1_a h z ∼ 0.15
6B;m`2 8XR, GBM2b, 1tT2+i2/ ;`Qri? +m`p2b b 7mM+iBQM Q7 +QbKB+ iBK2 UQ` `2/b?B7iV 7Q`
KbbBp2 ?HQ2b #b2/ QM i?2 JBHH2MMBmK bBKmHiBQM UaT`BM;2H 2i HX kyy8V- BM r?B+? r2 7QHHQr2/
i?2b2 ?HQ2b i }t2/ +QKQpBM; MmK#2` /2MbBivX "Hm2, h?2 :*Gaa +Hmbi2` bKTH2 bim/B2/ BM
p/"R9X _2/, GQr `2/b?B7i +Hmbi2` bKTH2 bim/B2/ ?2`2X Sm`TH2, h?2 *LP*R +Hmbi2` bKTH2
bim/B2/ #v JmxxBM 2i HX UkyydVX h?2 +Hmbi2` bKTH2b `2 HBMF2/ #v i?2 2pQHmiBQM`v ;`Qri?
+m`p2bX
h?2 qB/2@6B2H/ *K2` Uq6*V Bb M QTiB+H KQbB+ +K2` +QMbBbiBM; Q7 9
+?BTb- r?B+? Bb KQmMi2/ QM i?2 Ab+ L2riQM h2H2b+QT2 UALhV QM G SHKX
Aib }2H/@Q7@pB2r U6QoV Bb `Qm;?Hv jy×jy `+KBM- r?B+? BM+Hm/2b bT+2b #2ir22M
+?BTb- b22 i?2 mTT2` H27i TM2H Q7 6B;X 8XkX h?2 6Qo Q7 i?2 KQbB+ Bb bKHH2` i?M
J2;*K- M/ HbQ /Q2b MQi 2MiB`2Hv +Qp2` i?2 7mHH 2ti2Mi Q7 i?2 HQr@z +Hmbi2`b
rBi?BM i?2B` T`QD2+i2/ pB`BH `/BBX AM Q`/2` iQ bim/v i?2 /Bbi`B#miBQM M/
T`QT2`iB2b Q7 ;HtB2b i?i 2ti2M/ i H2bi mT iQ i?2 +Hmbi2` pB`BH `/BB- r2 TTHv
/Bi?2`2/ TQBMiBM; bi`i2;vX h?2 M;mH` bBx2 Q7 i?2 pB`BH `/Bmb /2T2M/b
#Qi? QM i?2 +Hmbi2` iQiH Kbb M/ Bib M;mH` /BK2i2` /BbiM+2 Ui?`Qm;?
`2/b?B7iVX Pm` TT`Q+? Bb iQ iF2 d- N Q` Rk TQBMiBM;b T2` +Hmbi2`- /2T2M/BM;
QM i?2B` M;mH` bBx2bX "b2/ QM M miQKi2/ i2bi Q7 3y-yyy /Bz2`2Mi TQBMiBM;
+QM};m`iBQMb r2 7QmM/ i?i i?2b2 +M #2 +QK#BM2/ iQ +Qp2` =N3W Q7 i?2
`2 +QMiBM2/ rBi?BM T`QD2+i2/ `/BB Q7 RyyyǴ- RkyyǴ M/ R9yyǴ U`2bT2+iBp2HvV
7`QK i?2B` +2Mi`2b iQ bi+F2/ /2Ti? Q7 i H2bi j TQBMiBM;b- b22 6B;X 8XkX "v
8XkX .h Po1_oA1q S_P*1aaAL:
NN
6B;m`2 8Xk, lTT2` H27i TM2H, 6Qm` **.b BM i?2 q6* KQbB+- b?QrBM; ;Tb #2ir22M +?BTbX
Pi?2` TM2Hb, Pm` QTiBKBb2/ TQBMiBM; bi`i2;v UQi?2` M;mH` b+H2 i?M mTT2` H27i TM2HVb?QrBM; ?Qr r2 +Qp2` i?2 `2 rBi?BM i?2 2biBKi2/ pB`BH `/Bmb #v mbBM; d- N Q` Rk /Bi?2`bX
h?2 `2 r?2`2 i?2 /2Ti? Bb i H2bi j TQBMiBM;b- +Q``2bTQM/BM; iQ Rkyyb BMi2;`iBQM- Bb
K`F2/X
mbBM; 2tTQbm`2 iBK2b Q7 9yyb BM i?2 u@ M/ i@#M/- r2 `2+? /2Ti? Q7 i
H2bi Rkyyb Qp2` UT`+iB+HHvV i?2 2MiB`2 +Hmbi2` pB`BH `/BmbX L2` i?2 +Hmbi2`
+2Mi`2b i?2`2 `2 KQ`2 Qp2`HTTBM; TQBMiBM;b r?B+? 7m`i?2` 2M?M+2 i?2 /2Ti?X
aBM+2 i?2 J1L2*a M/ ***S +Hmbi2` bKTH2b `2 bT`2/ BM _- r2 ?p2 iQ
+QK#BM2 /i 7`QK Q#b2`pBM; `mMb BM /Bz2`2Mi b2bQMbX q2 +QKTBH2/ /i
b2i- iQiHHBM; 8j MB;?ib- b22 h#H2 8XkX
q?2`2b r2 mb2/ T`2@T`Q+2bb2/ J2;*K /i 7`QK i?2 1HBtB` TBT2HBM2i?2`2 Bb MQ bBKBH` Hi2`MiBp2 7Q` q6*X q2 i?2`27Q`2 +QKTQb2/ Qm` QrM `2@
/m+iBQM TBT2HBM2 BK2/ i T`Q/m+BM; BK;2b iQ K2bm`2 ~mt2b BM i?2 u@- M/
i@#M/b rBi? ?B;? T?QiQK2i`B+ ++m`+v M/ T`2+BbBQMX AM bmKK`v- r2 +QM@
bi`m+i +HB#`iBQM 7`K2b 7Q` 2+? `mM iQ bm#i`+i i?2 #Bb- /BpB/2 i?`Qm;?
*>Sh1_ 8X h>1 .Aah_A"lhAPL P6 ah1GG_ Jaa AL :Gsu
Ryy
*Glah1_a h z ∼ 0.15
h#H2 8Xk, a+?2/mH2/ Q#b2`piBQMb QM i?2 Ab+ L2riQM h2H2b+QT2 UALhV BM G SHK- mbBM;
i?2 qB/2 6B2H/ *K2` Uq6*V 7Q` iQiH Q7 8j MB;?ibX
u2`
kyRy
kyRy
kyRy
kyRy
kyRy
kyRR
kyRR
hQiH
JQMi?
CM
T`
Jv
P+i
LQp
T`
Jv
.vb
8@Rj
R9@R3
e@R8
d@R9
3@R9
9@d- jy
R@N
LmK#2` Q7 MB;?ib
N
8
Ry
3
d
8
N
8j
~i@}2H/b- M/ `2KQp2 7`BM;BM; Tii2`Mb 7`QK i?2 i@#M/X q2 B/2MiB7v M/
KbF TBt2Hb i?i ?p2 MQMHBM2` `2bTQMb2 iQ BM+QKBM; ~mt- M/ 7m`i?2` `2@
KQp2 +QbKB+ `vb #v mbBM; i?2 GTH+BM *QbKB+ _v A/2MiB}+iBQM K2i?Q/
UpM .QFFmK kyyRVX q2 +QMbi`m+i qQ`H/ *QQ`/BMi2 avbi2K Uq*aV 7Q`
2+? BK;2 #v +QKT`BM; rBi? +iHQ;m2b +QMbi`m+i2/ mbBM; i?2 J2;*K
/i 7Q` i?2b2 +Hmbi2` }2H/bX h?2 bi`QK2i`B+ `2bB/mHb ?p2 HQr b+ii2` i?i
Bb ivTB+HHv yXyj@yXR8Ǵ- +QMbBbi2Mi rBi? biiBbiB+H mM+2`iBMiB2b BM +2Mi`QB/ /2@
i2`KBMiBQMX q2 T2`7Q`K +?BT@#v@+?BT #+F;`QmM/ bm#i`+iBQM 7i2` KbFBM;
HH /2i2+i2/ Q#D2+ibX
aBKBH` iQ r?i rb /QM2 7Q` i?2 J2;*K /i- r2 +QMpQHp2 i?2 BK;2b
rBi? TQbBiBQM@/2T2M/2Mi F2`M2H iQ ?QKQ;2MBx2 i?2 Sa6 iQ +B`+mH` :mb@
bBMX h?2 6q>J bBx2 Q7 i?Bb :mbbBM 7Q` i?2 q6* /i Bb H`;2` i?M 7Q`
i?2 J2;*K BK;2b- ivTB+HHv `QmM/ kǴX _2HiBp2 b+HBM; Q7 i?2 T?QiQK2i`B+
x2`Q TQBMi #2ir22M 2tTQbm`2b Bb /2i2`KBM2/ #v +QMbB/2`BM; Q#D2+ib i?i `2
BK;2/ QM Qp2`HTTBM; T`ib #2ir22M 2tTQbm`2bX 7i2` i?2b2 bi2Tb- r2 +?B2p2
bvbi2KiB+ mM+2`iBMiv QM ~mt K2bm`2K2Mib bKHH2` i?M RW BM i?2 irQ
#M/bX
h?mb 7`- i?2 T?QiQK2i`B+ ~mt K2bm`2K2Mib ?p2 #22M b+H2/ iQ vB2H/ mMB@
7Q`K x2`Q TQBMi 7Q` 2+? }Hi2`X hQ +QMp2`i i?2 ~mt K2bm`2K2Mib BM /Bz2`2Mi
}Hi2`b iQ i?2 bK2 `2HiBp2 T?QiQK2i`B+ b+H2- r2 2tTHQBi i?2 mMBp2`bH T`QT2`@
iB2b Q7 i?2 bi2HH` HQ+mbX h?Bb K2i?Q/ Bb /2b+`B#2/ BM >B;? 2i HX UkyyNV- M/
r2 HbQ TTHB2/ i?Bb +HB#`iBQM i2+?MB[m2 iQ i?2 :*Gaa /i Ub22 p/"RjTT2M/Bt VX 6B;m`2 8Xj /2KQMbi`i2b i?Bb i2+?MB[m2 7Q` i?2 7Qm` #M/b pBH@
#H2 iQ mb- 7i2` b2H2+iBM; bi`b #b2/ QM i?2B` K2bm`2/ ~mt M/ M;mH` bBx2X
8XkX .h Po1_oA1q S_P*1aaAL:
RyR
6B;m`2 8Xj, h?2 bi2HH` HQ+mb BM k TM2Hb- +QK#BMBM; i?2 ugr UH27i TM2HV M/ gri U`B;?i TM2HV
T2`im`2 ~mt2b Q7 bi`bX _2/ HBM2b M/ Q`M;2 +QMiQm`b, +QHQm`b Q7 bi`b M/ R@σ `2;BQM Q7
BMi`BMbB+ b+ii2` BM i?2 *Qp2v 2i HX UkyydV +iHQ;m2- +QMp2`i2/ iQ i?2 *6>h }Hi2` b2iX "H+F
TQBMib, +QHQm`b Q7 bi`b BM i?2 }2H/ Q7 #2HH kR9k 7i2` +HB#`iBQMX "Hm2 ``Qr, :H+iB+ /mbi
`2//2MBM; p2+iQ` 7Q` i?Bb }2H/X
h?2 `2/ HBM2 M/ bbQ+Bi2/ R@σ `2;BQM Q7 BMi`BMbB+ b+ii2` UQ`M;2V `2 #b2/
QM i?2 *Qp2v 2i HX UkyydV +iHQ;m2 Q7 bi2HH` +QHQm`bX aBM+2 i?Bb `272`2M+2
bi2HH` +iHQ;m2 Bb #b2/ QM i?2 a.aa }Hi2` bvbi2K- r2 mb2 HBM2` +QHQm` i2`Kb
iQ +QMp2`i Bi iQ i?2 *6>h }Hi2` b2ik X *QHQm` i2`Kb `2bmHi BM `QiiBQMb M/
i`Mb7Q`KiBQMb Q7 i?2 bi2HH` HQ+mb BM i?Bb +QHQm`@+QHQm` THM2- M/ +M i?2`2@
7Q`2 #2 Q#iBM2/ 7`QK i?2 /Bbi`B#miBQM Q7 bi2HH` +QHQm`b Bib2H7X q2 2biBKi2 i?2
7QHHQrBM; HBM2` +QHQm` i2`K iQ Tmi i?2 q6* K2bm`2K2Mib QMiQ i?2 J2;*K
T?QiQK2i`B+ bvbi2KX
uJ2;*K = uq6* − 0.150 · (uq6* − gJ2;*K )
iJ2;*K = iq6* − 0.120 · (rJ2;*K − iq6* )
U8XRV
U8XkV
q2 mb2 KTb 7`QK a+?H2;2H 2i HX URNN3V iQ }M/ i?2 p2`;2 2tiBM+iBQM
+mb2/ #v /mbi BM i?2 JBHFv qv i?i Bb Q#b+m`BM; 2+? +Hmbi2`X aBM+2 i?2 ~mt
2tiBM+iBQM Bb rp2H2M;i? /2T2M/2Mi- r2 2biBKi2 i?2 2tiBM+iBQM BM 2+? #M/
k
?iiT,ffrrrjX+/+@++/X?B@B?XM`+@+M`+X;+X+fK2;TBT2f/Q+bf}Hi2`bX?iKH
*>Sh1_ 8X h>1 .Aah_A"lhAPL P6 ah1GG_ Jaa AL :Gsu
Ryk
*Glah1_a h z ∼ 0.15
b2T`i2Hv M/ +Q``2+i i?2 ~mt2b 7Q` i?Bb 2z2+iX h?2 +QKTHB+iBQM Bb i?i i?2
bi`b BM i?2 }2H/ rBHH ?p2 `M;2 Q7 /BbiM+2b iQ 1`i?- M/ i?mb bi`b i?i
`2 7m`i?2` rv ?p2 H`;2` KQmMi Q7 /mbi Q#b+m`iBQMX aBM+2 r2 +QMbB/2`
bi`b BM }t2/ rBM/Qr Q7 TT`2Mi K;MBim/2 U2X;X 18 < K;r < 20V- r2
2tT2+i i?2 `2//2` bi`b iQ #2 KQ`2 M2`#v M/ i?mb #2 KQbiHv BM 7`QMi Q7
i?2 /mbi +QHmKMX "Hm2` bi`b QM i?2 Qi?2` ?M/ ?p2 ?B;?2` HmKBMQbBiv
M/ i?2`27Q`2 `2 ivTB+HHv i H`;2` /BbiM+2 7`QK 1`i?X AM 6B;X 8Xj i?2
/mbi `2//2MBM; p2+iQ` Bb BM/B+i2/ BM #Qi? TM2Hb- M/ i?2 bi`b i i?2 `2/
UmTT2` `B;?iV T`i Q7 i?2 bi2HH` HQ+mb ?p2 #22M Qp2`@+Q``2+i2/ 7Q` :H+iB+
/mbi 2tiBM+iBQMX >Qr2p2`- i?2 2ti`;H+iB+ bQm`+2b BM r?B+? r2 `2 BMi2`2bi2/
`2 +Q``2+i2/ T`QT2`Hv 7Q` /mbiX AM }2H/b i?i `2 MQi bB;MB}+MiHv Q#b+m`2/ #v
:H+iB+ /mbi UBX2X r?2M i ?B;? :H+iB+ HiBim/2V i?2 bi2HH` HQ+mb +HB#`iBQM
i2+?MB[m2 rQ`Fb #2bi- bBM+2 i?2 b?T2 Q7 i?2 bi2HH` HQ+mb rBHH #2 H2bi z2+i2/X
h?2 J2;*K r@#M/ Bb +HB#`i2/ BM #bQHmi2 i2`Kb rBi? `2bT2+i iQ biM@
/`/ bi` }2H/b- M/ KQbi Q7 i?2b2 /i `2 iF2M mM/2` T?QiQK2i`B+ +QM/BiBQMbX
h?2`27Q`2 r2 /Dmbi i?2 u@- g @- M/ i@#M/ x2`Q@TQBMib iQ #`BM; i?2 bi`b BM
i?2 }2H/ BM HBM2 rBi? i?2 bi2HH` HQ+mb- M/ r2 F22T i?2 r@#M/ x2`Q@TQBMi mM@
+?M;2/X q2 +M i2bi i?2 `Q#mbiM2bb Q7 i?2 r@#M/ #bQHmi2 +HB#`iBQM BM i?2
7QHHQrBM; rvX q2 +Q``2+i i?2 x2`Q@TQBMib BM 2+? q6* 2tTQbm`2 7Q` /Bz2`@
2M+2b BM 2tTQbm`2 iBK2 M/ B`Kbb UmbBM; b `272`2M+2 9yyb M/ M B`Kbb
Q7 RXjVX h?Bb ;Bp2b M BM/B+iBQM Q7 i?2 iKQbT?2`B+ i`MbKBbbBQM- r?B+? r2
THQi b 7mM+iBQM Q7 iBK2 UC.VX aBM+2 KMv +Hmbi2`b r2`2 Q#b2`p2/ BM i?2 bK2
MB;?i- M/ BM KQbi MB;?ib i?2 +QM/BiBQMb +?M;2/ p2`v ;`/mHHv- QmiHB2`b BM
i?2b2 /B;`Kb `2 BM/B+iBp2 Q7 T`Q#H2Kb BM #bQHmi2 +HB#`iBQMX 6Q` 2tKTH2B7 7Q` ;Bp2M +Hmbi2` i?2 2biBKi2/ iKQbT?2`B+ i`MbKBbbBQM Bb bvbi2KiB+HHv
Qz@b2i 7Q` HH 2tTQbm`2b BM #Qi? }Hi2`b- i?Bb Bb bi`QM; BM/B+iBQM Q7 +HB#`@
iBQM T`Q#H2KX q2 mb2 i?Bb BM7Q`KiBQM iQ }M2@imM2 i?2 x2`Q@TQBMib 7m`i?2`X 6Q`
}2H/b i?i bmz2` 7`QK H`;2 :H+iB+ /mbi +QHmKM i?Bb Bb Qm` KBM K2i?Q/
7Q` T?QiQK2i`B+ +HB#`iBQMX h?2 TT`2Mi K;MBim/2 7i2` iKQbT?2`B+ 2t@
iBM+iBQM Bb ;Bp2M #v K = KR + Fλ × (B`Kbb − R)- r?2`2 KR Bb i?2 K;MBim/2
7Q` `272`2M+2 B`Kbb Q7 R- M/ Fλ Bb i?2 rp2H2M;i? /2T2M/2Mi 2tiBM+iBQM
+Q2{+B2MiX h?2 iKQbT?2`B+ 2tiBM+iBQM +Q2{+B2Mib BM i?2 u@- M/ i@#M/ r2
}M/ iQ #2 yX8y M/ yXye- `2bT2+iBp2HvX
"2+mb2 Q7 i?2 2t+2HH2Mi BK;2 [mHBiv M/ /2Ti? BM i?2 J2;*K r@#M/
bi+Fb- r2 mb2 i?2b2 b Qm` /2i2+iBQM BK;2bX 6Q` ;HtB2b rBi? `2/b?B7i z " 0.4
i?2 r@#M/ }Hi2` T`Q#2b i?2 `2bi@7`K2 a1. `2/r`/ Q7 i?2 4000˚
#`2F- r?B+?
KF2b i?2 Q#b2`p2/ r@#M/ ~mt `2bQM#H2 T`Qtv 7Q` bi2HH` KbbX q2 K2@
bm`2 T2`im`2 ~mt2b BM i?2 b22BM;@?QKQ;2MBx2/ BK;2b mbBM; :mbbBM r2B;?i
7mM+iBQM- r?B+? r2 /Dmbi BM bBx2 iQ ++QmMi 7Q` /Bz2`2Mi Sa6 bBx2bX hQ 2biBKi2
2``Q`b QM i?2b2 K2bm`2K2Mib- r2 `M/QKHv TH+2 T2`im`2b rBi? i?2 bK2
b?T2 QM i?2 b22BM;@?QKQ;2MBx2/ BK;2b M/ K2bm`2 i?2 /BbT2`bBQM BM i?2
#+F;`QmM/X aBM+2 i?2 ~mt K2bm`2K2Mib Q7 Qm` 7BMi bQm`+2b `2 #+F;`QmM/@
MQBb2 HBKBi2/- i?Bb rv r2 T`Q#2 i?2 /QKBMMi +QKTQM2Mi Q7 i?2 T2`im`2 ~mt
8XkX .h Po1_oA1q S_P*1aaAL:
Ryj
h#H2 8Xj, h?2 T?QiQK2i`B+ /i b2i mb2/ BM i?Bb bim/vX lMH2bb BM/B+i2/ Qi?2`rBb2- u@M/ i@#M/ T?QiQK2i`v Bb Q#iBM2/ mbBM; i?2 qB/2 6B2H/ *K2` i i?2 ALh- M/ g@- M/
r@#M/ T?QiQK2i`v +QK2b 7`QK J2;*K i i?2 *6>hX h?2 HBKBiBM; K;MBim/2b `2TQ`i2/
`2 K2/BM 8@σ ~mt K2bm`2K2Mi HBKBib 7Q` TQBMi bQm`+2b K2bm`2/ rBi? :mbbBM r2B;?i
7mM+iBQMX 6Q` HH +Hmbi2`b T`i 7`QK e88- r2 ?/ iQ 2tTM/ i?2 bBx2 Q7 i?2 :mbbBM T2`im`2
r2B;?i 7mM+iBQM bm#biMiBHHv iQ ++QKKQ/i2 i?2 ALh BK;2 [mHBivX
LK2
e88
Ryjj
Rye3
R3j8
RNR9
kykN
kyeN
kRRR
kR9k
kkeR
*PaJPa
uHBK
(K;" )
k8XN
k9Xy
k9X3
k9X8
k9Xy
k9Xk
k9Xy
k9X9
k9Xj
k9Xj
keXe
gHBK
(K;" )
keXy
k8Xy
k8XR
k9X3
k8XR
k9Xe
k8XR
k8Xk
k9X3
k8Xy
keXj#
rHBK
(K;" )
k8X8
k9X9
k9X9
k9X9
k9X8
k9Xy
k9X8
k9Xe
k9Xk
k9X9
keX9#
iHBK
(K;" )
k8Xy
kkXN
kjXe
kjXe
kjXk
kjX9
kjXk
kjXR
kkX8
kRX3
keXy#
J2;*K- *M/@6`M+2@>rBB h2H2b+QT2 U*6>hV
#
amT`BK2*K- am#`m
2``Q`X 6Q` i?2 q6* /i r2 +QKT`2 T2`im`2 ~mt K2bm`2K2Mib 7Q` 2+?
bQm`+2 BM i?2 BM/BpB/mH 2tTQbm`2b M/ Ui?`Qm;? bB;K@+HBTTBM;V +QK#BM2 i?Bb
BMiQ ~mt K2bm`2K2Mi M/ 2``Q`X lbBM; i?2b2 2biBKi2/ 2``Q`b r2 ;Bp2 i?2
K2/BM /2Ti? Q7 2+? BK;2 BM h#H2 8Xj- +QMbB/2`BM; QMHv TQbBiBQMb r?2`2 i?2
BK;2 /2Ti? Bb i H2bi RkyybX LQi2 i?i i?2 8@σ /2Ti? BM i?2b2 T2`im`2b Bb
HbQ z2+i2/ #v i?2 b22BM; BM i?2 q6* BK;2b- bBM+2 i?2 bBx2b Q7 i?2 T2`im`2b
M22/ iQ #2 2tTM/2/ T`QTQ`iBQMHHv iQ i?2 BK;2b rBi? BM72`BQ` AZX LQi2 i?i
7Q` +Hmbi2` #2HH e88 r2 ?p2 /22T 9@#M/ +Qp2`;2 rBi? *6>h J2;*KX
q2 KbF bi`b #`B;?i2` i?M o4R8 UmiQKiB+HHv b2H2+i2/ 7`QK i?2 :mB/2
ai` *iHQ; AA U:a*@AA GbF2` 2i HX kyy3VV M/ i?2B` /Bz`+iBQM bTBF2b M/
?HQ2b BM i?2 BK;2b- r?B+? ivTB+HHv +Qp2` 72r T2`+2Mi Q7 i?2 `2X h?2
/b?2/ HBM2 BM 6B;X 8X9 b?Qrb i?2 BK;2/ 7`+iBQM Q7 i?2 2Mb2K#H2 +Hmbi2` UBX2X
Ry +Hmbi2`b +QK#BM2/V QM i?2 /2i2+iBQM BK;2b b 7mM+iBQM Q7 `/BH 2ti2Mi
7`QK i?2 "*:- b b+H2/ rBi? i?2 pB`BH `/Bmb R200 Uh#H2 8XRVX h?2 /2i2+iBQM
BK;2b +Qp2` M `2 U2t+Hm/BM; HQ+iBQMb rBi? #`B;?i bi`bV H`;2` i?M i?2
pB`BH `/Bmb 7Q` 2+? +Hmbi2`X q2 HbQ b?Qr i?2 7`+iBQMH `2 +Qp2`2/ rBi?
9@#M/ T?QiQK2i`v U/2Ti? i H2bi Rkyyb BM 2+? #M/VX h?2 BMM2` #BM Bb
*>Sh1_ 8X h>1 .Aah_A"lhAPL P6 ah1GG_ Jaa AL :Gsu
Ry9
*Glah1_a h z ∼ 0.15
T`iHv +Qp2`2/ #v i?2 "*:- r?B+? /Q2b MQi HHQr 7Q` i?2 /2i2+iBQM Q7 bi2HHBi2
;HtB2b- M/ i?Bb `2 Bb i?2`27Q`2 HbQ KbF2/X
6B;m`2 8X9, 6`+iBQMHHv +Qp2`2/ `2
Q7 i?2 2Mb2K#H2 +Hmbi2` b 7mM+@
iBQM Q7 `/BH /BbiM+2 7`QK i?2 "*:X
.b?2/ HBM2, BK;2/ 7`+iBQM Q7 i?2
2Mb2K#H2 +Hmbi2` UBX2X Ry +Hmbi2`b +QK@
#BM2/V QM i?2 /2i2+iBQM BK;2bX h?Bb
2t+Hm/2b HQ+iBQMb rBi? #`B;?i bi`bX
.Qii2/ HBM2, 7`+iBQMH `2 +Qp2`2/
rBi? 9@#M/ T?QiQK2i`v U/2Ti? i
H2bi Rkyyb BM 2+? #M/VX h?2 2z2+@
iBp2 `2 BM i?2 BMM2` #BM Bb `2/m+2/
/m2 iQ i?2 TBt2Hb +Qp2`2/ #v i?2 "*:X
q2 T2`7Q`K irQ T`HH2H M/ UH`;2HvV BM/2T2M/2Mi MHvb2b iQ K2bm`2 i?2
`/BH bi2HH` Kbb /Bbi`B#miBQM BM i?2 2Mb2K#H2 +Hmbi2`X q2 i?2M +QKT`2
`2bmHib 7`QK i?2b2 MHvb2b b `Q#mbiM2bb i2biX
h?2 }`bi TT`Q+? Bb iQ 2biBKi2 T?QiQK2i`B+ `2/b?B7i 7Q` 2p2`v ;Htv BM
i?2 +Hmbi2` BK;2b- TTHv +mi BM `2/b?B7i bT+2 Uz < 0.3V M/ biiBbiB+HHv
bm#i`+i ;HtB2b BM i?2 7Q`2@- M/ #+F;`QmM/ #v TTHvBM; i?2 bK2 `2/b?B7i
+mi iQ i?2 `272`2M+2 *PaJPa }2H/X q2 mb2 ugri T?QiQK2i`B+ /i BM #Qi? Qm`
+Hmbi2` }2H/b M/ i?2 *PaJPa }2H/ iQ 2biBKi2 T?QiQK2i`B+ `2/b?B7ib mbBM;
i?2 1wu U"`KK2` 2i HX kyy3V T?QiQK2i`B+ `2/b?B7i +Q/2X q2 mb2 M r@#M/
b2H2+i2/ +iHQ;m2 7`QK i?2 *PaJPa }2H/ r?B+? ?b #22M +QMbi`m+i2/ BM i?2
bK2 rv b i?2 E@#M/ b2H2+i2/ +iHQ;m2 Q7 JmxxBM 2i HX UkyRj#VX h?2 }2H/
?b M 2z2+iBp2 `2 Q7 RXek /2;k - M/ r2 QMHv mb2 /i BM i?2 ugri@}Hi2`b iQ
T`QpB/2 7B` `272`2M+2 iQ Qm` +Hmbi2` bKTH2X
"2+mb2 Qm` #Hm2bi #M/ Bb i?2 u@#M/- Bi Bb /B{+mHi iQ +QMbi`BM i?2 HQ@
+iBQM Q7 i?2 4000˚
@#`2F 7Q` ;HtB2b i HQr Uz " 0.15V `2/b?B7i- bBM+2 i?2
#`2F Bb i?2M HQ+i2/ BM i?Bb }Hi2`X GBF2 KMv `2/b?B7i +Q/2b- 1wu TTHB2b ~mt@- M/ `2/b?B7i@#b2/ T`BQ`- r?B+? ;Bp2b i?2 `2/b?B7i T`Q##BHBiv /Bbi`B#miBQM
7Q` ;Htv Q7 ;Bp2M r@#M/ ~mt SUz -rVX h?Bb T`BQ` ?b bi`QM; 2z2+i BM
2biBKiBM; i?2 KQbi T`Q##H2 `2/b?B7i Q7 ;Htv r?2M i?2 u@g +QHQm` HQb2b Bib
+QMbi`BMBM; TQr2` Ub Bb i?2 +b2 7Q` `2/b?B7ib z " 0.15VX AM i?2 HQr `2/b?B7i
8XjX LGuaAa
Ry8
6B;m`2 8X8, G27i TM2H, aT2+i`Qb+QTB+ p2`bmb T?QiQK2i`B+ `2/b?B7ib 7Q` i?2 Ry +Hmbi2`b BM i?Bb
∆z
bim/vX PmiHB2`b- Q#D2+ib 7Q` r?B+? 1+z
> 0.15- `2 K`F2/ BM `2/X h?2 QmiHB2` 7`+iBQM Bb H2bb
∆z
i?M 2W- i?2 b+ii2` UBM 1+z V Q7 i?2 `2KBMBM; Q#D2+ib Bb σz = 0.033X _B;?i TM2H, aK2
7Q` i?2 *PaJPa }2H/- #mi QMHv mbBM; i?2 ugri@}Hi2`bX h?2 QmiHB2` 7`+iBQM M/ b+ii2` `2
bHB;?iHv H`;2` b `2bmHi Q7 /22T2` bT2+i`Qb+QTB+ /i UHbQ i ?B;?2` `2/b?B7i r?2`2 i?2 ugri
}Hi2`b HQb2 i?2B` +QMbi`BMBM; TQr2`VX
`2;BK2 Uz " 0.3V- i?2 +QKQpBM; pQHmK2 2H2K2Mi dVc /dz/dΩ Bb bi`QM; 7mM+@
iBQM Q7 `2/b?B7i U2X;X >Q;; RNNNV- #mi i?2 HmKBMQbBiv 7mM+iBQM /Q2b MQi 2pQHp2
bi`QM;Hv BM i?Bb `2/b?B7i `M;2 U2X;X JmxxBM 2i HX kyRjVX h?2`27Q`2 i?2 T`BQ`
BM i?Bb `2;BK2 Bb /2+`2bBM; `TB/Hv iQr`/b SUz -rV4y 7Q` z = 0- BM/2T2M/2MiHv
Q7 i?2 r@#M/ ~mtX *QMb2[m2MiHv- ++Q`/BM; iQ i?2 T`BQ`- Bi Bb Km+? KQ`2 HBF2Hv
iQ }M/ ;Htv i z = 0.2 +QKT`2/ iQ 2X;X z = 0.1X PM+2 }2H/ Bb +2Mi`2/
QM KbbBp2 +Hmbi2` i HQr `2/b?B7i- i?Bb T`BQ` Bb MQ HQM;2` TTHB+#H2 bBM+2
i?2 T`Q##BHBiv Q7 }M/BM; ;Htv iQ #2 i i?2 +Hmbi2` `2/b?B7i Bb bB;MB}+MiHv
BM+`2b2/X "2bB/2b i?2 ;2M2`H `2/b?B7i M/ ~mt@/2T2M/2M+2 Q7 i?2 T`BQ`- QM2
b?QmH/ i?2`27Q`2 BM+Hm/2 BM7Q`KiBQM QM 2X;X i?2 ;HtvǶb /BbiM+2 iQ i?2 +Hmb@
i2` +2Mi`2 iQ i?2 T`BQ`X h?Bb ?Qr2p2`- Bb #2vQM/ Qm` `2[mB`2K2Mib- bBM+2 r2
bm#i`+i i?2 }2H/ biiBbiB+HHv- M/ i?2 pQHmK2 UM/ i?2`27Q`2 i?2 MmK#2` Q7
+QMiKBMiBM; ;HtB2bV BM i?2 }2H/b Bb bKHH #2HQr z < 0.3X +Q``2+iBQM
QM i?2 T`BQ` rBHH QMHv z2+i `2/b?B7ib i HQr2` `2/b?B7i- M/ rBHH i?2`27Q`2 MQi
+?M;2 r?B+? ;HtB2b bm`pBp2 i?2 `2/b?B7i +miX 6Q` ;HtB2b rBi? T?QiQK2i`B+
`2/b?B7i #2HQr z1wu = 0.16 r2 TTHv bBKTH2 +Q``2+iBQM Q7 i?2 7Q`K T?QiQ@
z = 0.16 · (z1wu − 0.10)/0.06 iQ i?2 1wu QmiTmi- M/ THQi +QKT`BbQM
#2ir22M bT2+@z Ƕb M/ T?QiQ@z Ƕb BM 6B;X 8X8X q2 TTHv i?2 bK2 +Q``2+iBQM iQ
i?2 1wu QmiTmi QM i?2 *PaJPa +iHQ;m2X
aBM+2 i?2 /BbiM+2 KQ/mHmb Bb bi`QM; 7mM+iBQM Q7 `2/b?B7i BM i?Bb `2;BK2 bKHH mM+2`iBMiv BM T?QiQK2i`B+ `2/b?B7i rBHH `2bmHi BM `2HiBp2Hv H`;2 mM@
*>Sh1_ 8X h>1 .Aah_A"lhAPL P6 ah1GG_ Jaa AL :Gsu
Rye
*Glah1_a h z ∼ 0.15
+2`iBMiv BM HmKBMQbBiv UQ` bi2HH` KbbV Q7 ;HtvX :Bp2M i?i i?2 +Hmbi2`
`2/b?B7i Bb r2HH@FMQrM- r2 rBHH bbB;M i?2 /BbiM+2 KQ/mHmb Q7 i?2 +Hmbi2` iQ
2p2`v ;Htv BM i?2 +Hmbi2` }2H/bX AM Q`/2` iQ T`QT2`Hv bm#i`+i +QMiKBMiBM;
7Q`2@ M/ #+F;`QmM/ ;HtB2b- r2 HbQ bbB;M i?Bb /BbiM+2 KQ/mHmb iQ 2+?
;Htv BM i?2 `272`2M+2 *PaJPa }2H/ U7i2` TTHvBM; i?2 `2/b?B7i +miVX q2
i?2M mb2 i?2 a1.@}iiBM; +Q/2 6ah UE`B2F 2i HX kyyNV iQ 2biBKi2 i?2 bi2HH`@
Kbb@iQ@HB;?i `iBQ UJfGV UBM i?2 r@#M/V 7Q` 2+? ;HtvX 6Q` i?Bb r2 ;BM
bbmK2 i?2 bK2 `2/b?B7i M/ /BbiM+2 KQ/mHmb U+Q``2bTQM/BM; iQ i?2 +Hmbi2`V
7Q` 2+? ;HtvX h?2M BM 2+? Q7 i?2 `/BH #BMb Ur?B+? `2 b+H2/ #v i?2 bBx2
R200 Q7 2+? +Hmbi2`V r2 K2bm`2 i?2 `2 UBM M;mH` bBx2V i?i Bb MQi KbF2/
#v #`B;?i bi`b Ur?B+? Bb HbQ /Bz2`2Mi 7Q` 2+? +Hmbi2` i?`Qm;? Bib M;mH` /B@
K2i2` /BbiM+2V M/ 2biBKi2 i?2 2tT2+i2/ MmK#2` Q7 bQm`+2b BM i?Bb `2 BM
i?2 *PaJPa }2H/X q2 2biBKi2 i?2 iQiH bi2HH` Kbb M/ +Q``2bTQM/BM; 2``Q`
7Q` i?Qb2 bQm`+2b #v T2`7Q`KBM; b2`B2b Q7 Ry-yyy JQMi2@*`HQ `2HBbiBQMb Q7
i?2 #+F;`QmM/- #v `M/QKHv /`rBM; bQm`+2b 7`QK i?2 *PaJPa +iHQ;m2X
q2 bm#i`+i i?2 2biBKi2/ }2H/ pHm2b 7`QK i?2 `r MmK#2` +QmMib iQ Q#iBM
i?2 +Hmbi2` bi2HH` Kbb /2MbBiv T`Q}H2X AM TT2M/Bt 8X r2 T2`7Q`K +QM@
bBbi2M+v +?2+F Q7 i?Bb K2i?Q/ #v +QMbB/2`BM; i?2 bi2HH` Kbb /Bbi`B#miBQM Q7
;HtB2b HQ+i2/ 7` rv 7`QK i?2 +Hmbi2` +2Mi`2 M/ +QKT`BM; i?Bb iQ i?2
}2H/ bi2HH` Kbb /Bbi`B#miBQMX q2 }M/ MQ bB;MB}+Mi bvbi2KiB+ /Bz2`2M+2 #2@
ir22M i?2 }2H/ T`Q#2/ `QmM/ i?2 +Hmbi2` M/ i?2 `272`2M+2 *PaJPa }2H/r?B+? bi`2M;i?2Mb Qm` +QM}/2M+2 BM i?Bb K2i?Q/X
AM i?2 K2i?Q/ /2b+`B#2/ #Qp2- r2 bm#i`+i i?2 ;HtB2b BM i?2 7Q`2@- M/
#+F;`QmM/ biiBbiB+HHv #b2/ QMHv QM i?2 T?QiQK2i`B+ /iX >Qr2p2`- b /Bb@
+mbb2/ BM a2+iX 8Xk- r2 +M mb2 bm#biMiBH KQmMi Q7 bT2+i`Qb+QTB+ `2/b?B7ib
BM i?2 +Hmbi2` }2H/b 7`QK i?2 HBi2`im`2X AM i?Bb b2+QM/ TT`Q+? r2 K2bm`2
i?2 bi2HH` Kbb +QMiBM2/ BM bT2+i`Qb+QTB+HHv +QM}`K2/ +Hmbi2` K2K#2`b iQ
T`QpB/2 HQr2` HBKBi iQ i?2 7mHH bi2HH` Kbb /Bbi`B#miBQMX
aBM+2 i?2 bT2+i`Qb+QTB+ /i b2i Bb Q#iBM2/ 7i2` +QK#BMBM; b2p2`H /Bz2`@
2Mi bm`p2vb- i?2 rv i?2 bT2+i`Qb+QTB+ i`;2ib ?p2 #22M b2H2+i2/ Bb MQi 2bBHv
`2+QMbi`m+i2/X 6B;X 8Xe b?Qrb i?2 bT2+i`Qb+QTB+ +QKTH2i2M2bb 7Q` HH ;HtB2b
rBi? T?QiQK2i`B+ `2/b?B7i z < 0.3 b 7mM+iBQM Q7 bi2HH` Kbb UbbmKBM; i?2
bK2 /BbiM+2 KQ/mHmb b i?2 +Hmbi2` `2/b?B7iV- M/ 7Q` /Bz2`2Mi `/BH #BMbX
6Q` bi2HH` Kbb2b J" > RyRR J" - i?2 +QKTH2i2M2bb Bb p2`v ?B;? U> 80WVX
aBM+2 i?2b2 Q#D2+ib +QMbiBimi2 KQbi Q7 i?2 iQiH bi2HH` Kbb /Bbi`B#miBQM Ub22
p/"R9 U6B;X kV 7Q` i?Bb `;mK2MiV- r2 +M ;2i 7B`Hv +QKTH2i2 +2Mbmb Q7 bi2HH`
Kbb #v Dmbi +QMbB/2`BM; i?2 ;HtB2b 7Q` r?B+? r2 ?p2 bT2+i`Qb+QTB+ `2/@
b?B7iX LQi2 ?Qr2p2` i?i i?2 bi2HH` Kbb +QMiBM2/ BM i?2 bT2+i`Qb+QTB+HHv
+QM}`K2/ K2K#2`b Bb HQr2` HBKBi iQ i?2 iQiH- #mi bBM+2 i?2 bT2+i`Qb+QTB+
+QKTH2i2M2bb Bb MQi bi`QM; 7mM+iBQM Q7 `/BH /BbiM+2- r2 2tT2+i iQ KBbb
8X9X _1alGha L. *PJS_AaPL h GPq@z
Ryd
bBKBH` bi2HH` Kbb 7`+iBQM i /Bz2`2Mi /BbiM+2bX q2 Q#iBM bi2HH` Kbb
2biBKi2b 7Q` i?2b2 bT2+i`Qb+QTB+HHv +QM}`K2/ +Hmbi2` ;HtB2b mbBM; i?2 a1.
}iiBM; +Q/2 6ahX q2 `mM Ry-yyy JQMi2@*`HQ `2HBbiBQMb BM r?B+? r2 `M@
/QKHv /`r bT2+i`Qb+QTB+ K2K#2`b BM 2+? #BM iQ 2biBKi2 i?2 R@σ biiBbiB+H
mM+2`iBMiv QM 2+? /i TQBMiX
6B;m`2 8Xe, aT2+i`Qb+QTB+ +QK@
TH2i2M2bb 7Q` bQm`+2b rBi? T?Q@
iQK2i`B+ `2/b?B7i z < 0.3 b 7mM+iBQM Q7 bi2HH` Kbb UbbmKBM;
i?2 bK2 /BbiM+2 KQ/mHmb b i?2
+Hmbi2` `2/b?B7iVX h?2 7Qm` HBM2b
b?Qr /Bz2`2Mi `/BH #BMbX h?2
+QKTH2i2M2bb Bb bBKBH` 7Q` 2+?
#BM- M/ Bb H`;2` i?M 3yW 7Q`
bi2HH` Kbb2b J! > RyRR J! X
z
AM i?Bb b2+iBQM r2 T`2b2Mi i?2 ;Htv MmK#2` M/ bi2HH` Kbb /2MbBiv /Bbi`B@
#miBQMb Q7 i?2 Ry +Hmbi2`b r2 bim/v- #b2/ QM i?2 irQ BM/2T2M/2Mi MHvb2b
/2b+`B#2/ BM a2+iX 8XjX q2 +QKT`2 i?2b2 `2bmHib iQ HBi2`im`2 K2bm`2K2Mib i
+QKT`#H2 `2/b?B7ib (z < 0.3)X AM a2+iX 8X8 r2 /Bb+mbb TQbbB#H2 2pQHmiBQM`v
b+2M`BQ #v +QKT`BM; i?2b2 `2bmHib iQ K2bm`2K2Mib i ?B;?2` `2/b?B7ibX
A;MQ`BM; #`vQMB+ T?vbB+b- i?2 ;Htv MmK#2` /2MbBiv /Bbi`B#miBQM BM +Hmbi2`
?HQ2b +M #2 +QKT`2/ iQ i?2 /Bbi`B#miBQM Q7 bm#@?HQ2b BM L@#Q/v bBKmH@
iBQMb b i2bi Q7 Λ*.JX .m2 iQ K2`;2`b M/ BMi2`+iBQMb #2ir22M ;HtB2bi?2 MmK#2` /2MbBiv /Bbi`B#miBQM Q7 ;HtB2b Kv #2 /Bz2`2Mi 7Q` ;HtB2b rBi?
/Bz2`2Mi bi2HH` Kbb2bX 6B;m`2 8Xd b?Qrb i?2 T`QD2+i2/ ;Htv MmK#2` /2M@
bBiv /Bbi`B#miBQM 7Q` ;HtB2b rBi? bi2HH` Kbb2b 2t+22/BM; J" > RyN J" UH27i
TM2HV- M/ J" > RyRy J" U`B;?i TM2HV BM i?2 2Mb2K#H2 +Hmbi2`X h?2b2 +mib
`2 +?Qb2M iQ 7+BHBii2 +QKT`BbQMb rBi? HBi2`im`2 K2bm`2K2Mib Q7 /Bz2`2Mi
/2Ti?bX "27Q`2 bi+FBM; i?2 Ry +Hmbi2`b- i?2B` `/BH /BbiM+2b iQ i?2 "*:b `2
b+H2/ #v R200 - #mi i?2 "*:b i?2Kb2Hp2b `2 MQi BM+Hm/2/X h?2 #Hm2 TQBMib
b?Qr i?2 `r MmK#2` +QmMib- BM+Hm/BM; i?2 }2H/X 7i2` i?2 }2H/ U`2/ TQBMibV
Bb bm#i`+i2/- r2 Q#iBM i?2 #H+F /i TQBMib b Qm` 2biBKi2 7Q` i?2 +Hmbi2`X
*>Sh1_ 8X h>1 .Aah_A"lhAPL P6 ah1GG_ Jaa AL :Gsu
Ry3
*Glah1_a h z ∼ 0.15
6B;m`2 8Xd, :Htv MmK#2` /2MbBiv /Bbi`B#miBQMb BM i?2 Kbb `M;2 J! > RyN J! UH27i TM2HVM/ J! > RyRy J! U`B;?i TM2HV 7Q` i?2 2Mb2K#H2 +Hmbi2` i z ∼ 0.15X 1``Q` #`b ;Bp2
SQBbbQM bKTHBM; 2``Q`bX "H+F TQBMib rBi? i?2 #2bi }iiBM; T`QD2+i2/ L6q 7mM+iBQMb `2
Qm` #2bi 2biBKi2 7Q` i?2 +Hmbi2` MmK#2` +QmMibX Sm`TH2 TQBMib BM/B+i2 i?2 MmK#2` Q7
bT2+i`Qb+QTB+HHv +QM}`K2/ +Hmbi2` K2K#2`bX
q2 }i T`QD2+i2/ L6q T`Q}H2b iQ i?2 /i TQBMib- KBMBKBxBM; i?2 χ2 pHm2
M/ mbBM; i?2 `2@r2B;?i2/ +2Mi`2b Q7 i?2 k. MMmHmb@b?T2/ #BMbX h?2 #2bi
}iiBM; 7mM+iBQMb ;Bp2 `2bQM#H2 }ib iQ i?2 /i Ub22 i?2 `2/m+2/ χ2 pHm2b
BM h#H2 8X9VX q2 ;Bp2 i?2 #2bi@}iiBM; +QM+2Mi`iBQM T`K2i2`b M/ i?2B`
K`;BMHBx2/ 2``Q`b BM i?2 i#H2- M/ b?Qr i?2 #2bi@}iiBM; 7mM+iBQMb BM 6B;X 8XdX
h?2 Tm`TH2 TQBMib b?Qr i?2 MmK#2`b Q7 bT2+i`Qb+QTB+HHv +QM}`K2/ K2K#2`
;HtB2bX
q2 }M/ bB;MB}+Mi /Bz2`2M+2 BM i?2 #2bi }iiBM; +QM+2Mi`iBQM U1.69+0.09
−0.10
p2`bmb 2.26+0.19
−0.19 V #2ir22M i?2 /Bz2`2Mi Ui?Qm;? Qp2`HTTBM;V Kbb #BMb UJ" =
Ry9 J" M/ J" > RyRy J" - `2bT2+iBp2HvV- BM/B+iBM; i?i i?2 KQ`2 KbbBp2
;HtB2b `2 KQ`2 bi`QM;Hv +QM+2Mi`i2/ BM i?2 +Hmbi2` 2Mb2K#H2X h?2 2z2+i
Q7 /vMKB+H 7`B+iBQM- r?B+? Bb KQ`2 2{+B2Mi 7Q` KbbBp2 ;HtB2b- +M #2 i?2
+mb2 Q7 i?Bb Kbb b2;`2;iBQMX
h?2 MmK#2` /2MbBiv T`Q}H2b BM i?2 HBi2`im`2 i?i r2 +M +QKT`2 rBi?
?p2 #22M K2bm`2/ QM b?HHQr2` /iX GBM 2i HX Ukyy9V bim/v i?2 p2`;2
MmK#2` /2MbBiv T`Q}H2 Q7 bKTH2 Q7 Nj +Hmbi2`b i 0.01 < z < 0.09 rBi?
kJaa E@#M/ /iX h?2v `2 #H2 iQ K2bm`2 /QrM iQ K;MBim/2 HBKBi
Uo2;V Q7 Eb,HBK = 13.5- r?B+? +Q``2bTQM/b iQ J" ≈ RyRy J" i z = 0.05 U"2HH
/2 CQM; kyyRVX Hi?Qm;? i?2v bim/v bvbi2Kb rBi? HQr2` Kbb `M;2 i?M
8X9X _1alGha L. *PJS_AaPL h GPq@z
RyN
h#H2 8X9, S`K2i2`b /2b+`B#BM; i?2 #2bi }iiBM; L6q T`Q}H2 iQ i?2 `/BH /2MbBiv /Bbi`B#m@
iBQMbX _2/m+2/ χ2 pHm2b `2 ;Bp2M URy iQ Rk /2;`22b Q7 7`22/QK T2` +Hmbi2`VX
*Hmbi2`
e88
Ryjj
Rye3
R3j8
RNR9
kykN
kyeN
kRRR
kR9k
kkeR
2Mb2K#H2
ai2HH` Jbb
/2MbBiv
cL6q
χ2 /d.o.f.
+0.76
2.83−0.66
RXRN
5.53+2.42
RXy3
−1.71
1.07+0.71
yXde
−0.47
3.35+0.90
RXdj
−0.71
5.44+2.28
yXN8
−1.85
0.88+0.43
yXej
−0.24
1.74+0.62
RXkN
−0.48
3.87+1.28
yX3k
−1.04
0.93+0.28
yXjj
−0.24
+0.43
1.69−0.29
yX39
1.92+0.19
yX3R
−0.14
LmK#2` /2MbBiv
J" > RyN J"
cL6q
χ2 /d.o.f.
+0.52
3.78−0.47
RX8j
3.49+0.76
RXjN
−0.67
1.21+0.57
kXRj
−0.38
1.97+0.29
jX9k
−0.28
3.02+0.48
kXkd
−0.47
1.21+0.19
yX9e
−0.19
1.40+0.24
RXRy
−0.28
2.45+0.43
yXke
−0.38
0.83+0.14
yX33
−0.14
+0.29
1.88−0.19
yX3N
1.69+0.09
RXd9
−0.10
LmK#2` /2MbBiv
J" > RyRy J"
cL6q
χ2 /d.o.f.
+0.90
3.68−0.71
yXe8
4.16+1.52
yX3j
−1.19
1.16+0.57
RXyR
−0.43
3.25+0.71
RXed
−0.57
4.35+1.33
yXdd
−1.14
1.40+0.38
yX39
−0.38
2.07+0.71
yXN3
−0.52
2.73+0.81
yX8d
−0.57
1.21+0.33
yXNy
−0.28
+0.52
2.21−0.43
yX8N
2.26+0.19
RX9y
−0.19
r2 T`Q#2- i?2v }M/ MmK#2` /2MbBiv +QM+2Mi`iBQM Q7 c = 2.90+0.21
−0.22 - r?B+?
Bb +QKT`#H2 iQ i?2 pHm2 Q7 c = 2.26+0.19
i?i
r2
}M/
7Q`
i?2
?B;? Kbb
−0.19
;HtB2b UJ" > RyRy J" VX
"m/xvMbFB 2i HX UkyRkV K2bm`2 i?2 `/BH /Bbi`B#miBQM Q7 bi2HHBi2 ;HtB2b
BM ;`QmTb M/ +Hmbi2`b BM i?2 `M;2 0.15 < z < 0.40 7`QK i?2 a.aa ._dX
6Q` i?2 bi2HHBi2 ;HtB2b i?2v TTHv K;MBim/2 HBKBi Q7 Mr = −20.5X h?Bb
+Q``2bTQM/b iQ #Qmi J" = RyRy.8 J" 7Q` ;HtB2b rBi? ?B;? JfGX h?2 #2bi
}iiBM; +QM+2Mi`iBQM T`K2i2` Q7 c ∼ 2.6 i?2v }M/ Bb HbQ +QMbBbi2Mi rBi?
Qm` K2bm`2K2Mi 7Q` i?2 ?B;?@Kbb bKTH2X h?2v }M/ i?i i?2 +QM+2Mi`@
iBQM Q7 bi2HHBi2b 7HHb bHB;?iHv b i?2B` #`B;?iM2bb BM+`2b2b- #mi MQi2 i?i i?2v
+QKT`2/ bi2HHBi2b BM ?B;?2` HmKBMQbBiv `M;2 rBi? `2bT2+i iQ Qm` bim/vX
p/"R9 K2bm`2 i?2 MmK#2` /2MbBiv /Bbi`B#miBQM Q7 i?2 :*Gaa +Hmbi2` 2M@
b2K#H2 i z ∼ 1 /QrM iQ bi2HH` Kbb Q7 J" = RyRy.k J" X h?2v K2bm`2 M
L6q +QM+2Mi`iBQM T`K2i2` Q7 c = 5.14+0.54
−0.63 - r?B+? Bb bB;MB}+MiHv ?B;?2`
i?M i?2 pHm2 r2 }M/ 7Q` i?2 HQr@z bKTH2X +QKT`BbQM #2ir22M i?2 MmK@
#2` /2MbBiv /Bbi`B#miBQM M/ i?2 bi2HH` Kbb /2MbBiv /Bbi`B#miBQM T`2b2Mi2/ BM
p/"R9 bm;;2bib i?i i?2 KQ`2 KbbBp2 ;HtB2b `2 bBimi2/ +HQb2` iQr`/b i?2
+Hmbi2` +2Mi`2b i?M HQr2` Kbb ;HtB2b- r?B+? Bb [mHBiiBp2Hv +QMbBbi2Mi rBi?
i?2 i`2M/ r2 }M/ ?2`2X
*>Sh1_ 8X h>1 .Aah_A"lhAPL P6 ah1GG_ Jaa AL :Gsu
RRy
*Glah1_a h z ∼ 0.15
6B;m`2 8X3, ai2HH` Kbb /2MbBiv /Bbi`B#miBQM Q7 i?2 2Mb2K#H2 +Hmbi2` i z ∼ 0.15X "H+F
TQBMib rBi? +Q``2bTQM/BM; SQBbbQM bKTHBM; 2``Q`b `2 Qm` #2bi 2biBKi2 7Q` i?2 +Hmbi2` bi2HH`
Kbb /Bbi`B#miBQMX h?2 #2bi }iiBM; T`QD2+i2/ L6q 7mM+iBQM Bb HbQ b?QrMX h?2 Tm`TH2 TQBMib
;Bp2 i?2 bi2HH` Kbb /Bbi`B#miBQM BM bT2+i`Qb+QTB+HHv +QM}`K2/ +Hmbi2` K2K#2`bX
q?2`2b i?2 MmK#2` /2MbBiv Q7 ;HtB2b +M +?M;2 b `2bmHi Q7 K2`;2`bi?2 bi2HH` Kbb /2MbBiv Bb MQi BKK2/Bi2Hv z2+i2/ #v bm+? T`Q+2bb2b B7 r2
B;MQ`2 i?2 #mBH/@mT Q7 A*G M/ bi2HH` Kbb BM i?2 +2Mi`H ;HtB2b- #2+mb2
i?2b2 +QKTQM2Mib `2 MQi BM+Hm/2/ BM i?2b2 T`Q}H2bX 6B;m`2 8X3 b?Qrb i?2
`/BH /Bbi`B#miBQM Q7 bi2HH` Kbb BM i?2 2Mb2K#H2 +Hmbi2`X _/BH /BbiM+2b
`2 MQ`KHBb2/ #v i?2 +Hmbi2`bǶ b+H2 `/BB R200 X "H+F /i TQBMib ;Bp2 i?2
#+F;`QmM/@bm#i`+i2/ UBX2X #Hm2 KBMmb `2/V +Hmbi2` bi2HH` Kbb /Bbi`B#miBQMX
1``Q`b `2 SQBbbQM bKTHBM; 2``Q`b- +QKT`2/ iQ r?B+? i?2 bi2HH` Kbb 2``Q`b
Q7 BM/BpB/mH ;HtB2b +M #2 B;MQ`2/X h?2 Tm`TH2 TQBMib b?Qr i?2 MmK#2`b Q7
bT2+i`Qb+QTB+HHv +QM}`K2/ K2K#2` ;HtB2bX h?2 bT2+i`Qb+QTB+ +QKTH2i2M2bb
BM i2`Kb Q7 iQiH bi2HH` Kbb Bb H`;2` i?M 8yW- M/ /Q2b MQi bB;MB}+MiHv /2@
T2M/ QM `/BH /BbiM+2 U+7X 6B;X 8XeVX ai2HH` Kbb /Bbi`B#miBQMb 7Q` BM/BpB/mH
+Hmbi2`b `2 T`2b2Mi2/ BM 6B;bX 8XN 8XRyX
q2 }i T`QD2+i2/ L6q T`Q}H2 iQ i?2 #H+F /i TQBMib- KBMBKBxBM; i?2 χ2
pHm2 M/ mbBM; i?2 `2@r2B;?i2/ +2Mi`2b Q7 i?2 k. MMmHmb@b?T2/ #BMbX h?2
#2bi }iiBM; 7mM+iBQM ;Bp2b `2bQM#H2 }i iQ i?2 /i Ub22 i?2 `2/m+2/ χ2 pHm2
8X9X _1alGha L. *PJS_AaPL h GPq@z
RRR
6B;m`2 8XN, ai2HH` Kbb /2MbBiv /Bbi`B#miBQM Q7 i?2 BM/BpB/mH +Hmbi2`bX "H+F TQBMib rBi?
+Q``2bTQM/BM; SQBbbQM bKTHBM; 2``Q`b `2 Qm` #2bi 2biBKi2 7Q` i?2 +Hmbi2` bi2HH` Kbb /Bb@
i`B#miBQMX h?2 #2bi }iiBM; T`QD2+i2/ L6q 7mM+iBQMb `2 HbQ b?QrMX h?2 Tm`TH2 TQBMib ;Bp2
i?2 bi2HH` Kbb /Bbi`B#miBQM BM bT2+i`Qb+QTB+HHv +QM}`K2/ +Hmbi2` K2K#2`bX
*>Sh1_ 8X h>1 .Aah_A"lhAPL P6 ah1GG_ Jaa AL :Gsu
RRk
*Glah1_a h z ∼ 0.15
6B;m`2 8XRy, 6B;m`2 8XN +QMiBMm2/XXX
BM h#H2 8X9VX h?2 #2bi }iiBM; +QM+2Mi`iBQM T`K2i2` 7Q` i?2 2Mb2K#H2 Bb c =
1.92+0.19
−0.14 X 1``Q`b QM i?Bb T`K2i2` `2 K`;BMHBx2/ Qp2` i?2 MQ`KHBbiBQMM/ i?2 #2bi }iiBM; L6q T`Q}H2 Bb b?QrM BM 6B;X 8X3X q?2M r2 }i T`QD2+i2/
L6q T`Q}H2 iQ i?2 bT2+i`Qb+QTB+ /i UTm`TH2 TQBMibV r2 }M/ c = 2.21+0.19
−0.28 r?B+? ;`22b iQ rBi?BM R@σ rBi? i?2 T?QiQK2i`B+ 2biBKi2X h?2 MQ`KHBbiBQM
Bb /Bz2`2Mi #v yXkk /2tX h?2 7+i i?i i?2 #+F;`QmM/ bm#i`+iBQM K2i?Q/
vB2H/b i?2 bK2 +QM+2Mi`iBQM T`K2i2` Bb bi`QM; `Q#mbiM2bb i2biX
q2 HbQ }i T`QD2+i2/ L6q T`Q}H2b iQ i?2 bi2HH` Kbb /Bbi`B#miBQMb 7Q` i?2
BM/BpB/mH +Hmbi2`b U6B;bX 8XN 8XRyV- M/ T`2b2Mi i?2 #2bi@}iiBM; +QM+2Mi`iBQM
T`K2i2`b BM h#H2 8X9X Hi?Qm;? i?2 mM+2`iBMiB2b QM i?2 +QM+2Mi`iBQM
T`K2i2`b `2 `2HiBp2Hv H`;2 /m2 iQ HQr2` MmK#2` biiBbiB+b +QKT`2/ iQ i?2
2Mb2K#H2- i?2 b+ii2` #2ir22M i?2 BM/BpB/mH K2bm`2K2Mib b22Kb iQ #2 H`;2`
i?M i?2 K2bm`2K2Mi 2``Q`bX aQK2 bQm`+2b Q7 i?Bb BMi`BMbB+ b+ii2` Kv #2
/Bz2`2Mi Q`B2MiiBQMb QM i?2 bFv- +2Mi`QB/BM; mM+2`iBMiB2b M/ /Bz2`2Mi ?HQ
8X8X h>1 1oPGoAL: ah1GG_ Jaa .Aah_A"lhAPL
RRj
Kbb bb2K#Hv ?BbiQ`B2b 7Q` i?2 +Hmbi2`bX q2 K2bm`2 i?2 BMi`BMbB+ b+ii2` BM
i?2 +QM+2Mi`iBQM T`K2i2` #v KBMBKBxBM; i?2 HQ;@HBF2HB?QQ/
− 2 HM L = 2
n
'
i=1
HM wi +
)
n (
'
ci − c2Mb2K#H2 2
i=1
wi
,
U8XjV
r?2`2 BM/2t i `mMb Qp2` i?2 Ry +Hmbi2`b BM Qm` bKTH2- M/ r?2`2 wi Bb +QK#BMiBQM Q7 biiBbiB+H mM+2`iBMiB2b QM 2+? BM/BpB/mH
K2bm`2K2Mi M/
*
2
2
:mbbBM BMi`BMbB+ b+ii2` σc,BMi - bm+? i?i wi =
σc,i
+ σc,
BMi X a22 HbQ
>Q2Fbi` 2i HX UkyRRV 7Q` +QKT`2?2MbBp2 /2b+`BTiBQM Q7 i?Bb K2i?Q/ iQ 2b@
iBKi2 i?2 BMi`BMbB+ b+ii2`X q2 }M/ M BMi`BMbB+ b+ii2` BM i?2 +QM+2Mi`iBQM
T`K2i2` Q7 σc,BMi = 0.70+0.33
−0.22 UQ` σHQ;Ry c,BMi = 0.25 ± 0.05 /2tVX
JmxxBM 2i HX UkyydV K2bm`2 i?2 E@#M/ HmKBMQbBiv T`Q}H2b 7Q` bi+F
Q7 R8 *LP*R Uu22 2i HX RNNeV +Hmbi2`b BM i?2 `2/b?B7i `M;2 0.2 < z < 0.5X
AM i?Bb `2/b?B7i `M;2- i?2 HmKBMQbBiv BM i?2 E@#M/ Bb 2tT2+i2/ iQ #2 ;QQ/
T`Qtv 7Q` bi2HH` KbbX h?2v }M/ +QM+2Mi`iBQM Q7 i?2 HmKBMQbBiv /2MbBiv
Q7 c = 4.28 ± 0.70X Hi?Qm;? i?2 `2/b?B7i `M;2 Q7 i?2 *LP*R bKTH2 Bb
/Bz2`2Mi 7`QK Qm`b- i?2v `2 TT`QtBKi2 T`Q;2MBiQ`b Q7 i?2 bKTH2 r2 bim/v
Ub22 6B;X 8XRVX
AM p/"R9 r2 T`2b2Mi i?2 bi2HH` Kbb /2MbBiv /Bbi`B#miBQM Q7 i?2 :*Gaa
+Hmbi2` bKTH2 i z ∼ 1- M/ }M/ `2HiBp2Hv ?B;? +QM+2Mi`iBQM Q7 c =
7.12+1.53
−0.99 X h?2b2 bvbi2Kb `2 HBF2Hv iQ ;`Qr BMiQ +Hmbi2`b i?i `2 QMHv 7+iQ`
Q7 ∼ 2 H2bb KbbBp2 i?M i?2 HQr@z +Hmbi2`b bim/B2/ BM i?Bb TT2`X *QKT`@
BbQMb KQM; i?2b2 `2bmHib BM/B+i2 i?i i?2 bi2HH` Kbb /Bbi`B#miBQM BM +Hmbi2`b
2pQHp2b bB;MB}+MiHv Qp2` +QbKB+ iBK2X
q2 ?p2 T2`7Q`K2/ K2bm`2K2Mi Q7 i?2 bi2HH` Kbb /Bbi`B#miBQM BM +Hmbi2`b
BM i?2 HQ+H U0.07 < z < 0.26V lMBp2`b2X AM 6B;X 8XRR r2 +QKT`2 i?Bb K2@
bm`2K2Mi iQ `2bmHib 7`QK i?2 :*Gaa M/ *LP*R bm`p2vb- r?B+? bm;;2bib
i?i i?2 bi2HH` Kbb /Bbi`B#miBQM 2pQHp2b bB;MB}+MiHv #2ir22M z ∼ 1 M/ i?2
HQ+H lMBp2`b2X
q2 MQi2 i?i i?2 +QM+2Mi`iBQM T`K2i2`b r2 `2 +QKT`BM; `2 /2}M2/
rBi? `2bT2+i iQ i?2 +Hmbi2` b+H2 `/BB R200 - r?B+? +Q``2bTQM/ iQ T?vbB+H
bBx2 Q7 ∼ 1 JT+ 7Q` :*Gaa- M/ R200 ∼ k JT+ 7Q` i?2 HQr@z bKTH2X A7 i?2
+`BiB+H /2MbBiv ρ+`Bi - rBi? `2bT2+i iQ r?B+? i?2 b+H2 `/BB `2 /2}M2/- 2pQHp2bi?2 K2bm`2/ +QM+2Mi`iBQMb rBHH +?M;2- 2p2M B7 i?2 T?vbB+H T`Q}H2 `2KBMb
+QMbiMi Qp2` iBK2 UTb2m/Q@2pQHmiBQM- 2X;X .B2K2` 2i HX kyRjVX LQM2i?2H2bb+Hmbi2`b BM i?Bb Kbb `2;BK2 U1014 < M200 /J" < 1015 V `2 2tT2+i2/ iQ ;`Qr #v
7+iQ` Q7 ∼ 3.0 #2ir22M z = 1 M/ z = 0 Uq2+?bH2` 2i HX kyykc aT`BM;2H 2i HX
kyy8VX AM 6B;X 8XRk r2 +QKT`2 i?2 +Hmbi2` bi2HH` Kbb /2MbBiv T`Q}H2b i i?2
*>Sh1_ 8X h>1 .Aah_A"lhAPL P6 ah1GG_ Jaa AL :Gsu
RR9
*Glah1_a h z ∼ 0.15
6B;m`2 8XRR, "H+F HBM2b, h?2 L6q +QM+2Mi`iBQM BM i?2 bKTH2 Q7 `2Ht2/ ?HQ2b 7`QK
.mzv 2i HX Ukyy3V b 7mM+iBQM Q7 `2/b?B7iX .Qii2/ M/ /b?2/, >HQ2b Q7 ;Bp2M Kbb
b 7mM+iBQM Q7 `2/b?B7iX aQHB/, L6q +QM+2Mi`iBQM Q7 ?HQ i?i Bb 2pQHpBM; BM Kbb- rBi?
b+ii2` ;Bp2M #v i?2 b?/2/ `2;BQMX h?2 7mHH bKTH2 7`QK .mzv 2i HX Ukyy3V ?b bHB;?iHv
HQr2` p2`;2 +QM+2Mi`iBQM- #mi H`;2` b+ii2`X "Hm2, ai2HH` Kbb /2MbBiv +QM+2Mi`iBQM
BM :*Gaa 7`QK p/"R9X Sm`TH2, E@#M/ HmKBMQbBiv /2MbBiv +QM+2Mi`iBQM BM *LP*R 7`QK
JmxxBM 2i HX UkyydVX _2/, ai2HH` Kbb /2MbBiv +QM+2Mi`iBQM 7Q` i?2 +Hmbi2`b mb2/ BM i?Bb
bim/vX h?2 /b?2/ 2``Q` #` QM i?2 K2M `2T`2b2Mib i?2 #2bi@}i HQ;@MQ`KH BMi`BMbB+ b+ii2`
QM i?2 +QM+2Mi`iBQMX _2/ TQBMib ;Bp2 K2bm`2/ +QM+2Mi`iBQMb 7Q` i?2 BM/BpB/mH +Hmbi2`b BM
J1L2*af***SX
bK2 T?vbB+H b+H2- bQ i?i r2 +B`+mKp2Mi i?2 2z2+i Q7 Tb2m/Q@2pQHmiBQM- M/
bim/v /B`2+iHv ?Qr i?2 T`Q}H2b Q7 i?2b2 +Hmbi2`b 2pQHp2 bBM+2 z ∼ 1X :Bp2M i?i
i?2 +m``2Mi HQr@z bKTH2 Bb 7+iQ` ∼ 1.7 KQ`2 KbbBp2 i?M i?2 /2b+2M/Mib
7`QK :*Gaa `2 2tT2+i2/ iQ #2 Ub22 6B;X 8XRV- M/ i?2 `2HiBQM #2ir22M
0.71±0.04
bi2HH` Kbb M/ ?HQ Kbb M" ∝ M500
7`QK GBM 2i HX UkyRkV UHbQ b22
p/"R9 U6B;X8VV- r2 KmHiBTHB2/ i?2 HQr@z T`Q}H2 #v 7+iQ` Q7 yXd iQ #2ii2`
`2b2K#H2 i?2 2tT2+i2/ /2b+2M/Mi bKTH2 7`QK :*GaaX h?2 2t+i pHm2 Q7
i?Bb +Q``2+iBQM 7+iQ` /Q2b MQi ?p2 bB;MB}+Mi BKT+i QM i?2 BMi2`T`2iiBQMX
6B;m`2 8XRk bm;;2bib i?i- Hi?Qm;? i?2 iQiH bi2HH` Kbb Q7 i?2b2 +Hmbi2`b
;`Qrb bm#biMiBHHv bBM+2 z ∼ 1- i?2 bi2HH` Kbb /2MbBiv BM i?2 +Hmbi2` +Q`2 U_
I yXk JT+V /`QTb bB;MB}+MiHv /m`BM; i?2 bK2 T2`BQ/X aBM+2 BM Qm` MHvbBb
r2 /B/ MQi iF2 ++QmMi Q7 i?2 A*G +QKTQM2Mi- M/ 2t+Hm/2/ i?2 "*:b 7`QK
i?2 }i- i?2 #mBH/@mT Q7 bi2HH` Kbb BM i?2b2 +QKTQM2Mib Kv #2 `2bTQMbB#H2
7Q` i?2 Q#b2`p2/ 2pQHmiBQMX
JbbBp2 ;HtB2b +HQb2 iQ i?2 "*: `2 2tT2+i2/ iQ K2`;2 rBi? i?2 +2Mi`H
;Htv QM `2HiBp2Hv b?Q`i iBK2@b+H2- M/ THv /QKBMMi `QH2 BM i?2 #mBH/@
8X8X h>1 1oPGoAL: ah1GG_ Jaa .Aah_A"lhAPL
RR8
6B;m`2 8XRk, "H+F bQHB/, h?2 p2`;2 bi2HH` Kbb /2MbBiv T`Q}H2 Q7 :*Gaa- BM T?vbB+H
mMBibX "H+F /b?2/, h?2 bi2HH` Kbb /2MbBiv T`Q}H2 i HQr@z- i i?2 bK2 T?vbB+H b+H2X "Hm2
bQHB/, h?2 p2`;2 bi2HH` Kbb /2MbBiv T`Q}H2b Q7 i?2 bi`@7Q`KBM; ;HtB2b BM :*Gaa- r?B+?
Bb i?2 KQbi `2+2MiHv ++`2i2/ TQTmHiBQM Q7 ;HtB2bX a?/2/ `2;BQMb K`F R@σ mM+2`iBMiv
`2;BQMb QM i?2 L6q T`K2i2`bX h?2 Q`M;2 `2;BQM K`Fb i?2 T`i Q7 i?2 z ∼ 1 T`Q}H2 i?i
Bb BM 2t+2bb Q7 i?2 z ∼ 0.15 T`Q}H2X
mT Q7 bi2HH` Kbb BM i?2 "*: U2X;X "m`F2 *QHHBMb kyRjc GB/KM 2i HX kyRjVX
a2p2`H bim/B2b ?p2 7QmM/ i?i i?2 bi2HH` Kbb BM +2Mi`H ;HtB2b Bb `2Hi2/
iQ i?2 ?HQ Kbb Q7 i?2 bvbi2K U2X;X GB/KM 2i HX kyRkc "2?`QQxB 2i HX kyRj0.5
p/"R9V- rBi? `2HiBQM i?i Bb T`QtBKi2Hv M"*: ∝ M200
BM i?Bb Kbb M/
`2/b?B7i `2;BK2X A7 r2 BMi2;`i2 i?2 Kbb 2M+HQb2/ BM i?2 z $ 1 T`Q}H2 i?i Bb
BM 2t+2bb Q7 i?2 z $ 0.15 T`Q}H2 UBX2X- i?2 Q`M;2 `2;BQM BM 6B;X 8XRkV- r2 }M/
i?i i?Bb Bb QM p2`;2 #Qmi 2 × 1011 M" T2` +Hmbi2`X :Bp2M i?i i?2 "*:b
BM i?2 :*Gaa +Hmbi2`b ?p2 ivTB+H bi2HH` Kbb2b Q7 M","*: $ 3 × 1011 M"
Up/"R9- h#H2 kV- M/ i?2 ?HQ Kbb2b `2 2tT2+i2/ iQ ;`Qr #v 7+iQ` Q7 ∼ 3
bBM+2 z ∼ 1- r2 }M/ i?i i?2 ;`Qri? Q7 i?2 bi2HH` Kbb BM i?2 +2Mi`H ;HtB2b
+M `2/BHv 2tTHBM i?2 /2+`2bBM; T`Q}H2X
6m`i?2`KQ`2- /vMKB+H BMi2`+iBQMb #2ir22M ;HtB2b BM i?2 +Hmbi2` Kv
H2/ iQ #mBH/@mT Q7 i?2 A*G +QKTQM2MiX :QMxH2x 2i HX UkyRjV K2bm`2 i?2
+QMi`B#miBQM Q7 i?2 "*:YA*G +QKTQM2Mi iQ i?2 iQiH HmKBMQbBiv Q7 bKTH2
Q7 ;Htv ;`QmTb M/ +Hmbi2`b i z ∼ 0.1 U7Q` 2biBKi2b Q7 i?2 A*G +QKTQM2MiHbQ b22 wB#2iiB 2i HX kyy8c aM/ 2i HX kyRRVX :QMxH2x 2i HX UkyRjV }M/ i?i
*>Sh1_ 8X h>1 .Aah_A"lhAPL P6 ah1GG_ Jaa AL :Gsu
RRe
*Glah1_a h z ∼ 0.15
i?2 "*:YA*G 7`+iBQM Bb /2+`2bBM; 7mM+iBQM Q7 bvbi2K Kbb UQ` p2HQ+Biv
/BbT2`bBQMV- M/ Bb #Qmi jyW Q7 i?2 iQiH HmKBMQbBiv rBi?BM R500 7Q` bvbi2Kb
rBi? σ = 1000 FK b−R X `QmM/ z ∼ 1- i?2 bi2HH` Kbb 7`+iBQM BM i?2 A*G
Bb 2tT2+i2/ iQ #2 bB;MB}+MiHv HQr2` U"m`F2 2i HX kyRkV Ui?Bb i`2M/ Bb HbQ
`2T`Q/m+2/ rBi? b2KB@MHviB+ KQ/2Hb- *QMiBMB 2i HX UkyRjVVX h?2 /2p2HQTK2Mi
Q7 M A*G +QKTQM2Mi Kv i?2`27Q`2 HbQ +QMi`B#mi2 iQ M 2pQHmiBQM BM i?2
Q#b2`p2/ bi2HH` Kbb /2MbBiv T`Q}H2X
am#biMiBH ;`Qri? QMiQ i?2 QmibFB`ib Q7 i?2 +Hmbi2`b Bb HbQ `2[mB`2/ iQ
2tTHBM i?2 Q#b2`p2/ 2pQHmiBQM bBM+2 z ∼ 1X AM 6B;X 8XRk r2 b?Qr i?2 bi2HH`
Kbb /2MbBiv T`Q}H2 Q7 i?2 bi`@7Q`KBM; ;HtB2b BM :*Gaa- r?B+? `2 2t@
T2+i2/ iQ #2 ++`2i2/ 7`QK i?2 }2H/ `2HiBp2Hv `2+2MiHv +QKT`2/ iQ i?2 KQ`2
+QM+2Mi`i2/ [mB2b+2Mi TQTmHiBQM Up/"R9VX :Bp2M i?i i?Bb TQTmHiBQM Bb /2@
b+`B#2/ #v `/BH /Bbi`B#miBQM i?i Bb bBKBH` BM b?T2 iQ i?2 iQiH bi2HH`
Kbb /Bbi`B#miBQM i HQr2` `2/b?B7i- +QMiBMmiBQM Q7 bi`@7Q`KiBQM M/ +@
+`2iBQM i i?2b2 HQ+iBQMb +QmH/ 2tTHBM i?2 bi2HH` Kbb /2MbBiv 2pQHmiBQM QM
i?2 QmibFB`ibX
lM/2` i?2 bbmKTiBQM i?i ;HtB2b TQTmHi2 bm#@?HQ2b M/ i?i i?2b2
bvbi2Kb `2 ++`2i2/ QMiQ i?2 +Hmbi2`b bBM+2 z = 1- Bi Bb 2tT2+i2/ i?i /`F@
Kii2` ?HQ2b HbQ ++`2i2 Kii2` QMiQ i?2 QmibFB`ibX h?Bb 2z2+i Bb BM/22/
Q#b2`p2/ BM L@#Q/v bBKmHiBQMb U.mzv 2i HX kyy3V- B7 i?2b2 bBKmHiBQMb `2
+QKT`2/ QM i?2 bK2 T?vbB+H b+H2X h?2 bm#biMiBH /Bz2`2M+2 #2ir22M i?2
+QM+2Mi`iBQM bBKmHi2/ rBi? L@#Q/v +Q/2b M/ i?2 Q#b2`p2/ /Bbi`B#miBQM Q7
bi2HH` Kbb Kv #2 `2+QM+BH2/ #v KQ/B7vBM; i?2 bi2HH` Kbb 7`+iBQM Q7 BM@
7HHBM; ?HQ2b BM b2KB@MHviB+ KQ/2HbX h?2 Q#b2`p2/ 2pQHmiBQM Q7 i?2 bi2HH`
Kbb /Bbi`B#miBQM Bb HbQ bi`BM;2Mi i2bi 7Q` 2tBbiBM; M/ 7mim`2 ?v/`Q/vMKB+H
bBKmHiBQMb U2X;X a+?v2 2i HX kyRyc *2M kyR9VX
:Bp2M i?2 bB;MB}+Mi 2pQHmiBQM i?i Bb Q#b2`p2/ #2ir22M i?2 :*Gaa bKTH2
M/ i?2 HQr@z /2b+2M/Mi bKTH2- r2 ?p2 iQ +QMbB/2` i?2 TQbbB#BHBiv i?i i?Bb
BM72``2/ 2pQHmiBQM Bb +mb2/ #v i?2 rv i?2b2 bKTH2b `2 b2H2+i2/X aBM+2 Bi
Bb BKTQbbB#H2 iQ b2H2+i +Hmbi2` bKTH2 #b2/ QM ?HQ Kbb- /Bz2`2Mi b2H2+iBQM
K2i?Q/b Us@`v- aw@- Q` ;Htv b2H2+iBQMbV TQi2MiBHHv `2bmHi BM #Bb2/ bKTH2
Q7 +Hmbi2`bX
h?2 :*Gaa bKTH2 +QMbBbib Q7 Ry +Hmbi2`b /`rM 7`QK i?2 9k /2;`22
aTBix2` /TiiBQM Q7 i?2 _2/@b2[m2M+2 *Hmbi2` am`p2v UaT_*a- JmxxBM
2i HX kyyNc qBHbQM 2i HX kyyNc .2K`+Q 2i HX kyRyVX *Hmbi2`b BM aT_*a
r2`2 /2i2+i2/ mbBM; i?2 `2/@b2[m2M+2 /2i2+iBQM K2i?Q/ /2p2HQT2/ #v :H//2`b
u22 UkyyyV- M/ 2tTM/2/ QM BM JmxxBM 2i HX Ukyy3VX AM bmKK`v- i?Bb
/2i2+iBQM K2i?Q/ rb TTHB2/ iQ i?2 QTiB+HYAM7`_2/ /i BM aT_*a- bQ
i?i i?2 z $ −3.6µK +QHQm` rb mb2/ iQ /2i2+i +Hmbi2`b i `2/b?B7ib z > 0.8 7i2`
+QMpQHpBM; i?2 ;Htv MmK#2` /2MbBiv KTb rBi? M 2tTQM2MiBH F2`M2H Ub22
8X8X h>1 1oPGoAL: ah1GG_ Jaa .Aah_A"lhAPL
RRd
:H//2`b u22 kyyy- 1[X jVX _B+?M2bb2b r2`2 K2bm`2/ BM }t2/ T2`im`2b rBi?
`/Bmb Q7 8yy FT+- 7i2` r?B+? i?2 `B+?2bi bvbi2Kb r2`2 +QMbB/2`2/ 7Q` 7QHHQr@
mT T?QiQK2i`v M/ bT2+i`Qb+QTvX JmxxBM 2i HX UkyRkV /2b+`B#2b ?Qr i?Bb
:*Gaa 7QHHQr@mT bKTH2 rb /`rM 7`QK i?2 `B+?2bi bvbi2Kb 7i2` QTiBKBbBM;
i?2 `2/b?B7i #b2HBM2 M/ 2Mbm`BM; bT`2/ BM _ 7Q` Q#b2`piBQMH +QMp2MB2M+2X
h?2 }t2/ T2`im`2 Q7 8yy FT+ KF2b i?2 `B+?M2bb b2H2+iBQM BM/2T2M/2Mi QM
+QM+2Mi`iBQMX >Qr2p2`- r2 ?p2 iQ 2tTHQ`2 i?2 TQbbB#BHBiv i?i `B+?M2bb M/
+QM+2Mi`iBQM `2 +Q``2Hi2/ [mMiBiB2b bm+? i?i `B+?M2bb b2H2+iBQM BM/B`2+iHv
#Bb2b Qm` bKTH2 iQr`/b ?B;?fHQr +QM+2Mi`iBQMbX
h?2 biiBbiB+b BM i?2 :*Gaa bKTH2 `2 BMbm{+B2Mi iQ bim/v TQbbB#H2
i`2M/ #2ir22M `B+?M2bb M/ +QM+2Mi`iBQM i z ∼ 1X h?2`27Q`2 r2 2tKBM2
i?Bb mbBM; i?2 HQr@z bKTH2- 7Q` r?B+? r2 `2 #H2 iQ K2bm`2 +QM+2Mi`iBQM
7Q` 2+? BM/BpB/mH +Hmbi2`X Hi?Qm;? i?2 +m``2Mi bKTH2 Q7 Ry +Hmbi2`b Bb
HBKBi2/- r2 }M/ ?BMi Q7 +Q``2HiBQM #2ir22M `B+?M2bb UK2bm`2/ #v +QmMiBM;
HH ;HtB2b KQ`2 KbbBp2 i?M M" > 1010 J" rBi?BM `/Bmb Q7 1.2 R200 #+F;`QmM/ bm#i`+i2/V M/ +QM+2Mi`iBQM- rBi? aT2`KM `MF +Q2{+B2Mi
Q7 ρ = −0.62X h?Bb M2;iBp2 +Q``2HiBQM Kv MQi +QK2 b bm`T`Bb2 ;Bp2M
i?2 FMQrM Kbb@+QM+2Mi`iBQM `2HiBQM U2X;X *QK2`7Q`/ Li`DM kyydc
JM/2H#mK 2i HX kyy3V- M/ Kbb@`B+?M2bb `2HiBQM U2X;X M/`2QM >m`M
kyRyc "m2` 2i HX kyRkVX aT2+B}+HHv- i?2 irQ `B+?2bi bvbi2Kb UkR9k M/
kykNV TT2` iQ ?p2 i?2 HQr2bi +QM+2Mi`iBQMbX h?2`27Q`2- B7 i?2 bK2 Bb i`m2
i ?B;?2` `2/b?B7i- i?2 +m``2Mi bKTH2 /Q2b MQi bmTTQ`i i?2 B/2 i?i `B+?M2bb
b2H2+iBQM rQmH/ `2bmHi BM +Hmbi2` bKTH2 rBi? bi2HH` Kbb /Bbi`B#miBQMb i?i
`2 ?B;?Hv +QM+2Mi`i2/X q2 rBHH 2tTM/ i?2 bKTH2 iQ jy@9y +Hmbi2`b- r?B+?
rBHH HHQr mb iQ bim/v TQbbB#H2 +Q``2HiBQM #2ir22M `B+?M2bb M/ +QM+2Mi`iBQM
7Q` +Hmbi2`b BM bBKBH` U/vMKB+HV Kbb #BMbX
AM i?Bb i?2bBb- r2 T`Q+22/ iQ i2bi TQi2MiBH #Bb BM i?2 b2H2+iBQM Q7 :*Gaa
#v +QKT`BM; i?2 /vMKB+H Kbb2b Q7 i?2 :*Gaa bKTH2 iQ i?2 hBMF2` 2i HX
Ukyy3V +mKmHiBp2 ?HQ Kbb 7mM+iBQM #b2/ QM qJSd +QbKQHQ;v- r?B+?
r2 /Q BM 6B;X 8XRjX :Bp2M i?2 2z2+iBp2 `2 Q7 9RXN b[m`2 /2;`22b r2 2biBKi2
i?2 2z2+iBp2 pQHmK2 Q7 i?2 aT_*a bm`p2v U7`QK r?B+? :*Gaa rb b2H2+i2/V
BM i?2 `2/b?B7i bHB+2 0.86 < z < 1.34 M/ MQ`KHBb2 i?2 +mKmHiBp2 MmK#2`
/2MbBiv Q7 i?2 :*Gaa +Hmbi2`b Qp2` i?Bb pQHmK2X i i?2 ?B;?@Kbb 2M/ Q7
i?2 /Bbi`B#miBQM r2 2tT2+i SQBbbQM b+ii2`- M/ i?2`2 Bb b+ii2` BM i?2 Kbb@
`B+?M2bb `2HiBQM iQ #2 +QMbB/2`2/X h?2 i2M :*Gaa bvbi2Kb `2 i?2`27Q`2
MQi M2+2bb`BHv i?2 KQbi KbbBp2 QM2bX "b2/ QM i?Bb +QKT`BbQM- r2 2biBKi2
i?i BM :*Gaa r2 T`Q#2 `QmM/ RyW Q7 i?2 +Hmbi2`b BM i?2 aT_*a pQHmK2
`QmM/ i?2 K2/BM Kbb Q7 i?2 :*Gaa bKTH2 UM200 $ 1014.3 J" VX
q2 +QMbB/2` i?2 TQbbB#BHBiv i?i i?2 +Hmbi2`b T`Q#2/ #v :*Gaa `2 i?2
RyW rBi? i?2 ?B;?2bi +QM+2Mi`iBQMb BM i?2 bBKmHiBQMX 6B;m`2 8XR9 b?Qrb
i?2 :*Gaa 2Mb2K#H2 p2`;2 bi2HH` Kbb +QM+2Mi`iBQM rBi? :mbbBM
T`Q##BHBiv /Bbi`B#miBQM `QmM/ c = 7.12X h?2 .mzv 2i HX Ukyy3V HQ;@MQ`KH
+QM+2Mi`iBQM /Bbi`B#miBQM 7Q` +Hmbi2`@bBx2/ ?HQ2b BM L@#Q/v bBKmHiBQMb `2
*>Sh1_ 8X h>1 .Aah_A"lhAPL P6 ah1GG_ Jaa AL :Gsu
RR3
*Glah1_a h z ∼ 0.15
6B;m`2 8XRj, "H+F bQHB/ HBM2, hBMF2` 2i HX Ukyy3V +mKmHiBp2 Kbb 7mM+iBQM i z = 1 7Q`
qJSd +QbKQHQ;vX "H+F /Qii2/ HBM2b, hBMF2` 2i HX Ukyy3V +mKmHiBp2 Kbb 7mM+iBQMb i
z = 0.86 M/ z = 1.34- r?B+? `2 i?2 `2/b?B7i HBKBib rBi?BM r?B+? i?2 :*Gaa +Hmbi2`b `2
b2H2+i2/X _2/ /b?2/ HBM2, +mKmHiBp2 Kbb 7mM+iBQM Q7 i?2 Ry :*Gaa +Hmbi2`b- MQ`KHBb2/
#v i?2 iQiH pQHmK2 Q7 aT_*aX
6B;m`2 8XR9, "H+F bQHB/ HBM2,
:*Gaa 2Mb2K#H2 p2`;2 bi2H@
H` Kbb +QM+2Mi`iBQM rBi? :mbbBM T`Q##BHBiv /Bbi`B#miBQM
`QmM/ c = 7.12X HbQ b?QrM
`2 i?2 HQ;@MQ`KH +QM+2Mi`iBQM
/Bbi`B#miBQM 7Q` +Hmbi2`b rBi? i?2
bK2 Kbb M/ `2/b?B7i b i?2
:*Gaa bKTH2 7Q` i?2 `2Ht2/
?HQ2b BM .mzv 2i HX Ukyy3V U"Hm2
/Qii2/ HBM2V- M/ i?2B` 7mHH bKTH2
U_2/ /b?2/ HBM2VX
8XeX alJJ_u L. *PL*GlaAPLa
RRN
HbQ b?QrM- #Qi? 7Q` i?2B` `2Ht2/ M/ 7mHH bKTH2 U?HQ2b r2`2 +i2;Q`Bx2/
#b2/ QM i?2 /BbiM+2 #2ir22M i?2 KQbi #QmM/ T`iB+H2 M/ i?2 +2Mi`2 Q7 Kbb
BM i?2 bBKmHiBQMVX h?2 `2Ht2/ bKTH2 ?b bHB;?iHv ?B;?2` +QM+2Mi`iBQM
Q7 c4jXjy +QKT`2/ iQ c4kX39 7Q` i?2 7mHH bKTH2- #mi ?b bKHH2` b+ii2`
Uσ(HQ;Ry c)4yXRR /2t p2`bmb yXR8 /2t 7Q` i?2 7mHH bKTH2VX q?2`2 i?2 .mzv
2i HX Ukyy3V /Bbi`B#miBQMb Qp2`HT rBi? i?2 :*Gaa T`Q##BHBiv /Bbi`B#miBQMi?2b2 irQ /Bbi`B#miBQMb `2 bBKBH`X
q2 T2`7Q`K bBKTH2 i2bi BM r?B+? r2 `M/QKHv bKTH2 Ryy +QM+2Mi`iBQMb
7`QK i?2 .mzv 2i HX Ukyy3V `2HiBQMbX q2 /Q i?Bb 7Q` Ryyy /Bz2`2Mi `2HBb@
iBQMb M/ 2+? iBK2 p2`;2 i?2 Ry KQbi +QM+2Mi`i2/ QM2bX AM QMHv jW Q7
i?2 `2HBbiBQMb r2 }M/ H`;2` p2`;2 i?M i?2 K2bm`2/ +QM+2Mi`iBQM 7`QK
:*Gaa Uc = 7.12+1.53
−0.99 V- iFBM; ++QmMi HbQ Q7 i?2 2``Q` QM i?Bb K2bm`2/
+QM+2Mi`iBQMX h?2`27Q`2- 2p2M mM/2` i?2 KQbi +QMb2`piBp2 bbmKTiBQM i?i
`B+?M2bb b2H2+iBQM Bb +QKTH2i2Hv #Bb2/ iQr`/b i?2 KQbi +QM+2Mi`i2/ ;Htv
+Hmbi2`b- i?2`2 Bb QMHv jW T`Q##BHBiv i?i r2 K2bm`2 M p2`;2 +QM+2M@
i`iBQM 7Q` :*Gaa Q7 c = 7.12+1.53
−0.99 X JQ`2Qp2`- b r2 `;m2/ BM p/"R9- i?2
K2bm`2/ +QM+2Mi`iBQM Q7 c $ 7.12 Bb HQr2` HBKBi B7 r2 BM+Hm/2 mM+2`iBMiB2b
`BbBM; 7`QK KBbHB;MK2Mib #2ir22M i?2 "*:b M/ i?2 Ǵi`m2Ǵ +Hmbi2` +2Mi`2bX
:Bp2M i?2b2 `;mK2Mib- Bi Bb mMHBF2Hv i?i #Qi? i?2 Q#b2`p2/ 2pQHmiBQM bBM+2
z ∼ 1- M/ i?2 /Bz2`2M+2 #2ir22M i?2 T`2/B+iBQMb 7`QK L@#Q/v bBKmHiBQMb
M/ Q#b2`piBQMb i i?Bb `2/b?B7i- `2 QMHv M 2z2+i Q7 i?2 rv i?2 :*Gaa
bKTH2 Bb b2H2+i2/X
AM i?Bb TT2` r2 bim/v i?2 `/BH ;Htv MmK#2` /2MbBiv M/ bi2HH` Kbb
/2MbBiv BM bKTH2 Q7 Ry ;Htv +Hmbi2`b i 0.07 < z < 0.26X h?2b2 +Hmbi2`b
`2 /`rM 7`QK i?2 JmHiB@1TQ+? L2`#v *Hmbi2` am`p2v UJ1L2*aV M/ i?2
*M/BM *Hmbi2` *QKT`BbQM S`QD2+i U***SVX TT`QtBKi2Hv jyyy K2K#2`
;HtB2b BM i?2b2 +Hmbi2`b ?p2 #22M B/2MiB}2/ #v b2p2`H bT2+i`Qb+QTB+ bm`p2vb
BM i?2 HBi2`im`2X q2 +QKTBH2/ +iHQ;m2b Q7 ugri@#M/ T?QiQK2i`v iQ 2biBKi2
T?QiQK2i`B+ `2/b?B7ib M/ bi2HH` Kbb2b 7Q` 2+? +Hmbi2` }2H/X
q2 K2bm`2 i?2 ;Htv MmK#2` /2MbBiv /Bbi`B#miBQM BM irQ UQp2`HTTBM;V
bi2HH` Kbb #BMb- M/ }M/ i?i i?2 ?B;?2` Kbb ;HtB2b UJ" > RyRy J" V
`2 +QM+2Mi`i2/ KQ`2 bi`QM;Hv Uc = 2.26+0.19
−0.19 V i?M ;HtB2b rBi? Kbb2b
J" > RyN J" Uc = 1.69+0.09
−0.10 VX h?Bb Q#b2`p2/ Kbb b2;`2;iBQM Bb 2tT2+i2/
7`QK i?2 T`Q+2bb Q7 /vMKB+H 7`B+iBQMX q2 }M/ [mHBiiBp2 ;`22K2Mi #2@
ir22M i?2b2 K2bm`2K2Mib M/ i?2 HBi2`im`2 K2bm`2K2Mib Q7 ;Htv /Bbi`B@
#miBQMb BM HQr@z +Hmbi2`bX
q2 K2bm`2 i?2 `/BH bi2HH` Kbb /2MbBiv T`Q}H2 BM irQ rvb- }M/BM; bBK@
BH` `2bmHib UrBi?BM R@σ mM+2`iBMivVX h?2 biiBbiB+H bm#i`+iBQM K2i?Q/ `2HB2b
2t+HmbBp2Hv QM i?2 T?QiQK2i`B+ BM7Q`KiBQMX 6Q` i?2 bT2+i`Qb+QTB+ TT`Q+?
*>Sh1_ 8X h>1 .Aah_A"lhAPL P6 ah1GG_ Jaa AL :Gsu
Rky
*Glah1_a h z ∼ 0.15
r2 mb2 i?2 T?QiQK2i`v QMHv iQ K2bm`2 bi2HH` Kbb2b 7Q` i?2 bT2+i`Qb+QTB+HHv
B/2MiB}2/ +Hmbi2` K2K#2`bX h?2 bi2HH` Kbb /Bbi`B#miBQM BM i?2 2Mb2K#H2 +Hmb@
i2` Bb r2HH }ii2/ #v T`QD2+i2/ L6q T`Q}H2 rBi? +QM+2Mi`iBQM c = 1.92+0.19
−0.14 X
6`QK i?2 K2bm`2/ +QM+2Mi`iBQMb 7Q` i?2 BM/BpB/mH bvbi2Kb- r2 2biBKi2 M
BMi`BMbB+ b+ii2` Q7 σc,BMi = 0.70+0.33
−0.22 UQ` σHQ;Ry c,BMi = 0.25 ± 0.05 /2tVX aQK2
bQm`+2b i?i Kv +QMi`B#mi2 iQ i?Bb BMi`BMbB+ b+ii2` `2 /Bz2`2Mi Q`B2MiiBQMb
QM i?2 bFv- +2Mi`QB/BM; mM+2`iBMiB2b M/ /Bz2`2Mi ?HQ Kbb bb2K#Hv ?BbiQ`B2b
7Q` i?2 +Hmbi2`bX
h?2 +Hmbi2` bKTH2 r2 bim/v Bb +HQb2 BM ?HQ Kbb iQ i?2 HBF2Hv /2b+2M/Mi
TQTmHiBQM Q7 i?2 z ∼ 1 :*Gaa +Hmbi2` bKTH2 Up/"R9V- 7Q` r?B+? bi2HH`
Kbb +QM+2Mi`iBQM Q7 c = 7.12+1.53
−0.99 rb 2biBKi2/X +QKT`BbQM rBi? i?2b2
K2bm`2K2Mib bm;;2bib i?i i?2`2 Bb bB;MB}+Mi 2pQHmiBQM BM i?2 bi2HH` Kbb
/2MbBiv /Bbi`B#miBQM bBM+2 z ∼ 1X q2 +QKT`2 i?2 bi2HH` Kbb /2MbBiv /Bbi`B@
#miBQMb #2ir22M i?2 irQ 2TQ+?b QM i?2 bK2 T?vbB+H b+H2- b?QrBM; i?i i?2
bi2HH` Kbb /2MbBiv BM i?2 +Hmbi2` +Q`2b U_IyXk JT+V ?b iQ /2+`2b2 bBM+2
z ∼ 1X q2 `;m2 i?i i?Bb Kv #2 `2Hi2/ iQ i?2 #mBH/@mT Q7 i?2 A*GY"*:
+QKTQM2Mi Qp2` +QbKB+ iBK2X
#mBH/@mT Q7 bi2HH` Kbb QMiQ i?2 QmibFB`ib U_=yXj JT+V Bb 7m`i?2` `2@
[mB`2/ iQ Ki+? i?2 Q#b2`p2/ bi2HH` Kbb /Bbi`B#miBQM BM i?2 /2b+2M/Mi TQT@
mHiBQMX :Bp2M i?i i?2 /`F Kii2` ?HQ2b BM L@#Q/v bBKmHiBQMb `2 HbQ
7QmM/ iQ ++`2i2 Kii2` QMiQ i?2 Qmi2` T`ib- +QKT`BbQM #2ir22M Q#b2`p@
iBQMb M/ bBKmHiBQM ?b i?2 TQi2MiBH iQ +QMbi`BM i?2 bi2HH` Kbb 7`+iBQM Q7
?HQ2b i?i `2 #2BM; ++`2i2/ #v i?2 +Hmbi2`bX
"b2/ QM Q#b2`piBQMb K/2 rBi? i?2 Ab+ L2riQM h2H2b+QT2 i?`Qm;? T`Q;`K
A.b ARyLyye- ARySyy8- ARy"Lyyj- ARy"Syy8- ARRLyyN- ARRSyRjX q2
i?MF JHBM o2HM/2`- 1KK :`Q+mii- G`b EQ2Mb M/ *i?2`BM2 >2vKMb
7Q` ?2HT BM +[mB`BM; i?2 /iX h?2 Ab+ L2riQM h2H2b+QT2 Bb QT2`i2/ QM i?2
BbHM/ Q7 G SHK #v i?2 Ab+ L2riQM :`QmT BM i?2 aTMBb? P#b2`piQ`BQ
/2H _Q[m2 /2 HQb Jm+?+?Qb Q7 i?2 AMbiBimiQ /2 bi`Q7őbB+ /2 *M`BbX
q2 +QKT`2 i?2 aJ6 Q7 ;HtB2b BM i?2 *PaJPa }2H/- b 2biBKi2/ mbBM;
T?QiQK2i`v BM i?2 ugri@#M/b- rBi? i?2 aJ6 Q7 ;HtB2b BM i?2 Qmi2`KQbi
`2b Q7 i?2 +Hmbi2` }2H/bX aBM+2 i?2 /BbiM+2 iQ i?2 +Hmbi2` +2Mi`2 Bb H`;2`
i?M i?2 pB`BH `/Bmb UQ` R200 V- i?2 +Hmbi2` Bb 2tT2+i2/ iQ QMHv #2 K`;BMHHv
Qp2`@/2Mb2 +QKT`2/ iQ i?2 }2H/ BM i?i `2;BK2X h?mb r2 mb2 i?Bb +QKT`BbQM
b +QMbBbi2M+v +?2+F #2ir22M i?2 /Bz2`2Mi bm`p2vb M/ }Hi2` b2ibX
8XX *PLaAah1L*u *>1*Ea
RkR
6B;m`2 8XR8, h?2 aJ6 Q7 e88 UiQTV M/ R3j8 U#QiiQKV BM irQ `/BH #BMbX G27i, h?2
+Hmbi2` BMM2` T`i U_IR200 VX _B;?i, i?2 Qmi2` T`i 1.5R200 < _ < 1.7R200 X h?2 2tT2+i2/
#+F;`QmM/ U}2H/V +QmMib 7`QK i?2 *PaJPa bm`p2v `2 BM/B+i2/ BM `2/- M/ i?2 #H+F TQBMib
`2 i?2 #+F;`QmM/ bm#i`+i2/ pHm2bX h?2 Qmi2` `/BH #BM b?Qrb QMHv KBH/ Qp2`@/2MbBiv Q7
+QmMib +QKT`2/ iQ i?2 }2H/ pHm2bX
*>Sh1_ 8X h>1 .Aah_A"lhAPL P6 ah1GG_ Jaa AL :Gsu
Rkk
*Glah1_a h z ∼ 0.15
q2 Q#iBM i?2 bi2HH` Kbb2b 7`QK i?2 a1.@}iiBM; +Q/2 6ah- r?2`2 r2
}t i?2 `2/b?B7i iQ i?2 K2/BM `2/b?B7i Q7 i?2 +Hmbi2`X h?Bb Bb i?mb MQ T`QT2`
}2H/ aJ6- bBM+2 HH /BbiM+2 KQ/mHB `2 2[mH iQ i?2 +Hmbi2`bǶX >Qr2p2`- mTQM
bm#i`+iBM; i?2 *PaJPa }2H/ pHm2 7`QK i?2 +Hmbi2`@}2H/ +QmMib- r2 Q#iBM
i?2 bi2HH` Kbb 7mM+iBQM BM i?Bb Qmi2` `/BH #BM Q7 i?2 +Hmbi2`X h?2 T?QiQK2i`B+
/i Q7 i?2 *PaJPa }2H/ Bb bm#biMiBHHv U∼ R@k K;bV /22T2` i?M Qm`
+Hmbi2` /i- H2/BM; iQ /Bz2`2Mi bi2HH` Kbb +QKTH2i2M2bb HBKBi Ub22 i?2
/Bz2`2M+2 BM i?2 /`QT BM ;Htv +QmMib i i?2 HQr@Kbb 2M/ Q7 i?2 aJ6 7Q` i?2
/Bz2`2Mi bm`p2vbVX 6Q` i?2 rQ`F T`2b2Mi2/ BM i?Bb TT2`- i?2 BM+QKTH2i2M2bb
BM i?i `2;BK2 /Q2b MQi bB;MB}+MiHv z2+i i?2 bi2HH` Kbb /Bbi`B#miBQM UMQ`
i?2 MmK#2` /2MbBiv /Bbi`B#miBQM 7Q` bQm`+2b rBi? bi2HH` Kbb 2t+22/BM; 109 VX
6Q` i?2 K2bm`2K2Mi Q7 i?2 +Hmbi2` ;Htv bi2HH` Kbb 7mM+iBQM BM i?Bb +Hmbi2`
bKTH2 UpM /2` "m`; 2i HX- BM T`2TV- r2 rBHH T2`7Q`K b2`B2b Q7 bBKmHiBQMb
iQ bb2bb M/ +Q``2+i 7Q` i?2 bi2HH` Kbb BM+QKTH2i2M2bb i HQr2` Kbb2bX
*?Ti2`
e
h?2 lo ;Htv GmKBMQbBiv
6mM+iBQM i z4j@8 7`QK i?2
*6>h G2;+v am`p2v .22T
}2H/b
q2 K2bm`2 M/ bim/v i?2 2pQHmiBQM Q7 i?2 lo ;Htv GmKBMQbBiv 6mM+iBQM
UG6V i z 4j@8 7`QK i?2 H`;2bi ?B;?@`2/b?B7i bm`p2v iQ /i2- i?2 .22T T`i Q7
i?2 *6>h G2;+v am`p2vX q2 HbQ ;Bp2 ++m`i2 2biBKi2b Q7 i?2 a6_ /2MbBiv
i i?2b2 `2/b?B7ibX q2 +QMbB/2` ∼ Ryy yyy GvKM@#`2F ;HtB2b i z ≈ jXRjX3 9X3 b2H2+i2/ 7`QK p2`v /22T ugriz BK;2b Q7 i?Bb /i b2i M/ 2biBKi2
i?2B` `2bi@7`K2 Reyy³ HmKBMQbBiv 7mM+iBQMX .m2 iQ i?2 H`;2 bm`p2v pQHmK2+QbKB+ p`BM+2 THvb M2;HB;B#H2 `QH2X 6m`i?2`KQ`2- r2 K2bm`2 i?2 #`B;?i 2M/
Q7 i?2 G6 rBi? mMT`2+2/2Mi2/ biiBbiB+H ++m`+vX *QMiKBMiBQM 7`+iBQMb
7`QK bi`b M/ HQr@z ;Htv BMi2`HQT2`b `2 2biBKi2/ 7`QK bBKmHiBQMbX 6`QK
i?2b2 bBKmHiBQMb i?2 `2/b?B7i /Bbi`B#miBQMb Q7 i?2 GvKM@#`2F ;HtB2b BM
i?2 /Bz2`2Mi bKTH2b `2 2biBKi2/- M/ i?Qb2 `2/b?B7ib `2 mb2/ iQ +?QQb2
#M/b M/ +H+mHi2 F@+Q``2+iBQMb bQ i?i i?2 G6b `2 +QKT`2/ i i?2 bK2
`2bi@7`K2 rp2H2M;i?X hQ +Q``2+i 7Q` BM+QKTH2i2M2bb- r2 bim/v i?2 /2i2+iBQM
`i2 Q7 bBKmHi2/ ;HtB2b BMD2+i2/ iQ i?2 BK;2b b 7mM+iBQM Q7 K;MBim/2
M/ `2/b?B7iX q2 2biBKi2 i?2 +QMi`B#miBQM Q7 b2p2`H bvbi2KiB+ 2z2+ib BM i?2
MHvbBb iQ i2bi i?2 `Q#mbiM2bb Q7 Qm` `2bmHibX q2 }M/ i?2 #`B;?i 2M/ Q7 i?2
G6 Q7 Qm` u@/`QTQmi bKTH2 iQ /2pBi2 bB;MB}+MiHv 7`QK a+?2+?i2` 7mM+iBQMX
A7 r2 KQ/B7v i?2 7mM+iBQM #v `2+2MiHv T`QTQb2/ K;MB}+iBQM KQ/2H- i?2
}i BKT`Qp2bX 6Q` i?2 }`bi iBK2 BM M G": bKTH2- r2 +M K2bm`2 /QrM iQ
i?2 /2MbBiv `2;BK2 r?2`2 K;MB}+iBQM z2+ib i?2 b?T2 Q7 i?2 Q#b2`p2/ G6
Rkj
#2+mb2 Q7 i?2 p2`v #`B;?i M/ ``2 ;HtB2b r2 `2 #H2 iQ T`Q#2 rBi? i?Bb
/i b2iX q2 }M/ M BM+`2b2 BM i?2 MQ`KHBbiBQM- φ∗ - Q7 i?2 G6 #v 7+iQ`
Q7 kX8 #2ir22M z ≈ 5 M/ z ≈ 3X h?2 7BMi@2M/ bHQT2 Q7 i?2 G6 /Q2b MQi 2pQHp2
bB;MB}+MiHv #2ir22M z ≈ 5 M/ z ≈ 3X q2 /Q MQi }M/ bB;MB}+Mi 2pQHmiBQM Q7
i?2 +?`+i2`BbiB+ K;MBim/2 BM i?2 bim/B2/ `2/b?B7i BMi2`pH- TQbbB#Hv #2+mb2
Q7 BMbm{+B2Mi FMQrH2/;2 Q7 i?2 bQm`+2 `2/b?B7i /Bbi`B#miBQMX h?2 a6_ /2MbBiv
Bb 7QmM/ iQ BM+`2b2 #v 7+iQ` Q7 ∼k 7`QK z ≈ 5 iQ z ≈ 4X h?2 2pQHmiBQM
7`QK z ≈ 4 iQ z ≈ 3 Bb H2bb 2KBM2MiX
_2K+Q 6XCX pM /2` "m`;- >2M/`BF >BH/2#`M/i- h?QKb 1`#2M
bi`QMQKv bi`QT?vbB+b- oQHmK2 8kj- d9 UkyRyV
Rk9
eXRX ALh_P.l*hAPL
Rk8
h?2 7Q`KiBQM M/ 2pQHmiBQM Q7 ;HtB2b `MF KQM; i?2 #B; [m2biBQMb BM b@
i`QMQKv M/ biBHH rBi +QKTH2i2 2tTHMiBQMX ++Q`/BM; iQ +m``2Mi i?2Q`vi?2 7Q`KiBQM Q7 /`F Kii2` ?HQ2b #v ;`pBiiBQMH BMbi#BHBiB2b Bb M 2bb2MiBH
}`bi bi2T BM i?2 7Q`KiBQM Q7 ;HtB2b U1;;2M 2i HX RNekVX ai`b `2 #2HB2p2/ iQ
7Q`K r?2M ;b +QQHb i i?2 +2Mi`2b Q7 i?2b2 ?HQ2b Uq?Bi2 _22b RNd3V- M/
KF2 mT i?2 T`i Q7 i?2 ;Htv i?i r2 +M Q#b2`p2X MmK#2` Q7 T?vbB+H
T`Q+2bb2b bi`QM;Hv z2+i i?Bb #`vQMB+ Kbb bb2K#Hv- HBF2 i?2 ?v/`Q/vMK@
B+b Q7 i?2 ;b- 722/#+F T`Q+2bb2b #v bmT2`MQp2 M/ bi2HH` rBM/b- TQbbB#Hv
K;M2iB+ }2H/b- i?2 `QH2 Q7 :L- Q` i?2 2z2+ib Q7 ;Htv@;Htv BMi2`+iBQMb
M/ K2`;2`bX 6Q` i?2b2 `2bQMb i?2 KQ/2HHBM; Q7 ;Htv 7Q`KiBQM /2T2M/b QM
KMv 7`22 T`K2i2`b M/ Bb MQi p2`v r2HH +QMbi`BM2/X
Pp2` i?2 Tbi /2+/2 i?2 ?B;? `2/b?B7i mMBp2`b2 ?b #2+QK2 ++2bbB#H2
Q#b2`piBQMHHv i?`Qm;? i?2 mb2 Q7 T?QiQK2i`B+ i2+?MB[m2bX "v /2i2+iBQM Q7 i?2
bT2+i`H /Bb+QMiBMmBiv /m2 iQ i?2 `2/b?B7i2/ GvKM@#`2F BM KmHiB@rp2H2M;i?
}Hi2` b2i- H`;2 M/ +H2M bKTH2b Q7 ?B;? `2/b?B7i bi`@7Q`KBM; ;HtB2b +M
#2 b2H2+i2/ Uai2B/2H 2i HX RNNe- RNNNc :BpHBb+Q kyykV- rBi? HQr KQmMib
Q7 +QMiKBMiBQMX h?2b2 bKTH2b +M #2 mb2/ iQ bim/v b2p2`H T`QT2`iB2b Q7
i?2 2`Hv mMBp2`b2X 6Q` 2tKTH2- #v K2bm`BM; i?2 +Q``2HiBQM 7mM+iBQM Q7
i?2b2 GvKM@#`2F :HtB2b UG":bV M/ +QKT`BM; Bi rBi? i?2 +Q``2HiBQM Q7
/`F Kii2`- i?2 +?`+i2`BbiB+ Kbb Q7 i?2B` ?HQ2b +M #2 /2i2`KBM2/ U2X;X
:BpHBb+Q .B+FBMbQM kyyRc Pm+?B 2i HX kyy9#c >BH/2#`M/i 2i HX kyy8- kyydkyyNVX >m##H2 aT+2 h2H2b+QT2 Q#b2`piBQMb Q7 G":b `2 mb2/ iQ bim/v ?Qr
+2`iBM KQ`T?QHQ;B+H ivT2b 2pQHp2 rBi? iBK2 USB`xFH 2i HX kyy8VX bim/v Q7
i?2 2pQHmiBQM Q7 i?2 lo GmKBMQbBiv 6mM+iBQM UG6V Uai2B/2H 2i HX RNNe- RNNNc
arB+FB h?QKTbQM kyyec "Qmr2Mb 2i HX kyydV- r?B+? Bb i?2 K2bm`2 Q7 i?2
MmK#2` Q7 ;HtB2b T2` mMBi pQHmK2 b 7mM+iBQM Q7 HmKBMQbBiv- Bb MQi?2`
7mM/K2MiH T`Q#2 BM ;Htv 7Q`KiBQM M/ 2pQHmiBQM- #2+mb2 Q7 Bib +HQb2
`2HiBQM iQ bi` 7Q`KiBQM T`Q+2bb2bX
a2p2`H i2+?MB[m2b +M #2 mb2/ iQ 2biBKi2 i?2 bi` 7Q`KiBQM `i2 Ua6_V
BM ;HtB2b- KQbiHv #b2/ QM i?2 2tBbi2M+2 Q7 KbbBp2- vQmM; bi`b- BM/B+iBp2
Q7 `2+2Mi bi` 7Q`KiBQMX +QKKQMHv mb2/ rv iQ T`Q#2 i?2 2tBbi2M+2 Q7
KbbBp2 bi`b Bb i?2 >α HmKBMQbBiv UE2MMB+mii RN3jV- #2+mb2 >α T?QiQMb
Q`B;BMi2 7`QK i?2 ;b BQMBx2/ #v i?2 `/BiBQM Q7 KbbBp2 bi`bX b2+QM/
bi` 7Q`KiBQM BM/B+iQ` Bb i?2 BM7``2/ UA_V HmKBMQbBiv Q`B;BMiBM; 7`QK /mbi
+QMiBMmmK 2KBbbBQM UE2MMB+mii RNN3c >B`b?Bi 2i HX kyyjVX h?2 #bQ`TiBQM
+`Qbb b2+iBQM Q7 /mbi Bb bi`QM;Hv T2F2/ BM i?2 lo- M/ i?2`27Q`2 i?2 2tBbi2M+2
Q7 lo 2KBiiBM;- BX2X KbbBp2- bi`b Bb T`Q#2/ BM/B`2+iHvX h?B`/Hv- i?2 lo
+QMiBMmmK Bb mb2/ b bi` 7Q`KiBQM T`Q#2- rBi? i?2 KBM /pMi;2b #2BM;
i?i i?2 lo@2KBbbBQM Q7 i?2 vQmM; bi2HH` TQTmHiBQM Bb directly Q#b2`p2/mMHBF2 BM >@α M/ A_ bim/B2bX 6m`i?2`KQ`2- i?Bb i2+?MB[m2 +M #2 TTHB2/ 7`QK
i?2 ;`QmM/ iQ bi`@7Q`KBM; ;HtB2b Qp2` rB/2 `M;2 Q7 `2/b?B7ibX >2M+2- Bi
*>Sh1_ eX h>1 lo :Gsu GlJALPaAhu 6lL*hAPL h z 4j@8
Rke
6_PJ h>1 *6>h G1:*u al_o1u .11S 6A1G.a
Bb biBHH i?2 KQbi TQr2`7mH T`Q#2 Q7 +QbKQHQ;B+H 2pQHmiBQM Q7 i?2 a6_ UJ/m
2i HX RNNeVX >Qr2p2`- BM7Q`KiBQM #Qmi i?2 BMBiBH Kbb 7mM+iBQM UAJ6VM/ T`iB+mH`Hv i?2 2tiBM+iBQM #v /mbi `2 `2[mB`2/ iQ 2biBKi2 i?2 iQiH bi`
7Q`KiBQM `i2X
AM i?Bb TT2` r2 2biBKi2 i?2 lo G6 i `2/b?B7ib z 4j@8 7`QK i?2 *M/@
6`M+2@>rBB@h2H2b+QT2 G2;+v am`p2v U*6>hGaV .22T- bm`p2v +Qp2`BM; 9
b[m`2 /2;`22b BM 7Qm` BM/2T2M/2Mi }2H/b bT`2/ +`Qbb i?2 bFvX aBM+2 Qm` bK@
TH2b- i /Bz2`2Mi `2/b?B7ib- `2 HH 2ti`+i2/ 7`QK i?2 bK2 /ib2i- i?Bb ;Bp2b
M 2t+2HH2Mi QTTQ`imMBiv iQ bim/v TQbbB#H2 2pQHmiBQM Q7 i?2 G6 BM i?Bb `2/b?B7i
BMi2`pHX a2p2`H bvbi2KiB+ 2z2+ib i?i M22/ iQ #2 +QMbB/2`2/ r?2M +QKT`@
BM; `2bmHib i /Bz2`2Mi `2/b?B7ib 7`QK /Bz2`2Mi bm`p2vb U2X;X bQm`+2 2ti`+iBQMKbFBM;- Sa6@KQ/2HHBM;- 2i+XV +M #2 pQB/2/ r?2M i?2 /Bz2`2Mi `2/b?B7i bK@
TH2b `2 2ti`+i2/ 7`QK i?2 bK2 bm`p2vX .m2 iQ i?2 H`;2 pQHmK2b r2 T`Q#2
rBi? Qm` 9 b[m`2 /2;`22 bm`p2v- i?2 BM~m2M+2 Q7 +QbKB+ p`BM+2 QM i?2 b?T2
Q7 i?2 2biBKi2/ G6 Bb M2;HB;B#H2 Uh`2MiB aiBp2HHB kyy3V- b r2 2tT2+i +QbKB+
p`BM+2 iQ z2+i Qm` MmK#2` +QmMib QMHv i i?2 R@8W H2p2H UaQK2`pBHH2 2i HX
kyy9VX q2 +M bim/v i?2 #`B;?i 2M/ Q7 i?2 G6 rBi? mMT`2+2/2Mi2/ ++m`+vb i?2b2 Q#D2+ib `2 ``2 M/ r2 `2 #H2 iQ K2bm`2 /QrM iQ p2`v HQr /2MbB@
iB2bX h?Bb HHQrb mb iQ bim/v i?2 2z2+i i?i K;MB}+iBQM ?b QM i?2 Q#b2`p2/
/Bbi`B#miBQM Ub22 `2+2Mi `2bmHib #v CBM GBK kyRyV- M/ bim/v TQbbB#H2
/2pBiBQM 7`QK i?2 +QKKQMHv mb2/ a+?2+?i2` 7mM+iBQMX 6m`i?2`KQ`2- ;Bp2M
i?2 /2Ti? Q7 i?2 bi+F2/ BK;2b- r2 +M T`Q#2 i?2 7BMi 2M/ Q7 i?2 HmKBMQbBiv
7mM+iBQM rBi? +QKT`#H2 T`2+BbBQM b i?2 /22T2bi ;`QmM/ #b2/ bm`p2vb ?p2
/QM2 #27Q`2 UarB+FB h?QKTbQM kyyeVX
h?2 bi`m+im`2 Q7 i?Bb TT2` Bb b 7QHHQrb, AM a2+iX eXk r2 /2b+`B#2 i?2 /i
b2i r2 mb2- i?2 G": b2H2+iBQM +`Bi2`B b r2HH b i?2 bBKmHiBQMb i?i H2/ iQ i?2
`2/b?B7i /Bbi`B#miBQMb M/ +QMiKBMiBQM 7`+iBQMbX AM a2+iX eXj i?2 bm`p2vǶb
+QKTH2i2M2bb M/ i?2 2z2+iBp2 bm`p2v pQHmK2b `2 2biBKi2/X AM a2+iX eX9 r2
T`Q+22/ rBi? i?2 `2bmHiBM; 2biBKi2/ G6b- T`2b2Mi i?2 #2bi@}iiBM; a+?2+?i2`
T`K2i2`b- M/ b?Qr ?Qr bBKTH2 K;MB}+iBQM KQ/2H +M bB;MB}+MiHv BK@
T`Qp2 i?2 [mHBiv Q7 i?2 }iX h?2 lo HmKBMQbBiv /2MbBiB2b UloG.V M/ a6_
/2MbBiB2b Ua6_.V `2 2biBKi2/ #b2/ QM i?2 K2bm`2/ G6bX q2 HbQ 2H#Q`i2
QM i?2 `Q#mbiM2bb Q7 Qm` `2bmHibX AM a2+iX eX8 r2 +QKT`2 i?2b2 iQ T`2pBQmb
/2i2`KBMiBQMb Q7 i?2 lo G6 M/ a6_. 7`QK i?2 HBi2`im`2X AM a2+iX eXe r2
}MBb? rBi? bmKK`v M/ T`2b2Mi Qm` +QM+HmbBQMbX
q2 mb2 i?2 " K;MBim/2b bvbi2K UPF2 :mMM RN3jV i?`Qm;?Qmi M/
/QTi Λ*.J +QbKQHQ;v rBi? ΩK = 0.3- ΩΛ = 0.7 M/ >y = dy FK b−R JT+−R X
eXkX .h aJSG1a
Rkd
6Q` i?Bb rQ`F r2 KF2 mb2 Q7 Tm#HB+Hv pBH#H2 /i 7`QK i?2 *6>hGa .22T- bm`p2v mbBM; J2;*K KQmMi2/ i i?2 T`BK2 7Q+mb Q7 i?2 *6>h r?B+? +Qp2`b
7Qm` BM/2T2M/2Mi }2H/b Q7 R b[m`2 /2;`22 2+?X AK;2b `2 iF2M BM i?2 }Hi2`b
ugriz M/ `2 T`2@T`Q+2bb2/ mbBM; i?2 1HBtB` bvbi2K UJ;MB2` *mBHHM/`2
kyy9VX AK;2 `2/m+iBQM Bb /QM2 mbBM; i?2 h>1GA TBT2HBM2 U1`#2M 2i HX kyy8c
>BH/2#`M/i 2i HX kyyeV- H2/BM; iQ TT`QtBKi2 5σ TQBMi bQm`+2 HBKBib Q7 kdX8kdXN- kdXN- kdXd M/ keX8 7Q` i?2 ugriz #M/b- `2bT2+iBp2HvX h?2 HBKBib 7Q` 2+?
Q7 i?2 }2H/b HB2 rBi?BM yXk K; 7`QK i?2b2 p2`;2 pHm2bX
aQm`+2 1ti`+iQ` U"2`iBM `MQmib RNNeV Bb mb2/ iQ +`2i2 KmHiB@+QHQm`
+iHQ;m2X hQiH i@#M/ K;MBim/2b `2 K2bm`2/ BM E`QM@HBF2 T2`im`2b UE`QM
RN3yV mbBM; a1ti`+iQ`Ƕb lhP K;MBim/2bX 1p2`v BK;2 Bb bKQQi?2/ #v +QM@
pQHmiBQM rBi? :mbbBM }Hi2` iQ Ki+? i?2 b22BM; Q7 i?2 BK;2 rBi? i?2 rQ`bi
b22BM; pHm2 UivTB+HHv i?2 u@#M/VX h?2b2 +Q``2+iBQMb `2 ivTB+HHv bKHH @ HH
#M/b ?p2 b22BM; #2HQr R `+b2+X h?2 /mH@BK;2 KQ/2 Q7 a1ti`+iQ` Bb i?2M
mb2/ rBi? i?2 mM+QMpQHp2/ i@#M/ 7Q` bQm`+2 /2i2+iBQM M/ BbQT?QiH K;MB@
im/2b 7`QK i?2 +QMpQHp2/ #M/b iQ 2biBKi2 +QHQm`bX M 2ti2MbBp2 /2b+`BTiBQM
Q7 i?2 /i `2/m+iBQM M/ +iHQ;m2 +`2iBQM Bb ;Bp2M BM 1`#2M 2i HX UkyyNV
M/ >BH/2#`M/i 2i HX UkyyNVX
u g
r
*H2M bKTH2b Q7 u@- g @- M/ r@/`QTQmib `2 b2H2+i2/ #b2/ QM i?2 7QHHQrBM;
b2H2+iBQM +`Bi2`B U>BH/2#`M/i 2i HX kyyNV,
u−/`QTQmib : 1.0 < (u − g) ∧ −1.0 < (g − r) < 1.2 ∧
1.5 · (g − r) < (u − g) − 0.75,
g−/`QTQmib : 1.0 < (g − r) ∧ −1.0 < (r − i) < 1.0 ∧
1.5 · (r − i) < (g − r) − 0.80,
r−/`QTQmib : 1.2 < (r − i) ∧ −1.0 < (i − z) < 0.7 ∧
1.5 · (i − z) < (r − i) − 1.00.
UeXRV
UeXkV
UeXjV
6m`i?2`KQ`2- Bi Bb `2[mB`2/ i?i HH G":b ?p2 a1ti`+iQ` *Gaanah_
T`K2i2` Q7 *Gaanah_ < yXN- i?i g @/`QTQmib `2 MQi /2i2+i2/ BM uM/ i?i r@/`QTQmib `2 M2Bi?2` /2i2+i2/ BM u MQ` BM g X LQi2 i?i i?2 +QHQm`
b2H2+iBQM +`Bi2`B Q7 i?2 u@/`QTQmi bKTH2 BM >BH/2#`M/i 2i HX UkyyNV `2
T`2iiv +QMb2`piBp2X q2 `2Ht2/ i?2 u − g +mi bHB;?iHv iQ KF2 i?2 b2H2+iBQM
KQ`2 +QKT`#H2 iQ 2X;X ai2B/2H 2i HX UkyyjV- ai2B/2H 2i HX Ukyy9V M/ arB+FB
h?QKTbQM UkyyeVX
*>Sh1_ eX h>1 lo :Gsu GlJALPaAhu 6lL*hAPL h z 4j@8
Rk3
6_PJ h>1 *6>h G1:*u al_o1u .11S 6A1G.a
6B;m`2 eXR, 6`QK H27i iQ `B;?i i?2 MmK#2` +QmMib Q7 i?2 m@- ;@- M/ `@/`QTQmib BM i?2 *6>hGa
.22T- b b2H2+i2/ #v i?2 +QHQm` +`Bi2`B Q7 1[bX eXR@eXjX
h?Bb `2bmHib BM i?2 b2H2+iBQM Q7 8y33y u@- jekke g @- M/ RR9RR r@/`QTQmib BM
iQiH Qp2` i?2 7Qm` }2H/bX h?2B` K;MBim/2 /Bbi`B#miBQMb `2 b?QrM BM 6B;X eXRX
LQi2 i?2 /Bz2`2M+2b BM /2Ti? Q7 i?2 BM/BpB/mH }2H/bX
h?2 KDQ`Biv Q7 i?2 b2H2+i2/ bQm`+2b Bb iQQ 7BMi iQ KF2 bT2+i`Qb+QTB+ `2/b?B7i
/2i2`KBMiBQM TQbbB#H2- M/ i?2 #`B;?i2` +M/B/i2b ?p2 MQi bT2+i`Qb+QTB+HHv
#22M Q#b2`p2/ v2iX 6Q` i?Bb `2bQM >BH/2#`M/i 2i HX UkyyNV 2biBKi2/ i?2
`2/b?B7i /Bbi`B#miBQMb #v K2Mb Q7 T?QiQK2i`B+ `2/b?B7ib M/ bBKmHiBQMbX
h?`Qm;?Qmi i?Bb TT2` r2 rBHH mb2 i?2 K2M `2/b?B7i pHm2b 7`QK bBKm@
HiBQMb #b2/ QM bvMi?2iB+ i2KTHi2b #v "`mxmH X *?`HQi URNNjV- #2BM;
< z >∼
= jXR- jX3 M/ 9Xd 7Q` i?2 u@- g @- M/ r@/`QTQmib `2bT2+iBp2HvX q2
2biBKi2 i?2 mM+2`iBMiv BM i?2 K2M `2/b?B7ib iQ yXR 7Q` i?2 i?`22 /`QTQmi
bKTH2bX
AM Q`/2` iQ //`2bb i?2 KQmMi Q7 +QMiKBMiBQM BM Qm` G": bKTH2b>BH/2#`M/i 2i HX UkyyNV +QMbB/2` i?2 TQbbB#BHBiB2b Q7 bi`b M/ HQr@z ;HtB2b
b+ii2`BM; BM i?2 b2H2+iBQM #Qt2bX :HtB2b `2 bBKmHi2/ #b2/ QM i2KTHi2b
7`QK i?2 HB#``v Q7 "`mxmH X *?`HQi URNNjV- r?BH2 i?2 +QHQm`b Q7 bi`b
BM i?2 }2H/b `2 2biBKi2/ #b2/ QM i?2 h_AG1:G ;H+iB+ KQ/2H U:B``/B
2i HX kyy8VX *QMiKBMiBQM 7`+iBQMb `2 b?QrM ;`T?B+HHv BM 6B;X eXkX
ai2HH` +QMiKBMiBQM Bb M2;HB;B#H2 7Q` i?2 #`B;?i2` Q#D2+ib- b i?2 b2H2+iBQM
#Qt2b bi22` rv 7`QK i?2 bi2HH` HQ+mbX 6Q` 7BMi Q#D2+ib BM i?2 u@- M/ g @
/`QTQmi bKTH2b- i?2 bi2HH` +QMiKBMiBQM BM+`2b2b b `2bmHi Q7 T?QiQK2i`B+
b+ii2`X
h?2 +QMiKBMiBQM #v HQr@z ;HtB2b Bb M2;HB;B#H2 BM i?2 u@/`QTQmi bK@
TH2- b i?2 GvKM #`2F 7Q` z ∼ 3 ;Htv Bb biBHH #Hm2@r`/ Q7 i?2 z ∼ 0
"HK2`f9yyy³ #`2FX 6Q` ?B;?2` `2/b?B7ib i?Bb +2b2b iQ #2 i?2 +b2- bQ i?i
i?2 g @- M/ r@/`QTQmi bKTH2b bmz2` 7`QK bB;MB}+Mi +QMiKBMiBQM 7`+iBQM
eXjX LGuaAa @ al_o1u *PJSG1h1L1aa
RkN
6B;m`2 eXk, *QMiKBMiBQM 7`+iBQMb Q7 bi`b M/ HQr@z ;HtB2b BM i?2 /`QTQmi bKTH2bX
"Hm2 '@bvK#QHb +QMM2+i2/ #v /b?2/ HBM2 b?Qr i?2 bi2HH` +QMiKBMiBQM 7`+iBQM #b2/ QM
;H+iB+ KQ/2HX "H+F b[m`2b +QMM2+i2/ #v i?2 bQHB/ HBM2 b?Qr i?2 iQiH +QMiKBMiBQM
7`+iBQM 7`QK >BH/2#`M/i 2i HX UkyyNVX
i i?2 #`B;?i 2M/- r?2`2 i?2 G": TQTmHiBQM Bb bT`b2X 6BMi HQr@z Q#D2+ib
`2 HBF2Hv iQ b+ii2` BMiQ i?2 b2H2+iBQM #Qt BM 2+? Q7 i?2 bKTH2b- bQ i?i i?2
+QMiKBMiBQM 7`+iBQMb `2 BM+`2b2/ ?2`2X
aBM+2 i?2 +QMiKBMiBQM 7`+iBQMb `2 HQr i i?2 #`B;?i 2M/ Q7 i?2 u@
/`QTQmib- r2 ?p2 i?2 TQi2MiBH iQ T`Q#2 i?2 G6 iQ p2`v HQr G": ;Htv
/2MbBiB2bX q2 BMbT2+i i?2 3y #`B;?i2bi Q#D2+ib Ur" < 23.2V BM i?2 u@/`QTQmi
bKTH2 #v 2v2 M/ `2KQp2 Q#pBQmb bTm`BQmb bQm`+2b- jy BM iQiHX bi`QM;#mi +2`iBMHv bHB;?iHv bm#D2+iBp2- `2D2+iBQM +`Bi2`BQM Bb i?2 bBx2 Q7 i?2 `2;BQM
BM r?B+? i?2 ~mt Bb K2bm`2/- BX2X i?2 ?H7@HB;?i `/Bmb URj Q#D2+ib `2D2+i2/VX
aQm`+2b i?i `2 +H2`Hv #H2M/2/ #v #`B;?i M2B;?#Qm` Uk Q#D2+ibV- b r2HH b
bQm`+2b i?i ?p2 iQQ H`;2 TT`2Mi bBx2 Uj Q#D2+ibVX HbQ M bi2`QB/ i`+F
?b #22M `2KQp2/X
AM i?2 g @- M/ r@/`QTQmi bKTH2 r2 /Q MQi T`Q#2 i?2b2 HQr U" yXyR K;−1
`+KBM−2 V G": ;Htv /2MbBiB2b- bBM+2 i?2b2 TQBMib `2 mM`2HB#H2 /m2 iQ i?2
?B;? +QMiKBMiBQM 7`+iBQMb 7`QK HQr@z Q#D2+ib Ub22 6B;X eXkVX h?Bb T`Q?B#Bib
bim/v Q7 i?2 #`B;?i 2M/ Q7 i?2 G6 7Q` i?2 g @- M/ r@/`QTQmib mMiBH i?2 Mim`2
Q7 i?2 BM/BpB/mH bQm`+2b ?b #22M p2`B}2/X
q2 mb2 /2iBH2/ KQ/2HHBM; TT`Q+? iQ 2biBKi2 i?2 +QKTH2i2M2bb Q7 i?2
bm`p2v b 7mM+iBQM Q7 K;MBim/2 M/ `2/b?B7i- 7Q` 2+? Q7 i?2 /`QTQmi bKTH2bX
q2 // `iB}+BH Q#D2+ib iQ Qm` BK;2b- rBi? +QHQm`b `2T`2b2MiiBp2 Q7 bi`@
7Q`KBM; ;HtB2b- M/ i`v iQ `2+Qp2` i?2K 7QHHQrBM; i?2 bK2 bQm`+2 2ti`+iBQM
M/ +QHQm` b2H2+iBQM +`Bi2`B b 7Q` i?2 `2H /iX q2 BMp2biB;i2 ?Qr i?2
BM+`2bBM; b+ii2` BM i?2 +QHQm`b 7Q` 7BMi2` Q#D2+ib BM~m2M+2b i?2 +QKTH2i2M2bb
*>Sh1_ eX h>1 lo :Gsu GlJALPaAhu 6lL*hAPL h z 4j@8
Rjy
6_PJ h>1 *6>h G1:*u al_o1u .11S 6A1G.a
b 7mM+iBQM Q7 K;MBim/2X 6m`i?2`KQ`2- QM2 2tT2+ib i?i- 7Q` 7BMi2` /`QTQmi
Q#D2+ib- i?2 `2/b?B7i /Bbi`B#miBQM Q7 i?2b2 Q#D2+ib #`Q/2Mb /m2 iQ i?2 bK2
2z2+iX >2M+2 r2 rBHH HbQ KQ/2H i?Bb b 7mM+iBQM Q7 `2/b?B7iX
q2 /2b+`B#2 Qm` }/m+BH KQ/2H a1.b- bBx2b M/ b?T2b Q7 i?2 bBKmHi2/
Q#D2+ib #2HQrX h?2 bbmKTiBQMb r2 KF2- `2 i2bi2/ BM a2+iX eX9Xj iQ 2biBKi2
i?2 `Q#mbiM2bb Q7 i?2 `2bmHibX
h?2 "`mxmH X *?`HQi URNNjV bi2HH` TQTmHiBQM bvMi?2bBb HB#``v Bb mb2/
iQ b2i mT Qm` }/m+BH ;Htv a1. KQ/2Hc Ryy Jv` QH/ ;Htv i2KTHi2 rBi?
+QMbiMi bi` 7Q`KiBQMX JBHH2` a+HQ URNdNV AJ6 Bb bbmK2/X h?2 QTiB+H
/2Ti? Q7 M2mi`H ?v/`Q;2M- b 7mM+iBQM Q7 `2/b?B7i- Bb KQ/2HH2/ ++Q`/BM; iQ
J/m URNN8VX
h?Bb i2KTHi2 Bb `2//2M2/ #v i?2 bi`#m`bi 2tiBM+iBQM Hr 7`QK *Hx2iiB
2i HX UkyyyV- rBi? /Bbi`B#miBQM BM E(B − V )X h?Bb /Bbi`B#miBQM r2 +?QQb2
bm+? i?i i?2 lo@+QMiBMmmK bHQT2b i?i r2 K2bm`2 7`QK i?2 /i `2 Ki+?2/
r?2M r2 mb2 Qm` }/m+BH i2KTHi2 b #b2X hQ K2bm`2 i?2 lo@+QMiBMmmK
bHQT2b- r2 mb2 +QHQm` `2/r`/ Q7 Reyy `2bi@7`K2- BX2X i?2 r − i +QHQm` 7Q` i?2
u@/`QTQmib M/ i?2 i − z +QHQm` 7Q` i?2 g @/`QTQmibX 6Q` i?2 r@/`QTQmib r2 +M
MQi T2`7Q`K bBKBH` K2bm`2K2Mi #2+mb2 r2 /Q MQi ?p2 Q#b2`piBQMb BM #M/ `2/r`/ Q7 i?2 z @#M/X h?2`27Q`2 r2 rBHH mb2 i?2 bK2 /Bbi`B#miBQM Q7
/mbi b r2 }M/ 7Q` i?2 g @/`QTQmibX
6B;m`2 eXj,
h?2 /Bbi`B#miBQM Q7 lo@
+QMiBMmmK bHQT2b 7Q` i?2 u@/`QTQmib b
K2bm`2/ #v i?2 r − i +QHQm` 7`QK i?2
*6>h /i U#H+FV +QKT`2/ rBi? i?2 Qmi@
+QK2b 7`QK bBKmHiBQMbX h?2 +QHQm` Bb
K2bm`2/ BM T`i Q7 i?2 bT2+i`mK rBi?Qmi
bi`QM; 72im`2b- `2/r`/ Q7 ReyyX "Qi? M
QH/2` i2KTHi2 M/ ?B;?2` KQmMi Q7 /mbi
`2bmHi BM `2//2` lo +QHQm`X h?2 KQmMi
Q7 /mbi r2 M22/ iQ // i?2`27Q`2 /2T2M/b
QM i?2 ;2 Q7 i?2 #b2 i2KTHi2X 6Q` i?2
u@/`QTQmib r2 }M/ i?i mMB7Q`K /Bbi`B#m@
iBQM Q7 /mbi rBi? yXR< E(B − V ) <yX9
;Bp2b ;QQ/ }i iQ i?2 /i- r?2M i?2
i2KTHi2 Bb Ryy Jv` QH/ rBi? +QMbiMi
KQmMi Q7 bi` 7Q`KiBQM UTm`TH2VX
6Q` i?2 u@/`QTQmib r2 }M/ i?i mMB7Q`K /mbi /Bbi`B#miBQM rBi? `2//2MBM;
#2ir22M rBi? yXR< E(B − V ) <yX9 ;Bp2b ;QQ/ }i iQ i?2 /i- b22 6B;X eXjX
6Q` i?2 g @/`QTQmib r2 K2bm`2 H`;2` bT`2/ BM lo@+QMiBMmmK bHQT2b- M/
}M/ `2bQM#H2 }i r?2M mbBM; mMB7Q`K /mbi /Bbi`B#miBQM rBi? `2//2MBM;
eXjX LGuaAa @ al_o1u *PJSG1h1L1aa
RjR
#2ir22M yXy< E(B − V ) <yX8X Ai b?QmH/ #2 MQi2/ i?i i?2 ;2 M/ KQmMi
Q7 /mbi ii2MmiBQM Q7 i?2 i2KTHi2 `2 ?B;?Hv /2;2M2`i2- bQ i?i /Bz2`2Mi
+QK#BMiBQMb Q7 i?2b2 T`K2i2`b }i i?2 lo@+QMiBMmmK bHQT2b BM i?2 /iX Ai Bb
2bT2+BHHv BKTQ`iMi iQ +Q``2+iHv Ki+? i?2 /Bbi`B#miBQM Q7 i?2 lo@+QMiBMmmK
bHQT2b 7`QK i?2 /i rBi? i?2 KQ/2H ;HtB2b- bBM+2 M BM+`2b2 U/2+`2b2V BM i?2
;2 Q7 i?2 ;Htv KQ/2H i2KTHi2 ?b bBKBH` 2z2+i QM i?2 G6 b M BM+`2b2
U/2+`2b2V Q7 i?2 KQmMi Q7 /mbiX q2 rBHH 2H#Q`i2 QM i?Bb BM a2+iX eX9XjX A7
r2 K2bm`2 i?2 lo@+QMiBMmmK bHQT2b BM Qm` /i 7Q` /Bz2`2Mi K;MBim/2 #BMbr2 /Q MQi }M/ bB;MB}+Mi 2pQHmiBQMX h?2`27Q`2 r2 rBHH mb2 /Bbi`B#miBQM Q7
/mbi ii2MmiBQM BM Qm` bBKmHiBQMb i?i Bb BM/2T2M/2Mi Q7 K;MBim/2X
G":b ?p2 ivTB+H ?H7@HB;?i `/BB Q7 r1/2 ∼ yXRǴ@yXjǴ U:BpHBb+Q 2i HX RNNeV
M/ i?mb `2 mM`2bQHp2/ #v i?2 *6>h M/ +M #2 i`2i2/ b TQBMi bQm`+2bX b
i?2 bBx2 Q7 i?2 Sa6 BM i?2 *6>h BK;2b Bb bi`QM;Hv TQbBiBQM /2T2M/2Mi- r2
?p2 iQ /Ti i?2 BMD2+i2/ bQm`+2b ++Q`/BM;HvX q2 T`K2i`Bx2 i?2 Sa6 #v JQzi T`Q}H2+
( )2 ,−β
R
I = I0 1 + (21/β − 1) ·
,
UeX9V
R0
BM r?B+? β M/ R0 `2 i?2 T`K2i2`b i?i r2 /Ti iQ /Dmbi i?2 b?T2 M/
bBx2 Q7 i?2 T`Q}H2 `2bT2+iBp2HvX I0 `2T`2b2Mib i?2 ~mt MQ`KHBbiBQMX
AM Q`/2` iQ K2bm`2 i?2 Sa6 b 7mM+iBQM Q7 TQbBiBQM 7Q` i?2 /Bz2`2Mi }Hi2`b
M/ }2H/b- r2 }`bi b2H2+i b2p2`H ?mM/`2/ bi`b #b2/ QM i?2B` K;MBim/2b M/
?H7@HB;?i `/BB- BM 2+? }2H/ M/ 2+? }Hi2`X q2 K2bm`2 i?2 8yW M/ NyW
~mt `/BB Q7 i?2b2 bi`b- `8y M/ `Ny - mbBM; a1ti`+iQ`X h?2 `iBQ Q7 i?2b2 ~mt
`/BB mMB[m2Hv /2i2`KBM2b i?2 JQzi@β T`K2i2`- r?B+?- BM +QK#BMiBQM rBi?
2Bi?2` QM2 Q7 i?2 ~mt `/BB- ;Bp2b i?2 JQzi T`Q}H2 `/Bmb R0 7Q` 2+? bi`X q2
}M/ i?i i?2 JQzi@β T`K2i2` Bb 7B`Hv +QMbiMi Qp2` i?2 }2H/b M/ }Hi2`b
(β ≈ 4.0) M/ QMHv R0 +?M;2b bB;MB}+MiHvX hQ KQ/2H R0 b 7mM+iBQM Q7
TQbBiBQM- r2 }i k@/BK2MbBQMH TQHvMQKBH 7mM+iBQM iQ i?2 a1ti`+i2/ pHm2b
7Q` r50 X h?Bb +QMbi`BMb i?2 Sa6 bBx2 QM 2p2`v TQbBiBQM- 7Q` 2p2`v }2H/ M/
}Hi2`X
q2 }M/ i?i i?2`2 Bb ∼jyW /Bz2`2M+2 BM R0 #2ir22M i?2 BK;2 +2Mi2`
M/ #QmM/`B2bX b i?Bb- BM Qm` ;`QmM/@#b2/ rB/2@}2H/ bm`p2v- Bb #v 7` i?2
/QKBMiBM; 2z2+i BM i?2 TT`2Mi bm`7+2 #`B;?iM2bb2b Q7 Qm` bQm`+2b- r2 /Q
MQi bbmK2 M BMi`BMbB+ bBx2 /Bbi`B#miBQM 7Q` i?2 bQm`+2b BM i?2 KBM bBKmHiBQMb
Q7 i?Bb TT2`X
A7 r2 +QMbB/2` +2`iBM BMi`BMbB+ K;MBim/2 /Bbi`B#miBQM Q7 ;HtB2b- i?2 `2+Qp@
2`2/ /Bbi`B#miBQM 7i2` bQm`+2 2ti`+iBQM M/ +QHQm` b2H2+iBQM rBHH HQQF /Bz2`2Mi
/m2 iQ biiBbiB+H ~m+imiBQMb BM i?2 K2bm`2K2MiX AM Qm` MHvbBb r2 ii2KTi
iQ +Q``2+i 7Q` i?Bb 2z2+i +HH2/ 1//BM;iQM #Bb U1//BM;iQM RNRjc h22`BFQ`TB
*>Sh1_ eX h>1 lo :Gsu GlJALPaAhu 6lL*hAPL h z 4j@8
Rjk
6_PJ h>1 *6>h G1:*u al_o1u .11S 6A1G.a
kyy9VX Ai Bb ?`/ iQ 2biBKi2 i?Bb #Bb MHviB+HHv #2+mb2 i?2 bBx2 Q7 i?2 K;@
MBim/2 b+ii2` Bb M BM+`2bBM; 7mM+iBQM Q7 K;MBim/2X HbQ- r?2M TT`Q+?BM;
i?2 +QKTH2i2M2bb HBKBi Q7 i?2 bm`p2v- QMHv i?2 #`B;?i2` Q#D2+ib rBHH #2 /2i2+i2/X
q?i ;2M2`HHv ?TT2Mb Bb i?i BMi`BMbB+HHv 7BMi Q#D2+ib rBHH QM p2`;2 HQQF
#`B;?i2` i?M i?2v `2X
h?2 1//BM;iQM #Bb +M #2 2biBKi2/ #v +QKT`BM; i?2 BMi`BMbB+ K;MB@
im/2b Q7 i?2 BMD2+i2/ bQm`+2b iQ i?2 `2+Qp2`2/ K;MBim/2bX am+? +QKT`BbQM Bb
b?QrM BM 6B;X eX9- bi`2bbBM; i?2 BKTQ`iM+2 Q7 i?i 2z2+i 7Q` 7BMi K;MBim/2bX
6B;m`2 eX9, h?2 /Bz2`2M+2 #2@
ir22M `2+Qp2`2/ M/ BMD2+i2/
bQm`+2 K;MBim/2b b 7mM+iBQM
Q7 `2+Qp2`2/ K;MBim/2 7Q` i?2
r@/`QTQmibX aBKBH` i`2M/b T@
T2` BM i?2 Qi?2` /`QTQmi bK@
TH2bX h?2 2``Q` #`b `2~2+i i?2
b+ii2` 7`QK i?2 7Qm` }2H/bX bBKBH` 2z2+i b b?QrM `QmM/
K`2+ = 25.3- MK2Hv M BM@
+`2b2 Q7 K`2+ − KBMD - Bb 7QmM/
#v "Qmr2Mb 2i HX Ukyye- 6B;XRNVr?2`2 Q#b2`piBQMb r2`2 mb2/
`i?2` i?M bBKmHiBQMbX
q2 rMi iQ BMD2+i bQm`+2b rBi? i?2 bK2 K;MBim/2 /Bbi`B#miBQM b i?2
BMi`BMbB+ /Bbi`B#miBQM- iQ ;2i M mM#Bb2/ `2bmHiX b i?2 #Bb Bb 2tT2+i2/ iQ
#2 H`;2bi 7Q` 7BMi2` bQm`+2b- Bi Bb 2bT2+BHHv BKTQ`iMi iQ +Q``2+iHv KQ/2H i?2
7BMi@2M/ Q7 i?2 BMi`BMbB+ /Bbi`B#miBQMX >2`2 r2 /QTi G6 i?i Bb +QMbBbi2Mi
rBi? i?2 /22T2bi G": bm`p2v- +QM/m+i2/ #v "Qmr2Mb 2i HX UkyydVX
6QHHQrBM; i?Bb /QTi2/ BMi`BMbB+ /Bbi`B#miBQM r2 BMD2+i 20 000 bQm`+2b BM 2+? Q7
i?2 BK;2b- 7Q` ey 2[mH `2/b?B7i bi2Tb #2ir22M z = 0.0 M/ z = 6.0X hQ p2`B7v
i?i i?2 BMD2+i2/ bQm`+2b /Q MQi bB;MB}+MiHv BM~m2M+2 2+? Qi?2` #v #H2M/BM;MQ` i?i i?2 #+F;`QmM/ Bb BM~m2M+2/ bB;MB}+MiHv- r2 T2`7Q`K i?2 7QHHQrBM;
i2bibX q2 BMD2+i i?2 bK2 20 000 bQm`+2b BM 9 bi;2b- 8yyy bQm`+2b 2+?- M/
/Q i?B`/ MHvbBb r?2`2 r2 BMD2+i 100 000 bQm`+2b BM iQiHX AM 6B;X eX8 i?2
`2+Qp2`2/ 7`+iBQMb Q7 bQm`+2b i?i HbQ biBb7v Qm` g @/`QTQmi +`Bi2`B `2 b?QrM
b 7mM+iBQM Q7 K;MBim/2- 7Q` QM2 T`iB+mH` `2/b?B7i bi2TX PMHv 7Q` 7BMi
K;MBim/2b /Q2b i?2 100 000 +m`p2 /2pBi2 7`QK i?2 Qi?2` QM2b- r?B+? `2
B/2MiB+H BM i?Bb `2;BK2X AM 6B;X eXe i?2 /Bbi`B#miBQM Q7 `2+Qp2`2/ g @/`QTQmib
rBi? M BMi`BMbB+ K;MBim/2 Q7 m = 25.0 Bb b?QrM b 7mM+iBQM Q7 `2+Qp2`2/
K;MBim/2X q2 +QM+Hm/2 i?i i?2 BMD2+iBQM Q7 20 000 bQm`+2b /Q2b MQi BM~m2M+2
eXjX LGuaAa @ al_o1u *PJSG1h1L1aa
Rjj
i?2 BK;2b bm+? i?i i?2 T?QiQK2i`v rQmH/ #2 T2`im`#2/ bB;MB}+MiHvX bBKBH` #2?pBQm` Bb 2tT2+i2/ 7Q` i?2 u@ M/ r@/`QTQmi bKTH2bX
6B;m`2 eX8, h?2 `2+Qp2`2/ 7`+iBQM Q7 BM@
D2+i2/ bQm`+2b i?i HbQ biBb7v i?2 g@
/`QTQmi +`Bi2`B- b 7mM+iBQM Q7 i@#M/
K;MBim/2- 7Q` R `2/b?B7i bi2TX h?`22
+m`p2b `2 ;Bp2M 7Q` /Bz2`2Mi KQmMib Q7
BMD2+i2/ bQm`+2b- iQ b22 r?2i?2`- M/ ?Qri?2 T`2b2M+2 Q7 i?2b2 bQm`+2b BM~m2M+2b i?2
T?QiQK2i`v Q7 i?2 MHvbBbX
6B;m`2 eXe, h?2 /Bbi`B#miBQM Q7 K2@
bm`2/ bQm`+2 K;MBim/2b 7Q` TQTmHiBQM
Q7 BMD2+i2/ bBKmHi2/ bQm`+2b rBi? BMi`BM@
bB+ i@#M/ K;MBim/24k8Xy- 7Q` R `2/b?B7i
bi2TX h?`22 +m`p2b `2 ;Bp2M 7Q` /Bz2`@
2Mi KQmMib Q7 BMD2+i2/ bQm`+2b- iQ b22
r?2i?2`- M/ ?Qr- i?2 T`2b2M+2 Q7 i?2b2
bQm`+2b BM~m2M+2b i?2 T?QiQK2i`v Q7 i?2
MHvbBbX
h?2 +Hmbi2`BM; Q7 G":b Bb MQi iF2M BMiQ ++QmMiX q2 bbmK2 i?Bb 2z2+i iQ
#2 BMbB;MB}+Mi 7Q` 2biBKiBM; +QKTH2i2M2bb- b i?2 +Q``2HiBQM H2M;i?- r?B+?
Bb ivTB+HHv `QmM/ 8 JT+ U>BH/2#`M/i 2i HX kyyNV- Bb p2`v bKHH +QKT`2/ iQ
i?2 bm`p2v pQHmK2X h?2`27Q`2 r2 bT`2/ Qm` bBKmHi2/ bQm`+2b mMB7Q`KHv Qp2`
i?2 BK;2bX
L2ti r2 /2}M2 i?2 7mM+iBQM p(m, z) iQ #2 i?2 MmK#2` Q7 bQm`+2b `2+Qp2`2/
rBi? M Q#b2`p2/ K;MBim/2 BM i?2 BMi2`pH [m; m + ∆m]- M/ `2 b2H2+i2/ b
/`QTQmib- /BpB/2/ #v i?2 MmK#2` Q7 BMD2+i2/ bQm`+2b rBi? M BMi`BMbB+ K;MB@
im/2 BM i?2 bK2 BMi2`pH [m; m+∆m] M/ `2/b?B7i BM i?2 BMi2`pH [z; z +∆z]X
LQi2 i?i i?2 /2}MBiBQM Q7 p(m, z) Bb bHB;?iHv /Bz2`2Mi +QKT`2/ iQ i?2 QM2
mb2/ BM 2X;X arB+FB h?QKTbQM UkyyeV- b i?2v /Q MQi iF2 1//BM;iQM #Bb
BMiQ ++QmMiX AM Qm` /2}MBiBQM- p(m, z) +QmH/ TQi2MiBHHv #2 > R b `2bmHi Q7
i?Bb #Bb +Q``2+iBQMX
*>Sh1_ eX h>1 lo :Gsu GlJALPaAhu 6lL*hAPL h z 4j@8
Rj9
6_PJ h>1 *6>h G1:*u al_o1u .11S 6A1G.a
h?2 2z2+iBp2 pQHmK2b UV277 V Q7 Qm` bm`p2v `2 ;Bp2M #v
#
dV*
V277 (m) = Af
p(m, z)dz,
dz
UeX8V
*
r?2`2 Af Bb i?2 }2H/ `2 BM b[m`2 `+KBMmi2b- M/ dV
Bb i?2 +QKQpBM;
dz
pQHmK2 T2` b[m`2 `+KBMmi2- r?B+? /2T2M/b QM i?2 /QTi2/ +QbKQHQ;vX
h?2 K;MBim/2 Bb K2bm`2/ BM i?2 r@- i@- M/ z @#M/b 7Q` i?2 u@- g @- M/
r@/`QTQmi bKTH2b- `2bT2+iBp2HvX h?2b2 #M/b T`Q#2 ~mt i TT`QtBKi2Hv
Reyy³ `2bi@7`K2 Q7 i?2 bQm`+2b i i?2 2tT2+i2/ K2M `2/b?B7ib- bQ i?i QMHv
KBMQ` F@+Q``2+iBQM rBHH #2 bm{+B2Mi iQ +QKT`2 i?2 `2bmHib 7Q` i?2 /Bz2`2Mi
2TQ+?b /B`2+iHv- b22 i?2 mTT2` TM2H Q7 6B;X eXdX q2 i`Mb7Q`K i?2 TT`2Mi
K;MBim/2b iQ #bQHmi2 K;MBim/2b M/ T2`7Q`K F@+Q``2+iBQM iQ `2bi@7`K2
rp2H2M;i? Q7 Reyy³ mbBM; i?2 K2M `2/b?B7ib 7Q` 2+? Q7 i?2 /`QTQmi bKTH2bBX2X r2 bbmK2 HH bQm`+2b iQ #2 i i?2 bK2 `2/b?B7iX
h?2 mM+2`iBMiB2b BM i?2 K2M `2/b?B7ibR `2 2tT2+i2/ iQ #2 TT`QtBKi2Hv
0.1 7Q` i?2 i?`22 /`QTQmi bKTH2b- b `;m2/ BM a2+iX eXkXjX h?Bb H2/b iQ
mM+2`iBMiB2b BM #Qi? /BbiM+2 KQ/mHmb M/ F@+Q``2+iBQM- `2bmHiBM; BM bvb@
i2KiB+ 2``Q` BM i?2 #bQHmi2 K;MBim/2b Q7 Qm` 2biBKi2/ G6- b22 i?2 HQr2`
TM2H Q7 6B;X eXdX h?2 }MH mM+2`iBMiB2b `2 #Qmi yXyd- yXy8 M/ yXy9 BM i?2
#bQHmi2 K;MBim/2 7Q` i?2 u@- g @- M/ r@/`QTQmi bKTH2b- `2bT2+iBp2HvX
z
7i2` /BpB/BM; i?2 MmK#2` +QmMib #v V277 - r?B+? +Q``2+ib 7Q` BM+QKTH2i2M2bb
M/ 1//BM;iQM #Bb- M/ bm#i`+iBM; i?2 /BbiM+2 KQ/mHmb M/ i?2 F@+Q``2+iBQM
7`QK i?2 TT`2Mi K;MBim/2b- r2 Q#iBM i?2 G6 BM #bQHmi2 K;MBim/2b i
ReyyX
_2bmHib 7`QK i?2 7Qm` }2H/b `2 #BMM2/ iQ ∆K;4yXj- +QK#BM2/- M/ b?QrM
BM 6B;X eX3 M/ h#H2 eXRX lM+2`iBMiB2b BM i?2 K;MBim/2 /B`2+iBQM `2 /m2
iQ mM+2`iBMiB2b BM i?2 `2/b?B7i /Bbi`B#miBQM Q7 bQm`+2 ;HtB2bX h?2 7Qm` BM/2@
T2M/2Mi MHvb2b Q7 i?2 }2H/b HHQr mb iQ 2biBKi2 }2H/@iQ@}2H/ p`BiBQMb 7Q`
2+? Q7 i?2 /i TQBMibX o2`iB+H 2``Q` #`b `2~2+i 2Bi?2` i?Bb mM+2`iBMiv- Q`
R
LQi2 i?i r2 KF2 mb2 Q7 irQ /Bz2`2Mi `2/b?B7i /Bbi`B#miBQMb BM Qm` MHvbBbX hQ
2biBKi2 #Qi? i?2 F@+Q``2+iBQM M/ i?2 2z2+iBp2 pQHmK2b r2 mb2 i?2 /Bbi`B#miBQM ;Bp2M #v
i?2 bBKmHiBQMb /2b+`B#2/ BM a2+iX eXj- r?BH2 r2 mb2 i?2 /Bbi`B#miBQM 7`QK i?2 bBKmHiBQMb
7`QK >BH/2#`M/i 2i HX UkyyNV iQ b?B7i i?2 G6 BM i?2 K;MBim/2 /B`2+iBQMX h?2 `2/b?B7i
/Bbi`B#miBQM 7`QK i?2 Hii2` bBKmHiBQMb `2 2tT2+i2/ iQ #2 KQ`2 `2HB#H2 #2+mb2 i?2v
iF2 rB/2 p`B2iv Q7 i2KTHi2 ;Htv KQ/2Hb BMiQ ++QmMi- #mi r2 +MMQi mb2 i?2K 7Q`
2z2+iBp2 pQHmK2b F@+Q``2+iBQMb #2+mb2 Q7 +QKTmiiBQMH +QMbi`BMibX _i?2` r2 ?p2
iQ bBKmHi2 i?Qb2 rBi? bBM;H2 i2KTHi2X
eX9X _1alGha
Rj8
6B;m`2 eXd, lTT2` TM2H, F@+Q``2+iBQM iQ
Reyy³ 7Q` i?2 J2;*K riz }Hi2`b- b 7mM+@
iBQM Q7 `2/b?B7i #b2/ QM i?2 Ryy Jv` QH/ +QM@
iBMmQmbHv bi`@7Q`KBM; i2KTHi2 rBi? /mbi i@
i2MmiBQM Q7 E(B − V )4yXk8X h?2 p2`;2
`2/b?B7ib 7`QK i?2 bBKmHiBQMb M/ i?2B` mM@
+2`iBMiB2b `2 `2T`2b2Mi2/ #v ?Q`BxQMiH 2``Q`
#`bX h?Bb H2/b iQ +Q``2bTQM/BM; 2``Q` BM i?2
F@+Q``2+iBQMX GQr2` TM2H, a?B7ib 7`QK TT`@
2Mi K;MBim/2b BM i?2 J2;*K riz }Hi2`biQ #bQHmi2 K;MBim/2b i Reyy³X h?2 .Bb@
iM+2 JQ/mHmb M/ F@+Q``2+iBQM `2 iF2M BMiQ
++QmMiX h?2 mM+2`iBMiB2b BM i?2 p2`;2 `2/@
b?B7ib Q7 i?2 bKTH2b H2/ iQ mM+2`iBMiB2b BM
i?2 #bQHmi2 K;MBim/2bX
6B;m`2 eX3, h?2 G6b Q7 G":b BM i?2 *6>[email protected] }2H/bX .i TQBMib M/ #2bi@}iiBM;
a+?2+?i2` 7mM+iBQMb `2 b?QrM 7Q` i?2 uU#Hm2V@- gU;`22MV@- M/ rU`2/V@/`QTQmibX 6Q` H2;B#BHBiv
r2 TTHB2/ bKHH Qzb2i QM i?2 t@tBb pHm2b Q7 i?2 g@- M/ r@ /`QTQmibX h?2 /b?2/ #Hm2
+m`p2 b?Qrb i?2 #2bi }iiBM; a+?2+?i2` 7mM+iBQM 7Q` i?2 u@/`QTQmib 7i2` K;MB}+iBQM 2z2+ib
?p2 #22M BM+Hm/2/- b /2b+`B#2/ BM a2+iX eX9XRX
*>Sh1_ eX h>1 lo :Gsu GlJALPaAhu 6lL*hAPL h z 4j@8
Rje
6_PJ h>1 *6>h G1:*u al_o1u .11S 6A1G.a
h#H2 eXR, h?2 2biBKi2/ G6b 7`QK i?2 *6>hGa .22TX
MReyy,"
@kjXky
@kkXNy
@kkXey
@kkXjy
@kkXyy
@kRXdy
@kRX9y
@kRXRy
@kyX3y
@kyX8y
@kyXky
@RNXNy
@RNXey
@RNXjy
@RNXyy
@R3Xdy
u@/`QTQmib
φk [10−3
JT+−j K;−R ]
yXyyR ± yXyyR
yXyyR ± yXyyR
yXyyd ± yXyyk
yXykk ± yXyyd
yXy8d ± yXyky
yXRRj ± yXyk3
yXk89 ± yXykd
yX9Nd ± yXyeR
yXd33 ± yXRRy
RXR33 ± yXked
RXd98 ± yXjdd
kXk9y ± yXjdj
kXdNN ± yX8RN
jXdj9 ± yX3ej
9Xdky ± yX3ee
jXk8k ± RX8y3
g @/`QTQmib
φk [10−3
JT+−j K;−R ]
@
@
yXyy9 ± yXyyk
yXyRe ± yXyyj
yXyj8 ± yXyy8
yXy3e ± yXyRy
yXRey ± yXykd
yXk3d ± yXyey
yX8yN ± yXyeR
yXdk3 ± yXyed
RXyye ± yXy9y
RX9e8 ± yXR9d
RXd8e ± yXyej
kXkjy ± yXjy8
kX9NN ± yX8e9
jXyj3 ± yXjdy
r@/`QTQmib
φk [10−3
JT+−j K;−R ]
@
@
yXyyk ± yXyyk
yXyRy ± yXyyk
yXyjk ± yXyRy
yXye8 ± yXyR8
yXRkR ± yXyRe
yXkj9 ± yXyk3
yXj93 ± yXyk8
yX9N9 ± yXy8y
yXdy3 ± yXyjy
RXRkj ± yXkRR
RX9ke ± yXkkN
RXek9 ± yXyN8
RX3RN ± yXejy
@
i?2 SQBbbQM MQBb2 i2`K- r?B+?2p2` Bb H`;2biX lbmHHv i?2 }2H/@iQ@}2H/ p`BM+2
/QKBMi2bX b +QMb2[m2M+2 Q7 i?2 rv i?2b2 `2 +QKTmi2/- SQBbbQM MQBb2 Bb
Hrvb iF2M BMiQ ++QmMiX
q2 }i a+?2+?i2` 7mM+iBQM Ua+?2+?i2` RNdeV iQ i?2 #BMM2/ /i TQBMib-
φ(M )dM = 0.4 HM(10)φ∗ 100.4(α+1)(M
∗
−M )
2tT(−100.4(M
∗
−M )
),
UeXeV
rBi? M ∗ #2BM; i?2 +?`+i2`BbiB+ K;MBim/2- α #2BM; i?2 7BMi@2M/ bHQT2- M/
φ∗ #2BM; i?2 Qp2`HH MQ`KHBbiBQMX
lbBM; χ2 biiBbiB+b QM i?`22 /BK2MbBQMH ;`B/ Q7 5003 /Bz2`2Mi a+?2+?i2`
T`K2i2` +QK#BMiBQMb- r2 }M/ i?2 KBMBKH pHm2 Uχ2KBM V 7Q` 2+? Q7 i?2
/`QTQmi bKTH2b vB2H/BM; i?2 #2bi }i pHm2bX hQ 2biBKi2 i?2 2``Q`b BM i?2
}ii2/ T`K2i2`b- r2 T`QD2+i i?2 j@/BK2MbBQMH /Bbi`B#miBQM Q7 χ2 iQ j THM2b
#v iFBM; i?2 KBMBKmK χ2 HQM; i?2 T`QD2+i2/ /BK2MbBQMX AM 6B;X eXN i?2
e3XjW M/ N8X9W +QM}/2M+2 H2p2Hb `2 b?QrM- r?B+? +Q``2bTQM/ iQ ∆χ2 4kXj
M/ eXRd rBi? `2bT2+i iQ χ2Kin X AM h#H2 eXk r2 ;Bp2 i?2 e3XjW +QM}/2M+2 H2p2Hb
QM 2+? BM/BpB/mH T`K2i2`- +Q``2bTQM/BM; iQ ∆χ2 4RXyX
LQi2- ?Qr2p2`- i?i i?Bb 2``Q` 2biBKi2 bbmK2b :mbbBM 2``Q`b- M/ i?i
i?2 2``Q`b QM i?2 /i TQBMib `2 BM/2T2M/2MiX 1bT2+BHHv 7Q` i?2 u@/`QTQmib
i?Bb Bb T`Q##Hv MQi i?2 +b2X h?2 MQ`KHBbiBQM Q7 i?2 G6 b22Kb iQ #2 bvb@
i2KiB+HHv bHB;?iHv /Bz2`2Mi 7Q` 2+? Q7 i?2 }2H/b Ub22 HbQ 6B;X eXRV- ;BpBM;
eX9X _1alGha
Rjd
6B;m`2 eXN, h?2 e3W M/ N8W HBF2HB?QQ/ +QMiQm`b 7Q` /Bz2`2Mi a+?2+?i2` T`K2i2` +QK#B@
MiBQMbX a?QrM `2 i?2 `2bmHib 7Q` i?2 u@/`QTQmib i z ∼ 3 U#Hm2- bQHB/V- i?2 g@/`QTQmib i
z ∼ 4 U;`22M- /QibV- M/ i?2 r@/`QTQmib i z ∼ 5 U`2/- /b?@/QibVX h?2 u@/`QTQmi +QMiQm`b
`2T`2b2Mi i?2 #2bi a+?2+?i2` T`K2i2`b r?2M r2 BM+Hm/2 K;MB}+iBQM 2z2+ib- b /2b+`B#2/
BM a2+iX eX9XRX
bvbi2KiB+ mM+2`iBMiv BM φ∗ Q7 #Qmi jyWX 6Q` i?2 u@/`QTQmib i?Bb 2z2+i
Bb H`;2bi #2+mb2 Q7 bHB;?iHv KQ`2 mM+2`iBM ~mt +HB#`iBQM BM i?2 u@#M/
+QKT`2/ iQ i?2 g @ M/ r@#M/bX h?2 2z2+iBp2 }Hi2` i?`Qm;?Tmi +?M;2b rBi?
iBK2 BM i?2 lo b i?2 iKQbT?2`2 Bb +?M;BM;- M/ HbQ i?2 +K2` Bb H2bb
b2MbBiBp2 BM i?Bb rp2H2M;i? `2;BK2 `2bmHiBM; BM H`;2` b?Qi@MQBb2X
.m2 iQ BM?QKQ;2M2BiB2b BM i?2 Kii2` /Bbi`B#miBQM #2ir22M /BbiMi bQm`+2b
M/ i?2 Q#b2`p2`- Ti?b Q7 T?QiQMb ;2i bHB;?iHv T2`im`#2/X h?Bb `2bmHib BM /BbiQ`iBQM Q7 i?2 b?T2 M/ K;MB}+iBQM Q7 /BbiMi bQm`+2bX q?2M bQm`+2
Bb K;MB}2/ #v 7+iQ` µ- i?2 ~mt ;2ib #QQbi2/ #v i?2 bK2 KQmMiX PM2
+M `2Hi2 M BMi`BMbB+ HmKBMQbBiv /Bbi`B#miBQM iQ M Q#b2`p2/ /Bbi`B#miBQM B7
i?2 K;MB}+iBQM /Bbi`B#miBQM Bb FMQrM- b rb b?QrM #v CBM GBK UkyRyVX
>BH#2`i 2i HX UkyydV 2biBKi2 K;MB}+iBQM /Bbi`B#miBQMb 7Q` /Bz2`2Mi bQm`+2
`2/b?B7ib #v b?QQiBM; `M/QK `vb i?`Qm;? b2`B2b Q7 H2Mb THM2b +`2i2/ 7`QK
*>Sh1_ eX h>1 lo :Gsu GlJALPaAhu 6lL*hAPL h z 4j@8
Rj3
6_PJ h>1 *6>h G1:*u al_o1u .11S 6A1G.a
h#H2 eXk, +QKT`BbQM #2ir22M i?2 #2bi }iiBM; a+?2+?i2` T`K2i2`b M/ i?2B` e3W
+QM}/2M+2 BMi2`pHb 7Q` i?2 u@- g@- M/ r@/`QTQmibX
aKTH2
u
g
r
u#
J∗lo −20.94+0.14
−0.13
−20.84+0.09
−0.09
−20.94+0.10
−0.11
−20.84+0.15
−0.13
φ∗
(10−3 JT+−3 )
1.79+0.51
−0.38
1.36+0.23
−0.20
0.83+0.15
−0.14
2.11+0.63
−0.45
α
−1.65+0.12
−0.11
−1.56+0.08
−0.08
−1.65+0.09
−0.08
−1.60+0.14
−0.11
χ2 //Q7
0.52
0.36
0.19
0.41
.m2 iQ mM+2`iBMiB2b BM i?2 `2/b?B7i /Bbi`B#miBQMb i?2`2 Bb M //BiBQMH
2``Q` +QKTQM2Mi Q7 yXyd- yXy8- M/ yXy9 BM i?2 2biBKi2/ J∗lo 7Q` i?2 u@g @- M/ r@/`QTQmi bKTH2b- `2bT2+iBp2HvX
#
"2bi@}ii2/ a+?2+?i2` T`K2i2`b 7Q` KQ/2H r?2`2 i?2 7mM+iBQM Bb KQ/@
B}2/ rBi? K;MB}+iBQM /Bbi`B#miBQMX
i?2 JBHH2MMBmK aBKmHiBQMX h?2 rB/i? Q7 i?2 K;MB}+iBQM /Bbi`B#miBQM Bb
7QmM/ iQ BM+`2b2 rBi? BM+`2bBM; bQm`+2 `2/b?B7i- M/ i?2 T2F TQbBiBQM Q7 i?2
/Bbi`B#miBQM /2+`2b2b bHB;?iHv rBi? BM+`2bBM; bQm`+2 `2/b?B7iX
J;MB}+iBQM +M ++QmMi 7Q` bi`QM; /2pBiBQM 7`QK a+?2+?i2` 7mM+iBQM
r?2`2 i?2 bHQT2 Q7 i?2 BMi`BMbB+ HmKBMQbBiv /Bbi`B#miBQM Bb p2`v bi22T- b22 CBM
GBK UkyRyVX q2 bi`2bb ;BM i?i r2 K2bm`2 i?2 G6 7`QK pQHmK2 i?i
Bb Km+? H`;2` i?M ?b #22M mb2/ #27Q`2X h?2 #`B;?i 2M/ Q7 Qm` g @- M/ r@
/`QTQmi bKTH2b bmz2`b 7`QK BM+`2bBM; KQmMib Q7 +QMiKBMiBQMX PMHv 7Q`
i?2 u@/`QTQmib r2 T`Q#2 i?2 /Bbi`B#miBQM Q7 u@/`QTQmib i i?2 #`B;?i 2M/ /QrM
iQ /2MbBiv Q7 10−6 K;−1 JT+−3 X q2 mb2 i?2 K;MB}+iBQM /Bbi`B#miBQM 7Q`
bQm`+2 `2/b?B7i Q7 z = 3.1 i?i rb FBM/Hv T`QpB/2/ #v ai27M >BH#2`i iQ
BKT`Qp2 Qm` KQ/2H iQ i?2 /iX
q`BiBM; i?2 G6 b 7mM+iBQM Q7 K;MBim/2- r2 mb2 i?2 7QHHQrBM; 2[miBQM
iQ +Q``2+i i?2 a+?2+?i2` 7mM+iBQM 7Q` K;MB}+iBQM 2z2+ibX Ai Bb 2[mBpH2Mi iQ
i?2 2tT`2bbBQM mb2/ #v CBM GBK UkyRyVX
#
φ(mobs ) = dµ P (µ) φ∗ (mobs + 2.5 HQ;(µ)),
UeXdV
r?2`2 φ∗ Bb i?2 a+?2+?i2` 7mM+iBQM /2}M2/ #v 1[X eXeX h?2 M2r 7mM+iBQM vB2H/b
bHB;?iHv #2ii2` }i iQ i?2 #`B;?i 2M/ Q7 i?2 G6- `2/m+BM; i?2 7Q`KH χ2 //Q7
7`QK yX8k iQ yX9RX 6BM/ i?2 M2r a+?2+?i2` T`K2i2`b- iQ;2i?2` rBi? i?2B`
e3XjW +QM}/2M+2 H2p2Hb BM h#H2 eXk- M/ i?2B` k@/BK2MbBQMH e3XjW M/ N8X9W
+QM}/2M+2 +QMiQm`b THQii2/ BM 6B;X eXNX h?2 #2bi }iiBM; 7mM+iBQM Bb i?2 /b?2/
+m`p2 BM 6B;X eX3X
eX9X _1alGha
RjN
b i?2 #`B;?i b2H2+i2/ u@/`QTQmib `2 HBF2Hv iQ #2 bB;MB}+MiHv K;MB}2/- r2
2tT2+i i?2K iQ TT2` +HQb2 iQ KbbBp2 7Q`2;`QmM/ ;Htv Q` ;`QmT Q7 ;HtB2b
i?i +ib b H2MbX q2 BMbT2+i2/ i?2 #`B;?i2bi UrAB <kjXkV u@/`QTQmib #v 2v2
M/ }M/ i?i i?Bb Bb BM/22/ i?2 +b2 7Q` KMv Q7 i?2KX LQi2 i?i i?2 KQ/2H Bb
biBHH mM+2`iBM b i?2 JBHH2MMBmK bBKmHiBQM /Q2b MQi BM+Hm/2 #`vQMB+ Kii2`M/ bbmK2b σ8 = 0.9 UaT`BM;2H 2i HX kyy8V- r?2`2 `2+2Mi 2biBKi2b BM/B+i2
HQr2` pHm2 `QmM/ yX3 UEQKibm 2i HX kyRyVX HbQ- BM i?2 K;MB}+iBQM
T`Q##BHBiv /Bbi`B#miBQM i?2 TQbbB#BHBiv Q7 KmHiBTHv BK;2/ bvbi2Kb Bb B;MQ`2/X
hQ `mH2 Qmi +QMiKBMiBQM BM i?2 G": bKTH2 i i?2 #`B;?i 2M/ Q7 i?2 G6- i?2
Mim`2 Q7 2+? #`B;?i Q#D2+i ?b iQ #2 p2`B}2/ bT2+i`Qb+QTB+HHvX
biiBbiB+HHv Km+? #2ii2` bKTH2 +M #2 b2H2+i2/ 7`QK i?2 *6>h G2;+v
am`p2v qB/2- +QMbBbiBM; Q7 Rdy b[m`2 /2;`22 BK;BM; BM ugriz Q7 b?HHQr2`
/2Ti?X q2 H2p2 i?Bb 7Q` 7mim`2 bim/B2bX
L2ti r2 2biBKi2 i?2 lo HmKBMQbBiv /2MbBiv UloG.V i i?2 /Bz2`2Mi 2TQ+?bX
hQ #2 #H2 iQ +QKT`2 Qm` `2bmHib rBi? i?2 `2bmHib 7`QK T`2pBQmb bim/B2b- r2 rBHH
BMi2;`i2 i?2 /i TQBMib /QrM iQ L = 0.3L∗z=3 - r?2`2 L∗z=3 (= N.9 × Ryk3 2`;
b−1 >x−1 i Reyy˚
V Bb i?2 +?`+i2`BbiB+ HmKBMQbBiv Q7 Qm` u@/`QTQmi bKTH2X
_2bmHib `2 b?QrM BM i?2 Q//@MmK#2`2/ `Qrb Q7 *QHX j BM h#H2 eXjX >Qr2p2`7Q` bi22T 7BMi@2M/ bHQT2b Q7 α < −1.6- KQ`2 i?M 8yW Q7 i?2 lo HmKBMQbBiv
Bb 2tT2+i2/ iQ #2 2KBii2/ #v HQr2` HmKBMQbBiv bQm`+2bX h?2`27Q`2 r2 rBHH KF2
b2+QM/ 2biBKi2 Q7 i?2 lo HmKBMQbBiv /2MbBiv #v BMi2;`iBM; i?2 #2bi@}iiBM;
a+?2+?i2` 7mM+iBQM Qp2` HH HmKBMQbBiB2bX h?Bb `2bmHib BM
ρlo = φ∗ L∗ Γ(α + 2),
UeX3V
r?2`2 Γ Bb 1mH2`Ƕb :KK 7mM+iBQMX Hi?Qm;? i?Bb 7mHH BMi2;`H Q7 i?2 G6
/2T2M/b bi`QM;Hv QM mM+2`iBMiB2b BM i?2 7BMi@2M/ bHQT2- r2 mb2 Bi iQ T`QpB/2
M mTT2` HBKBi iQ i?2 loG.X h?2 `2bmHib `2 b?QrM BM i?2 2p2M@MmK#2`2/ `Qrb
Q7 *QHX j BM h#H2 eXjX
h?2 2z2+iBp2 2tiBM+iBQM BM i?2 lo Bb bi`QM; 7mM+iBQM Q7 i?2 KQmMi Q7
/mbiX i i?2b2 ?B;? `2/b?B7ib Uz ! 3V i?2 QMHv 2biBKi2 7Q` i?2 KQmMi Q7 /mbi
Bb #b2/ QM K2bm`2 Q7 i?2 lo +QMiBMmmK bHQT2X LQi2 ?Qr2p2` i?i i?2`2 Bb
bi`QM; /2;2M2`+v #2ir22M i?2 ;2 M/ i?2 KQmMi Q7 /mbi BM i?2 i2KTHi2
B7 i?2 `2bi@7`K2 A_ Bb MQi +Qp2`2/- b22 2X;X STQpB+? 2i HX UkyyRVX
"Qmr2Mb 2i HX UkyyNV `2+2MiHv K2bm`2/ i?2 lo@+QMiBMmmK bHQT2 Q7 G":b
i ?B;? `2/b?B7ib 7`QK /22T >ah /i- 7`QK r?B+? i?2 KQmMi Q7 /mbi Q#b+m@
`iBQM +QmH/ #2 2biBKi2/ b 7mM+iBQM Q7 G": K;MBim/2X h?2 pHm2b i?2v
}M/ i i?2 +?`+i2`BbiB+ K;MBim/2b Q7 Qm` bKTH2b `2 E(B − V ) = 0.15 7Q`
z = 3, 4- M/ E(B − V ) = 0.10 7Q` i?2 z ∼ 5 bKTH2X "Qmr2Mb 2i HX UkyyNV
}M/ /2+`2bBM; KQmMi Q7 /mbi 7Q` 7BMi2` K;MBim/2bX 6Q` +QMbBbi2M+v r2
*>Sh1_ eX h>1 lo :Gsu GlJALPaAhu 6lL*hAPL h z 4j@8
R9y
6_PJ h>1 *6>h G1:*u al_o1u .11S 6A1G.a
h#H2 eXj, h?2 ρlo M/ ρa6_ 7Q` i?2 /Bz2`2Mi /`QTQmi bKTH2bX h?2 }`bi HBM2b 7Q` 2+?
bKTH2 +Q``2bTQM/ iQ bmKb Qp2` i?2 /i TQBMib /QrM iQ L = 0.3L∗z=3 r?BH2 i?2 b2+QM/ HBM2b
+Q``2bTQM/ iQ BMi2;`Hb Qp2` i?2 #2bi@}i a+?2+?i2` 7mM+iBQMbX
aKTH2
AMi2;`H HBKBi
u
L > 0.3L∗z=3
a+?2+?i2`
L > 0.3L∗z=3
a+?2+?i2`
L > 0.3L∗z=3
a+?2+?i2`
g
r
ρlo [1026
2`; b >x−R JT+−j ]
1.73 ± 0.09
4.41
1.07 ± 0.03
2.62
0.80 ± 0.03
2.19
−R
ρa6_
[J v`−R JT+−j ],#
0.129+0.064
−0.036
yXR89
0.078+0.032
−0.019
yXyNk
0.027+0.013
−0.007
yXyj3
.m2 iQ mM+2`iBMiB2b BM i?2 `2/b?B7i /Bbi`B#miBQMb- i?2`2 Bb M //BiBQMH
2``Q` +QKTQM2Mi Q7 ∼dW- ∼8W- M/ ∼9W BM i?2 2biBKi2/ ρlo M/ ρa6_
pHm2b 7Q` i?2 u@- g @- M/ r@/`QTQmi bKTH2b- `2bT2+iBp2HvX
#
*Q``2+i2/ 7Q` /mbi 2tiBM+iBQM mbBM; i?2 HmKBMQbBiv /2T2M/2Mi +Q``2+iBQM
7+iQ`b 7`QK "Qmr2Mb 2i HX UkyyNVX avbi2KiB+ 2``Q`b b `2bmHi 7`QK
i?2 ;2@/mbi /2;2M2`+v `2 HbQ BM+Hm/2/X
rBHH mb2 i?2 `2HiBQMb?BTb i?2v 2biBKi2 iQ +Q``2+i 7Q` /mbi 2tiBM+iBQM BM Qm`
/i- M/ MQi i?2 pHm2b 7`QK a2+iX eXjXRX
J2m`2` 2i HX URNNNV }M/ `2HiBQM #2ir22M i?2 lo@+QMiBMmmK bHQT2 M/
i?2 2tiBM+iBQM #v /mbiX "Qmr2Mb 2i HX UkyyNV mb2 i?Bb `2HiBQM M/ }M/- mTQM
BMi2;`iBM; /QrM iQ L = 0.3L∗z=3 - /2MbBiv +Q``2+iBQM 7+iQ`b Q7 6.0+1.8+2.1
−1.4−1.6 +0.7+1.0
5.8+0.8+2.1
M/
2.7
7Q`
i?2
i?`22
`2/b?B7i
bKTH2b`2bT2+iBp2HvX
"Qi?
−0.7−1.5
−0.5−0.7
`M/QK 2``Q`b M/ bvbi2KiB+ 2``Q`b `2 [mQi2/ U"Qmr2Mb 2i HX kyyNVX
q2 MQr +QMp2`i i?2 lo HmKBMQbBiv /2MbBiv BMiQ i?2 bi` 7Q`KiBQM `i2
/2MbBiv- ρa6_ - i i?2 /Bz2`2Mi 2TQ+?b mbBM; UJ/m 2i HX RNN3V-
LU V = 8.0 × 10
27
(
a6_
M v`−R
)
2`; b−R >x−R .
UeXNV
h?Bb `2HiBQM bbmK2b yXR@Rk8J aHT2i2` AJ6 M/ +QMbiMi bi` 7Q`KiBQM
`i2 Q7 ! Ryy Jv`X h?2 `2bmHiBM; 2biBKi2b Q7 ρa6_ `2 b?QrM BM *QHX 9 Q7
h#H2 eXj- r?2`2 r2 ?p2 +Q``2+i2/ 7Q` /mbi 2tiBM+iBQMX AM a2+iX eX8X9 r2
+QKT`2 i?2b2 2biBKi2b iQ pHm2b `2TQ`i2/ BM T`2pBQmb bim/B2bX
LQi2- ?Qr2p2`- i?i bQK2 bQm`+2b HBF2 :L- r?B+? KB;?i #2 BM+Hm/2/ BM
Qm` /`QTQmi bKTH2b- // iQ i?2 iQiH lo HmKBMQbBiv /2MbBiv BM i?2 lMBp2`b2i?Qm;? /Q MQi +QMi`B#mi2 iQ i?2 a6_.X
eX9X _1alGha
R9R
Pm` }/m+BH i2KTHi2 KQ/2H Bb Ryy Jv` QH/ +QMiBMmQmbHv bi`@7Q`KBM; ;Htv
rBi? mMB7Q`K /Bbi`B#miBQM Q7 /mbi +2Mi`2/ `QmM/ E(B − V )4yXk8X h?Bb /mbi
/Bbi`B#miBQM rb +?Qb2M bm+? i?i i?2 /Bbi`B#miBQM Q7 lo@+QMiBMmmK bHQT2b
Q7 i?2 `2+Qp2`2/ bBKmHi2/ bQm`+2b Ki+?2b i?2 /Bbi`B#miBQM Q7 lo@+QMiBMmmK
bHQT2b BM i?2 `2H /i Ub22 6B;X eXjVX q2 i2bi bQK2 Q7 i?2 bbmKTiBQMb r2
K/2 BM a2+iX eXjXR #v +?2+FBM; i?2B` BM~m2M+2 QM i?2 }MH G6bX
b `272`2M+2 a1. r2 mb2 Ryy Jv` QH/ ;Htv KQ/2H rBi? +QMbiMi bi`
7Q`KiBQM M/ bBM;H2 /mbi ii2MmiBQM pHm2 Q7 E(B − V )4yXk8X q2 +QMbB/2`
`2//2` U#Hm2`V i2KTHi2b #v 2Bi?2` BM+`2bBM; U/2+`2bBM;V i?2 ;2 Q7 i?2 bi`@
7Q`KBM; T2`BQ/- Q` BM+`2bBM; U/2+`2bBM;V i?2 KQmMi Q7 /mbiX AM 6B;X eXRy
i?2 +QHQm`b Q7 i?2b2 Hi2`MiBp2 i2KTHi2b- b i?2v rQmH/ #2 K2bm`2/ #v i?2
J2;*K ugriz }Hi2` b2i- `2 b?QrM b 7mM+iBQM Q7 `2/b?B7iX b i?2 [mHBiv Q7
i?2 a+?2+?i2` }i Bb ?B;? BM HH +b2b Uχ2 //Q7 < 1.0V- r2 T`2b2Mi i?2 /Bz2`2M+2b
#v +QKT`BM; i?2 a+?2+?i2` T`K2i2`b,
Ç h?2 7BMi@2M/ bHQT2 α /2T2M/b QM i?2 +QHQm` Q7 i?2 bT2+i`H i2KTHi2X
AM i?2 g @- M/ r@/`QTQmi bKTH2b- `2//2` i2KTHi2b i2M/ iQ ;Bp2 bi22T2`
α i?M #Hm2` i2KTHi2bX h?2 `2bQM 7Q` i?Bb Bb b 7QHHQrb- rBi? i?2 g @
/`QTQmib b M 2tKTH2X aQm`+2b BM i?2 b2H2+iBQM #Qt ?p2 `2/ Q#b2`p2/
g − i +QHQm`bX 6Q` 7BMi K;MBim/2b UMQi2 i?i i?2 `272`2M+2 K;MBim/2
Bb K2bm`2/ BM i?2 i@#M/V- i?2 g @#M/ K;MBim/2 2t+22/b i?2 HBKBiBM;
K;MBim/2 Q7 i?2 bm`p2vX PMHv HQr2` HBKBi QM g − r +M i?2M #2 ;Bp2M
M/ i?2 bQm`+2 KQp2b Qmi Q7 i?2 /`QTQmi b2H2+iBQM #QtX h?2 K;MB@
im/2 i r?B+? i?Bb ?TT2Mb /2T2M/b QM i?2 g − i +QHQm` Q7 i?2 i2KTHi2X
b i?2 p2`;2 g − i +QHQm` BM i?2 b2H2+iBQM #Qt Bb `2//2` 7Q` `2/ i2K@
THi2b U6B;X eXRyV- i?2 /2i2+iBQM `i2 Q7 `2/ bQm`+2b Bb bmTT`2bb2/ i 7BMi
K;MBim/2bX h?Bb `;mK2Mi ?QH/b 7Q` Mv `2/ i2KTHi2 BM i?2 g @- M/
r@/`QTQmi bKTH2bX 6B;X eXRy BM/B+i2b i?i i?2 QTTQbBi2 2z2+i ?TT2Mb
BM i?2 u@/`QTQmi bKTH2 b i?2 u−r +QHQm` Bb ;2M2`HHv #Hm2` U`2//2`V 7Q`
`2//2` U#Hm2`V i2KTHi2b BM i?2 b2H2+iBQM #QtX h?Bb 2z2+i Bb BM/22/ HbQ
BM72``2/ 7`QK i?2 bBKmHiBQMbX h?2`2 Bb M //BiBQMH 2z2+i /m2 iQ i?2
`2[mB`2K2Mi i?i g @/`QTQmib `2 MQi /2i2+i2/ BM u- M/ i?i r@/`QTQmib
`2 M2Bi?2` /2i2+i2/ BM g MQ` BM uX h?Bb bmTT`2bb2b i?2 /2i2+iBQM Q7 #`B;?i
g @- M/ r@/`QTQmib- 2bT2+BHHv i HQr `2/b?B7ibX h?2 #Hm2` i?2 u−i +QHQm`
7Q` i?2 g @/`QTQmib UBX2X i?2 #Hm2` i?2 i2KTHi2V- i?2 bi`QM;2` i?Bb 2z2+i
BbX bBKBH` `;mK2Mi ?QH/b 7Q` i?2 r@/`QTQmibX h?2`27Q`2 i?2 V277 Ƕb
`2 ?B;?2` BM i?2 7BMi K;MBim/2 `2;BK2- bQ i?i i?2 G6b `2 HQr2` i
i?Bb 2M/X h?2 `M;2b Q7 #2bi@}ii2/ α pHm2b- 7Q` i?2 i2KTHi2 bT2+i` r2
+QMbB/2`2/- `2 −1.82 < α < −1.38 7Q` i?2 u@- −1.82 < α < −1.42 7Q`
i?2 g @- M/ −2.14 < α < −1.40 7Q` i?2 r@/`QTQmi bKTH2X
Ç h?2 +?`+i2`BbiB+ K;MBim/2- M ∗ - /Q2b MQi b2MbBiBp2Hv /2T2M/ QM i?2
*>Sh1_ eX h>1 lo :Gsu GlJALPaAhu 6lL*hAPL h z 4j@8
R9k
6_PJ h>1 *6>h G1:*u al_o1u .11S 6A1G.a
6B;m`2 eXRy, h?2 ;`2v TQBMib `2T`2b2Mi i?2 +QHQm`b Q7 Ry-yyy Q#D2+ib BM }2H/ R Q7 i?2 *6>hGa
.22TX h?2 #H+F #Qt2b `2 /2}M2/ #v 1[bX eXR@eXj M/ `2 mb2/ iQ b2H2+i u@UiQT TM2HbV- g@
UKB//H2 TM2HbV- M/ r@U#QiiQK TM2HbV /`QTQmibX h?2 +QHQm`2/ i`+Fb `2T`2b2Mi i?2 +QHQm`b
Q7 i2KTHi2 ;Htv b 7mM+iBQM Q7 zX h?2v `2 2pHmi2/ i BMi2`pHb Q7 ∆z4yXRX h?2
bvK#QHb K`F `2/b?B7ib 7`QK kX8 iQ jX8- 7`QK jXk iQ 9Xk M/ 7`QK 9Xk iQ 8Xk 7Q` u@- g@- M/
r@/`QTQmib `2bT2+iBp2HvX h?2 ;`22M +m`p2 rBi? ×@bvK#QHb `2T`2b2Mib `272`2M+2 KQ/2H- Ryy
Jv` QH/ +QMiBMmQmbHv bi`@7Q`KBM; i2KTHi2 rBi? /mbi ii2MmiBQM Q7 E(B − V )4yXk8X AM
i?2 H27i TM2Hb r2 +QMbB/2` `2//2` U#Hm2`V i2KTHi2b #v BM+`2bBM; U/2+`2bBM;V i?2 i2KTHi2
;2- b22 i?2 `2/ U#Hm2V +m`p2b M/ i?2 $ U♦V@bvK#QHbX AM i?2 `B;?i TM2Hb r2 +QMbB/2` `2//2`
U#Hm2`V i2KTHi2b #v BM+`2bBM; U/2+`2bBM;V i?2 KQmMi Q7 /mbi BM i?2 i2KTHi2- b22 i?2 `2/
U#Hm2V +m`p2b M/ i?2 $ U♦V@bvK#QHbX LQi2 i?i r2 mb2 /Bbi`B#miBQM Q7 /mbi BM Qm` }/m+BH
MHvbBb Ub22 a2+iX eXjXRVX
eX9X _1alGha
R9j
i2KTHi2 bT2+i`mK +?Qb2MX h?2 `M;2b Q7 #2bi@}ii2/ M ∗ pHm2b- 7Q` i?2
i2KTHi2 bT2+i` r2 +QMbB/2`2/- `2 −20.88 < M ∗ < −20.72 7Q` i?2 u@−21.06 < M ∗ < −20.74 7Q` i?2 g @- M/ −21.26 < M ∗ < −20.88 7Q`
i?2 r@/`QTQmi bKTH2X >Qr2p2`- MQi?2` bvbi2KiB+ mM+2`iBMiv BM i?Bb
T`K2i2` Bb /m2 iQ i?2 mMFMQrM `2/b?B7i /Bbi`B#miBQM Q7 bQm`+2 ;HtB2bb22 6B;X eXd- r?B+? /2T2M/b QM i?2 KBt Q7 i2KTHi2b mb2/ #v >BH/2#`M/i
2i HX UkyyNVX
Ç h?2 MQ`KHBbiBQM φ∗ /2+`2b2b UBM+`2b2bV r?2M i?2 7BMi@2M/ bHQT2
#2+QK2b bi22T2` Ub?HHQr2`VX h?2 #2bi@}i a+?2+?i2` T`K2i2`b KQp2
i?2M BM i?2 /B`2+iBQM Q7 i?2 /2;2M2`+v Q7 i?2 2HHBTb2 BM i?2 mTT2` H27i
T`i Q7 6B;X eXNX h?2 `M;2b Q7 #2bi@}ii2/ φ∗ pHm2b (10−3 JT+−3 )- 7Q`
i?2 i2KTHi2 bT2+i` r2 +QMbB/2`2/- `2 1.36 < φ∗ < 2.89 7Q` i?2 [email protected] < φ∗ < 1.74 7Q` i?2 g @- M/ 0.39 < φ∗ < 1.12 7Q` i?2 r@/`QTQmi
bKTH2X
aQK2 bim/B2b U2X;X arB+FB h?QKTbQM kyyeV KF2 mb2 Q7 bi`#m`bi
i2KTHi2 BMbi2/ Q7 +QMiBMmQmbHv bi`@7Q`KBM; KQ/2HX h?2 bi2HH` TQTmHiBQM
BM bi`#m`bi i2KTHi2 Bb QH/2` QM p2`;2- M/ i?2`27Q`2 i?2 +QHQm`b rBHH #2
`2//2`X >Qr2p2`- 7Q` i2KTHi2 ;2 Q7 Ryy Jv` i?2 /Bz2`2M+2 BM +QHQm`b Bb
p2`v bKHHX q2 +QKT`2 i?2 a+?2+?i2` T`K2i2`b i?i r2 K2bm`2 7i2` mbBM;
Qm` `272`2M+2 KQ/2H UBX2X Ryy Jv` +QMiBMmQmbHv bi`@7Q`KBM; i2KTHi2 rBi?
/mbi `2//2MBM; Q7 E(B − V )4yXk8V rBi? KQ/2H r?2`2 r2 +?M;2 i?2 bi`@
7Q`KiBQM Hr iQ bi`#m`biX q2 }M/ i?2 a+?2+?i2` T`K2i2`b iQ +?M;2 BM
i?2 /B`2+iBQMb i?i `2 2tT2+i2/ 7Q` `2//2` i2KTHi2- b 2tTHBM2/ #Qp2X
>Qr2p2` i?2 /Bz2`2M+2b `2 BMbB;MB}+Mi bBM+2 i?2v `2 Km+? bKHH2` i?M i?2
biiBbiB+H 2``Q`b QM i?2 a+?2+?i2` T`K2i2`bX
q2 bi`2bb ;BM i?i r2 mb2 KBt Q7 /mbi KQmMib BM Qm` biM/`/ MH@
vbBb iQ Ki+? i?2 lo@+QMiBMmmK bHQT2 /Bbi`B#miBQM i?i Bb K2bm`2/ 7`QK i?2
/iX 1bT2+BHHv 7Q` i?2 u@- M/ g @/`QTQmib i?Bb Tmib bi`QM; +QMbi`BMib QM i?2
+QK#BMiBQM Q7 i?2 ;2 M/ i?2 KQmMi Q7 /mbi BM i?2 KQ/2H i2KTHi2- bQ i?i
r2 +M `2/m+2 i?2 bvbi2KiB+ 2``Q` iQ KBMBKmKX
hQ DmbiB7v i?2 bbmKTiBQMb r2 KF2 `2;`/BM; i?2 b?T2b Q7 Qm` bBKmHi2/
bQm`+2b r2 HbQ 2biBKi2/ i?2 bvbi2KiB+ 2``Q` QM i?2 G6 /m2 iQ i?Bb +QK@
TQM2MiX "2+mb2 r2 2tT2+i bBKBH` `2bmHib BM i?2 i?`22 /`QTQmi bKTH2b- r2
QMHv `mM i?2b2 bBKmHiBQMb 7Q` i?2 g @/`QTQmibX q2 BMD2+i bQm`+2b i?i `2 yXy8Ǵ
H`;2` i?M i?2 K2bm`2/ TQbBiBQM@/2T2M/2Mi Sa6- M/ +QKT`2 pHm2b Q7 JQ7@
7i T`K2i2` β = 3.0 M/ β = 5.0 rBi? Qm` }/m+BH β = 4.0 T`K2i2`X q2
}M/ i?2 7QHHQrBM;,
Ç b 2tT2+i2/- α #2+QK2b bi22T2` 7Q` KQ`2 2ti2M/2/ bQm`+2b UBX2X BM+`2b@
BM; i?2 R0 Q` /2+`2bBM; β V- b i?Bb +mb2b i?2 T2F bm`7+2 #`B;?iM2bb iQ
/`QTX h?Bb QMHv bB;MB}+MiHv z2+ib i?2 V277 Ƕb i i?2 7BMi 2M/ Q7 i?2 G6X
1biBKiBQMb Q7 α `M;2 7`QK −1.94 < α < −1.36X bBKBH` +?M;2 Bb
*>Sh1_ eX h>1 lo :Gsu GlJALPaAhu 6lL*hAPL h z 4j@8
R99
6_PJ h>1 *6>h G1:*u al_o1u .11S 6A1G.a
2tT2+i2/ 7Q` i?2 u@- M/ r@ /`QTQmi bim/B2bX h?2 Qi?2` a+?2+?i2` T`K@
2i2`b- φ∗ M/ M ∗ - i?2M HbQ +?M;2 bHB;?iHv b i?2v KQp2 BM i?2 /B`2+iBQM
Q7 i?2 /2;2M2`+v BM 6B;X eXNX
6m`i?2`KQ`2 r2 }M/ i?i- #b2/ QM i?2 /Bz2`2Mi i2KTHi2 bT2+i`- i?2
2biBKi2/ lo HmKBMQbBiv /2MbBiv p`B2bX h?2 `M;2b `2- mTQM BMi2;`iBQM
/QrM iQ L < 0.3L∗z=3 - BM mMBib [Ryke 2`; b−R >x−R JT+−j ]- 1.30 < ρlo < 1.98
7Q` i?2 u@- 0.92 < ρlo < 1.15 7Q` i?2 g @- M/ 0.80 < ρlo < 0.92 7Q` i?2
r@/`QTQmibX
AM Q`/2` iQ BHHmbi`i2 i?2 2z2+i i?i i?2 1//BM;iQM #Bb +M ?p2 QM G6
2biBKiBQMb r2 `2T2i Qm` MHvbBb rBi? bHB;?iHv +?M;2/ p(m, z)X AM i?2 +QK@
TH2i2M2bb bBKmHiBQMb r2 #BM i?2 `2+Qp2`2/ bQm`+2b #v i?2B` BMi`BMbB+ K;MBim/2
BMbi2/ Q7 i?2B` `2+Qp2`2/ K;MBim/2X .QBM; bQ H2p2b i?2 1//BM;iQM #Bb mM@
+Q``2+i2/X q2 }M/ i?i i?2 a+?2+?i2` }i iQ i?2 `2bmHiBM; G6b `2 MQi b ;QQ/
b 7Q` Qm` biM/`/ MHvbBb- 2bT2+BHHv 7Q` i?2 g @- M/ r@/`QTQmib- r?2`2 r2
}M/ i?i χ2KBM //Q7 rQmH/ #2 RXy M/ jXy- `2bT2+iBp2HvX 6Q` i?2 u@/`QTQmib i?2
#2bi@}iiBM; T`K2i2`b `2 MQi +?M;2/ bB;MB}+MiHv- #mi 7Q` i?2 g @- M/ r@
/`QTQmib i?2 7BMi@2M/ bHQT2 bi22T2Mb r?BH2 i?2 MQ`KHBbiBQM Q7 i?2 a+?2+?i2`
7mM+iBQM /2+`2b2bX
LQi2 i?i r2 /B/ MQi ++QmMi 7Q` i?2 T`2b2M+2 Q7 GvKM@ α 2KBbbBQM BM Qm`
bBKmHiBQMb- Hi?Qm;? i?Bb HBM2 +H2`Hv +QMi`B#mi2b iQ #`Q/#M/ ~mt2bX a?TH2v
2i HX UkyyjV K2bm`2/ i?2 +QMi`B#miBQM Q7 i?Bb HBM2 BM i?2 bT2+i` Q7 z ∼ 3
G":b M/ +QM+Hm/2/ i?i QMHv ∼ 25W Q7 i?2 bKTH2 b?Qr2/ bB;MB}+Mi Gv α
2KBbbBQM bm+? i?i 1qUGvαV > 20- b22 HbQ _2//v 2i HX Ukyy3VX Hi?Qm;?
i?2 `2HiBp2 +QMi`B#miBQM Q7 i?Bb HBM2 Bb i?Qm;?i iQ BM+`2b2 iQr`/b ?B;?2`
`2/b?B7i M/ 7BMi2` +QMiBMmmK HmKBMQbBiv- i?Bb ?b MQi #22M [mMiB}2/ v2iX
q2 rBHH i?2`27Q`2 /2b+`B#2 TQbbB#H2 #Bbb2b /m2 iQ i?2 T`2b2M+2 Q7 i?Bb HBM2 BM
i?2 K2bm`2K2Mi Q7 i?2 G6 QMHv [mHBiiBp2HvX
A7 i?2 HBM2 TT2`b BM 2KBbbBQM- Bi +QMi`B#mi2b iQ i?2 ~mt BM i?2 *6>h g @
#M/ 7Q` `2/b?B7ib Q7 #Qmi 2.5 < z < 3.5- BM i?2 r@#M/ 7Q` `2/b?B7ib Q7 #Qmi
3.7 < z < 4.6- BM i?2 i@#M/ 7Q` `2/b?B7ib Q7 #Qmi 4.8 < z < 5.9- M/ BM i?2
z @#M/ 7Q` `2/b?B7ib Q7 #Qmi z > 5.8X 6QHHQrBM; i?2 `2/b?B7i /Bbi`B#miBQMb 7`QK
>BH/2#`M/i 2i HX UkyyNV- r2 2tT2+i i?i i?2 HBM2 T`2/QKBMMiHv +QMi`B#mi2b iQ
i?2 KB//H2 #M/ BM irQ +QHQm` b2H2+iBQM 7Q` i?2 u@- M/ r@ /`QTQmi bKTH2bKQpBM; i?2 bQm`+2 iQ i?2 mTT2` H27i BM 6B;X eXRyX h?Bb 2z2+i +mb2b i?2 2z2+iBp2
pQHmK2b iQ `Bb2- i?2`2#v HQr2`BM; i?2 G6 K2bm`2K2MiX A7 i?2 HBM2 BM/22/ ;2ib
bi`QM;2` i 7BMi K;MBim/2b- i?Bb rQmH/ #Bb i?2 G6 K2bm`2K2Mi M/ `2bmHib
BM b?HHQr2` HT?X AM Qm` g @/`QTQmi bKTH2 i?2 HBM2 Bb 2tT2+i2/ iQ +QMi`B#mi2
iQ i?2 ~mt BM #Qi? i?2 r@ M/ i@#M/- /2T2M/BM; QM i?2 `2/b?B7i Q7 i?2 T`iB+mH`
bQm`+2X AM i?2 +b2 r?2`2 i?2 HBM2 7HHb BM i?2 r@#M/- i?2 2z2+iBp2 pQHmK2b `Bb2
M/ i?2 G6 r2 K2bm`2/ Bb iQQ ?B;?X 6Q` i?2 `2/b?B7ib r?2`2 i?2 HBM2 7HHb BM i?2
i@#M/- i?2 bQm`+2b rQmH/ KQp2 iQ i?2 `B;?i BM 6B;X eXRy bQ i?i i?2 2z2+iBp2
pQHmK2b `2 /2+`2b2/ M/ i?2 G6 BM+`2b2bX hQ 2biBKi2 r?B+? 2z2+i T`2pBHb-
eX8X *PJS_AaPL qAh> S_1oAPla .1h1_JALhAPLa
R98
i?2 `2/b?B7i /Bbi`B#miBQM M22/b iQ #2 K2bm`2/ bT2+i`Qb+QTB+HHvX aQK2 Q#D2+ib
b?Qr Gv@α BM #bQ`TiBQM `i?2` i?M 2KBbbBQM- r?B+? rQmH/ ;Bp2 i?2 QTTQbBi2
2z2+iX
LQi2 i?i "Qmr2Mb 2i HX UkyydV KQ/2H i?2 +QMi`B#miBQM Q7 Gvα BM i?2
K2bm`2K2Mi Q7 i?2B` G6- #v mbBM; bBKTH2 KQ/2H r?2`2 jjW Q7 i?2 z ∼ 4 − 5
G":b ?p2 1qUGv α V4 8y - BM/2T2M/2Mi Q7 i?2 +QMiBMmmK HmKBMQbBivX h?2v
}M/ i?i i?Bb z2+ib i?2 MQ`KHBbiBQM Q7 i?2 G6 #v QMHv ∼ 10WX >Qr2p2`- r2
bi`2bb ;BM i?i i?2 K2bm`2 Q7 α KB;?i #2 #Bb2/ B7 i?2 bi`2M;i? Q7 i?2 HBM2
/2T2M/b QM i?2 +QMiBMmmK HmKBMQbBivX
Hi?Qm;? r2 +M K2bm`2 i?2 lo HmKBMQbBiv /2MbBiv rBi? ;`2i ++m`+vM 2biBKi2 Q7 i?2 a6_ .2MbBiv /2T2M/b b2MbBiBp2Hv QM i?2 /mbi 2tiBM+iBQM
+Q``2+iBQMX lbBM; i?2 T`2b+`BTiBQM 7`QK "Qmr2Mb 2i HX UkyyNV- r2 }M/ i?i
i?2 a6_ .2MbBiv b?Qrb bB;MB}+Mi BM+`2b2 #v 7+iQ` Q7 9@8 #2ir22M z ∼ 5
M/ z ∼ 3 X
q2 }M/ bi`QM; BM+`2b2 BM φ∗ #2ir22M z ∼ 5 M/ z ∼ 3 #v 7+iQ` Q7
∗
kX8- r?B+? Bb `Q#mbi `2bmHiX h?2 +?`+i2`BbiB+ K;MBim/2- Mlo
- ?Qr2p2`
Bb MQi p2`v r2HH +QMbi`BM2/ #v Qm` /i b2iX h?Bb Bb /m2 iQ mM+2`iBMiB2b BM
i?2 `2/b?B7i /Bbi`B#miBQMb Q7 i?2 bQm`+2 ;HtB2b- b i?2`2 `2 MQ bT2+i`Qb+QTB+
∗
/i pBH#H2X Pm` /i `2 +QMbBbi2Mi rBi? MQM@2pQHpBM; Mlo
U∼ −20.9V
#2ir22M z ∼ 5 M/ z ∼ 3X Pm` /i /Q MQi b?Qr M 2pQHmiBQM Q7 i?2 7BMi@2M/
bHQT2- M/ BM/B+i2 α ∼ −1.6 BM i?Bb 2TQ+?X
"27Q`2 r2 +QKT`2 Qm` `2bmHib 7`QK 2+? Q7 i?2 bKTH2b rBi? a+?2+?i2` T`K@
2i2`b `2TQ`i2/ 7`QK T`2pBQmb /2i2`KBMiBQMb BM i?2 HBi2`im`2- i?2`2 `2 72r
i?BM;b i?i b?QmH/ #2 MQi2/X q2 rBHH +QKT`2 `2bmHib i `2/b?B7ib Q7 around j9 M/ 8X h?2 G":b `2 ;2M2`HHv b2H2+i2/ 7`QK /Bz2`2Mi bm`p2vb M/ }Hi2` b2ibM/ i?2`27Q`2 BMi`BMbB+HHv bHB;?iHv /Bz2`2Mi ;HtB2b Kv #2 b2H2+i2/- bim/B2/
M/ +QKT`2/X HbQ i?2 `2bi@7`K2 rp2H2M;i? i r?B+? i?2 G6 Bb 2biBKi2/p`B2bX q2 +QKT`2/ i?2 G6b i Reyy³- r?BH2 2X;X arB+FB h?QKTbQM UkyyeV
K2bm`2/ i?2 G6 i Rdyy³- M/ 2X;X :BpHBb+Q 2i HX Ukyy9V /B/ i?2B` MH@
vbBb i R8yy³X aQK2 Q7 i?2 bim/B2b /2b+`B#2/ #2HQr KF2 mb2 Q7 B/2MiB+H Q`
T`iBHHv Qp2`HTTBM; /ib2ibX Pm` MHvbBb- QM i?2 +QMi``v- Bb +QKTH2i2Hv
BM/2T2M/2Mi 7`QK T`2pBQmb /2i2`KBMiBQMb- 2t+2Ti 7Q` i?2 /mbi 2tiBM+iBQM +Q`@
`2+iBQM BM Qm` a6_ /2MbBiv 2biBKi2X 6m`i?2`KQ`2 i?2 2``Q`b Q7 b2p2`H Qi?2`
bim/B2b +QmH/ #2 mM/2`2biBKi2/ #2+mb2 QMHv i?2 SQBbbQM MQBb2 +QKTQM2Mi
Bb iF2M BMiQ ++QmMi- b Qi?2` MQBb2 +QKTQM2Mib U2X;X +QbKB+ p`BM+2V `2
/B{+mHi iQ 2biBKi2 rBi? i?2 ivTB+H bKHH bm`p2v pQHmK2b Q7 Qi?2` bm`p2vbX
*>Sh1_ eX h>1 lo :Gsu GlJALPaAhu 6lL*hAPL h z 4j@8
R9e
6_PJ h>1 *6>h G1:*u al_o1u .11S 6A1G.a
HbQ MQi2 i?i r2 +QKT`2 Qm` k@/BK2MbBQMH 2``Q` 2HHBTb2b rBi? R@/BK2MbBQMH
2``Q` #`b i?i r2`2 iiBM2/ 7i2` K`;BMHBxBM; Qp2` i?2 irQ Qi?2` a+?2+?i2`
T`K2i2`bX h?Bb /BHmi2b BM7Q`KiBQM QM /2;2M2`+B2b #2ir22M a+?2+?i2` T@
`K2i2`bX 6Q` i?2b2 `2bQMb i?2 +QKT`BbQMb BM i?Bb b2+iBQM rBHH #2 `i?2`
[mHBiiBp2- M/ `2 K2Mi iQ Tmi Qm` `2bmHib BMiQ +QMi2tiX *QKT`BbQMb Q7 i?2
a+?2+?i2` T`K2i2`b `2 b?QrM BM h#H2 eX9- M/ BM 6B;bX eXRR- eXRk eXRjM/ rBHH #2 /Bb+mbb2/ #2HQrX
h#H2 eX9, Pm` 2biBKi2/ a+?2+?i2` T`K2i2`b +QKT`2/ rBi? pHm2b `2TQ`i2/ BM i?2 HBi2`@
im`2- 7Q` i?2 i?`22 /`QTQmi bKTH2bX
_272`2M+2
MU∗ V
u@/`QTQmib
h?Bb rQ`F- a+?2+?i2`
−20.94+0.14
−0.13
h?Bb rQ`F- a+?2+?i2`YJ;MB}+iBQM
−20.84+0.15
−0.13
_2//v ai2B/2H UkyyNV
−20.97 ± 0.14
arB+FB h?QKTbQM UkyyeV
−20.90+0.22
−0.14
`MQmib 2i HX Ukyy8V
−21.08 ± 0.45
SQHB 2i HX UkyyRV
−20.84 ± 0.37
ai2B/2H 2i HX URNNNV
−21.04 ± 0.15
g@/`QTQmib
h?Bb rQ`F
−20.84 ± 0.09
"Qmr2Mb 2i HX UkyydV
−20.98 ± 0.10
uQb?B/ 2i HX UkyyeV
−21.14+0.14
−0.15
arB+FB h?QKTbQM UkyyeV
−21.0+0.4
−0.5
:BpHBb+Q Ukyy8V
−21.20 ± 0.04
Pm+?B 2i HX Ukyy9V
−21.0 ± 0.1
ai2B/2H 2i HX URNNNV
−21.05
r@/`QTQmib
h?Bb rQ`F
−20.94+0.10
−0.11
"Qmr2Mb 2i HX UkyydV
−20.64 ± 0.13
P2b+? 2i HX UkyydV
−20.78 ± 0.16
Ari 2i HX UkyydV
−21.28 ± 0.38
uQb?B/ 2i HX UkyyeV
−20.72+0.16
−0.14
:BpHBb+Q Ukyy8V
−21.06 ± 0.05
Pm+?B 2i HX Ukyy9V
−20.3 ± 0.2
(10
−3
φ∗
JT+−3 )
α
1.79+0.51
−0.38
2.11+0.63
−0.45
1.71 ± 0.53
1.70+0.59
−0.32
1.62 ± 0.90
2.3
1.4
−1.65+0.12
−0.11
−1.60+0.14
−0.11
−1.73 ± 0.13
−1.43+0.17
−0.09
−1.47 ± 0.21
−1.37 ± 0.19
−1.60 ± 0.13
1.36+0.23
−0.20
1.3 ± 0.2
1.46+0.41
−0.35
0.85+0.53
−0.45
1.20 ± 0.03
1.2 ± 0.2
1.1
−1.56 ± 0.08
−1.73 ± 0.05
−1.82 ± 0.09
−1.26+0.40
−0.36
−1.64 ± 0.10
−2.2 ± 0.2
−1.6 U}t2/V
0.83+0.15
−0.14
1.0 ± 0.3
0.9 ± 0.3
0.41+0.29
−0.30
1.23+0.44
−0.27
0.83 ± 0.03
2.4 ± 1.0
−1.65+0.09
−0.08
−1.66 ± 0.09
−1.54 ± 0.10
−1.48+0.38
−0.32
−1.82 U}t2/V
−1.51 ± 0.18
−1.6 U}t2/V
z
q2 +QKT`2 i?2 `2bmHib 7`QK Qm` u@/`QTQmi bKTH2 rBi? b2p2`H a+?2+?i2` T@
`K2i2`b `2TQ`i2/ BM i?2 HBi2`im`2X arB+FB h?QKTbQM UkyyeV 2biBKi2/ i?2
G6 7`QK i?2 E2+F /22T }2H/b- 7`QK Un GR@b2H2+i2/ bi`@7Q`KBM; ;HtB2bX h?2B`
eX8X *PJS_AaPL qAh> S_1oAPla .1h1_JALhAPLa
R9d
6B;m`2 eXRR, *QKT`BbQM i z ∼ 3X h?2 2HHBTb2b `2T`2b2Mi i?2 e3W M/ N8W +QM}/2M+2
+QMiQm`b 7Q` /Bz2`2Mi a+?2+?i2` T`K2i2` +QK#BMiBQMb- #b2/ QM Qm` bim/vX h?2 2``Q` #`b
`2~2+i i?2 e3W +QM}/2M+2 HBKBib QM i?2 `2bmHib 7`QK T`2pBQmb bim/B2bX Pm` `2bmHib ;`22
rBi?BM i?2 R@σ H2p2H rBi? KQbi Q7 i?2 Qi?2` /2i2`KBMiBQMbX
6B;m`2 eXRk, aBKBH` b 6B;X eXRR- #mi MQr +QKT`BbQM i z ∼ 4X
*>Sh1_ eX h>1 lo :Gsu GlJALPaAhu 6lL*hAPL h z 4j@8
R93
6_PJ h>1 *6>h G1:*u al_o1u .11S 6A1G.a
bm`p2v `2 Bb #Qmi ey iBK2b bKHH2` i?M i?2 *6>[email protected] h?2 /2Ti? Q7
i?2B` Q#b2`piBQMb Bb bHB;?iHv /22T2` i?M Qm`b- #mi /m2 iQ Qm` 1//BM;iQM #Bb
+Q``2+iBQM- r2 `2 #H2 iQ T`Q#2 i?2 G6b /QrM iQ bBKBH` K;MBim/2bX _2//v
ai2B/2H UkyyNV 2biBKi2 G6 i z ∼ 3- 7`QK jR bTiBHHv BM/2T2M/2Mi }2H/b?pBM; iQiH `2 Q7 #Qmi [m`i2` Q7 Qm`bX h?2B` bKTH2 +QMiBMb b2p2`H
i?QmbM/b Q7 bT2+i`Qb+QTB+ `2/b?B7ib i z 4k@jX `MQmib 2i HX Ukyy8V KBMHv
7Q+mbb2/ QM i?2 ;Htv G6 i HQr2` `2/b?B7ib U0.2 ≤ z ≤ 1.2V 7`QK GALEX @
/i- #mi i?2B` `2/b?B7i `M;2 rb 2ti2M/2/ mbBM; Rdj ;HtB2b i z ∼ 3 7`QK
i?2 >.6 bKTH2X SQHB 2i HX UkyyRV mb2/ i?2 >.6@L- >.6@a M/ [email protected]
bKTH2b iQ 2biBKi2 i?2 G6 BM i?2 `M;2 2.5z3.5X h?2B` bKTH2 rb i?2`27Q`2
b2H2+i2/ 7`QK p2`v bKHH pQHmK2- r?B+? KF2b i?2B` `2bmHib bmb+2TiB#H2 iQ
+QbKB+ p`BM+2X ai2B/2H 2i HX URNNNV TBQM22`2/ i?Bb rQ`F- M/ 2biBKi2/ i?2
lo G6 7`QK yXkj /2;2 Q7 KQ/2`i2Hv /22T /iX h?2B` bim/v rb bmTTQ`i2/ #v
bT2+i`Qb+QTB+ `2/b?B7i bKTH2X h?Bb /i Bb BM+Hm/2/ BM i?2 bim/v #v _2//v
ai2B/2H UkyyNVX
Pm` `2bmHib ;`22 rBi?BM i?2 1 − σ H2p2H rBi? i?2 `2bmHib 7`QK T`2pBQmb
/2i2`KBMiBQMb i z ∼ 3X LQi2 i?i i?2 Qi?2` /i TQBMib HB2 BM i?2 /B`2+iBQM
Q7 i?2 2HQM;i2/ 2HHBTb2- M/ i?2`27Q`2 BM i?2 /B`2+iBQM Q7 i?2 /2;2M2`+v r2
}M/X
z
Pm` g @/`QTQmi bKTH2 Bb +QKT`2/ rBi? i?2 z ∼ 4 bKTH2 7`QK arB+FB h?QKTbQM UkyyeV- b2H2+i2/ 7`QK i?2 GRI }Hi2` b2ib QM i?2 E2+F i2H2b+QT2X
h?2B` `2 Bb B/2MiB+H iQ i?2 QM2 7`QK r?B+? i?2 z ∼ 3 G6 rb 2biBKi2/X
ai2B/2H 2i HX URNNNV HbQ 2biBKi2/ i?2 z ∼ 4 G6 rBi? bBKBH` }Hi2` b2i b
arB+FB h?QKTbQM UkyyeV- #mi /B/ MQi T`Q#2 /22T 2MQm;? iQ #2 #H2 iQ
+QMbi`BM i?2 7BMi@2M/ bHQT2 αX h?Bb T`K2i2` rb b2i 2[mH iQ i?2 pHm2
7QmM/ i z = 3- MK2Hv α = −1.6X uQb?B/ 2i HX UkyyeV T`2b2Mi2/ i?2 G6 7Q`
j3y3 BRiǶ@b2H2+i2/ G":b- b2H2+i2/ 7`QK i?2 am#`m .22T 6B2H/ T`QD2+iX Pm+?B
2i HX Ukyy9V b2H2+i2/ z ∼ 4 G": bKTH2 7`QK am#`m BK;BM;- bmTTQ`i2/
#v bKTH2 Q7 38 bT2+i`Qb+QTB+HHv B/2MiB}2/ Q#D2+ibX :BpHBb+Q 2i HX Ukyy9V
mb2/ ∼yXyN /2;2 bKTH2 7`QK i?2 :PP.a iQ 2biBKi2 G6 7Q` B450 V606 z850 @
b2H2+i2/ G":bX "Qmr2Mb 2i HX UkyydV mb2/ i?2 /22T >ah *a }2H/b- BM+Hm/BM;
i?2 >l.6 M/ i?2 :PP.a- iQ b2H2+i bKTH2 Q7 9edR "@/`QTQmib- 7`QK r?B+?
i?2v 2biBKi2/ i?2 lo G6 iQ M1600,AB = −16.26X
qBi? i?Bb /i b2i r2 ?p2 #22M #H2 iQ K2bm`2 i?2 a+?2+?i2` T`K2i2`b
7Q` i?2 g @/`QTQmi bKTH2 rBi? p2`v ?B;? biiBbiB+H ++m`+vX LQi2 ?Qr2p2`
i?i b2p2`H bvbi2KiB+ mM+2`iBMiB2b- r?B+? r2 +QKK2Mi mTQM BM a2+iX eX9Xj`2 MQi BM+Hm/2/ BM Qm` 2``Q` 2HHBTb2bX Pm` `2bmHib ;`22 rBi?BM i?2 1 − σ
H2p2H rBi? KMv Q7 i?2 z ∼ 4 `2bmHib BM i?2 HBi2`im`2X >Qr2p2`- i?2`2 Bb biBHH
bQK2 i2MbBQM BM K2bm`2K2Mib Q7 i?2 7BMi@2M/ bHQT2 αX h?2 +?`+i2`BbiB+
eX8X *PJS_AaPL qAh> S_1oAPla .1h1_JALhAPLa
R9N
6B;m`2 eXRj, aBKBH` b 6B;X eXRR- #mi MQr +QKT`BbQM i z ∼ 5X
6B;m`2 eXR9, ρa6_ b 7mM+iBQM Q7 `2/b?B7i M/ +QbKB+ iBK2X .Qii2/, a6_.
mM+Q``2+i2/ 7Q` /mbiX aQHB/, i?2 /mbi +Q``2+i2/ a6_.- r?2`2 r2 mb2 HmKB@
MQbBiv /2T2M/2Mi /mbi +Q``2+iBQM 7+iQ` 7`QK "Qmr2Mb 2i HX UkyyNVX LQi2 i?i
r2 BM+Hm/2/ #Qi? `M/QK M/ bvbi2KiB+ 2``Q`b BM Qm` /mbi +Q``2+iBQM- mMHBF2
KQbi Qi?2` bim/B2bX
*>Sh1_ eX h>1 lo :Gsu GlJALPaAhu 6lL*hAPL h z 4j@8
R8y
6_PJ h>1 *6>h G1:*u al_o1u .11S 6A1G.a
K;MBim/2- J∗lo - r2 K2bm`2- Bb bHB;?iHv 7BMi2` i?M i?2 pHm2b r2 7QmM/ BM
i?2 HBi2`im`2X
z
i z ∼ 5- Ari 2i HX UkyydV `2TQ`i2/ i?2 lo G6 7`QK +QK#BMiBQM Q7 >.6
M/ am#`m BK;2b- iQiHHBM; bm`p2v `2 #Qmi RfN Q7 Qm`bX P2b+? 2i HX
UkyydV #b2/ i?2B` bim/v QM TT`QtBKi2Hv Ryy G":b 7`QK p2`v /22T *a M/
LA*JPa BK;BM;X uQb?B/ 2i HX UkyyeV HbQ /2}M2/ z ∼ 5 bKTH2 7`QK i?2B`
Q#b2`piBQMb- +QK#BMBM; V i$ z $ M/ Ri$ z $ b2H2+i2/ Q#D2+ib- b /B/ Pm+?B 2i HX
Ukyy9VX :BpHBb+Q 2i HX Ukyy9V b2H2+i2/ kd8 V606 i775 z850 G":b iQ 2biBKi2
z ∼ 5 lo G6X "Qmr2Mb 2i HX UkyydV HbQ K2bm`2/ bKTH2 Q7 R9Re o@
/`QTQmib 7`QK i?2B` /22T >ah *a bKTH2- r?B+? `2bmHi2/ BM M 2biBKiBQM
Q7 i?2 lo G6 /QrM iQ M1600,AB = −17.16X
aBKBH` iQ i?2 a+?2+?i2` T`K2i2`b 7QmM/ 7Q` z ∼ 4- i?2`2 Bb H`;2
/Bb+`2TM+v BM i?2 HBi2`im`2 7Q` i?2 a+?2+?i2` T`K2i2`b i z ∼ 5X h?2
biiBbiB+H mM+2`iBMiB2b BM i?2 a+?2+?i2` T`K2i2`b Bb p2`v bKHH 7Q` Qm` r@
/`QTQmi bKTH2X LQi2 ?Qr2p2` i?i b2p2`H bvbi2KiB+ mM+2`iBMiB2b `2 MQi
BM+Hm/2/ BM i?2b2 2``Q` 2HHBTb2b- b22 a2+iX eX9XjX Pm` `2bmHib ;`22 `2bQM#Hv
r2HH- rBi?BM i?2 1 − σ H2p2H- rBi? KMv T`2pBQmb /2i2`KBMiBQMb i z ∼ 5X
AM 6B;X eXR9 r2 +QKT`2 i?2 a6_ /2MbBiv pHm2b ;Bp2M BM h#H2 eXj iQ pHm2b
`2TQ`i2/ #v a+?BKBMQpB+? 2i HX Ukyy8V- r?Q K/2 mb2 Q7 HQr@z :G1s /i_2//v ai2B/2H UkyyNV i BMi2`K2/Bi2 z - M/ "Qmr2Mb 2i HX UkyyNV i ?B;?
z X h?2 mM+Q``2+i2/ a6_.b `2 BM ;QQ/ ;`22K2Mi rBi? 2+? Qi?2` M/ b?Qr bKQQi? `2/b?B7i 2pQHmiBQMX >Qr2p2`- Bi Bb +H2` i?i i?2 /mbi +Q``2+iBQM Bb i?2
KDQ` mM+2`iBMiv #2+mb2 Q7 i?2 ;2@/mbi /2;2M2`+vX q2 mb2 i?2 bK2 /mbi
+Q``2+iBQM b "Qmr2Mb 2i HX UkyyNV M/ HbQ BM+Hm/2 bvbi2KiB+ mM+2`iBMiB2b
BM i?2 2``Q` #`bX
AM i?Bb TT2` r2 mb2 i?2 *6>h G2;+v am`p2v .22T }2H/b iQ 2biBKi2 i?2 lo
GmKBMQbBiv 6mM+iBQMb Q7 i?2 H`;2bi u- g @- M/ r@/`QTQmib bKTH2b iQ /i2X b
Qm` bKTH2b `2 HH 2ti`+i2/ 7`QK i?2 bK2 /ib2i i?Bb bim/v Bb B/2HHv bmBi2/
iQ bim/v iBK2 2pQHmiBQM Q7 i?2 HmKBMQbBiv 7mM+iBQM BM i?2 `2/b?B7i `2;BK2
z = 3 − 5X h?MFb iQ i?2 H`;2 pQHmK2b r2 T`Q#2 rBi? Qm` 9 b[m`2 /2;`22
bm`p2v- +QbKB+ p`BM+2 THvb M2;HB;B#H2 `QH2 BM Qm` MHvbBbX q2 `2 MQr
#H2 iQ bim/v i?2 #`B;?i 2M/ Q7 i?2 HmKBMQbBiv 7mM+iBQM rBi? mMT`2+2/2Mi2/
++m`+vX 6m`i?2`KQ`2- ;Bp2M i?2 /2Ti? Q7 i?2 bi+F2/ J2;*K BK;2b- r2
eXeX alJJ_u *PL*GlaAPLa
R8R
T`Q#2 i?2 7BMi 2M/ Q7 i?2 HmKBMQbBiv 7mM+iBQM rBi? +QKT`#H2 T`2+BbBQM b
i?2 /22T2bi ;`QmM/ #b2/ bm`p2vb ?p2 /QM2 #27Q`2X h?Bb mMB[m2 +QK#BMiBQM
;Bp2b mb i?2 QTTQ`imMBiv iQ MQi QMHv 2biBKi2 i?2 a+?2+?i2` T`K2i2`b 7Q` i?2
/Bz2`2Mi HmKBMQbBiv 7mM+iBQMb- #mi HbQ iQ bim/v TQbbB#H2 /2pBiBQM 7`QK i?Bb
+QKKQMHv mb2/ }iX
AM i?2 u@- M/ g @/`QTQmi bKTH2b Q7 Qm` bm`p2v r2 `2 #H2 iQ K2bm`2
i?2 lo +QMiBMmmK bHQT2 /B`2+iHv 7`QK i?2 /iX h?Bb HHQrb mb iQ bBKmHi2
bQm`+2b i?i ?p2 i?2 bK2 /Bbi`B#miBQM Q7 lo bHQT2b- r?B+? Bb BKTQ`iMi 7Q`
M ++m`i2 2biBKi2 Q7 i?2 a+?2+?i2` T`K2i2`bX
q2 }M/ i?2 7BMi@2M/ bHQT2 α iQ MQi 2pQHp2 bB;MB}+MiHv BM i?2 `2/b?B7i
`M;2 r2 T`Q#2- M/ iQ ?p2 pHm2 Q7 `QmM/ −1.6X h?Bb T`K2i2` ?Qr2p2`Bb MQi p2`v bi`QM;Hv +QMbi`BM2/ #v Qm` ;`QmM/ #b2/ bm`p2v- b i?Bb T`K2i2`
/2T2M/b QM bQK2 Q7 i?2 bbmKTiBQMb K/2X
∗
q2 /Q MQi }M/ bB;MB}+Mi 2pQHmiBQM BM Mlo
- M/ `;m2 i?i i?Bb KB;?i #2
/m2 iQ BMbm{+B2Mi FMQrH2/;2 Q7 i?2 `2/b?B7i /Bbi`B#miBQM Q7 i?2 bQm`+2 ;HtB2bX
h?2 +QMp2`bBQM Q7 TT`2Mi iQ #bQHmi2 K;MBim/2b /2T2M/b bi`QM;Hv QM i?2b2
/Bbi`B#miBQMb- M/ M mM+2`iBMiv BM i?2 /BbiM+2 KQ/mHmb /B`2+iHv T`QT;i2b
∗
BMiQ M 2[mH mM+2`iBMiv BM Mlo
X h?Bb T`K2i2` Bb i?2`27Q`2 TQQ`Hv +QM@
bi`BM2/ #v i?Bb bim/v- mMiBH KQ`2 `2HB#H2 `2/b?B7i /Bbi`B#miBQM Bb pBH#H2X
q2 }M/ bi`QM; 2pQHmiBQM BM φ∗ - r?B+? r2 `;m2 iQ #2 bB;MB}+MiX h?2
MQ`KHBbiBQM Q7 i?2 G": /2MbBiv- φ∗ - BM+`2b2b #v 7+iQ` Q7 ∼ 2.5 7`QK
z ≈ 5 iQ z ≈ 3- M BM+`2b2 i?i +MMQi #2 2tTHBM2/ #v Mv +?M;2 BM i?2
bbmKTiBQMb i2bi2/X q2 i?2`27Q`2 +QM+Hm/2 i?i i?2 lo HmKBMQbBiv /2MbBiv Bb
BM+`2bBM; BM i?2 +Q``2bTQM/BM; 2TQ+?- BM rv i?i /Q2b MQi bi`QM;Hv /Bz2`
rBi? K;MBim/2X
h?2 a6_ .2MbBiv /Q2b BM+`2b2 bB;MB}+MiHv- #v 7+iQ` Q7 ∼ 3- #2ir22M
z ∼ 5 M/ z ∼ 4X q2 }M/ bKHH2`- #mi H2bb bB;MB}+Mi BM+`2b2 #2ir22M
z ∼ 4 M/ z ∼ 3X
qBi? Qm` 9 b[m`2 /2;`22 bm`p2v r2 T`Q#2 /2MbBiB2b i?i `2 i H2bi 7Qm`
iBK2b HQr2` i?M Mv Q7 i?2 bim/B2b r2 +QKT`2/ Qm` `2bmHib iQX q2 }M/ bm#biMiBH /2pBiBQM 7`QK i?2 a+?2+?i2` 7mM+iBQM i i?2 #`B;?i 2M/ 7Q` i?2 u@
/`QTQmib- r?2`2 i?2 G": /2MbBiB2b `2 p2`v HQrX q2 }M/ i?i i?2 /2pBiBQM +M
#2 ii`B#mi2/ iQ K;MB}+iBQM 2z2+ib i?i `Bb2 7`QK BM?QKQ;2M2BiB2b BM i?2
Kii2` /Bbi`B#miBQM #2ir22M i?2 G":b M/ i?2 Q#b2`p2`X q2 }i M BKT`Qp2/
a+?2+?i2` 7mM+iBQM i?i Bb +Q``2+i2/ 7Q` K;MB}+iBQM M/ }M/ i?i i?2 [mHBiv
Q7 i?2 }i BKT`Qp2b bB;MB}+MiHvX AMi`BMbB+HHv i?2 /Bbi`B#miBQM Q7 HmKBMQbBiB2b
/Q2b i?2`27Q`2 MQi /2pBi2 bB;MB}+MiHv 7`QK a+?2+?i2` KQ/2HX qBi? i?Bb /i
b2i r2 ?p2 #22M i?2 }`bi iQ #2 #H2 iQ K2bm`2 ?BMi Q7 i?Bb K;MB}+iBQM
BKT`BMi QM z ∼ 3 G": bKTH2X
*>Sh1_ eX h>1 lo :Gsu GlJALPaAhu 6lL*hAPL h z 4j@8
R8k
6_PJ h>1 *6>h G1:*u al_o1u .11S 6A1G.a
q2 i?MF ai27M >BH#2`i 7Q` bmTTHvBM; i?2 K;MB}+iBQM /Bbi`B#miBQM 7Q` bQm`+2b
i Qm` `2/b?B7i Q7 BMi2`2biX q2 `2 ;`i27mH iQ EQM`/ EmBDF2M- _v+?`/
"Qmr2Mb- Gm/QpB+ pM q2`#2F2 M/ J`BDM 6`Mt 7Q` i?2 BMi2`2biBM; /Bb+mb@
bBQMb r2 ?/ M/ i?2B` bm;;2biBQMb iQ BKT`Qp2 i?2 [mHBiv Q7 i?Bb `2b2`+?X q2
i?MF >2MF >Q2Fbi` 7Q` i?2 bmTTHv Q7 TQr2`7mH *SlǶb iQ T2`7Q`K i?2 bBKmH@
iBQMb rBi?- M/ mb27mH +QKK2Mib QM i?2 TT2`X q2 HbQ i?MF i?2 MQMvKQmb
`272`22 7Q` /2iBH2/ `2TQ`i rBi? MB+2 bm;;2biBQMb 7Q` i?Bb TT2`X
"b2/ QM Q#b2`piBQMb Q#iBM2/ rBi? J2;S`BK2fJ2;*K- DQBMi T`QD2+i
Q7 *6>h M/ *1f.SLA- i i?2 *M/@6`M+2@>rBB h2H2b+QT2 U*6>hV
r?B+? Bb QT2`i2/ #v i?2 LiBQMH _2b2`+? *QmM+BH UL_*V Q7 *M/- i?2 AM@
biBimi LiBQMH /2b a+B2M+2b /2 HǶlMBp2`b Q7 i?2 *2Mi`2 LiBQMH /2 H _2+?2`+?2
a+B2MiB}[m2 U*L_aV Q7 6`M+2- M/ i?2 lMBp2`bBiv Q7 >rBBX h?Bb rQ`F Bb
#b2/ BM T`i QM /i T`Q/m+ib T`Q/m+2/ i h1_SAs M/ i?2 *M/BM b@
i`QMQKv .i *2Mi`2 b T`i Q7 i?2 *M/@6`M+2@>rBB h2H2b+QT2 G2;+v
am`p2v- +QHH#Q`iBp2 T`QD2+i Q7 L_* M/ *L_aX
q2 `2 ;`i27mH iQ i?2 *6>hGa bm`p2v i2K 7Q` +QM/m+iBM; i?2 Q#b2`@
piBQMb M/ i?2 h1_SAs i2K 7Q` /2p2HQTBM; bQ7ir`2 mb2/ BM i?Bb bim/vX
q2 +FMQrH2/;2 mb2 Q7 i?2 *M/BM bi`QMQKv .i *2Mi`2 QT2`i2/ #v
i?2 .QKBMBQM bi`QT?vbB+H P#b2`piQ`v 7Q` i?2 LiBQMH _2b2`+? *QmM+BH
Q7 *M/Ƕb >2`x#2`; AMbiBimi2 Q7 bi`QT?vbB+bX >> Bb bmTTQ`i2/ #v i?2 1m@
`QT2M .l1G _hL- T`QD2+i J_hL@*h@kyye@yjeRjjX h1 Bb bmTTQ`i2/ #v
i?2 1m`QT2M .l1G _hL- i?2 :2`KM JBMBbi`v 7Q` a+B2M+2 M/ 1/m+iBQM
U"J"6V i?`Qm;? i?2 .1au T`QD2+i ǵ:oP AAAǶ- M/ i?2 .2mib+?2 6Q`b+?mM;b@
;2K2BMb+?7i i?`Qm;? i?2 T`QD2+ib a*>L j9kfd @ R M/ 1_ jkdfj @ R rBi?BM
i?2 S`BQ`Biv S`Q;`KK2 RRddX
"B#HBQ;`T?v
#xDBM- EX LX- /2HKM@J+*`i?v- CX EX- ;Ƀ2`Qb- JX X- 2i HX kyyN- TCaR3k- 89j
?M- *X SX- H2tM/`Qz- _X- HH2M/2 S`B2iQ- *X- 2i HX kyRj- `sBp 2@T`BMib
M/`2QM- aX kyRy- JL_a- 9yd- kej
M/`2QM- aX kyRk- - 893- 3j
M/`2QM- aX >m`M- JX X kyRy- JL_a- 9y9- RNkk
`MQmib- aX- a+?BKBMQpB+?- .X- AH#2`i- PX- 2i HX kyy8- TC- eRN- G9j
"?û- uX JX- J+*`i?v- AX :X- "HQ;?- JX GX- 6QMi- X aX kyRj- JL_a- 9jyjyRd
"H/`v- AX EX- "HQ;?- JX GX- "Qr2`- _X :X- 2i HX kyye- JL_a- jdj- 9eN
"HQ;?- JX GX- "H/`v- AX EX- LB+?QH- _X- 2i HX kyy9- TC- eR8- GRyR
"HQ;?- JX GX- J+*`i?v- AX :X- "Qr2`- _X :X- 1F2- oX _X kyy3- JL_a- j38Ryyj
"HQ;?- JX GX- J+:22- aX GX- qBHKM- .X CX- 2i HX kyRR- JL_a- 9Rk- kjyj
"HQ;?- JX GX- JQ``Bb- aX GX- u22- >X EX *X- *`H#2`;- _X :X- 1HHBM;bQM- 1X RNNNTC- 8kd- 89
"biBM- LX- *Qp2v- EX _X- J2v2`- JX _X kyRy- _- 93- jjN
"m2`- X >X- "Hiv- *X- 1HHKM- LX- 2i HX kyRk- TC- d9N- 8e
"22`b- hX *X- 6HvMM- EX- :2#?`/i- EX RNNy- C- Ryy- jk
"2?`QQxB- SX aX- *QM`Qv- *X- q2+?bH2`- _X >X kyRy- TC- dRd- jdN
"2?`QQxB- SX aX- q2+?bH2`- _X >X- *QM`Qv- *X kyRj- TC- ddy- 8d
"2HH- 1X 6X /2 CQM;- _X aX kyyR- TC- 88y- kRk
"2HH- 1X 6X- J+AMiQb?- .X >X- Eix- LX- q2BM#2`;- JX .X kyyj- TCa- R9N- k3N
"2MM2ii- *X GX- G`bQM- .X- q2BHM/- CX GX- 2i HX kyRj- TCa- ky3- ky
"2MbQM- X CX- G+2v- *X :X- "m;?- *X JX- *QH2- aX- 6`2MF- *X aX kyyk- JL_ajjj- R8e
"2`iBM- 1X kyye- BM bi`QMQKB+H aQ+B2iv Q7 i?2 S+B}+ *QM72`2M+2 a2`B2b- oQHX
R8j
R89
"A"GAP:_S>u
j8R- bi`QMQKB+H .i MHvbBb aQ7ir`2 M/ avbi2Kb so- 2/X *X :#`B2H*X `pBb2i- .X SQMx- aX 1M`B[m2- RRk
"2`iBM- 1X `MQmib- aX RNNe- a- RRd- jNj
"BH/72HH- *X- >Q2Fbi`- >X- "#mH- X- 2i HX kyRk- JL_a- 9k8- ky9
"BMM2v- CX h`2KBM2- aX kyy3- :H+iB+ .vMKB+b, a2+QM/ 1/BiBQM US`BM+2iQM
lMBp2`bBiv S`2bbV
"BpBMQ- X- Ei;2`i- SX- h?QKb- hX- /KB- *X kyyk- - j3d- 3
"HF2bH22- CX SX- 6`Mt- JX- SQbiKM- JX- 2i HX kyyj- TC- 8Ne- GR9j
"HMiQM- JX _X- 1Bb2Mbi2BM- .X- >Q;;- .X qX- a+?H2;2H- .X CX- "`BMFKMM- CX
kyy8- TC- ekN- R9j
"QHxQM2HH- JX- EQpÍ- EX- SQxx2iiB- GX- 2i HX kyRy- - 8k9- de
"Q`;MB- aX- :B``/B- JX- *`H#2`;- _X :X- u22- >X EX *X- 1HHBM;bQM- 1X RNNNTC- 8kd- 8eR
"Qmr2Mb- _X CX- AHHBM;rQ`i?- :X .X- "HF2bH22- CX SX- 6`Mt- JX kyye- TC- e8j8j
"Qmr2Mb- _X CX- AHHBM;rQ`i?- :X .X- 6`Mt- JX- 2i HX kyyN- `sBp 2@T`BMib
"Qmr2Mb- _X CX- AHHBM;rQ`i?- :X .X- 6`Mt- JX- 6Q`/- >X kyyd- TC- edy- Nk3
"Qmr2Mb- _X CX- AHHBM;rQ`i?- :X .X- P2b+?- SX X- 2i HX kyRk- TC- d89- 3j
"Qr2`- _X :X- "2MbQM- X CX- *`BM- _X X kyRk- JL_a- 9kk- k3Re
"Qr2`- _X :X- "2MbQM- X CX- JH#QM- _X- 2i HX kyye- JL_a- jdy- e98
"QvHM@EQH+?BM- JX- "mHHQ+F- CX aX- ETHBM;?i- JX kyRR- JL_a- 9R8- G9y
"QvHM@EQH+?BM- JX- aT`BM;2H- oX- q?Bi2- aX .X JX- C2MFBMb- X- G2KbQM- :X
kyyN- JL_a- jN3- RR8y
"`KK2`- :X "X- pM .QFFmK- SX :X- *QTTB- SX kyy3- TC- e3e- R8yj
"`KK2`- :X "X- q?BiF2`- EX 1X- pM .QFFmK- SX :X- 2i HX kyRR- TC- djN- k9
"`mxmH- :X *?`HQi- aX kyyj- JL_a- j99- Ryyy
"`mxmH X- :X *?`HQi- aX RNNj- TC- 9y8- 8j3
"`vM- :X GX LQ`KM- JX GX RNN3- TC- 9N8- 3y
"m/xvMbFB- CX JX- EQTQbQp- aX 1X- J+*`i?v- AX :X- "2HQFm`Qp- oX kyRj- JL_a
"m/xvMbFB- CX JX- EQTQbQp- aX 1X- J+*`i?v- AX :X- J+:22- aX GX- "2HQFm`QpoX kyRk- JL_a- 9kj- Ry9
"mHHQ+F- CX aX kyRy- `sBp 2@T`BMib
"mM/v- EX- 1HHBb- _X aX- *QMb2HB+2- *X CX- 2i HX kyye- TC- e8R- Rky
"m`F2- *X *QHHBMb- *X X kyRj- JL_a- 9j9- k38e
"m`F2- *X- *QHHBMb- *X X- aiQii- CX SX- >BHiQM- JX kyRk- JL_a- 9k8- ky83
"mi+?2`- >X P2KH2`- C`X- X RNd3- TC- kRN- R3
*Hx2iiB- .X- `Kmb- GX- "Q?HBM- _X *X- 2i HX kyyy- TC- 8jj- e3k
*TF- SX- mbb2H- >X- DBFB- JX- 2i HX kyyd- TCa- Rdk- NN
*`BHHB- *X GX qHi2`- 6X kyRj- _- 8R- Ry8
*`H#2`;- _X :X- u22- >X EX *X- 1HHBM;bQM- 1X RNNd- TC- 9d3- 9ek
*`H#2`;- _X :X- u22- >X EX *X- 1HHBM;bQM- 1X- 2i HX RNNe- TC- 9ek- jk
*`H#2`;- _X :X- u22- >X EX *X- 1HHBM;bQM- 1X- 2i HX RNNd#- TC- 938- GRj
"A"GAP:_S>u
R88
*`H#2`;- _X :X- u22- >X EX *X- 1HHBM;bQM- 1X- 2i HX RNNd+- TC- 9de- Gd
*2M- _X kyR9- TC- d3R- j3
*?#`B2`- :X kyyj- SaS- RR8- dej
*HQr2- .X- J`F2pBi+?- JX- "`/Í- JX- 2i HX kyRk- TC- d83- Rk3
*QH2- aX- LQ`#2`;- SX- "m;?- *X JX- 2i HX kyyR- JL_a- jke- k88
*QHH2bb- JX- .HiQM- :X- J//Qt- aX- 2i HX kyyR- JL_a- jk3- RyjN
*QK2`7Q`/- CX JX Li`DM- SX kyyd- JL_a- jdN- RNy
*QMiBMB- 1X- .2 Gm+B- :X- oBHHHQ#Qb- X- "Q`;MB- aX kyRj- `sBp 2@T`BMib
*QQT2`- JX *X- *QBH- X GX- :2`F2- "X 6X- 2i HX kyRy- JL_a- 9yN- jjd
*Qp2v- EX _X- Ap2xBÉ- ʇX- a+?H2;2H- .X- 2i HX kyyd- C- Rj9- kjN3
*mbrQ`i?- aX CX- Ev- aX hX- "iiv2- _X X- h?QKb- SX X kyRj- `sBp 2@T`BMib
.HH o2++?B- *X a+?v2- CX kyy3- JL_a- j3d- R9jR
.2 Gm+B- :X "HBxQi- CX kyyd- JL_a- jd8- k
.2 Gm+B- :X- q2BMKMM- aX- SQ;;BMiB- "X JX- `;ƦM@aHKM+- X- w`BibFv.X kyRk- JL_a- 9kj- Rkdd
.2K`+Q- _X- qBHbQM- :X- JmxxBM- X- 2i HX kyRy- TC- dRR- RR38
.B2K2`- "X- JQ`2- aX- E`pibQp- X oX kyRj- TC- dee- k8
.QH;- EX- "Q`;MB- aX- Jm`Mi2- :X- aT`BM;2H- oX kyyN- JL_a- jNN- 9Nd
.`2bbH2`- X RN3y- TC- kje- j8R
.`2bbH2`- X- aKBH- AX- SQ;;BMiB- "X JX- 2i HX RNNN- TCa- Rkk- 8R
.mzv- X _X- a+?v2- CX- Ev- aX hX- .HH o2++?B- *X kyy3- JL_a- jNy- Ge9
1//BM;iQM- X aX RNRj- JL_a- dj- j8N
17bii?BQm- :X kyyy- JL_a- jRd- eNd
1;;2M- PX CX- GvM/2M@"2HH- .X- aM/;2- X _X RNek- TC- Rje- d93
1`#2M- hX- >BH/2#`M/i- >X- G2`+?bi2`- JX- 2i HX kyyN- - 9Nj- RRNd
1`#2M- hX- a+?B`K2`- JX- .B2i`B+?- CX SX- 2i HX kyy8- bi`QMQKBb+?2 L+?`B+?i2Mjke- 9jk
1p``/- X 1X- "BH2F- CX- "mb?- JX- 2i HX kyy3- TC- edk- Rkk
6#BM- X *X kyRk- _- 8y- 988
6//- .X- :B``/B- JX- :Bm`B+BM- :X- J`/B`QbbBM- 6X- J2xx2iiB- JX RNNe- TC9dj- edy
6Q`/- CX- >BH/2#`M/i- >X- oM q2`#2F2- GX- 2i HX kyRj- `sBp 2@T`BMib
:KQr- :X RN93- Lim`2- Rek- e3y
:Q- GX- Lp``Q- CX 6X- *QH2- aX- 2i HX kyy3- JL_a- j3d- 8je
:?B;M- aX- JQQ`2- "X- :Qp2`MiQ- 6X- 2i HX kyyy- TC- 899- eRe
:BpHBb+Q- JX kyyk- _- 9y- 8dN
:BpHBb+Q- JX kyy8- L2r bi`QMQKv _2pB2r- 9N- 99y
:BpHBb+Q- JX .B+FBMbQM- JX kyyR- TC- 88y- Rdd
:BpHBb+Q- JX- .B+FBMbQM- JX- 62`;mbQM- >X *X- 2i HX kyy9- TC- eyy- GRyj
:BpHBb+Q- JX- ai2B/2H- *X *X- J++?2iiQ- 6X .X RNNe- TC- 9dy- R3N
:BHHBb- "X _X- >m/bQM- JX CX- 1`#2M- hX- 2i HX kyRj- JL_a- 9jR- R9jN
R8e
"A"GAP:_S>u
:BQ/BMB- aX- 6BMQ;m2MQp- X- SB2`BMB- .X- 2i HX kyRk- - 8j3- Ry9
:BQ/BMB- aX- SB2`BMB- .X- 6BMQ;m2MQp- X- 2i HX kyyN- TC- dyj- N3k
:B``/B- GX- :`Q2M2r2;2M- JX X hX- >ixBKBMQ;HQm- 1X- / *Qbi- GX kyy8- 9je- 3N8
:B``/B- JX- "BpBMQ- X- :Bm`B+BM- :X- J`/B`QbbBM- 6X- J2xx2iiB- JX RNNjTC- 9y9- j3
:B``/B- JX J2xx2iiB- JX kyyR- TC- 893- dN
:H//2`b- JX .X u22- >X EX *X kyyy- C- Rky- kR93
:QMxH2x- X >X- aBpMM/K- aX- w#Hm/Qz- X AX- w`BibFv- .X kyRj- TC- dd3R9
:QMxH2x- X >X- w`BibFv- .X- w#Hm/Qz- X AX kyyd- TC- eee- R9d
:mMM- CX 1X :Qii- AAA- CX _X RNdk- TC- Rde- R
:mQ- ZX- q?Bi2- aX- GB- *X- "QvHM@EQH+?BM- JX kyRy- JL_a- 9y9- RRRR
>BM2b- *X SX- S2`2B`- JX CX- aM/2`bQM- X CX _X- 2i HX kyRk- TC- d89- Nd
>BM2b- *X SX- S2`2B`- JX CX- aKBi?- :X SX- 2i HX kyRj- TC- dd8- Rke
>2M`B[m2b- "X JX "X- q?Bi2- aX .X JX- G2KbQM- :X- 2i HX kyRk- JL_a- 9kR- kNy9
>B;?- 6X qX- aim##b- *X qX- _2bi- X- aiH/2`- "X- *?HHBb- SX kyyN- C- Rj3RRy
>BH#2`i- aX- q?Bi2- aX .X JX- >`iHT- CX- a+?M2B/2`- SX kyyd- JL_a- j3k- RkR
>BH/2#`M/i- >X- `MQmib- aX- *TF- SX- 2i HX kyRy- - 8kj- jR
>BH/2#`M/i- >X- "QKMb- .X CX- 1`#2M- hX- 2i HX kyy8- - 99R- Ny8
>BH/2#`M/i- >X- 1`#2M- hX- .B2i`B+?- CX SX- 2i HX kyye- - 98k- RRkR
>BH/2#`M/i- >X- 1`#2M- hX- EmBDF2M- EX- 2i HX kyRk- JL_a- 9kR- kj88
>BH/2#`M/i- >X- JmxxBM- X- 1`#2M- hX- 2i HX kyRR- TC- djj- Gjy
>BH/2#`M/i- >X- SB2HQ`x- CX- 1`#2M- hX- 2i HX kyyd- - 9ek- 3e8
>BH/2#`M/i- >X- SB2HQ`x- CX- 1`#2M- hX- 2i HX kyyN- - 9N3- dk8
>BH/2#`M/i- >X- pM q2`#2F2- GX- a+Qii- .X- 2i HX kyRj- JL_a- 9kN- jkjy
>BHiQM- JX- >bb2H}2H/- JX- aB7ƦM- *X- 2i HX kyRj- JL_a- 9j8- j9eN
>B`b?Bi- >X- "mi- oX- AMQm2- X EX kyyj- - 9Ry- 3j
>Q2Fbi`- >X kyyd- JL_a- jdN- jRd
>Q2Fbi`- >X- .QM?m2- JX- *QMb2HB+2- *X CX- J+LK`- "X _X- oQBi- :X JX
kyRR- TC- dke- 93
>Q2Fbi`- >X- 6`Mt- JX- EmBDF2M- EX kyyy- TC- 8jk- 33
>Q2Fbi`- >X- J?/pB- X- "#mH- X- "BH/72HH- *X kyRk- JL_a- 9kd- RkN3
>Q;;- .X qX RNNN- `sBp bi`QT?vbB+b 2@T`BMib
>m- qX q?Bi2- JX RNNe- TC- 9dR- jy
>m##H2- 1X >mKbQM- JX GX RNjR- TC- d9- 9j
>m##H2- 1X SX RNke- TC- e9- jkR
AH#2`i- PX- aHpiQ- JX- G2 6HQ+Ƕ?- 1X- 2i HX kyRy- TC- dyN- e99
Ari- AX- P?i- EX- hKm`- LX- 2i HX kyyd- JL_a- jde- R88d
CBM- "X GBK- JX kyRy- `sBp 2@T`BMib
"A"GAP:_S>u
R8d
ETi2vM- CX *X RNkk- TC- 88- jyk
EmzKMM- :X- >2+FKM- hX JX- q?Bi2- aX .X JX- 2i HX kyyj- JL_a- j9R- jj
EmzKMM- :X- q?Bi2- aX .X JX- >2+FKM- hX JX- 2i HX kyy9- JL_a- j8j- dRj
E2MMB+mii- C`X- _X *X RN3j- TC- kdk- 89
E2MMB+mii- C`X- _X *X RNN3- _- je- R3N
EHvTBM- X- E`pibQp- X oX- oH2Mxm2H- PX- S`/- 6X RNNN- TC- 8kk- 3k
EMQ#2H- *X- GBHHv- aX CX- EQpÍ- EX- 2i HX kyRj- TC- deN- k9
EQKibm- 1X- aKBi?- EX JX- .mMFH2v- CX- 2i HX kyRy- `sBp 2@T`BMib
EQpÍ- EX- GBHHv- aX CX- EMQ#2H- *X- 2i HX kyR9- JL_a- 9j3- dRd
E`pibQp- X oX "Q`;MB- aX kyRk- _- 8y- j8j
E`B2F- JX- pM .QFFmK- SX :X- G##û- AX- 2i HX kyyN- TC- dyy- kkR
E`QM- _X :X RN3y- TCa- 9j- jy8
E`QmT- SX kyyR- JL_a- jkk- kjR
EmBDF2M- EX kyye- - 98e- 3kd
EmBDF2M- EX kyy3- - 93k- Ry8j
G;M€- hX 6X- J`iBM2i- LX- .m``2i- 6X- 2i HX kyRj- - 888- ee
GTQ`i2- *X 6X SX- q?Bi2- aX .X JX- L#- hX- :Q- GX kyRj- JL_a- 9j8- NyR
G`bQM- _X "X- hBMbH2v- "X JX- *H/r2HH- *X LX RN3y- TC- kjd- eNk
GbF2`- "X JX- GiiMxB- JX :X- J+G2M- "X CX- 2i HX kyy3- C- Rje- dj8
G2mi?m/- X- :2Q`;2- JX _X- "2?`QQxB- SX aX- 2i HX kyRk- TC- d9e- N8
G2mi?m/- X- hBMF2`- CX- "mM/v- EX- 2i HX kyRk#- TC- d99- R8N
GB/KM- *X- A+Q#mi- :X- "m2`- X 1X- 2i HX kyRj- JL_a- 9jj- 3k8
GB/KM- *X- am?2`HB- CX- JmxxBM- X- 2i HX kyRk- JL_a- 9kd- 88y
GBHHv- aX CX- G2 62p`2- PX- >KK2`- 6X- *`KTiQM- .X RNNe- TC- 9ey- GR
GBM- uX@hX JQ?`- CX CX kyy9- TC- eRd- 3dN
GBM- uX@hX- JQ?`- CX CX- aiM7Q`/- aX X kyy9- TC- eRy- d98
GBM- uX@hX- aiM7Q`/- aX X- 1Bb2M?`/i- SX _X JX- 2i HX kyRk- TC- d98- Gj
GQMb/H2- *X CX- aKBi?- >X 1X- _QrM@_Q#BMbQM- JX- 2i HX kyyj- SaS- RR8- 3Nd
J/m- SX RNN8- TC- 99R- R3
J/m- SX- 62`;mbQM- >X *X- .B+FBMbQM- JX 1X- 2i HX RNNe- JL_a- k3j- Rj33
J/m- SX- SQxx2iiB- GX- .B+FBMbQM- JX RNN3- TC- 9N3- Rye
J;MB2`- 1X X *mBHHM/`2- CX@*X kyy9- SaS- RRe- 99N
J?DM- aX- JKQM- :X X- _v+?m/?m`v- aX kyRR- JL_a- 9Re- k33k
J?/pB- X- >Q2Fbi`- >X- "#mH- X- "HK- .X .X- *TF- SX GX kyyd- TCee3- 3ye
JM/2H#mK- _X- a2HDF- lX- >B`i- *X JX kyy3- CX *QbKQHQ;v bi`QT`iX S?vbX3- e
J`+?2bBMB- .X- pM .QFFmK- SX :X- 6ƺ`bi2` a+?`2B#2`- LX JX- 2i HX kyyN- TCdyR- Rde8
J`i2H- >X- "`B- SX- "`BiQ- qX kyRk- TC- d8d- 93
J`iBM- .X *X- 6MbQM- CX- a+?BKBMQpB+?- .X- 2i HX kyy8- TC- eRN- GR
R83
"A"GAP:_S>u
J+*`i?v- AX :X- 6`2MF- *X aX- 6QMi- X aX- 2i HX kyy3- JL_a- j3j- 8Nj
J+*`+F2M- >X CX- JBHpM;@C2Mb2M- "X- .mMHQT- CX- 2i HX kyRk- - 899- R8e
J+:22- aX GX- "HQ;?- JX GX- "Qr2`- _X :X- 6QMi- X aX- J+*`i?v- AX :X kyyNJL_a- 9yy- Njd
J+:22- aX GX- "HQ;?- JX GX- qBHKM- .X CX- 2i HX kyRR- JL_a- 9Rj- NNe
J2m`2`- :X _X- >2+FKM- hX JX- *Hx2iiB- .X RNNN- TC- 8kR- e9
JBHH2`- :X 1X a+HQ- CX JX RNdN- TCa- 9R- 8Rj
JQF- X- "HQ;?- JX GX- J+:22- aX GX- 2i HX kyRj- JL_a- 9jR- RyNy
JQQ`2- "X- Eix- LX- GF2- :X- .`2bbH2`- X- P2KH2`- X RNNe- Lim`2- jdN- eRj
JQ`M- aX JX- 1HHBb- _X aX- h`2m- hX- 2i HX kyyd- TC- edR- R8yj
JQbi2`- "X SX- L#- hX- q?Bi2- aX .X JX kyRj- JL_a- 9k3- jRkR
JQbi2`- "X SX- aQK2`pBHH2- _X aX- JmH#2ib+?- *X- 2i HX kyRy- TC- dRy- Nyj
JmHHBb- *X _X- _QbiB- SX- GK2`- :X- 2i HX kyy8- TC- ekj- G38
JmM`B- 1X- "BpBMQ- X- "Q`;MB- aX- Jm`Mi2- :X- 6#DM- .X kyRj- JL_a9jy- kej3
JmxxBM- X- J`+?2bBMB- .X- ai27MQM- JX- 2i HX kyRj- TC- ddd- R3
JmxxBM- X- J`+?2bBMB- .X- ai27MQM- JX- 2i HX kyRj#- TCa- kye- 3
JmxxBM- X- qBHbQM- :X- G+v- JX- u22- >X EX *X- aiM7Q`/- aX X kyy3- TCe3e- Nee
JmxxBM- X- qBHbQM- :X- u22- >X EX *X- 2i HX kyRk- TC- d9e- R33 UJRkV
JmxxBM- X- qBHbQM- :X- u22- >X EX *X- 2i HX kyyN- TC- eN3- RNj9
JmxxBM- X- u22- >X EX *X- >HH- SX "X- 1HHBM;bQM- 1X- GBM- >X kyyd- TC- e8NRRye
L;B- .X E`pibQp- X oX kyy8- TC- eR3- 88d
LMiBb- CX "X- _2iim`- X- GB/KM- *X- 2i HX kyRj- - 88e- RRk
Li`DM- SX- EM2B#- CX@SX- aKBH- AX kyyk- TC- 83y- GRR
Lp``Q- CX 6X- 6`2MF- *X aX- q?Bi2- aX .X JX RNNd- TC- 9Ny- 9Nj
Lp``Q- CX 6X- Gm/HQr- X- aT`BM;2H- oX- 2i HX kyRy- JL_a- 9yk- kR
L2iQ- X 6X- :Q- GX- "2ii- SX- 2i HX kyyd- JL_a- j3R- R98y
L2rKM- X "X- h`2m- hX- 1HHBb- _X aX- aM/- .X CX kyRj- TC- de8- k8
LQ#H2- X :X- q2##- hX JX X- JmxxBM- X- 2i HX kyRj- TC- de3- RR3
LQ2bF2- EX :X- q2BM2`- "X CX- 6#2`- aX JX- 2i HX kyyd- TC- eey- G9j
P2b+?- SX X- aiBp2HHB- JX- *`QHHQ- *X JX- 2i HX kyyd- TC- edR- RkRk
PF2- CX "X :mMM- CX 1X RN3j- TC- kee- dRj
PKM- EX X- >m/bQM- JX CX- "2?`QQxB- SX aX kyRj- JL_a- 9jR- kjyd
Pm+?B- JX- a?BKbFm- EX- PFKm`- aX- 2i HX kyy9- TC- eRR- eey
Pm+?B- JX- a?BKbFm- EX- PFKm`- aX- 2i HX kyy9#- TC- eRR- e38
STQpB+?- *X- .B+FBMbQM- JX- 62`;mbQM- >X *X kyyR- TC- 88N- eky
Si2H- aX :X- >QH/2M- "X SX- E2HbQM- .X .X- 2i HX kyRk- TC- d93- Gkd
Si2H- aX :X- >QH/2M- "X SX- E2HbQM- .X .X- AHHBM;rQ`i?- :X .X- 6`Mt- JX kyyNTC- dy8- Ged
"A"GAP:_S>u
R8N
S2M;- uX@DX- GBHHv- aX CX- EQpÍ- EX- 2i HX kyRy- TC- dkR- RNj
S2M;- uX@DX- GBHHv- aX CX- _2MxBMB- X- *`QHHQ- JX kyRk- TC- d8d- 9
Sû`2x@:QMx€H2x- SX :X- _B2F2- :X >X- oBHH`- oX- 2i HX kyy3- TC- ed8- kj9
S2`HKmii2`- aX- H/2`BM;- :X- :QH/?#2`- :X- 2i HX RNNN- TC- 8Rd- 8e8
SB`xFH- LX- JH?Qi`- aX- _?Q/b- CX _X- *?mM- sX kyy8- BM "mHH2iBM Q7 i?2
K2`B+M bi`QMQKB+H aQ+B2iv- oQHX jd- "mHH2iBM Q7 i?2 K2`B+M bi`QMQKB+H
aQ+B2iv- RRN8ĜY
SHM2HH2b- aX- "Q`;MB- aX- .QH;- EX- 2i HX kyRj- JL_a- 9jR- R93d
SQ;;BMiB- "X JX- `;ƦM@aHKM+- X- w`BibFv- .X- 2i HX kyyN- TC- eNj- RRk
SQ;;BMiB- "X JX- "`B/;2b- hX CX- EQKBvK- uX- 2i HX kyy9- TC- eyR- RNd
SQ;;BMiB- "X JX- aKBH- AX- .`2bbH2`- X- 2i HX RNNN- TC- 8R3- 8de
SQHB- 6X- J2M+B- LX- :BHHQM;Q- 1X- 2i HX kyyR- TC- 88R- G98
S`2bb- qX >X a+?2+?i2`- SX RNd9- TC- R3d- 9k8
_B+?QQ`- X M/`2QM- aX kyRk- - 89j- RN
_bKmbb2M- CX- JmH+?2v- CX aX- "B- GX- 2i HX kyRk- TC- d8d- Rkk
_2//v- LX X ai2B/2H- *X *X kyyN- TC- eNk- dd3
_2//v- LX X- ai2B/2H- *X *X- S2iiBMB- JX- 2i HX kyy3- TCa- Rd8- 93
_27`2;B2`- X kyyj- JL_a- jj3- j8
_B2bb- X :X- 6BHBTT2MFQ- X oX- *?HHBb- SX- 2i HX RNN3- C- RRe- RyyN
_BM2b- EX- :2HH2`- JX CX- .B72`BQ- X- Em`ix- JX CX kyRj- TC- ded- R8
_m#BM- oX *X 6Q`/- C`X- qX EX RNdy- TC- R8N- jdN
_m/MB+F- :X- pQM /2` GBM/2M- X- S2HHƦ- _X- 2i HX kyyN- TC- dyy- R88N
aHT2i2`- 1X 1X RN88- TC- RkR- ReR
aM/- .X CX- :`?K- JX GX- "BH/72HH- *X- 2i HX kyRR- TC- dkN- R9k
aM/2`b- .X "X- aHpiQ- JX- mbb2H- >X- 2i HX kyyd- TCa- Rdk- 3e
a`Q- X- JQ?`- CX CX- "xBM- :X- .QH;- EX kyRj- TC- ddk- 9d
arB+FB- JX h?QKTbQM- .X kyye- TC- e9k- e8j
a+?rBMbFB- EX- h?QKb- .X- a`xB- JX- 2i HX kyyd- JL_a- j3k- R9R8
a+?v2- CX- .HH o2++?B- *X- "QQi?- *X JX- 2i HX kyRy- JL_a- 9yk- R8je
a+?2+?i2`- SX RNde- TC- kyj- kNd
a+?BKBMQpB+?- .X- AH#2`i- PX- `MQmib- aX- 2i HX kyy8- TC- eRN- G9d
a+?H2;2H- .X CX- 6BMF#2BM2`- .X SX- .pBb- JX RNN3- TC- 8yy- 8k8
a+QpBHH2- LX- mbb2H- >X- "2MbQM- X- 2i HX kyyd- TCa- Rdk- R8y
a2`2MQ- JX *QpQM2- :X kyRj- JL_a
a?TH2v- X 1X- ai2B/2H- *X *X- S2iiBMB- JX- /2H#2`;2`- EX GX kyyj- TC- 833- e8
a?2H/QM- 1X aX- CQ?MbiQM- .X 1X- JbD2/B- JX- 2i HX kyyN- TC- dyj- kkjk
aB7ƦM- *X- J2MMi2m- 6X- >bb2H}2H/- JX- 2i HX kyRj- TC- ddk- k8
aKBi?- :X SX- E?Qb`Qb??B- >X :X- .`Bmb?- X- 2i HX kyRy- JL_a- 9yN- ReN
aKBi?- _X CX- Gm+2v- CX _X- >KK2`- .X- 2i HX kyRy#- JL_a- 9y3- R9Rd
aQ#`H- .X- "2bi- SX LX- aKBH- AX- 2i HX kyRR- JL_a- 9RR- ed8
aQK2`pBHH2- _X aX- G22- EX- 62`;mbQM- >X *X- 2i HX kyy9- TC- eyy- GRdR
Rey
"A"GAP:_S>u
aT`BM;2H- oX- q?Bi2- aX .X JX- C2MFBMb- X- 2i HX kyy8- Lim`2- 9j8- ekN
ai2B/2H- *X *X- /2H#2`;2`- EX GX- :BpHBb+Q- JX- .B+FBMbQM- JX- S2iiBMB- JX
RNNN- TC- 8RN- R
ai2B/2H- *X *X- /2H#2`;2`- EX GX- a?TH2v- X 1X- 2i HX kyyj- TC- 8Nk- dk3
ai2B/2H- *X *X- :BpHBb+Q- JX- S2iiBMB- JX- .B+FBMbQM- JX- /2H#2`;2`- EX GX
RNNe- TC- 9ek- GRdY
ai2B/2H- *X *X- a?TH2v- X 1X- S2iiBMB- JX- 2i HX kyy9- TC- ey9- 8j9
hH- hX- pM .QFFmK- SX :X- 6`Mt- JX- 2i HX kyRj- TC- deN- jR
h`Mm- .X aX- >m/bQM- JX CX- "HQ;?- JX GX- 2i HX kyRk- `sBp 2@T`BMib
h22`BFQ`TB- SX kyy9- - 9k9- dj
h?QKb- .X- J`biQM- *X- a+?rBMbFB- EX- a`xB- JX- aBHF- CX kyRy- JL_a9y9- Rdd8
hBMF2`- CX- E`pibQp- X oX- EHvTBM- X- 2i HX kyy3- TC- e33- dyN
h`M- EX@oX >X- 6`Mt- JX- AHHBM;rQ`i?- :X .X- 2i HX kyyd- TC- eeR- d8y
h`2MiB- JX aiBp2HHB- JX kyy3- TC- ede- ded
h`2m- hX- 1HHBb- _X aX- EM2B#- CX@SX- 2i HX kyyj- TC- 8NR- 8j
pM .H2M- JX SX- a+?v2- CX- "QQi?- *X JX- .HH o2++?B- *X kyRR- JL_a9R8- je9N
pM /2M "Qb+?- 6X *X- [mBMQ- .X- uM;- sX- 2i HX kyy3- JL_a- j3d- dN
pM /2` "m`;- _X 6X CX- >BH/2#`M/i- >X- 1`#2M- hX kyRy- - 8kj- d9
pM /2` "m`;- _X 6X CX- JmxxBM- X- >Q2Fbi`- >X- 2i HX kyRj- - 88d- R8
Up/"RjV
pM /2` "m`;- _X 6X CX- JmxxBM- X- >Q2Fbi`- >X- 2i HX kyR9- - 8eR- dN
Up/"R9V
pM .QFFmK- SX :X kyyR- SaS- RRj- R9ky
pM .QFFmK- SX :X- 6`Mt- JX- 6#`B+Mi- .X- E2HbQM- .X .X- AHHBM;rQ`i?- :X .X
RNNN- TC- 8ky- GN8
omH+MB- "X- SQ;;BMiB- "X JX- `;ƦM@aHKM+- X- 2i HX kyRR- JL_a- 9Rkk9e
omH+MB- "X- SQ;;BMiB- "X JX- 6bMQ- :X- 2i HX kyRk- JL_a- 9ky- R93R
omH+MB- "X- SQ;;BMiB- "X JX- 6BMM- _X X- 2i HX kyRy- TC- dRy- GR
omH+MB- "X- SQ;;BMiB- "X JX- P2KH2`- X- 2i HX kyRj- - 88y- 83
q2+?bH2`- _X >X- "mHHQ+F- CX aX- S`BK+F- CX _X- E`pibQp- X oX- .2F2H- X kyykTC- 8e3- 8k
q2BMKMM- aX JX- EmzKMM- :X- pQM /2` GBM/2M- X- .2 Gm+B- :X kyRyJL_a- 9ye- kk9N
q2BMKMM- aX JX- Sb[mHB- X- PTT2M?2BK2`- "X .X- 2i HX kyRk- `sBp 2@T`BMib
q2ix2H- X _X- hBMF2`- CX GX- *QM`Qv- *X kyRk- JL_a- 9k9- kjk
q2ix2H- X _X- hBMF2`- CX GX- *QM`Qv- *X- pM /2M "Qb+?- 6X *X kyRj- JL_a9jk- jje
q?BiF2`- EX 1X- G##û- AX- pM .QFFmK- SX :X- 2i HX kyRR- TC- dj8- 3e
q?Bi2- aX .X JX _22b- JX CX RNd3- JL_a- R3j- j9R
"A"GAP:_S>u
ReR
qBHHBKb- _X CX- Zm/`B- _X 6X- 6`Mt- JX- pM .QFFmK- SX- G##û- AX kyyNTC- eNR- R3dN
qBHbQM- :X- JmxxBM- X- u22- >X EX *X- 2i HX kyyN- TC- eN3- RN9j
qQQ- CX- .2F2H- X- 6#2`- aX JX- 2i HX kyRj- JL_a- 9k3- jjye
qQ`i?2v- :X RNN9- TCa- N8- Ryd
qm- SX@6X- :H- _X _X- G2Kmt- "X *X- 2i HX kyRj- `sBp 2@T`BMib
qmvib- aX- G##û- AX- 6`Mt- JX- 2i HX kyyd- TC- e88- 8R
uM- _X- L2rKM- CX X- 6#2`- aX JX- 2i HX kyyN- JL_a- jN3- dj8
u22- >X EX *X- 1HHBM;bQM- 1X- *`H#2`;- _X :X RNNe- TCa- Ryk- keN
uQb?B/- JX- a?BKbFm- EX- Eb?BFr- LX- 2i HX kyye- TC- e8j- N33
wB#2iiB- aX- q?Bi2- aX .X JX- a+?M2B/2`- .X SX- "`BMFKMM- CX kyy8- JL_aj83- N9N
wrB+Fv- 6X RNjj- >2Hp2iB+ S?vbB+ +i- e- RRy
L2/2`HM/b2 aK2MpiiBM;
ǴHb D2 B2ib MB2i QT 22M 22MpQm/B;2 KMB2` FmMi mBiH2;;2M
/M #2;`BDT D2 ?2i MB2i ;Q2/ ;2MQ2;XǴ
@H#2`i 1BMbi2BM
PMb T2`bT2+iB27 QT /2 THib pM /2 K2Mb?2B/ BM ?2i mMBp2`bmK ?227i xB+? /2
7;2HQT2M 22mr2M bi2`F QMirBFF2H/X hQi KBM/2` /M k8 K2Mb2HBDF2 ;2M2`iB2b
;2H2/2M rb ?2i ;2Q+2Mi`Bb+?2 KQ/2H- r`BM /2 `/2 ?2i +2Mi`mK pM ?2i
mMBp2`bmK BMM22Ki- MQ; /2 H;2K22M M;2MQK2M #2b+?`BDpBM; pM ?2i ?22HHX
aBM/b/B2M ?2##2M MB2mr2 BMxB+?i2M iQi 22M ;2?22H M/2` #22H/ ;2H2B/X wQ r2`/
BM /2 Re/2 22mr ?2i ?2HBQ+2Mi`Bb+?2 KQ/2H- r`BM /2 THM2i2M xB+? `QM/ 22M
biiBQMB`2 wQM #2r2;2M- ;27Q`KmH22`/ /QQ` QXX LB+QHb *QT2`MB+mb 2M :HB@
H2Q :HBH2BX .Bi KQ/2H pQQ`xB2i BM 22M 22MpQm/B;2`2 2M 2H2;Mi2`2 #2b+?`BDpBM;
pM /2 THM22i#M2M BM ?2i xQMM2bi2Hb2HX PQF r2i2M r2 Mm /i /2 M/2`2 bi2``2M
M /2 ?2K2H 2B;2Mb+?TT2M ?2##2M /B2 p2`;2HBDF#` xBDM K2i /2 F2MK2`F2M
pM QMx2 wQM- H?Q2r2H x2 QT MxB2MHBDF ;`Qi2`2 7biM/2M biMX
PK /2 2MQ`K2 7biM/2M BM ?2i ?22HH i2 #2b+?`BDp2M Bb ?2i ;2#`mBF2HBDF /2x2
mBi i2 /`mFF2M K2i #2?mHT pM /2 HB+?ibM2H?2B/X Hb 22M HB+?ibi`H BM /2 H2;2
`mBKi2 pM ?2i ?22HH `2Bbi- H2;i /2x2 T2` b2+QM/2 22M BM/`mFr2FF2M/2 7biM/ 7
pM QM;2p22` jyyXyyy FKX .2 7biM/ M` /2 JM Bb xQǶM j3yXyyy FK- Q7i2r2H
`mBK ûûM HB+?ib2+QM/2X .2 wQM bii QT xQǶM +?i HB+?iKBMmi2M- ri #2i2F2Mi
/i r2 /2 wQM 2B;2MHBDF xB2M xQHb ?BD +?i KBMmi2M ;2H2/2M bi`H/2X .2 7biM/
iQi /2 22`bipQH;2M/2 bi2` Bb K22` /M pB2` HB+?iD`- 22M i`2z2M/2 BHHmbi`iB2 pM
/2 mBi;2bi`2Fi?2B/ pM ?2i ?22HHX .2x2 2BM/B;?2B/ pM /2 HB+?ibM2H?2B/ xQ`;i 2`
QQF pQQ` /i r2 #BMM2M /2 bi2``2MFmM/2 2z2+iB27 i2`m;FBDF2M BM /2 iBD/ Hb r2
?2i p2``2 ?22HH #2bim/2`2MX
.2 J2HFr2; #2bii mBi xQǶM Ryy KBHD`/ bi2``2M- p2`/22H/ Qp2` 22M /mMM2
Rej
Re9
L1.1_GL.a1 aJ1LohhAL:
b+?BD7 K2i 22M /BK2i2` pM QM;2p22` RyyXyyy HB+?iD`X .2 wQM #2pBM/i xB+?
BM ûûM pM /2 bTB`H`K2M #BMM2M /2x2 b+?BD7X AM /2 irBMiB;2` D`2M pM /2
pQ`B;2 22mr r2`/ /mB/2HBDF /i /2 J2HFr2; MB2i mMB2F Bb- K` /i 2` p2H2
bi2``2Mbi2Hb2Hb #2biM QT MQ; ;`Qi2`2 7biM/2MX .2 M/`QK2/M2p2H Bb ?2i
K22bi M#BD2 bi2``2Mbi2Hb2H /i pM p2`;2HBDF#`2 ;`QQii2 Bb Hb /2 J2HFr2;2M bii QT 22M 7biM/ pM xQǶM k-8 KBHDQ2M HB+?iD`X J2i /2x2 QMi/2FFBM;
pQM/ K2M QQF /i M;2MQ2; HH2 bi2``2Mbi2Hb2Hb pM QMb 7 #2r2;2M- 2M r2H
K2i 22M bM2H?2B/ /B2 HBM2B` iQ2M22Ki K2i ?mM 7biM/X .2 BKTHB+iB2 pM /2x2
r`;2MQK2M mBi/BDBM; pM ?2i ?22HH Bb /i /2 #2biM/b/2H2M pM ?2i ?22HH
BM ?2i p2`H2/2M /B+?i2` QT 2HF` ;2TFi KQ2i2M ?2##2M ;2x2i2M- 2M /Bi ?227i
;2H2B/ iQi /2 Q2`FMHi?2Q`B2X
.2 Q2`FMHi?2Q`B2 Bb BM /2 HQQT pM /2 D`2M p2`}DM/ /QQ` p2`b+?BHH2M/2
r`M2KBM;2M i2 +QK#BM2`2MX oQH;2Mb /2x2 i?2Q`B2 Bb ?2i ?22HH xQǶM Rj-3 KBH@
D`/ D` ;2H2/2M mBi 22M bBM;mH`Bi2Bi QMibiM- 2M Bb bBM/b/B2M 7;2FQ2H/ 2M BM
QKpM; iQ2;2MQK2M iQi ?2i ?mB/B;2 ?22HHX >B2`#BD xBDM HH2 bi`m+im`2M ;2pQ`K/
/B2 ?2i ?22HH `BDF Bbc pM /2 ;`QQibi2 p2`xK2HBM; bi2``2Mbi2Hb2Hb iQi THM2i2M
xQHb /2 `/2X H?Q2r2H /Bi KQ/2H BM 22`bi2 BMbiMiB2 KBbb+?B2M #Bx` xH FHBM@
F2M- FmMM2M p22H r`;2MQK2M p2`b+?BDMb2H2M BM ?2i ?22HH ?B2`/QQ` p2`FH`/
rQ`/2MX wQ ?227i /2 K2iBM; pM /2 ;HQ2/ pM /2 Q2`FMH- BM /2 pQ`K pM
FQbKBb+?2 +?i2`;`QM/bi`HBM;- BM kyye /2 LQ#2HT`BDb pQQ` /2 Limm`FmM/2
QT;2H2p2`/- 2M /Bi rQ`/i ;2xB2M Hb ?2i #2HM;`BDFbi2 `;mK2Mi pQQ` /2 Q2`@
FMHi?2Q`B2X aBM/b /2 Q2`FMH ?227i /2 xr`i2F`+?i 2`pQQ` ;2xQ`;/ /i ?2i
+QMi`bi imbb2M ?Q;2 2M H;2 /B+?i?2B/b;2#B2/2M BM /2 HQQT pM /2 iBD/ bi22/b
;`Qi2` Bb ;2rQ`/2M- 2M QQF /Bi Bb r`;2MQK2M BM /2 p2`/2HBM; pM Ki2`B2 BM
?2i ?22HHX
>Hp2`r2;2 /2 kybi2 22mr r2`/ MQ; 22M M/2`2 ;`Qi2 QMi/2FFBM; ;2/MX
.2 #2r2;BM; pM bi2``2M BM bi2``2Mbi2Hb2Hb 2M /2 #2r2;BM; pM bi2``2Mbi2Hb2Hb
BM +Hmbi2`b pM bi2``2Mbi2Hb2Hb- FmMM2M HH22M #2;`2T2M rQ`/2M Hb 2` #mBi2M /2
Ki2`B2 /B2 r2 FmMM2M xB2M- 22M MxB2MHBDF2 ?Q2p22H?2B/ Ki2`B2 Mr2xB; Bb
/B2 MB2i /B`2+i r`M22K#` BbX M;2xB2M /2x2 /QMF2`2 Ki2`B2 ;22M HB+?i
mBibi`Hi- Bb ?2i #2biM 2`pM mBibHmBi2M/ 7 i2 H2B/2M M /2 ?M/ pM /2
xr`i2F`+?iX .QQ` p2`b+?BHH2M/2 K2iBM;2M i2 +QK#BM2`2M rQ`/i ;2b+?i /i
3yW pM /2 Kbb BM ?2i ?22HH /2 2B;2Mb+?TT2M pM /QMF2`2 Ki2`B2 ?227iX
oQH;2Mb ?2i biM/`/KQ/2H #BMM2M /2 FQbKQHQ;B2 U/2 Q2`FMHi?2Q`B2V bT22Hi
/QMF2`2 Ki2`B2 22M #2HM;`BDF2 `QH #BD ?2i pQ`K2M pM bi`m+im`2M BM ?2i ?22HH
/MFxBD /2 #BDxQM/2`2 2B;2Mb+?T /i /QMF2`2Ki2`B2/22HiD2b MB2i FmMM2M #Qi@
b2MX .2x2 2B;2Mb+?T xQ`;i 2` QQF pQQ` /i /2 pQ`KBM; pM bi`m+im`2M K2i
/QMF2`2 Ki2`B2 `2HiB27 KFF2HBDF i2 bBKmH2`2M Bb K2i /2 +QKTmi2`X PT /2
QKbH; pM /Bi T`Q27b+?`B7i xBDM ir22 ;2bBKmH22`/2 p2`/2HBM;2M pM /QMF2`2
Re8
NGC$1365$
NGC$4472$
6B;mm` dXR, GBMFb, oQQ`#22H/ pM 22M bTB`HpQ`KB; bi2Hb2H BM ?2i M#BD2 ?22HH- r`BM +iB27
bi2``2M rQ`/2M ;2pQ`K/X PQF /2 J2HFr2; #2?QQ`i iQi /Bi ivT2X _2+?ib, oQQ`#22H/ pM 22M
TbbB27 bi2Hb2H BM ?2i M#BD2 ?22HH- r`BM T`FiBb+? ;22M MB2mr2 bi2``2M QMibiMX
Ki2`B2 QT /2 +?i2`;`QM/ i2 xB2MX .2 pQQ`xBD/2 iQQMi /2 ;2bBKmH22`/2 p2`/2@
HBM; #BMM2M 22M ;`QQi pQHmK2 BM ?2i ?mB/B;2 ?22HH- i2`rBDH /2 +?i2`xBD/2 /2
p2`/2HBM; BM ?2ix2H7/2 pQHmK2 iQQMi- K` /M QT ?2i KQK2Mi /i ?2i ;2bB@
KmH22`/2 ?22HH KBM/2` /M pBD7 KBHD`/ D` Qm/ BbX Hb r2 /2x2 #2B/2 xBD/2M
K2i 2HF` p2`;2HBDF2M #HBDFi BM/2`// /i ?2i +QMi`bi imbb2M ?Q;2 2M H;2
/B+?i?2B/b;2#B2/2M iQ2M22Ki K2i /2 iBD/X .2 /QMF2`2Ki2`B2rQHF2M UQQF ?HQǶb
;2MQ2K/V /B2 QMibiM #BMM2M /2x2 bBKmHiB2 xBDM p2`/22H/ HM;b }HK2Mi2M- 2M
/2x2 p2`/2HBM; ?227i B2ib r2; pM 22M bTBMM2Mr2#X H?Q2r2H /2 p2`/2HBM; pM
/QMF2`2 Ki2`B2 MB2i /B`2+i r` i2 M2K2M Bb BM ?2i ?22HH- #HBDFi /2 p2`/2HBM;
pM bi2``2Mbi2Hb2Hb QT ;`Qi2 b+?H ;Q2/ Qp2`22M i2 FQK2M K2i /2 ;2bBKmH22`/2
p2`/2HBM; pM /QMF2`2 Ki2`B2X oQH;2Mb /2 i?2Q`B2 #2pBM/2M /2 bi2``2Mbi2Hb2Hb
BM QMb ?22HH xB+? /mb BM ?HQǶb pM /QMF2`2 Ki2`B2X PQF /Bi p2`KQ2/2M rQ`/i
#2p2biB;/ /QQ` BM/B`2+i2 K2iBM;2MX
PT `2HiB27 FH2BM2`2 b+?H- /2 b+?H pM /2 bi2``2Mbi2Hb2Hb x2H7- xBDM /2 2B@
;2Mb+?TT2M pM #`vQMBb+?2 Ki2`B2 UxQHb /2 /22HiD2b r` rBD pM ;2KFi
xBDMV pM ;`Qi2 BMpHQ2/ QT ?2i pQ`K2M pM bi2``2M- THM2i2M 2M mBi2BM/2HBDF
QQF /2 H2p2MbpQ`K2M QT `/2X .QQ` F2`M`2+iB2b BM /2 +2Mi` pM bi2``2M
rQ`/2M pQQ`i/m`2M/ MB2mr2 2H2K2Mi2M ;2pQ`K/- 2M /QQ` bi2HHB`2 rBM/2M 2M
bmT2`MQp@QMiTHQ{M;2M rQ`/2M /2x2 /22HiD2b ?2i ?22HH BM ;2#Hx2MX .QQ` /2`@
;2HBDF2 T`Q+2bb2M rQ`/i ?2i pQ`K2M pM MB2mr2 bi2``2M #2śMpHQ2/- HbK2/2
/QQ` /2 2M2`;2iBb+?2 bi`HBM; /B2 rQ`/i mBi;2xQM/2M rMM22` xr`i2 ;i2M BM
/2 +2Mi` pM bi2``2Mbi2Hb2Hb ;`Q2B2M /QQ` /2 Mrb pM MB2mr2 Ki2`B2X >2i
bK2MbT2H imbb2M /2x2 T`Q+2bb2M 2M /2 Mimm`FmM/B;2 T`BM+BT2b /B2 ?B2`#BD 22M
`QH bT2H2M xBDM xQ/MB; +QKTH2t /i 2` MQ; p22H QT2M p`;2M xBDM #2i`2z2M/2
/2 7Q`KiB2 2M 2pQHmiB2 pM bi2``2Mbi2Hb2HbX
Ree
L1.1_GL.a1 aJ1LohhAL:
:2;2p2M QMb mBi;2bi`2Fi2 ?22HH 2M /2 2MQ`K2 ?Q2p22H?2B/ bi2``2Mbi2Hb2Hb
UM` b+?iiBM; `QM/ /2 Ryy KBHD`/- K2i 2HF QQF `mrr2; Ryy KBHD`/ bi2``2MVBb ?2i QTK2`F2HBDF /i bi2``2Mbi2Hb2Hb ;`Q7r2; BM ir22 bQQ`i2M i2 +HbbB}+2`2M
xBDM- xB2 6B;X dXRX aTB`HpQ`KB;2 bi2Hb2Hb xBDM +iB27 BM ?2i pQ`K2M pM bi2``2Mc xQ
pQ`Ki /2 J2HFr2; i2;2MrQQ`/B; 2MF2H2 MB2mr2 bi2``2M T2` D`X .2 Mr2xB;@
?2B/ pM /2x2 DQM;2 bi2``2M ;227i bTB`HpQ`KB;2 bi2Hb2Hb 22M #Hmr2 FH2m`X >2i
ir22/2 ivT2 #2bii mBi bi2``2Mbi2Hb2Hb K2i 22M pF 2HHBTiBb+?2 pQ`K- r`BM
MB2i Q7 Mmr2HBDFb MB2mr2 bi2``2M rQ`/2M ;2pQ`K/X .QQ` ?2i ;2#`2F M DQM@
;2 bi2``2M ?2##2M /2x2 TbbB2p2 bi2Hb2Hb 22M `Q/2 FH2m`X o2`b+?BHH2M/2 7+iQ`2M
#2TH2M pM r2HF ivT2 22M ;2;2p2M bi2``2Mbi2Hb2H BbX oQQ`H /2 Kbb pM 22M
bi2Hb2H 2M /2 ?Q2p22H?2B/ M#m`B;2 bi2``2Mbi2Hb2Hb bT2H2M ?B2`#BD 22M #2HM;`BDF2
`QH- K` QQF /2 H227iBD/ pM ?2i ?22HH QT ?2i KQK2Mi /i r2 22M bi2``2M@
bi2Hb2H r`M2K2M Bb pM BMpHQ2/X AM ?2i H;2K22M ;2H/i /i bi2``2Mbi2Hb2Hb 22M
;`Qi2`2 FMb ?2##2M QK TbbB27 i2 xBDM M`Ki2 ?mM Kbb ?Q;2` Bb- x2 K22`
M#m`B;2 bi2``2Mbi2Hb2Hb ?2##2M 2M ?2i ?22HH Qm/2` Bb U/mb rMM22` r2 BM ?2i
M#BD;2H2;2M ?22HH FBDF2MVX .2`;2HBDF2 K2iBM;2M xBDM #2HM;`BDF pQQ` ?2i p2`@
}DM2M pM QMb #2;`BT pM /2 Mimm`FmM/B;2 T`Q+2bb2M /B2 i2M ;`QM/bH; HB;;2M
M ?2i i`Mb7Q`K2`2M pM #Hmr2 +iB2p2 bi2``2Mbi2Hb2Hb M` `Q/2 TbbB2p2
bi2``2Mbi2Hb2HbX
PK i2 #2;`BDT2M ?Q2 bi2``2Mbi2Hb2Hb ;2pQ`K/ rQ`/2M BM /Bi /QQ` /QMF2`2 K@
i2`B2 ;2/QKBM22`/2 ?22HH- 2M QK/i /2 i`Mb7Q`KiB2 pM bi2``2Mbi2Hb2Hb pM
p2`b+?BHH2M/2 7+iQ`2M 7?MF2HBDF Bb- Bb ?2i pM #2HM; QK /2 BMpHQ2/ pM Kb@
b- QK;2pBM; 2M /2 H227iBD/ pM ?2i ?22HH HQb pM 2HF` i2 #2b+?Qmr2MX wQ Bb
?2i #BDpQQ`#22H/ MQ; QM/mB/2HBDF r2HF2 T`Q+2bb2M T`2+B2b xQ`;2M pQQ` ?2i /Q@
p2M U/XrXxX `QQ/ rQ`/2MV pM #Hmr2 bi2``2Mbi2Hb2Hb BM ;2#B2/2M K2i 22M ?Q;2
/B+?i?2B/ U/XrXxX bi2``2Mbi2Hb2Hb K2i p22H #m`2MVX 12M ;2`2Hi22`/2 p`; Bb ri
T`2+B2b ?2i p2`#M/ Bb imbb2M /2 p2`/2HBM; pM bi2HHB`2 Ki2`B2 2M /2 p2`/2HBM;
pM /QMF2`2 Ki2`B2X AM /Bi T`Q27b+?`B7i `B+?i2M r2 QMb QT /2`;2HBDF2 p`;2M
2M ;2#`mBF2M r2 T`2+B2x2 r`M2KBM;2M pM /2 K22bi2 KbbB2p2 bi`m+im`2M
/B2 ;2pQ`K/ xBDM BM ?2i ?22HH- MK2HBDF +Hmbi2`b pM bi2``2Mbi2Hb2Hb- QK QMx2
?mB/B;2 i?2Q`B2ďM i2 FmMM2M iQ2ib2M 2M p2`/2` i2 p2`}DM2MX aT2+B}2F bii /2
p`; +2Mi`H ri /2 BMpHQ2/ pM xmHF2 2ti`2K2 QK;2pBM;2M Bb QT /2 2pQHmiB2
pM bi2``2Mbi2Hb2HbX
AM >QQ7/bimF R ;2p2M r2 K22` +?i2`;`QM/BM7Q`KiB2 2M BMi`Q/m+2`2M
r2 #2;`BTT2M r` BM /2 `2bi pM ?2i T`Q27b+?`B7i QT pQQ`i;2#Qmr/ rQ`/iX
*2Mi`H BM /Bi T`Q27b+?`B7i bii ?2i F`Fi2`Bb2`2M pM bi2``2Mbi2Hb2Hb M /2
?M/ pM ?mM bi2HHB`2 KbbX .2x2 FmMM2M r2 b+?ii2M /QQ` i2 FBDF2M ?Q2p22H
HB+?i 22M bi2``2Mbi2Hb2H mBibi`Hi BM p2`b+?BHH2M/2 FH2m`2MX H?Q2r2H /2 bi2HHB`2
Kbb K` 22M FH2BM /22H Bb pM /2 iQiH2 Kbb Ur2HF2 rQ`/i ;2/QKBM22`/
Red
/QQ` /QMF2`2 Ki2`B2 2M ;b imbb2M /2 bi2``2MV- ;227i /Bi p22H BM7Q`KiB2 Qp2`
Mimm`FmM/B;2 T`Q+2bb2M /B2 22M `QH bT2H2M #BD ?2i pQ`K2M pM bi2``2MX
AM /2 >QQ7/bimFF2M k@9 #2bim/2`2M r2 /2 p2`/2HBM; pM bi2HHB`2 Ki2`B2
BM iB2M +Hmbi2`b BM ?2i DQM;2 ?22HH- iQ2M ?2i ?22HH QM;2p22` /2 ?2H7i pM xBDM
?mB/B;2 H227iBD/ ?/X >2i ;2#`mBF pM ;2pQ2HB;2 r`M2KBM;2M pM i2H2b+QT2M
QT *?BHB- >rBB 2M QQF /2 aTBix2` `mBKi2i2H2b+QQT- ;227i QMb 22M ;2/2iBHH22`/2
FBDF QT /2x2 DQM;2 bvbi2K2M /B2 iQi /mbp2` QM;2ďp2M`/ Bb BM /2 HBi2`imm`X
.2 +?i2`xBD/2 pM /Bi T`Q27b+?`B7i iQQMi 22M 7QiQ pM ûûM pM /2x2 +Hmbi2`b;2+QMbi`m22`/ /QQ` K22`/2`2 r`M2KBM;2M i2 +QK#BM2`2MX
AM >QQ7/bimF k #2bim/2`2M r2 bT2+B}2F /2 p2`/2HBM; pM bi2``2Mbi2Hb2Hb BM
/2x2 +Hmbi2`b Hb 7mM+iB2 pM ?mM bi2HHB`2 Kbb 2M p2`;2HBDF2M /Bi K2i bi2``2M@
bi2Hb2Hb 2`#mBi2MX q2 pBM/2M /i /2x2 Kbbp2`/2HBM;2M bB;MB}+Mi pM 2HF`
p2`b+?BHH2MX 1+?i2`- rMM22` r2 /2 ir22 ivT2M bi2``2Mbi2Hb2Hb HQb pM 2HF`
#2b+?Qmr2M- xB2M r2 /i 2HF ivT2 rQ`/i #2b+?`2p2M /QQ` 22M p2`/2HBM; /B2 QM@
7?MF2HBDF Bb pM /2 QK;2pBM;X >2i p2`b+?BH BM /2 iQiH2 Kbbp2`/2HBM; rQ`/i
/2`?Hp2 p2`QQ`xFi /QQ`/i /2 +Hmbi2`b QQF BM ?2i DQM;2 ?22HH H 22M `2HiB27
?QQ; MiH TbbB2p2 bi2``2Mbi2Hb2Hb #2pii2MX q2 p2`;2HBDF2M /2x2 K2iBM;2M
K2i 22M KQ/2H /i ?2i /Qp2M pM bi2``2Mbi2Hb2Hb #2b+?`BD7i 2M pBM/2M ?B2`K22
22M ;Q2/2 #2b+?`BDpBM; pM /2 /iX
>2i KQ/2H /i ?2i /Qp2M pM bi2``2Mbi2Hb2Hb #2b+?`BD7i- pQQ`bT2Hi BM QMx2
+Hmbi2`b /2 Mr2xB;?2B/ pM 22M TQTmHiB2 bi2``2Mbi2Hb2Hb /B2 `2+2Mi2HBDF 2M
#`mTi mBi;2/QQ7/ xBDMX .2x2 `2+2Mi mBi;2/QQ7/2 bi2``2Mbi2Hb2Hb ?2##2M bT2+B@
}2F2 F2MK2`F2M- 2M BM >QQ7/bimF j B/2MiB}+2`2M r2 /2x2 bi2Hb2Hb BM QMx2 iB2M
+Hmbi2`b BM ?2i DQM;2 ?22HHX q2 pBM/2M /i bi2``2Mbi2Hb2Hb pM /Bi ivT2 F2MK2`@
F2M/2 `2HiB2p2 bM2H?2/2M 2M TQbBiB2b ?2##2M i2M QTxB+?i2 pM /2 +Hmbi2`+2Mi`X
.Bi ?227i KQ;2HBDF i2 KF2M K2i 22M THQib2HBM;2 p2`rBD/2`BM; pM ?22i ;b mBi
/2x2 bi2``2Mbi2Hb2Hb- /i /`/QQ` MB2i K22` #2b+?BF#` Bb pQQ` ?2i pQ`K2M
pM bi2``2MX .QQ` /2x2 bim/B2 FmMM2M r2 xQ K22` H2`2M Qp2` ?2i T`Q+2b /i i2M
;`QM/bH; HB;i M ?2i /Qp2M pM bi2``2Mbi2Hb2Hb BM ?Q;2 /B+?i?2B/b;2#B2/2MX
AM >QQ7/bimF 9 p2`b+?mB7i QMx2 7Q+mb pM /2 BM/BpB/m2H2 bi2``2Mbi2Hb2Hb
#BMM2M /2 +Hmbi2`b M` /2 2B;2Mb+?TT2M pM /2 +Hmbi2`b x2H7X PT /2 b+?H
pM +Hmbi2`b p2`r+?i2M r2 /i QM;2p22` 3yW pM /2 Kbb /2 2B;2Mb+?TT2M
?227i pM /QMF2`2 Ki2`B2- 2M /i /2 #`vQMBb+?2 7`+iB2 U#2biM/2 mBi ;b 2M
bi2``2MV /mb M;2MQ2; ;2HBDF Bb M /2 ;2KB//2H/2 r`/2 BM ?2i ?22HHX .QQ` /2
iQiH2 ?Q2p22H?2B/ /QMF2`2 Ki2`B2- /B2 r2 KB//2Hb BM/B`2+i2 K2i?Q/2b FmMM2M
#2TH2M- 2M /2 bi2HHB`2 Ki2`B2 i2 p2`;2HBDF2M- FmMM2M r2 xQ B2ib H2`2M Qp2`
/2 2{+BďMiB2 r`K22 bi2``2M xB+? pQ`K2M BM +Hmbi2`b pM bi2``2Mbi2Hb2HbX PQF
FBDF2M r2 M` /2 `mBKi2HBDF2 p2`/2HBM; pM bi2HHB`2 Ki2`B2 BM /2x2 +Hmbi2`b
2M pBM/2M /i /2 T`Q}2H2M /B2 /2x2 p2`/2HBM; #2b+?`BDp2M K22` ;2TB2Fi xBDM /M
/2 p2`/2HBM; pM /QMF2`2 Ki2`B2 pQQ` /2`;2HBDF2 +Hmbi2`b BM /2 bBKmHiB2bX
AM >QQ7/bimF 8 #Qmr2M r2 ?B2`QT pQQ`i- 2M #2b+?`BDp2M 22M K2iBM; pM
/2 `mBKi2HBDF2 p2`/2HBM; pM bi2HHB`2 Ki2`B2 #BMM2M iB2M +Hmbi2`b pM bi2``2M@
bi2Hb2Hb BM ?2i M#BD2 ?22HH- QT #bBb pM r`M2KBM;2M ;2/M BM >rBB 2M
Re3
L1.1_GL.a1 aJ1LohhAL:
QT G SHKX .2 pQQ`xBD/2 pM /Bi T`Q27b+?`B7i Hi 22M FH2m`2M7QiQ pM ûûM
pM /2x2 +Hmbi2`b xB2MX PK/i /2x2 iB2M +Hmbi2`b BM ?2i M#BD2 ?22HH biM?2##2M x2 #BDM /2 ;2?2H2 H227iBD/ pM ?2i ?22HH ;2?/ QK xB+? iQi /2x2 bii
i2 QMirBFF2H2MX .QQ` /2x2 +Hmbi2`b i2 p2`;2HBDF2M K2i /2 +Hmbi2`b mBi ?2i DQM;2
?22HH U/XrXxX /2;2M2 /B2 r2 #2bim/22`/ ?2##2M /2 BM /2 ?QQ7/bimFF2M k@9VFmMM2M r2 #2bim/2`2M ?Q2 /2 `mBKi2HBDF2 p2`/2HBM; pM bi2HHB`2 Ki2`B2 2pQ@
Hm22`i BM /2 HQQT pM /2 iBD/X o2`;2H2F2M K2i /2 2pQHm2`2M/2 p2`/2HBM; pM
/QMF2`2 Ki2`B2 BM bBKmHiB2b- M2K2M r2 22M bB;MB}+Mi M/2`2 2pQHmiB2 r`
BM /2 p2`/2HBM; pM bi2HHB`2 Ki2`B2X q2 #2b+?Qmr2M p2`b+?BHH2M/2 b+2M`BQǶb
QK /2x2 p2`b+?BHH2M i2 FmMM2M p2`FH`2MX wQ Bb ?2i KQ;2HBDF /i /2 pQQ`bT2HHBM@
;2M pM bBKmHiB2b ?2`xB2M KQ2i2M rQ`/2M /QQ` ?2i iQ2pQ2;2M pM #`vQMBb+?2
T`Q+2bb2M- Q7 /i r2 22M /22H pM /2 bi2``2M MB2i FmMM2M r`M2K2M /QQ`/i
x2 i2 /Bzmmb p2`/22H/ xBDM imbb2M /2 bi2``2Mbi2Hb2Hb BMX
AM >QQ7/bimF e #2bim/2`2M r2 ?2i ?22HH xQHb ?2i 2` KBM/2` /M ir22
KBHD`/ D` M /2 Q2`FMH mBi x;- 22M T2`BQ/2 r`BM bi2``2Mbi2Hb2Hb x22` +iB27
r`2M BM ?2i pQ`K2M pM bi2``2MX .QQ` bT2+B}2F i2 7Q+mbb2M QT ?2i mBi;2bi`H/2
mHi`pBQH2ii2 HB+?i /QQ` /2x2 bi2``2Mbi2Hb2Hb- FmMM2M r2 22M BMp2Mi`BbiB2 K@
F2M pM /2 ?Q2p22H?2B/ bi2``2M /B2 ;2pQ`K/ rQ`/i T2` bi2``2Mbi2Hb2HX o2`;2H2F2M
K2i pQQ`;M/2 K2iBM;2M BM /2 HBi2`imm`- KF2M r2 ;2#`mBF pM r`M2KBM@
;2M pM 22M ;`Qi2` bimF M /2 ?2K2H- ri 22M biiBbiBb+? #2i2`2 `2T`2b2MiiB2
;227i pM ?2i iQiH2 ?22HHX J2i #2?mHT pM /2x2 K2iBM; FmMM2M r2 /2`;2HBDF2
p2`7;2H2;2M bi2``2Mbi2Hb2Hb x2H7b ;2#`mBF2M QK B2ib i2 H2`2M Qp2` /2 /QMF2`2K@
i2`B2p2`/2HBM; BM ?2i imbb2MHB;;2M/2 ?22HHX qi ?B2`M i2M ;`QM/bH; HB;i Bb
?2i p2`KQ;2M pM Kbb QK HB+?ibi`H2M 7 i2 #mB;2M- ri H2B/i iQi 22M r`@
;2MQK2M ?2H/2`?2B/bp2`/2HBM; /B2 M/2`b Bb /M /2 BMi`BMbB2F2 p2`/2HBM;X
.QQ` /2 r`M2KBM;2M /B2 #2b+?`2p2M biM BM /2 ?QQ7/bimFF2M pM /Bi
T`Q27b+?`B7i K2i KQ/2HH2M 2M bi22/b ;2pM+22`/2`2 bBKmHiB2b i2 p2`;2HBDF2MH2`2M r2 K22` Qp2` /2 Mimm`FmM/B;2 T`Q+2bb2M /B2 22M `QH bT2H2M #BD ?2i QMi@
biM pM bi`m+imm` BM ?2i ?22HH 2M /2 2pQHmiB2 pM bi2``2Mbi2Hb2HbX
*m``B+mHmK oBi2
PT jy T`BH RN3e #2M BF ;2#Q`2M BM G2B/2`/Q`T- r`M BF BM ?2i /Q`TD2 "2Mi@
?mBx2M QT;`Q2B/2X AM a2Ti2K#2` kyy9 #2;QM BF KBDM bim/B2 bi2``2MFmM/2 M
/2 lMBp2`bBi2Bi G2B/2M- r` BF pBD7 D` Hi2` +mK Hm/2 7bim/22`/2X :2/m`2M@
/2 /2x2 D`2M ?2# BF F2MMBb ;2KFi K2i p2`b+?BHH2M/2 QM/2`xQ2Fb`B+?iBM;2M
#BMM2M /2 bi2``2MFmM/2X wQ ?2# BF iBD/2Mb KBDM "+?2HQ`QM/2`xQ2F BM /2 QM/2`@
xQ2Fb;`Q2T pM .`X A;Mb aM2HH2M 22M xQ2FiQ+?i M` 2tQTHM2i2M QM/2`MQK2M2M K2i bm++2b 7;2bHQi2MX 12M D` Hi2` pQH;/2 22M MB2mr2 mBi/;BM; BM /2 ;`Q2T
pM .`X JB+?B2H >Q;2`?2BD/2- r`#BD BF ?2i ;2/`; 2M /2 bK2Mr2`FBM; imb@
b2M ;b 2M biQ7 BM /2 b+?BDp2M `QM/ DQM;2 bi2``2M QM/2`xQ+?iX AM ?2i F/2` pM
/Bi QM/2`xQ2F QM/2`MK BF 22M r`M22K`2Bb M` >rBBX hBD/2Mb KBDM Hi@
bi2 2M K22bi2 mBi;2#`2B/2 QM/2`xQ2F KFi2 BF F2MMBb K2i /2 2ti`;H+iBb+?2
bi2``2MFmM/2- QM/2` H2B/BM; pM .`X >2M/`BF >BH/2#`M/i 2M S`Q7X/`X EQ2M@
`/ EmBDF2MX .2 QMi2H#`2 bi2``2Mbi2Hb2Hb BM /2 mBi;2bi`2Fi?2B/ pM ?2i ?22HH
T`BFF2H/2M KBDM MB2mrb;B2`B;?2B/X
AM kyyN F`22; BF BM /2 QM/2`xQ2Fb;`Q2T pM .`X >2MF >Q2Fbi` /2 KQ@
;2HBDF?2B/ QK K2 KB//2Hb 22M T`QKQiB2TQbBiB2 p2`/2` i2 QMirBFF2H2M QT ?2i
;2#B2/ pM /2 2ti`;H+iBb+?2 bi2``2MFmM/2X JBDM r2i2Mb+?TT2HBDF2 `2bmHi@
i2M pM /2 /`QTpQH;2M/2 D`2M biM BM /Bi T`Q27b+?`B7i #2b+?`2p2MX PQF ?2#
BF /2 FMb ;2F`2;2M /2x2 i2 T`2b2Mi2`2M ;2/m`2M/2 BMi2`MiBQMH2 +QM72`2M@
iB2b BM a+?QiHM/- .mBibHM/- AiHBď 2M aTMD2X o2`/2` ?2# BF 2MF2H2 KH2M 22M
#2xQ2F ;2#`+?i M /2 o2`2MB;/2 aii2M QK BMi2MbB27 bK2M i2 r2`F2M K2i
+QHH2;Ƕb /`X :2/m`2M/2 je M+?i2M- p2`/22H/ Qp2` /2 D`2M kyRy 2M kyRR?2# BF bi`QMQKBb+?2 r`M2KBM;2M p2``B+?i QT /2 Ab+ L2riQM h2H2b+QQT BM
G SHKX .2 FQK2M/2 D`2M xH BF KBDM +``Bĕ`2 pQQ`ix2ii2M BM *1 a+Hv6`MF`BDF- BM /2 QM/2`xQ2Fb;`Q2T pM .`X JQMB[m2 `Mm/X
Lbi ?2i H2p2`2M pM /2x2 #BD/`;2 M /2 r2i2Mb+?T ?2# BF K2 QQF
QT M/2`2 ;2#B2/2M p2`/2` FmMM2M QMirBFF2H2MX wQ ?2# BF K2 D`2M HM; Hb
`Q2B2` 2M +Q+? BM;2x2i #BD bQTQb /2 oHB2i- 2M ?2# BF ?`/;2HQT2M #BD Gl>o
*m``BKmbX PQF #`+?i2M KBDM ;Bi` 2M TBMQ /2 MQ/B;2 ~2B/BM; 2M BMbTB`iB2X
ReN
LrQQ`/
Lm ?2i b+?`BDp2M pM /Bi T`Q27b+?`B7i +?i2` /2 `m; Bb- FBDF BF i2`m; QT 22M
BMi2`2bbMi2 iBD/ 2M H22`xK2 D`2MX >2i QM/2`xQ2F ri ?B2` #2b+?`2p2M bii
?/ BF MQQBi FmMM2M mBipQ2`2M xQM/2` /2 QMp2`;2i2HBDF2 bi2mM pM KBDM +QHH2@
;Ƕb- p`B2M/2M 2M 7KBHB2X :`; #2/MF BF KBDM Mbi2M ?B2`QM/2` pQQ` ?mM
#BD/`;2M M KBDM T2`bQQMHBDF2 QMirBFF2HBM;X
HH2`22`bi KBDM +QHH2;Ƕb pM /2 ai2``2r+?i G2B/2M- 2M BM ?2i #BDxQM/2`
/2 QM/2`xQ2Fb;`Q2T r` BF /22H pM ?2# KQ;2M mBiKF2MX >2M/`BF- Bi ?b
#22M ;`2i TH2bm`2 iQ rQ`F rBi? vQmX A H2`M2/ HQi- 2bT2+BHHv 7`QK vQm`
rQ`FBM; 2{+B2M+v- M/ i?Bb ?b #22M bi`QM; KQiBpiBQM 7Q` K2 iQ DQBM i?2
S?. T`Q;`KX "2`2MB+2- A p2`v Km+? TT`2+Bi2/ rQ`FBM; iQ;2i?2` rBi? vQm
7Q` b2p2`H KQMi?b ,@VX 1/Q- JHBM- 1HBb#2ii- ai27MB- hBK- J2`BDM- *`BbiƦ#H6#BM- C2`Q2M- _B+`/Q- JbbBKQ- J`+2HHQ- C2Hi2- J`;Qi- J`iBMc i?MFb 7Q`
i?2 7mM- M/ vQm` +QMi`B#miBQMb iQ ;`2i rQ`FBM; 2MpB`QMK2MiX
HbQ A rQmH/ HBF2 iQ i?MF HH Kv 7Q`K2` Q{+2@Ki2b- BM T`iB+mH` /K
M/ CvM2X /K- Bi rb ;`2i 7mM iQ rQ`F rBi? vQm- M/ A ?B;?Hv pHm2 HH
b+B2M+2 /Bb+mbbBQMb r2 ?/ /m`BM; i?2 Hbi 72r v2`bX HbQ A rBHH HQM; `2K2K#2`
Qm` #H+FD+F ;K2b BM Gb o2;b- Qm` ?BF2b HQM; bQK2 bi22T +HBzb- M/ vQm`
2p2`@+QMiBMmBM; +QKTHBMib #Qmi i?2 .mi+? r2i?2` M/ 7QQ/X CvM2- Bi ?b
#22M ;`2i iQ ;2i iQ FMQr vQm QM KQ`2 T2`bQMH H2p2H- QmibB/2 i?2 Q{+2X
A +QMbB/2` Kvb2H7 Hm+Fv i?i A K2i bm+? bT2+BH T2`bQM rBi? bm+? r`K
T2`bQMHBiv5 6m`i?2` A rQmH/ HBF2 iQ i?MF HH Qi?2` +QHH2;m2b- 2bT2+BHHv C2bb2.MBďH- _Q#- a?MMQM- _2MbF2- HHBbQM M/ JiiBX qBi?Qmi vQm i?2 +Qz22
M/ HmM+? #`2Fb rQmH/ M2p2` ?p2 #22M i?2 bK25 h2MbHQii2 ;i KBDM /MF
mBi M` .pB/- 1`BF- 1p2HBDM- GB2b#2i?- MBi 2M `i pQQ` ?mM T`FiBb+?2
QM/2`bi2mMBM; QT /2 ai2``2r+?iX
AM /2 HQQT pM KBDM S?. ?2# BF QQF BMi2`MiBQMH 22M QM/2`xQ2FbM2ir2`F
FmMM2M QT#Qmr2MX A rQmH/ HBF2 iQ i?MF Kv BMi2`MiBQMH +QHH2;m2b Q7 i?2
EB.a i2K- M/ HbQ i?2 aT_*af:*Gaa +QHH#Q`iBQM, BM T`iB+mH` :BH@
RdR
Rdk
L1.1_GL.a1 aJ1LohhAL:
HBM- *?`Bb- >Qr`/- h`+v- HHBbQM- JB+?2H- .2MMBb- M/ CmHB2X M/ /B`2+iHv
`2Hi2/ iQ i?2 i?2bBb Bib2H7c amxMM2- KMv i?MFb 7Q` vQm` ?2HT BM /2bB;MBM;
bm+? rQM/2`7mH i?2bBb +Qp2`5
"mBi2M /2 ai2``2r+?i ;M KBDM ;2/+?i2M mBi M` /2 KMM2M pM qB+@
Fu pQQ` /2 2TBb+?2 ;2p2+?i2M /B2 r2 bK2M T2` `Q2B#QQi QT K2MB; rQ2bi ri2`
?2##2M mBi;2pQ+?i2MX .2 #MM2M 3Y- ri BM i?2Q`B2 22M QMQp2`rBMM2HBDF ;2x2H@
b+?T rbX 12M ;2x2Hb+?T rb ?2i x2F2` ,@VX HH2 `Q2BTHQ2;D2b /B2 /2 7;2HQT2M
D`2M M` KBDM rBDx2 `/ rBH/2M HmBbi2`2MX AM ?2i #BDxQM/2` /2 KMM2M pM
hQp2`;B2i2` 2M /2 *Hm#3Y ;2MK/ uPGPX PQF KBDM K2/2@+Q+?2b 2M HH2 M@
/2`2 H2/2M pQQ` /2 ir22r2F2HBDFb2 #Q``2Hb BM ?2i +Hm#;2#QmrX JBDM KiD2b pM
*m``BKmb pQQ` 22M MiH KQQB2 ?`/HQQT@2bi72ii2b- K2i Hb ?QQ;i2TmMi QMx2
/22HMK2 M /2 _QS_mM BM kyRj, >2i rb 22M 7MibiBb+?2 2`p`BM;- r`@
#BD x2F2` /2 ?2H/2M//2M pM i2K #Hmr MB2i p2`;2i2M KQ;2M rQ`/2M5 E`HBhBKQ- LB2Hb- J`F- h?BDb 2M CmHBmbc QMx2 ?BF2@iQ+?i2M BM a+?QiHM/- wr2/2M/2 Sv`2M22ďM- ACbHM/ 2M "mH;`BD2 r`2M i2 2TBb+? pQQ` rQQ`/2MX >2i #HBD7i
#BDxQM/2` ?Q2 bM2H D2 22M ?2+?i2 #M/ QT#Qmri #BD ?2i bK2M /QQ`biM pM
QMi#2`BM;2M5 1M QQF KBDM }2ib@#m//vǶb 2M QMx2 MbiM/2 /2`/2 `2Bb M` /2
HT2M pQQ` 22M r22FD2 #2`;2M #2FHBKK2M 2M ##[Ƕ2MX
PQF K; BF K2x2H7 ;2HmFFB; T`BDx2M K2i 22M 7MibiBb+?2 7KBHB2X JBDM HB2p2
QK- QM/MFb ?` KQQB2 H227iBD/ MQ; HiBD/ ?`b+?2`T pM ;22bi- /` ?2# BF
p22H #2rQM/2`BM; pQQ`X J` #Qp2MH /2 bi2mM 2M QMpQQ`r`/2HBDF2 HB27/2 pM
KBDM Qm/2`b ?2##2M 2`pQQ` ;2xQ`;/ /i BF FQM QT;`Q2B2M iQi rB2 BF Mm #2MX
JBDM /MF#`?2B/ ;i M` ?2M mBi- 2M QQF M` KBDM HB27iHHB;2 xmbD2 /B2 K2
Hb T`MBK7 i2`xBD/2 xH biMX
_2K+Q 6XCX pM /2` "m`;
J`i kyR9X
h?2 iBK2 rBHH +QK2
r?2M- rBi? 2HiBQM
vQm rBHH ;`22i vQm`b2H7 ``BpBM;
i vQm` QrM /QQ`- BM vQm` QrM KB``Q`
M/ 2+? rBHH bKBH2 i i?2 Qi?2`Ƕb r2H+QK2M/ bv- bBi ?2`2X 1iX
uQm rBHH HQp2 ;BM i?2 bi`M;2` r?Q rb vQm` b2H7X
:Bp2 rBM2X :Bp2 #`2/X :Bp2 #+F vQm` ?2`i
iQ Bib2H7- iQ i?2 bi`M;2` r?Q ?b HQp2/ vQm
HH vQm` HB72- r?QK vQm B;MQ`2/
7Q` MQi?2`- r?Q FMQrb vQm #v ?2`iX
hF2 /QrM i?2 HQp2 H2ii2`b 7`QK i?2 #QQFb?2H7i?2 T?QiQ;`T?b- i?2 /2bT2`i2 MQi2bT22H vQm` QrM BK;2 7`QK i?2 KB``Q`X
aBiX 62bi QM vQm` HB72X
.2`2F qH+Qii

PowerPoint プレゼンテーション

Chapter 4

6 演算子の固有値、固有関数

「デマンド監視」「エネルギー監視」「ソラモニ 3G」の事業譲渡

Tabraino

1 量子反射と量子トンネル効果

e

Document

救急車同乗実習 - 松江生協病院

TS-M2M-0002v1.0.1 oneM2M 技術仕様書 －要求条件－ oneM2M

PowerPoint プレゼンテーション - ホーム