Chapter 4

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
*?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

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