BH連星合体イベントからの重力波
IMBH形成シナリオが，KAGRA で判別できるか．
重力波干渉計の話
Ringdown 波形の話
KAGRA/ETでの話
真貝寿明（大阪工大）
戎崎さん 神田さん
DECIGO/LISA
ではできる
2014年8月25日@理研東京
重力波干渉計の感度
LISA
DECIGO
LIGO
aLIGO
第3世代
(ET)
地上
スペース（計画のみ）
Pitkin+, Liv. Rev. Rel. 14 (2011) 5
第2世代
x10
LCGT
LCGT (varRSED, BWstudy2009)
LCGT (varRSEB, Bwstudy2009)
-20
10
Strain Equivalent Noise spectrum [1/√Hz]
advanced Virgo
advanced LIGO(ZERO DET, High P)
advanced LIGO(NS-NS)
-21
10
Einstein Telescope ET_B
ET_C
-22
10
-23
10
-24
10
6 7 8 9
10
2
3
4
5 6 7 8 9
100
frequency [Hz]
2
3
4
5 6 7 8 9
神田さん提供のKagra(LCGT)感度予想曲線(2013/3)
1000
BH#BH$merger$waveforms$(non$spinning)
Ajith+,(PRD77(2008)104017([arXiv:0710.2335]
Inspiral Phase
松林,真貝,戎崎, ApJ 614 (2004) 864
松林,真貝,戎崎, ApJ 614 (2004) 864
松林,真貝,戎崎, ApJ 614 (2004) 864
松林,真貝,戎崎, ApJ 614 (2004) 864
BH#BH$merger$waveforms$(non$spinning)
Ajith+,(PRD77(2008)104017([arXiv:0710.2335]
ここでは，BHBH合体のQNMを考える．
Black-Hole Ringdown waveform
10
h(t
19
M = 100M , a = 0.96, D = 1Mpc
t0 )
[s]
M = 1000M , a = 0.96, D = 1Mpc
h(t
t0 )
[s]
Ae
QNMの波形イメージ．
( fQNM /2(1 a)
0.45
)t
cos(2 fQNM t + ⇥0 )
BH quasi-normal ringing frequency (spin=0のとき)
f_QNM
1
78200 Hz
10
7820 Hz
100
782 Hz
1000
78.2 Hz
10000
7.82 Hz
LCGT
LCGT (varRSED, BWstudy2009)
LCGT (varRSEB, Bwstudy2009)
-20
10
advanced Virgo
Strain Equivalent Noise spectrum [1/√Hz]
Mtotal
advanced LIGO(ZERO DET, High P)
advanced LIGO(NS-NS)
-21
10
Einstein Telescope ET_B
ET_C
-22
10
-23
10
-24
10
6 7 8 9
10
2
3
4
5 6 7 8 9
100
frequency [Hz]
2
3
4
5 6 7 8 9
1000
神田さん提供のKagra(LCGT)感度予想曲線(2013/3)
fQNM
Black-Hole Ringdown frequency
fQNM
1000
c3
=
1
2 GM
0.63(1
0.3
a)
⇥
100
a = 0.98
a = 0.49
a=0
10
103
M/M
BHのKerrパラメータ依存性を考えたもの．
回転していると，QNM周波数は高くなるが，これはKagraでは見えやすくなるということ．
Signal-to-Noise Ratio (SNR)
Signal-to-Noise Ratio (SNR)
Signal-to-Noise Ratio (SNR)
Ringdown波形 のSNR (1)
？
Ringdown波形 のSNR (2)
0.10
0.08
0.06
3%
0.04
0.02
0.0
0.2
0.4
0.6
0.8
1.0
arXiv:0906.5423
MNRAS
Kato+, arXiv:0906.5423
MNRAS
KAGRA
BH Ringdown wave
(b) highly-spinning BHs
(a) non-spinning BHs
10-20
10-21
h
2560M
1280M
640M
320M
10-20
10-21
10-22
2560M
1280M
640M
320M
10-22
1 Mpc
1 Mpc
h
10-23
10-23
10 Mpc
10 Mpc
10-24
10-24
100 Mpc
100 Mpc
1 Gpc
1 Gpc
10
100
1000
10
fQNM [Hz]
100
fQNM [Hz]
Einstein Telescope
10-21
h
BH Ringdown wave
(b) highly-spinning BHs
(a) non-spinning BHs
10-20
1000
2560M
1280M
640M
320M
10-20
10-21
10-22
2560M
1280M
640M
320M
10-22
1 Mpc
10-23
1 Mpc
h
10-23
10 Mpc
10 Mpc
10-24
100 Mpc
10-24
100 Mpc
1 Gpc
1 Gpc
10
100
fQNM [Hz]
1000
10
100
fQNM [Hz]
1000
1Gpc先の感度
Kagra, BH
ringdown signal
KAGRA
SNR at d=1000 Mpc
100.0
a = 0.9
50.0
a = 0.5
10.0
a = 0.0
5.0
1.0
0.5
50
100
500
BH Mass (final BH)
1000
5000
[M ]
Einstein
Telescope,Telescope
BH ringdown signal
Einstein
a = 0.9
a = 0.5
SNR at d=1000 Mpc
2000
1000
a = 0.0
500
200
50
100
500
BH Mass (final BH)
1000
[M ]
5000
KAGRA
観測可能距離 (等質量連星合体)
Kagra, BH ringdown signal, spin a=0.9
Observable Distance [Mpc]
SNR=8
SNR=10
1000
SNR=100
10
1
SNR=10
1000
SNR=100
100
10
1
50
LCGT detection range (VRSE-D)
Detection Range (with optimal direction)
for CBC
| for BH QNM
SNR=3
|
SNR=3
SNR=8
|
SNR=8
SNR=100
|
SNR=100
10Mpc
0.01
0.001
10
0
10
1
2
10
mass of one star [Msolar]
(BH mass = 2M)
10
3
10
4
5000
13Gyr
[M ]
10Gyr
100Myr
0.1
1000
1Gyr
1
BH Mass (final BH)
[M ]
Look Back Time
10
5000
100Gpc
BH Mass (final BH)
1000
500
10Gpc
500
Luminocity Distance
100
1.4Msolar (Typical Neutron Star)
50
100
1Gpc
100
SNR=8
104
100Mpc
104
Cosmological Redshift : z
Observable Distance [Mpc]
105
Kagra, BH ringdown signal, spin a=0.0
105
Kanda+,
arXiv:1112.3092
KAGRA
(monopolistic growth)
観測可能距離 (非等質量連星合体)
Kagra, BH ringdown signal, spin a=0.9
Observable Distance [Mpc]
SNR=8
104
1000
100
SNR=10
SNR=100
10
1
50
100
500
BH Mass (final BH)
1000
[M ]
5000
Observable Distance [Mpc]
monopolistic growth
105
105
Kagra, BH ringdown signal, spin a=0.0
monopolistic growth
104
1000
SNR=8
SNR=10
100
SNR=100
10
1
20
50
100
200
BH Mass (final BH)
500
1000
[M ]
2000
Event Rate?
Event Rate?
Fraction Rate
1
Fraction
0.1
10-2
10-3
10-4
10-5
100
1000
104
BH Mass
105
106
KAGRA
(hierarchicalgrowth)
growth)
Event Rate (hierarchical
105
105
BH spin=0.9
SNR=8
BH spin=0.9
1000
1000
SNR=10
10
10
SNR=100
0.1
0.1
50
100
500
1000
10
5000
BH Mass
100
1000
Frequency
105
105
BH spin=0.0
BH spin=0.0
1000
1000
10
10
0.1
0.1
50
100
500
BH Mass
1000
5000
10
100
Frequency
1000
KAGRA
(monopolistic growth)
growth)
Event Rate (monopolistic
105
SNR=8
1000
105
BH spin=0.9
BH spin=0.9
1000
SNR=10
10
10
SNR=100
0.1
0.1
50
100
500
1000
10
BH Mass
105
BH spin=0.0
1000
1000
10
10
0.1
0.1
100
500
BH Mass
1000
Frequency
105
50
100
1000
5000
BH spin=0.0
10
100
Frequency
1000
BH連星合体イベントからの重力波
IMBH形成シナリオが，KAGRA で判別できるか．
KAGRAでも
できる
DECIGO/LISA
ではできる

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