初代星・初代銀河研究会2016@金沢

多重孤立BHの合体によるGW150914の説明© Illinois Relativity Group田川 寛通 (東京大学)
共同研究者:
梅村 雅之 (筑波大学)1

重力波イベントGW150914
Abbott et al. (2016)

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GW150914への進化モデル
Rodriguez et al. (2016)

1. 球状星団内での力
学的な進化

Belczynski et al. (2016)(e.g. Rodriguez et al. 2016)

2. 連星進化(e.g. Belczynski et al. 2016;
Marchant et al. 2016;de Mink & Mandel 2016)

我々は新たに “多重孤立BHからの進化’’ を提唱

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初代星からの多重孤立BH形成

Susa et al. (2014)

Heger & Woosley (2002)

2000 AU

BH
60

BH
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多重孤立BH形成とガスが豊富な環境
Tagawa, Umemura, Gouda, Yano & Yamai, 2015, MNRAS, 451, 2174
Tagawa, Umemura, Gouda, 2016, MNRAS, 462, 3812
First Objects
Mergerdense interstellar
cloud coresngas =105-7 cm-3

interstellar clouds
ngas <105 cm-3

galactic nuclear regions
ngas ≳ 107 cm-3 at ≲ 1pc

目的 : 多重孤立BHの進化により、GW150914のようなBH合体5が起こる条件を調べる

BH合体の素過程
重力波放出

力学的摩擦
BH

vBH
換算質量
周辺ガス

Bondi-Hoyle-Lyttleton
降着三体相互作用
vBH
Binary BHs
3rd BHPost-Newtonian N体シミュレーション
BHに関する加速度

𝑑 2 𝐫𝑖=2𝑑𝑡

𝑁BH−𝐺𝑚𝑗𝑗𝐫𝑖 − 𝐫𝑗𝐫𝑖 − 𝐫𝑗

3 + 𝑎PN,𝑖𝑗

初期条件+ 𝐚DF,𝑖 + 𝐚acc,𝑖 + 𝐚pot,𝑖パラメータ

ガス質量：105 Msun

1. 初期BH質量 (𝑚0 )合体条件：100 rsch

2. ガス降着率 (𝜀 = 𝑚 )計算時間：10 Gyr[pc]

ガスに関する加速度𝑚HL

3. 初期BH間典型的距離(𝑟typical )4. ガス密度 (𝑛gas )7

合体機構の分類
Type A

Type BGas drag-driven merger

Interplay-driven merger

3-bodygas-drag𝑛gas = 1012 cm−3𝑛gas = 109 cm−3

Gravitational Waves
Type CType D

Three body-driven merger

Accretion-driven merger𝑛gas = 106 cm−3𝑛gas = 107 cm−3初期と合体時のBH質量GW150914

𝑚0 ≳ 25 𝑀sun , type B or C
(𝑚~0.01 𝑚HL , 𝑟typical ≲ 1 pc)

孤立BH合体が期待される環境• 環境は 108 yrで変わる(AGN duty cycle, galactic rotation timescale)• 𝑡merge < 108 yr• 𝑡merge ∝ 𝑛gas −1 (Tagawa et al. 2015)→ 𝑛gas > 105 cm−3
環境:• Galactic nuclear regions (ngas ≳ 107 cm-3 at ≲ 1pc)
• Dense interstellar cloud cores (ngas =105-7 cm-3 )Event rate (LIGO O1)• 0.6-6 yr-1 in galactic nuclear regions• 2-20 yr-1 in dense interstellar cloud cores
円盤銀河の方が母銀河として好まれる

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結論1. 多重孤立BHによる合体によって、GW150914を説明できそう
2. 必要な条件は、
𝑚~0.01 𝑚HL , 𝑟typical ≲ 1 pc,𝑚0 ≳ 25 𝑀sun , type B or C𝑛gas > 105 cm−3 , 𝑡merge < 108 yr.

3. LIGO O1によるevent ratesは、• 0.6-6 yr-1 in galactic nuclear regions• 2-20 yr-1 in dense interstellar cloud cores
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Event rate in GMCs
• BH number in Milky Way sized galaxies～108 (Remillard et al. 2009)• Volume that BH would exist 10 kpc ×10 kpc ×1 kpc =100 kpc3
• Volume of GMC 10 pc ×10 pc × 10 pc ×1000 (number) =10-3 kpc3

• Averaged volume per one BH 100 kpc3/108=10-6 kpc3
• Averaged BH number in 1000 GMC 10-3 kpc3/10-6 kpc3=1000• In this case, about 100 GMC hold multiple BH system• Merger time is ～100 Myr (Tagawa et al. 2015)• Merger rate in one galaxy is 100 event/100 Myr=1 event Myr-1• Horizon distance by aLIGO Dh～(Mbinary=75 Msun)8 Gpc (z～1.1)• Comoving volume Vc=230 Gpc3

• Number density of MW sized galaxies～2e6/Gpc3• Number of galaxies, which is observed 230×2e6=5e8• If rate of massive BH to all BH is 10%,rate of massive BH-massive BH to all BH-BH is 1%• Event rate is 1 Myr-1 ×1% × 5e8=5 yr-1

Event rate for pop III BHs in GMCs
• If each mini halo of 105-106 Msun hold 100 pop III BHs,
MW sized galaxy hold pop III 107 BHs. (Ishiyama et al. 2016)• Most of pop III BHs possibly formed as multiple BH systems (Susa et al. 2014)• If all BHs are multiple system of 4 BHs,
25 GMCs hold multiple BH systems.

• Merger time is ～100 Myr• Merger rate in one galaxy is 25 event/100 Myr=0.25 event Myr-1• Horizon distance by aLIGO Dh～(Mbinary=75 Msun)8 Gpc (z～1.1)• Comoving volume Vc=230 Gpc3
• Number density of MW sized galaxies～2e6/Gpc3• Number of galaxies, which is observed 230×2e6=5e8• If rate of massive BH to all pop III BH is 50%,rate of massive BH-massive BH to all pop III BH-pop III BH is 25%• Event rate is 0.25Myr-1 ×25% × 5e8=23 yr-1

Event rate in GNRs
• About 3×106 stars exist in the 1 pc from SMBH (Alexander 2005), and about 1
BH exist per 1000 stars.
• Therefore, ～3×103 BHs may exist in GNRs.
• Merger time and AGN duty cycle are ～100 Myr• Merger rate in one galaxy is 3×103 event/100 Myr=30 event Myr-1• Horizon distance by aLIGO Dh～(Mbinary=75 Msun)8 Gpc (z～1.1)• Comoving volume Vc=230 Gpc3

• Number density of MW sized galaxies～2e6/Gpc3• Number of galaxies, which is observed 230×2e6=5e8• If rate of massive BH to all BH is 10%,rate of massive BH-massive BH to all BH-BH is 1%• Rate of merger phase (AGN phase) 100 Myr/10Gyr=1%• Event rate is 30 Myr-1 ×1% × 5e8 ×1%=2 yr-1