THE RATE OF GW CAPTURE OF STELLAR-MASS BHS IN NUCLEAR STAR CLUSTERS. Alexander Rasskazov & Bence Kocsis Eotvos University

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1 THE RATE OF GW CAPTURE OF STELLAR-MASS BHS IN NUCLEAR STAR CLUSTERS Alexander Rasskazov & Bence Kocsis Eotvos University

2 Merger rate density of events with e>0.1 in the LIGO band (>10 Hz), Gpc -3 yr -1 GW capture (single-single interactions) Hierarchical triples (Kozai-Lidov effect) Binary-single intercactions Nuclear star clusters Globular clusters Galactic field

3 HIERARCHICAL TRIPLES In GC: can form in binary-binary interactions 20% have e>0.1 Antonini et al % have e>0.9999

4 HIERARCHICAL TRIPLES In NSC: SMBH + binary BH Total rate: 1-3 Gpc -3 yr -1 (Hoang et al. 2018) Eccentric merger fraction:? In galactic field Antonini et al. 2017: total rate Gpc -3 yr -1, 3% have e> SIlsbee & Tremaine 2017: total rate Gpc -3 yr -1, few % have e>0.999

5 Merger rate density of events with e>0.1 in the LIGO band (>10 Hz), Gpc -3 yr -1 GW capture (single-single interactions) Hierarchical triples (Kozai-Lidov effect) Binary-single intercactions Nuclear star clusters? (Hoang+2018) Globular clusters 0.04 (Antonini+2016) Galactic field ? (Silsbee&Tremaine 2017) (Antonini+2017)

6 BINARY-SINGLE INTERACTIONS In GC 1-5% of all GC mergers have e>0.1 (Samsing 2018, Rodriguez+2018) Total rate 5-10 Gpc -3 yr -1 (Rodriguez+2016) In NSC Samsing 2018 Resonant interaction are rare due to high velocity dispersion

7 Merger rate density of events with e>0.1 in the LIGO band (>10 Hz), Gpc -3 yr -1 GW capture (single-single interactions) Hierarchical triples (Kozai-Lidov effect) Binary-single intercactions Nuclear star clusters? (Hoang+2018) 0? (Antonini & Rasio 2016) Globular clusters Galactic field 0.04 (Antonini+2016) ? (Silsbee&Tremaine 2017) (Antonini+2017) (Samsing+2018, Rodriguez+2018)?

8 Merger rate density of events with e>0.1 in the LIGO band (>10 Hz), Gpc -3 yr -1 GW capture (single-single interactions) Hierarchical triples (Kozai-Lidov effect) Binary-single intercactions Nuclear star clusters? (Hoang+2018) 0? (Antonini & Rasio 2016) Globular clusters Galactic field 0.04 (Antonini+2016) ? (Silsbee&Tremaine 2017) (Antonini+2017) (Samsing+2018, Rodriguez+2018)?

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BH NUMBER DENSITY Kroupa mass function for stars We assume all stars with M>Mcrit=20 produce BHs BH mass distribution f BH,init (m) / m, m min =5M <m<m max = 40M BH mass fraction apple init = mmin 2 m 2 max 0.03 m 1 min m 1 max

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DENSITY DISTRIBUTION Inside the sphere of influence the NSC is relaxed n(m, r) / r m mmax r infl = GM SBH 2 = 2.45 pc MSBH M 1/2 (O Leary et al. 2009) Outside the sphere of influence n / r 3.2 (Shodel et al. 2017)

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DYNAMICAL FRICTION t 1 DF =ln 4 G m 3 ln ln(m SBH /m) 13, Z 0 4 u 2 F (u)du, It increases the number of BHs ~3-4 times (the merger rate ~10 times) between different BH formation scenarios ξ No big difference [ ]

13 <latexit 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<latexit 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<latexit 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TOTAL MERGER 2 B = Z MSBH,max M B dn gal dm SBH dm SBH Intrinsic spread in M-σ relation adds a factor ~3 Event rate is almost indepenent of SBH mass dominated by low-mass galaxies - [ ] (Shankar et al. 2004)

14 <latexit 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<latexit sha1_base64="ez1cbp4lrwtj7mepdjrvglnwdgm=">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</latexit> <latexit sha1_base64="ez1cbp4lrwtj7mepdjrvglnwdgm=">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</latexit> TOTAL MERGER RATE Dominated by heavy BHs at log( 2 tot/ lnmtot q)[yr -1 Gpc -3 ] log( 2 tot/ lnmtot q)[yr -1 Gpc -3 ] log( 2 tot/ lnmtot q)[yr -1 Gpc -3 ]

15 <latexit 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<latexit sha1_base64="ey0tk359gldv35m9bjkmkmmprzq=">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</latexit> <latexit sha1_base64="ey0tk359gldv35m9bjkmkmmprzq=">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</latexit> <latexit sha1_base64="ey0tk359gldv35m9bjkmkmmprzq=">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</latexit> TOTAL MERGER RATE tot [yr -1 Gpc -3 ] = 1 = 2.35 = M SBH,min At β =1 and Mmin=10 5, tot 0.1yr 1 Gpc 3