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BH Dynamics in Globular Clusters

BH Dynamics in Globular Clusters. Ryan M. O’Leary, Natalia Ivanova, Frederic A. Rasio Northwestern University. Astrophysical Motivation. LIGO detection of BH-BH binary mergers in star clusters (Portegies Zwart & McMillan 2000) How often? When? Possible IMBH (~10 3 M  ) formation

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BH Dynamics in Globular Clusters

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  1. BH Dynamics in Globular Clusters Ryan M. O’Leary, Natalia Ivanova, Frederic A. Rasio Northwestern University

  2. Astrophysical Motivation • LIGO detection of BH-BH binary mergers in star clusters (Portegies Zwart & McMillan 2000) • How often? When? • Possible IMBH (~103 M) formation • Detection by LISA • Ultraluminous X-ray sources, i.e. MGG11 in M32 (Matsumoto et al. 2001; Strohmayer & Mushotzky 2003) • M15 and G1 in M31 (Gerssen et al. 2002,2003; van der Marel et al. 2002; Gebhardt, Rich, & Ho 2002; Baumgardt et al. 2003)

  3. Initial BH Population • We expect ~ 10-4 - 10-3 N BHs from stellar evolution (Salpeter, Standard Kroupa initial mass functions respectively) • Globular Clusters N ~ 105 – 106 • Expect a broad mass spectrum of BHs (Belczynski, Sadowski, & Rasio 2004)

  4. Dynamics • BHs concentrate in the core through mass segregation (Fregeau et al. 2002) • Decouple dynamically from rest of cluster, because most massive objects (Spitzer Instability) • BHs only interact with other BHs

  5. BH core dynamics • 3-body and 4-body interactions dominate • BH-BH binaries continuously harden • Get ejected from purely Newtonian recoil or merge from gravitational radiation (Peters 1964) • Binaries evolve from gravitational radiation (Peters 1964) • Recoil from gravitational wave emission in asymmetric BH-BH mergers (Fitchett 1983, Favata, Hughes, & Holz 2004) • Insignificant factors • Secular evolution of triples (Kozai Mechanism) • GR Bremsstrahlung (completely ignore, velocities too low)

  6. Previous Studies • Portegies Zwart & McMillan (2000) • Small direct N-body simulations without GR (NBH ~ 20, N =2048 or 4096) • Start all single 10 M BHs • 30% of BHs ejected in tight BH-BH binaries • 60% of BHs ejected as single BHs • <10% retained in cluster

  7. Previous Studies Escape Velocity km s-1 • Gültekin, Miller, & Hamiltonastro-ph/0402532 • Repeatedly interact 10 MBHs. Include GR between interactions. • Find efficiency too low to grow very massive objects. • Most interactions lead to some sort of ejection, not merger

  8. Our Method and Assumptions • Use realistic distribution of BH masses and binary separation(Belczynski, Sadowski, & Rasio 2004)

  9. BH Mass Function

  10. Our Method and Assumptions • Use realistic distribution of BH masses and binary separation (Belczynski, Sadowski, & Rasio 2004) • Place into constant density core and compute all interactions (3-body and 4-body) by direct integration (Using FewbodyFregeau et al. 2004) • Eject into Halo if necessary, reintroduce BHs from dynamical friction • Evolve binaries between interactions Peters (1964) • In some simulations, account for GR recoil (Fitchett 1983, Favata, Hughes, & Holz 2004)

  11. Results nc = 5 x 105 pc-3 σBH = 11.5 km s-1 trh = 3.2 x 108 yr M = 5 x 105 M NBH = 512 W0 = 9

  12. Results – Chirp Masses nc = 5 x 105 pc-3 σBH = 11.5 km s-1 trh = 3.2 x 108 yr M = 5 x 105 M NBH = 512 W0 = 9

  13. Results - eccentricity nc = 5 x 105 pc-3 σBH = 11.5 km s-1 trh = 3.2 x 108 yr M = 5 x 105 M NBH = 512 W0 = 9 Frequency of radiation two times orbital frequency

  14. Results nc = 5 x 105 pc-3 σBH = 11.5 km s-1 trh = 3.2 x 108 yr M = 5 x 105 M NBH = 512 W0 = 9 Mean Final BH Mass: 104 M Largest BH Mass: 295 M Standard Dev: 85 M Of 64 Runs

  15. Results – GR Recoil Maximum Recoil Velocity Core Escape Velocity: 57.6 km s-1 Halo Escape Velocity: 29.6 km s-1 Max. GR Recoil Vel vs. Avg Mass

  16. Conclusions • Clusters important factories for LIGO sources • Almost all mergers have negligible eccentricity • Chirp masses high with realistic mass function • Can detect mergers to larger distances, earlier times • Possible to get growth to IMBH • Mass spectrum of BHs contributes to more efficient BH-BH merger rate

  17. Chirp masses with recoil 20 Runs

  18. Probability distribution of mergers vs. time

  19. Eccentricity Dependence on Chirp mass

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