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 (~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)

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)

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

Myr 100

rhBH

seg tM

mt

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)

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

Previous Studies• Gültekin, Miller, &

Hamilton astro-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

Escape Velocity km s-1

Our Method and Assumptions

• Use realistic distribution of BH masses and binary separation (Belczynski, Sadowski, & Rasio 2004)

BH Mass Function

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 Fewbody Fregeau 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)

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

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

5/121

5/321

)(

)(

mm

mmM chirp

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

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

Results – GR RecoilCore Escape Velocity: 57.6 km s-1

Halo Escape Velocity: 29.6 km s-1

Maximum Recoil Velocity

km s-1 Avg M

0 104

60 75

65 54

70 35

80 33

Max. GR Recoil Vel vs. Avg Mass

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

Chirp masses with recoil

20 Runs

Probability distribution of mergers vs. time

Eccentricity Dependence on Chirp mass