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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 - PowerPoint PPT Presentation
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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