Stellar-mass black holes in star clusters: implications for gravitational wave radiation

Sambaran Banerjee, Holger Baumgardt, Pavel Kroupa
Argelander-Institut fur Astronomie, Auf dem Hugel 71, 53121, Bonn, Germany
Monthly Notices of the Royal Astronomical Society, Volume 402, Issue 1, pp. 371-380 (2009), arXiv:0910.3954 [astro-ph.SR] (20 Oct 2009)


   title={Stellar-mass black holes in star clusters: implications for gravitational-wave radiation},

   author={Banerjee, S. and Baumgardt, H. and Kroupa, P.},

   journal={Proceedings of the International Astronomical Union},






   publisher={Cambridge Univ Press}


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We study the dynamics of stellar-mass black holes (BH) in star clusters with particular attention to the formation of BH-BH binaries, which are interesting as sources of gravitational waves (GW). We examine the properties of these BH-BH binaries through direct N-body simulations of star clusters using the GPU-enabled NBODY6 code. We perform simulations of N <= 10^5 Plummer clusters of low-mass stars with an initial population of BHs. Additionally, we do several calculations of star clusters confined within a reflective boundary mimicking only the core of a massive cluster. We find that stellar-mass BHs with masses ~ 10 solar mass segregate rapidly into the cluster core and form a sub-cluster of BHs within typically 0.2 - 0.5 pc radius, which is dense enough to form BH-BH binaries through 3-body encounters. While most BH binaries are ejected from the cluster by recoils received during super-elastic encounters with the single BHs, few of them harden sufficiently so that they can merge via GW emission within the cluster. We find that for clusters with $N ga 5times 10^4$, typically 1 - 2 BH-BH mergers occur within them during the first ~ 4 Gyr of evolution. Also for each of these clusters, there are a few escaping BH binaries that can merge within a Hubble time, most of the merger times being within a few Gyr. These results indicate that intermediate-age massive clusters constitute the most important class of candidates for producing dynamical BH-BH mergers. Old globular clusters cannot contribute significantly to the present-day BH-BH merger rate since most of the mergers from them would have occurred earlier. In contrast, young massive clusters are too young to produce significant number of BH-BH mergers. Our results imply significant BH-BH merger detection rates for the proposed "Advanced LIGO" GW detector. (Abridged)
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