Black hole growth through hierarchical black hole mergers in dense star clusters: implications for gravitational wave detections. (arXiv:1811.03640v1 [astro-ph.HE])
<a href="http://arxiv.org/find/astro-ph/1/au:+Antonini_F/0/1/0/all/0/1">Fabio Antonini</a>, <a href="http://arxiv.org/find/astro-ph/1/au:+Gieles_M/0/1/0/all/0/1">Mark Gieles</a>, <a href="http://arxiv.org/find/astro-ph/1/au:+Gualandris_A/0/1/0/all/0/1">Alessia Gualandris</a>
In a star cluster with a sufficiently large escape velocity, black holes
(BHs) that are produced by BH mergers can be retained, dynamically form new
{BH} binaries, and merge again. This process can repeat several times and lead
to significant mass growth. In this paper, we calculate the mass of the largest
BH that can be formed through repeated mergers of stellar seed BHs and
determine how its value depends on the physical properties of the host cluster.
We adopt an analytical model in which the energy generated by the black hole
binaries in the cluster core is assumed to be regulated by the process of
two-body relaxation in the bulk of the system. This principle is used to
compute the hardening rate of the binaries and to relate this to the
time-dependent global properties of the parent cluster. We demonstrate that in
clusters with initial escape velocity $gtrsim 300rm km s^{-1}$ in the core
and density $gtrsim 10^5 M_odotrm pc^{-3}$, repeated mergers lead to the
formation of BHs in the mass range $100-10^5 ,M_odot$, populating any upper
mass gap created by pair-instability supernovae. This result is independent of
cluster metallicity and the initial BH spin distribution. We show that about
$10%$ of the present-day nuclear star clusters meet these extreme conditions,
and estimate that BH binary mergers with total mass $gtrsim 100,M _odot$
should be produced in these systems at a maximum rate $approx 0.05 ,rm
Gpc^{-3} yr^{-1}$, corresponding to one detectable event every few years with
Advanced LIGO/VIRGO at design sensitivity. The contribution of globular
clusters is likely to be negligible instead because the first BH merger remnant
escapes following the relativistic kick. A possible connection of our results
to the formation of massive BH seeds in galaxy nuclei and globular clusters is
discussed.
In a star cluster with a sufficiently large escape velocity, black holes
(BHs) that are produced by BH mergers can be retained, dynamically form new
{BH} binaries, and merge again. This process can repeat several times and lead
to significant mass growth. In this paper, we calculate the mass of the largest
BH that can be formed through repeated mergers of stellar seed BHs and
determine how its value depends on the physical properties of the host cluster.
We adopt an analytical model in which the energy generated by the black hole
binaries in the cluster core is assumed to be regulated by the process of
two-body relaxation in the bulk of the system. This principle is used to
compute the hardening rate of the binaries and to relate this to the
time-dependent global properties of the parent cluster. We demonstrate that in
clusters with initial escape velocity $gtrsim 300rm km s^{-1}$ in the core
and density $gtrsim 10^5 M_odotrm pc^{-3}$, repeated mergers lead to the
formation of BHs in the mass range $100-10^5 ,M_odot$, populating any upper
mass gap created by pair-instability supernovae. This result is independent of
cluster metallicity and the initial BH spin distribution. We show that about
$10%$ of the present-day nuclear star clusters meet these extreme conditions,
and estimate that BH binary mergers with total mass $gtrsim 100,M _odot$
should be produced in these systems at a maximum rate $approx 0.05 ,rm
Gpc^{-3} yr^{-1}$, corresponding to one detectable event every few years with
Advanced LIGO/VIRGO at design sensitivity. The contribution of globular
clusters is likely to be negligible instead because the first BH merger remnant
escapes following the relativistic kick. A possible connection of our results
to the formation of massive BH seeds in galaxy nuclei and globular clusters is
discussed.
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