Mergers of accreting stellar-mass black holes
  We present post-Newtonian $N$-body simulations on mergers of accreting
stellar-mass black holes (BHs), where such general relativistic effects as the
pericenter shift and gravitational wave (GW) emission are taken into
consideration. The attention is concentrated on the effects of the dynamical
friction and the Hoyle-Lyttleton mass accretion by ambient gas. We consider a
system composed of ten BHs with initial mass of $30~M_\odot$. As a result, we
show that mergers of accreting stellar-mass BHs are classified into four types:
a gas drag-driven, an interplay-driven, a three body-driven, or an
accretion-driven merger. We find that BH mergers proceed before significant
mass accretion, even if the accretion rate is $\sim10$ Eddington accretion
rate, and then all BHs can merge into one heavy BH. Using the simulation
results for a wide range of parameters, we derive a critical accretion rate
($\dot{m}_{\rm c}$), below which the BH growth is promoted faster by mergers.
Also, it is found that the effect of the recoil by the GW emission can reduce
$\dot{m}_{\rm c}$ especially in gas number density higher than $10^8~{\rm
cm}^{-3}$, and enhance the escape probability of merged BHs. Very recently, a
gravitational wave event, GW150914, as a result of the merger of a $\sim
30~M_\odot$ BH binary has been detected (Abbott et al. 2016). Based on the
present simulations, the BH merger in GW150914 is likely to be driven by
three-body encounters accompanied by a few $M_\odot$ of gas accretion, in
high-density environments like dense interstellar clouds or galactic nuclei.
