Merger of multiple accreting black holes concordant with gravitational
  wave events
  Recently, advanced Laser Interferometer Gravitational-Wave Observatory
(aLIGO) has detected black hole (BH) merger events, most of which are sourced
by BHs more massive than $30~M_\odot$. Especially, the observation of GW170104
suggests dynamically assembled binaries favoring a distribution of misaligned
spins. It has been argued that mergers of unassociated BHs can be engendered
through a "chance meeting" in a multiple BH system under gas-rich environments.
In this paper, we consider the merger of unassociated BHs, concordant with the
massive BH merger events. To that end, we simulate a multiple BH system with a
post-Newtonian $N$-body code incorporating gas accretion and general
relativistic effects. As a result, we find that gas dynamical friction
effectively promotes three-body interaction of BHs in dense gas of
$n_\mathrm{gas}\gtrsim 10^6\,\mathrm{cm}^{-3}$, so that BH mergers can take
place within $30$ Myr. This scenario predicts an isotropic distribution of spin
tilts. In the concordant models with GW150914, the masses of seed BHs are
required to be $\gtrsim 25~M_\odot$. The potential sites of such "chance
meeting" BH mergers are active galactic nucleus (AGN) disks and dense
interstellar clouds. Assuming the LIGO O1, we roughly estimate the event rates
for PopI BHs and PopIII BHs in AGN disks to be respectively $\simeq
1-2\,\mathrm{yr}^{-1}$ and $\simeq 1\,\mathrm{yr}^{-1}$. Multiple episodes of
AGNs may enhance the rates by roughly an order of magnitude. For massive PopI
BHs in dense interstellar clouds, the rate is $\simeq 0.02\,\mathrm{yr}^{-1}$.
Hence, high-density AGN disks are a more plausible site for mergers of chance
meeting BHs.
