Merger of multiple accreting black holes concordant with gravitational wave events

Abstract: 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.