Binary black hole mergers in gaseous disks: Simulations in general relativity

Abstract

Simultaneous gravitational and electromagnetic wave observations of merging black hole binaries (BHBHs) can provide unique opportunities to study gravitation physics, accretion, and cosmology. Here we perform fully general-relativistic, hydrodynamic simulations of equal-mass, nonspinning BHBHs coalescing in a circumbinary disk. We evolve the metric using the Baumgarte-Shapiro-Shibata-Nakamura (BSSN) formulation of Einstein's field equations with standard moving puncture gauge conditions. We handle the hydrodynamics via a high-resolution shock-capturing scheme. These initial simulations are exploratory in nature and simplified accordingly. We track the inspiral starting from a binary separation of $10M$, where $M$ is the total binary mass. We take the disks to have an inner radius at ${R}_{\mathrm{in}}\ensuremath{\approx}15M$ to account for the hollow created by the binary torques. Our disks extend to $R\ensuremath{\approx}65M$ and have an initial scale height of $H/R\ensuremath{\approx}0.03--0.11$. The gas is governed by a $\ensuremath{\Gamma}$-law equation of state, with $\ensuremath{\Gamma}$ equal to $5/3$, $4/3$, and 1.1. Disks are allowed to relax in the ``early inspiral'' epoch to provide quasistationary realistic initial data. We then evolve the spacetime metric and matter during the ``late inspiral and merger'' epochs. The later simulations are designed to track BHBH inspiral following disk-binary decoupling, through merger and ringdown, terminating before viscosity has time to fill the hollow about the black hole remnant. We compute the gas flow and accretion rate and estimate the electromagnetic luminosity due to bremsstrahlung and synchrotron emission as a perturbation for optically thin disks. The synchrotron component of the luminosity peaks in the infrared band and should be detectable by WFIRST and possibly the LSST for a ${10}^{8}{M}_{\ensuremath{\bigodot}}$ binary embedded in a disk with a density $n\ensuremath{\sim}{10}^{12}\text{ }\text{ }{\mathrm{cm}}^{\ensuremath{-}3}$ at $z=1$, beginning with a maximum value of $L\ensuremath{\sim}{10}^{46}{n}_{12}^{2}{M}_{8}^{3}\text{ }\text{ }\mathrm{erg}\text{ }{\mathrm{s}}^{\ensuremath{-}1}$ at decoupling, and decreasing steadily over a time scale of $\ensuremath{\sim}100{M}_{8}$ hours to a value of $L\ensuremath{\sim}{10}^{45}{n}_{12}^{2}{M}_{8}^{3}\text{ }\text{ }\mathrm{erg}\text{ }{\mathrm{s}}^{\ensuremath{-}1}$ at merger.