Hydrodynamical response of a circumbinary gas disc to black hole recoil and mass loss

Finding electromagnetic (EM) counterparts of future gravitational wave (GW) sources would bring rich scientific benefits. A promising possibility, in the case of the coalescence of a supermassive black hole binary (SMBHB), is that the prompt emission from merger-induced disturbances in a supersonic circumbinary disc may be detectable. We follow the post-merger evolution of a thin, zero-viscosity circumbinary gas disc with two-dimensional simulations, using the hydrodynamic code flash. We analyse perturbations arising from the 530 km s^-1 recoil of a 10⁶ M_⊙ binary, oriented in the plane of the disc, assuming either a non-radiative gamma-law or a pseudo-isothermal equation of state for the gas. We find that a single-armed spiral shock wave forms and propagates outwards, sweeping up ∼40 per cent of the mass of the disc. The morphology and evolution of the perturbations agrees well with those of caustics predicted to occur in a collisionless disc. Assuming that the disc radiates nearly instantaneously to maintain a constant temperature, we estimate the amount of dissipation and corresponding post-merger light curve. The luminosity rises steadily on the time-scale of months, and reaches few ×10⁴³ erg s^-1, corresponding to ≈10 per cent of the Eddington luminosity of the central SMBHB. We also analyse the case in which gravitational wave emission results in a 5 per cent mass loss in the merger remnant. The mass loss reduces the shock overdensities and the overall luminosity of the disc by ≈15-20 per cent, without any other major effects on the spiral shock pattern.