Shock propagation in accretion discs around merging black holes: self-similar solution

To date, the Laser Interferometer Gravitational-Wave Observatory (LIGO) and the Virgo gravitational wave detectors have registered several events due to merging binary black holes. It is considered that black holes are surrounded by the circumbinary accretion disc therefore such events must be followed by perturbation of the disc and an increase in the flux of electromagnetic radiation from these objects. Our recent numerical investigations have shown that the heating ofmatter caused by a shock wave leads to an increase in luminosity. This shock wave arises in the accretion disc due to the central object mass loss as a result of the radiation of gravitational waves. In this paper, a self-similar solution is considered. In this solution the accretion disc perturbation is described in a region, dominated by gas pressure, and the matter opacity is determined by Thomson electron scattering processes. Such an analytical model allows us to approximately estimate the magnitude of the electromagnetic response of the gravitational wave event without time-consuming numerical calculations.