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Abstract

We investigate the dynamics of a circumbinary disc that responds to the loss of mass and to the recoil velocity of the black hole produced by the merger of a binary system of supermassive black holes. More specifically, we perform the first two-dimensional general relativistic hydrodynamics simulations of \textit{extended} non-Keplerian discs and employ a new technique to construct a "shock detector", thus determining the precise location of the shocks produced in the accreting disc by the recoiling black hole. In this way we can study how the properties of the system, such as the spin, mass and recoil velocity of the black hole, affect the mass accretion rate and are imprinted on the electromagnetic emission from these sources. In contrast with what done in similar works, we here question the estimates of the bremsstrahlung luminosity when computed without properly taking into account the radiation transfer, thus yielding cooling times that are unrealistically short. At the same time we show, through an approximation based on the relativistic analogue of the isothermal evolution of \citet{Corrales2009}, that the luminosity produced can reach a peak value above $L \simeq 10^{43} {\rm erg/s} $ at about $\sim 20 {\rm d}$ after the merger of a binary with total mass $M\simeq 10^6 M_\odot$ and persist for several days at values which are a factor of a few smaller. If confirmed by more sophisticated calculations such a signal could indeed lead to an electromagnetic counterpart of the merger of binary black-hole system.