Vacuum electromagnetic counterparts of binary black-hole mergers

As one step towards a systematic modeling of the electromagnetic (EM) emission from an inspiralling black hole binary we consider a simple scenario in which the binary moves in a uniform magnetic field anchored to a distant circumbinary disc. We study this system by solving the Einstein-Maxwell equations in which the EM fields are chosen with strengths consistent with the values expected astrophysically and treated as test fields. Our initial data consists of a series of binaries with spins aligned or antialigned with the orbital angular momentum and we study the dependence of gravitational and EM signals with different spin configurations. Overall we find that the EM radiation in the lowest l = 2, m = 2 multipole accurately reflects the gravitational one, with identical phase evolutions and amplitudes that differ only by a scaling factor. This is no longer true when considering higher l modes, for which the amplitude evolution of the scaled EM emission is slightly larger, while the phase evolutions continue to agree. We also compute the efficiency of the energy emission in EM waves and find that it scales quadratically with the total spin and is given by E-EM(rad)/M similar or equal to 10(-15) (M/10(8)M(circle dot))(2)(B/10(4)G)(2), hence 13 orders of magnitude smaller than the gravitational energy for realistic magnetic fields. Although large in absolute terms, the corresponding luminosity is much smaller than the accretion luminosity if the system is accreting at near the Eddington rate. Most importantly, this EM emission is at frequencies of similar to 10(-4) (10(8)M(circle dot)/M) Hz, which are well outside those accessible to astronomical radio observations. As a result, it is unlikely that the EM emission discussed here can be detected directly and simultaneously with the gravitational-wave one. However, indirect processes, driven by changes in the EM fields behavior could yield observable events. In particular we argue that if the accretion rate of the circumbinary disc is small and sufficiently stable over the timescale of the final inspiral, then the EM emission may be observable indirectly as it will alter the accretion rate through the magnetic torques exerted by the distorted magnetic field lines.