Accurate Simulations of Binary Black-Hole Mergers in Force-Free Electrodynamics

We provide additional information on our recent study of the electromagnetic emission produced during the inspiral and merger of supermassive black holes when these are immersed in a force-free plasma threaded by a uniform magnetic field. As anticipated in a recent letter, our results show that although a dual-jet structure is present, the associated luminosity is ~ 100 times smaller than the total one, which is predominantly quadrupolar. We here discuss the details of our implementation of the equations in which the force-free condition is not implemented at a discrete level, but rather obtained via a damping scheme which drives the solution to satisfy the correct condition. We show that this is important for a correct and accurate description of the current sheets that can develop in the course of the simulation. We also study in greater detail the three-dimensional charge distribution produced as a consequence of the inspiral and show that during the inspiral it possesses a complex but ordered structure which traces the motion of the two black holes. Finally, we provide quantitative estimates of the scaling of the electromagnetic emission with frequency, with the diffused part having a dependence that is the same as the gravitational-wave one and that scales as L ~ Omega^{10/3-8/3}, while the collimated one scales as L ~ Omega^{5/3-6/3}, thus with a steeper dependence than previously estimated. We discuss the impact of these results on the potential detectability of dual jets from supermassive black holes and the steps necessary for more accurate estimates.