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

Abstract

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 non−coll EM ≈ Ω 10/3−8/3 , while the collimated one scales as L coll EM ≈ Ω 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.

Magnetosphere of a Kerr black hole immersed in magnetized plasma and its perturbative mode structure

“…After some lengthy calculations we can show that two factor equations for ∂ t S follow naturally from the determinant equation (up to O(a)). The first one 23) which is just the vacuum Teukolsky equation (before separating out the θ dependence) in the eikonal limit 2 . Therefore, clearly this family of modes are the "trapped" modes in the eikonal limit, as we have seen in the flat spacetime case.…”

Stability of force-free magnetospheres

“…MacDonald and Thorne [4] have formulated the force-free evolution equations in a 3 + 1 language, which serves as the foundation for most of the numerical investigations later on (e.g. [5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20]). Carter [21] and Uchida [22][23][24][25][26] instead constructed a unified spacetime description, recasting the dynamical variables into a pair of scalar Euler potentials.…”

Stability of exact force-free electrodynamic solutions and scattering from spacetime curvature

“…For the E · B = 0 constraint, we adopt a strategy similar in form to Ref. [27]. Specifically, we add a damping term −N δ(E · B)B/B 2 to ∂ t E, so that the full set of evolution equations becomes…”

“…[7,[9][10][11][12]) and numerically (e.g. [13][14][15][16][17][18][19][20][21][22][23][24][25][26][27][28]) study the solutions to the FFE equations.…”