Understanding possible electromagnetic counterparts to loud gravitational wave events: Binary black hole effects on electromagnetic fields

In addition to producing loud gravitational waves, the dynamics of a binary black hole system could induce emission of electromagnetic radiation by affecting the behavior of plasmas and electromagnetic fields in their vicinity. We study how the electromagnetic fields are affected by a pair of orbiting black holes through the merger. In particular, we show how the binary’s dynamics induce a variability in possible electromagnetically induced emissions as well as an enhancement of electromagnetic fields during the late-merge and merger epochs. These time dependent features will likely leave their imprint in processes generating detectable emissions and can be exploited in the detection of electromagnetic counterparts of gravitational waves.

Figure 1

Magnetic and electric field lines for $y=0$, $z\ge 0$ at $t=200M$ for a single black hole, together with the apparent horizon (inner circle, green) and the ergosphere (outer ellipse, magenta). The regions $x<0$ display the numerical solution, while Wald’s exact solution is shown in $x>0$.

Figure 2

$L_2$ and the $L_{\infty }$ norms of the physical constraint $\Vert Z\Vert$, which is kept under control through the evolution with a small increase at the merger. After it, the norms grow and oscillate for some period as the finest grid is destroyed and created a few times as required by the tolerance adopted at times $>38M$, the finest is destroyed for the last time and not needed anymore.

Figure 3

Magnetic (mostly vertical) and electric field lines at different phases during the evolution employing different scales for visualization purposes. The figures illustrate different stages: early when the black holes are separated, near merger, shortly after they merge, and at late times. The electric field lines are twisted around the black hole, while the magnetic lines slightly deform from their initial configuration aligned with the $z$ axis.

Figure 4

The top figure corresponds to the $l=m=2$ modes for $r{\Psi }_4$ and $r{\Phi }_2$ extracted at $r=40M$, rescaled properly with a factor $\approx 3\times {10}^6$ to fit in the same scale. The bottom figure illustrates the phase of these modes.

Figure 5

Total flux of gravitational and electromagnetic energy corresponding to the binary black hole case (integrated over the sphere surface $\Sigma$). The (integrate) electromagnetic energy flux has been rescaled by a factor $\approx {10}^{13}$ to make it appear clearly in the plot.

Figure 6

Electromagnetic energy density (normalized to the values at the initial time, far distances) at the $z=0$ plane for the binary black hole case at different times of the evolution. Energy contour plots are shown from 1.2 to 0.8 at intervals of 0.1.

Figure 7

Electric field lines at the plane $x=0$ for the binary black hole case at different times of the evolution. Notice that early on the field configuration is in agreement with the expected one from the membrane paradigm with two induced dipoles. As the black holes merge the configuration changes to a scenario consistent with that required in the Blandford-Znajek mechanism.

Figure 8

ISCO and ergosphere radii vs $a/M$. For $a>0.943M$ the ergosphere lies beyond the ISCO.