Electromagnetic luminosity of the coalescence of charged black hole binaries

The observation of a possible electromagnetic counterpart by the Fermi GBM group to the aLIGO detection of the merger of a black hole binary has spawned a number of ideas about its source. Furthermore, observations of fast radio bursts (FRBs) have similarly resulted in a range of new models that might endow black hole binaries with electromagnetic signatures. In this context, even the unlikely idea that astrophysical black holes may have significant charge is worth exploring, and here we present results from the simulation of weakly charged black holes as they orbit and merge. Our simulations suggest that a black hole binary with mass comparable to that observed in GW150914 could produce the level of electromagnetic luminosity observed by Fermi GBM ($10^{49}\mathrm{ergs}/\mathrm{s}$) with a nondimensional charge of $q\equiv Q/M={10}^{-4}$ assuming good radiative efficiency. However even a charge such as this is difficult to imagine avoiding neutralization long enough for the binary to produce its electromagnetic counterpart, and so this value would likely serve simply as an upper bound. On the other hand, one can equivalently consider the black holes as having acquired a magnetic monopole charge that would be easy to maintain and would generate an identical electromagnetic signature as the electric charges. The observation of such a binary would have significant cosmological implications, not the least of which would be an explanation for the quantization of charge itself. We also study such a magnetically charged binary in the force-free regime and find it much more radiative, reducing even further the requirements to produce the counterpart.

Figure 1

The dynamics of the binary system and its gravitational radiation. Top: The separation, $d$, as a function of time, obtained by the coordinate distance between the two minima of the conformal factor $\chi$. Middle: The real part of the $l=m=2$ mode of the Newman-Penrose scalar ${\mathrm{\Psi }}_4$. Bottom: The angular frequency of the binary obtained from the main gravitational-wave mode.

Figure 2

Electromagnetic and gravitational luminosities for the different electrovacuum configurations. Top: The gravitational luminosity (solid black) is the same among all cases. The electromagnetic luminosities vary for the different charge configurations. Bottom: The $\{+,+\}$ EM luminosity has been rescaled to show that the electromagnetic luminosity is proportional to the gravitational luminosity. Likewise, the $\{+,0\}$ EM luminosity has been rescaled showing that it is roughly a quarter of the luminosity of the $\{+,-\}$ case.

Figure 3

The electric field in the equatorial plane, $z=0$, for the electrovacuum case. Only a centered region of the computational domain is shown, spanning a width of four times the initial separation. Top: Before and Bottom: after the merger of the BBH system with $\{+,+\}$ charge configuration. After the merger, the electric field quickly settles to that of a spinning charge. The black holes are located where the field lines converge.

Figure 4

The main spin-weighted spherical-harmonic modes of the Newman-Penrose scalar ${\mathrm{\Phi }}_2$ describing the electromagnetic radiation for the different electrovacuum configurations. Top: The norms of the main modes. Bottom: The real part of the main modes.

Figure 5

Electromagnetic luminosities as a function of the angular frequency of the binary for the electrovacuum cases. Fits of these luminosities to a power law in the frequency are also shown (solid curves). Notice that the dependence of the luminosities on the orbital frequency follows that expected from a pair of orbiting charges, at least up to the plunge.

Figure 6

Electromagnetic and gravitational luminosities from the different cases in a force-free environment. Top: The gravitational luminosity (solid black) is shown for comparison with the previous electrovacuum cases. The electromagnetic luminosities vary for the different charge configurations. Bottom: The norms of the main spin-weighted spherical-harmonic modes of the Newman-Penrose scalar ${\mathrm{\Phi }}_2$, showing that the radiation is mainly dipolar.

Figure 7

The normalized luminosities emitted in a jet opening angle of 15° (which estimates the collimation of the radiation) for the force-free cases. The $\{+,-\}$ case is quite collimated during the inspiral and merger. In contrast, the collimation of the other two cases increases towards the merger as would be expected from a spinning black hole with magnetic monopole charge through the Blandford-Znajek mechanism.

Figure 8

Electromagnetic luminosities of the force-free cases as a function of the angular frequency of the binary. Fits of these luminosities to a power law in the frequency are also shown (solid curves).