Electromagnetic Emission post Spinning Black Hole-Magnetized Neutron Star Mergers

For a binary composed of a spinning black hole (BH) (with mass $gtrsim 7M_odot$) and a strongly magnetized neutron star (NS) (with surface magnetic field strength $B_{rm S,NS}gtrsim10^{12}$,G and mass $sim 1.4M_odot$), the NS as a whole will possibly eventually plunge into the BH. During the inspiral phase, the spinning BH could be charged to the Wald charge quantity $Q_{rm W}$ until merger in an electro-vacuum approximation. During the merger, if the spinning charged BH creates its own magnetosphere due to an electric field strong enough for pair cascades to spark, the charged BH would transit from electro-vacuum to force-free cases and could discharge in a time $gtrsim1~{rm ms}$. As the force-free magnetosphere is full of a highly conducting plasma, the magnetic flux over the NSs caps would be retained outside the BHs event horizon under the frozen-in condition. Based on this scenario, we here investigate three possible energy-dissipation mechanisms that could produce electromagnetic (EM) counterparts in a time interval of the BHs discharge post a BH-NS merger-induced gravitational wave event: (1) magnetic reconnection at the BHs poles would occur, leading to a millisecond bright EM signal, (2) a magnetic shock in the zone of closed magnetic field lines due to the detachment and reconnection of the entire BH magnetic field would probably produce a bright radio emission, e.g., a fast radio burst, and (3) the Blandford-Znajek mechanism would extract the BHs rotational energy, giving rise to a millisecond-duration luminous high-energy burst. We also calculate the luminosities due to these mechanisms as a function of BHs spin for different values of $B_{rm S,NS}$.