Electromagnetic counterparts and horizon geometry of binary black-hole mergers

Philipp Moesta

May 18, 2011

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Abstract: As one step towards a systematic modeling of the electromagnetic (EM) emission from an inspiralling black hole binary we consider a simple scenario in which the binary moves in a uniform magnetic field anchored to a distant circumbinary disc. We study this system by solving the Einstein-Maxwell equations in which the EM fields are chosen with strengths consistent with the values expected astrophysically and treated as test-fields. Our initial data consists of a series of binaries with spins aligned or anti-aligned with the orbital angular momentum and we study the dependence of gravitational and EM signals with different spin configurations. Overall we find that the EM radiation in the lowest l = 2, m = 2 multipole accurately reflects the gravitational one, with identical phase evolutions and amplitudes that differ only by a scaling factor. This is no longer true when considering higher l modes, for which the amplitude evolution of the scaled EM emission is slightly larger, while the phase evolutions continue to agree. We also compute the efficiency of the energy emission in EM waves and find that it scales quadratically with the total spin and is given by E^rad_EM / M ~ 10^-15 (M / 10^8 M_Sun)^2 (B / 10^4 G)^2, EM hence 13 orders of magnitude smaller than the gravitational energy for realistic magnetic fields. Additionally we present results obtained on the geometry of apparent horizons in head-on unequal-mass binary black-hole collisions. We use an harmonic evolution code to analyze some of the highly interesting features revealed by numerical simulations and connect this data with theorems from mathematical theory