Eccentric binary black-hole mergers: The transition from inspiral to plunge in general relativity

Abstract

We study the transition from inspiral to plunge in general relativity by computing gravitational waveforms of non-spinning, equal-mass black-hole binaries. We consider three sequences of simulations, starting with a quasi-circular inspiral completing 1.5, 2.3 and 9.6 orbits, respectively, prior to coalescence of the holes. For each sequence, the binding energy of the system is kept constant and the orbital angular momentum is progressively reduced, producing orbits of increasing eccentricity and eventually a head-on collision. We analyze in detail the radiation of energy and angular momentum in gravitational waves, the contribution of different multipolar components and the final spin of the remnant, comparing numerical predictions with the post-Newtonian approximation and with extrapolations of point-particle results. We find that the motion transitions from inspiral to plunge when the orbital angular momentum L = Lcrit ≃ 0.8M 2 . For L < Lcrit the radiated energy drops very rapidly. Orbits with L ≃ Lcrit produce our largest dimensionless Kerr parameter for the remnant, j = J/M 2 ≃ 0.724 ± 0.13 (to be compared with the Kerr parameter j ≃ 0.69 resulting from quasi-circular inspirals). This value is in good agreement with the value of 0.72 reported in [1]. These conclusions are quite insensitive to the initial separation of the holes, and they can be understood by extrapolating point particle results. Generalizing a model recently proposed by Buonanno, Kidder and Lehner [2] to eccentric binaries, we conjecture that (1) j ≃ 0.724 is close to the maximal Kerr parameter that can be obtained by any merger of non-spinning holes, and (2) no binary merger (even if the binary members are extremal Kerr black holes with spins aligned to the orbital angular momentum, and the inspiral is highly eccentric) can violate the cosmic censorship conjecture.

Black-hole binary simulations: The mass ratio10∶1

“…We follow the convention of [83] and normalize initial parameters relative to the total black hole mass M = M 1 + M 2 and dimensional diagnostic quantities by their total initial values; the Arnowitt-Deser-Misner (ADM) mass M ADM and the total initial angular momentum J ini . The initial tangential linear momentum P has been calculated from Eq.…”

Spin expansion for binary black hole mergers: New predictions and future directions

“…With the exception of a few papers (e.g. [44,45,46,47,48]), simulations of BBH mergers thus far have focused on circular orbits. Nevertheless, in Appendix E, we will explain the extension of our formalism to non-circular (eccentric) orbits.…”

Measuring orbital eccentricity and periastron advance in quasicircular black hole simulations

“…In Ref. [35], the authors studied the transition from inspiral to plunge in general relativity by computing gravitational waveforms of eccentric nonspinning, equal-mass blackhole binaries. They analyzed the radiation of energy and angular momentum in gravitational waves, the contribution of different multipolar components and the final spin of the remnant black hole.…”