Statistical studies of spinning black-hole binaries

Abstract

We study the statistical distributions of the spins of generic black-hole binaries during the inspiral and merger, as well as the distributions of the remnant mass, spin, and recoil velocity. For the inspiral regime, we start with a random uniform distribution of spin directions S1 and S2 over the sphere and magnitudes | S1/m 2 1 | = | S2/m 2 2 | = 0.97 for different mass ratios, where Si and mi are the spin-angular momentum and mass of the ith black hole. Starting from a fiducial initial separation of ri = 50M , we perform 3.5-post-Newtonian-order evolutions down to a separation of r f = 5M , where M = m1 + m2, the total mass of the system. At this final fiducial separation, we compute the angular distribution of the spins with respect to the final orbital angular momentum, L. We perform 16 4 = 65536 simulations for six mass ratios between q = 1 and q = 1/16 and compute

Dynamical shift condition for unequal mass black hole binaries

“…Most importantly, the simulations remained stable, without significantly changing the gravitational waves. The formula was later used successfully for the 10:1 mass-ratio in [9].…”

“…The form of η was chosen to have proper fall-off rates both at the punctures and at large distance from the binary. In [9], this approach was used successfully for mass ratio 10:1. (We note in passing that damping is useful in other gauges as well, e.g.…”

“…To date, the mass ratio furthest from equal masses that has been numerically simulated is 10:1 [8,9]. These simulations use the Baumgarte-Shapiro-Shibata-Nakamura (BSSN) formulation [10][11][12] with 1+log slicing, and thẽ Γ driver condition for the shift [13,14].…”

Modeling maximum astrophysical gravitational recoil velocities

“…For the low-spin simulations we used a constant η = 2, while for the α = 0.92 simulation we used a modification of the form proposed in [90],…”

“…Two astrophysically important regions of this parameter space remain challenging to describe accurately by numerical simulations: the small q limit, although recent development of the numerical techniques have produced a successful simulation of the last few orbits before the merger of a q = 1/100 binary [67], and the near maximal spin limit. The most recent simulations of highly-spinning BHBs was of non-precessing binaries with intrinsic spins α = 0.95 [68].…”