Gravitational radiation driven capture in unequal mass black hole encounters

Abstract

The gravitational radiation driven capture (GR capture) between unequal mass black holes without spinshas been investigated with numerical relativistic simulations. We adopt the parabolic approximation whichassumes that the gravitational wave radiation from a weakly hyperbolic orbit is the same as that from theparabolic orbit having the same pericenter distance. Using the radiated energies from the parabolic orbitsimulations, we have obtained the critical impact parameter (bcrit) for the GR capture for weakly hyperbolicorbit as a function of initial energy. The most energetic encounters occur around the boundary between thedirect merging and the fly-by orbits, and can emit several percent of total initial energy at the peak. Whenthe total mass is fixed, energy and angular momentum radiated in the case of unequal mass black holes aresmaller than those of equal mass black holes having the same initial orbital angular momentum for the flybyorbits.We have compared our results with two different post-Newtonian (PN) approximations, the exactparabolic orbit (EPO) and PN corrected orbit (PNCO).We find that the agreement between the EPO and thenumerical relativity breaks down for very close encounters (e.g., bcrit ≲ 100 M), and it becomes worse forhigher mass ratios. For instance, the critical impact parameters can differ by more than 50% from thoseobtained in EPO if the relative velocity at infinity v∞ is larger than 0.1 for the mass ratio of m1=m2¼ 16.The PNCO gives more consistent results than EPO, but it also underestimates the critical impact parameterfor the GR capture at bcrit ≲ 40 M.