Gravitational radiation driven capture in unequal mass black hole encounters

TL;DR

This study uses numerical relativity to analyze gravitational radiation capture in unequal mass black hole encounters, revealing the limitations of post-Newtonian approximations at close distances and high mass ratios.

Contribution

It introduces a parabolic approximation method to determine critical impact parameters for gravitational capture in unequal mass black holes, comparing results with post-Newtonian models.

Findings

Most energetic encounters occur near the boundary between merging and fly-by orbits.

Unequal mass black holes radiate less energy and angular momentum than equal mass ones at the same orbital angular momentum.

Post-Newtonian approximations diverge significantly from numerical relativity results at close encounters and high mass ratios.

Abstract

The gravitational radiation driven capture (GR capture) between unequal mass black holes without spins has been investigated with numerical relativistic simulations. We adopt the parabolic approximation which assumes that the gravitational wave radiation from a weakly hyperbolic orbit is the same as that from the parabolic orbit having the same pericenter distance. Using the radiated energies from the parabolic orbit simulations, we have obtained the critical impact parameter ($b_{\rm crit}$) for the GR capture for weakly hyperbolic orbit as a function of initial energy. The most energetic encounters occur around the boundary between the direct merging and the fly-by orbits, and can emit several percent of initial total ADM energy at the peak. When the total mass is fixed, energy and angular momentum radiated in the case of unequal mass black holes are smaller than those of equal mass black holes having the same initial orbital angular momentum for the fly-by orbits. We have compared our results with two different Post-Newtonian (PN) approximations, the exact parabolic orbit (EPO) and PN corrected orbit (PNCO). We find that the agreement between the EPO and the numerical relativity breaks down for very close encounters ($\it{e.g.}$, $b_{\rm crit} \lesssim 100$ M), and it becomes worse for higher mass ratios. For instance, the critical impact parameters can differ by more than $50\%$ from those obtained in EPO if the relative velocity at infinity $v_{\infty}$ is larger than 0.1 for the mass ratio of $m_{1}/m_{2}=16$. The PNCO gives more consistent results than EPO, but it also underestimates the critical impact parameter for the GR capture at $b_{\rm crit} \lesssim40$ M.