Getting a kick out of numerical relativity

TL;DR

This work addresses the problem of gravitational recoil from the merger of binary black holes by performing fully numerical relativity simulations of a nonspinning $1.5:1$ mass-ratio system using moving-puncture techniques and extracting gravitational radiation via $\psi_4$. It finds a recoil velocity in the range $86$--$116$ km s$^{-1}$ with a best estimate of $v_{\rm kick}=92\pm6$ km s$^{-1}$, and shows a roughly $40\%$ post-peak reduction due to phase evolution, consistent with early 2PN predictions. The results imply that black hole remnants can be ejected from low-mass halos at high redshift, affecting early SMBH assembly and halo occupation, while informing future studies of spins and other mass ratios through Fitchett scaling. This work highlights the importance of accurate numerical relativity for predicting recoil and its astrophysical consequences across cosmic time.

Abstract

Recent developments in numerical relativity have made it possible to follow reliably the coalescence of two black holes from near the innermost stable circular orbit to final ringdown. This opens up a wide variety of exciting astrophysical applications of these simulations. Chief among these is the net kick received when two unequal mass or spinning black holes merge. The magnitude of this kick has bearing on the production and growth of supermassive black holes during the epoch of structure formation, and on the retention of black holes in stellar clusters. Here we report the first accurate numerical calculation of this kick, for two nonspinning black holes in a 1.5:1 mass ratio, which is expected based on analytic considerations to give a significant fraction of the maximum possible recoil. We have performed multiple runs with different initial separations, orbital angular momenta, resolutions, extraction radii, and gauges. The full range of our kick speeds is 86--116 km s$^{-1}$, and the most reliable runs give kicks between 86 and 97 km s$^{-1}$. This is intermediate between the estimates from two recent post-Newtonian analyses and suggests that at redshifts $z\gtrsim 10$, halos with masses $\lesssim 10^9 M_\odot$ will have difficulty retaining coalesced black holes after major mergers.

Figures (2)

• Figure 1: The magnitude of the radiated momentum, as a function of time, from three different simulations. For initial coordinate separations of $d_{\rm init}=4.1M_0, 6.2M_0, {\rm and}\ 7.0M_0$, the final values of the kicks are respectively 113 km/s, 97 km/s, and 92 km/s. Also shown is the 2nd order post-Newtonian radiated momentum, which was computed from a low frequency cutoff commensurate with that of the $d_{\rm init}=7.0M_0$ simulation (see text for details). The excellent agreement of the post-Newtonian kick with that of the $d_{\rm init}=7.0M_0$ simulation over most of the first orbit, together with the agreement to within $6\%$ of the final kick from the $d_{\rm init}=7.0M_0$ simulation with that of the $d_{\rm init}=6.2M_0$ simulation, lends support to the accuracy of these results.
• Figure 2: Minimum mass of a dark matter halo at a given redshift required to retain the product of the merger of two nonspinning black holes with a mass ratio indicated on the curve. Details of the computation are in the text. Note that we use the Fit83 analytical estimate of the mass ratio dependence, assuming our numerical result of 92 km s$^{-1}$ for the mass ratio of 1.5:1. Then a mass ratio of 3:1 gives 140 km s$^{-1}$, a mass ratio of 5:1 gives 103 km s$^{-1}$, and a mass ratio of 10:1 gives 45 km s$^{-1}$. This figure indicates that early halos might lose merger remnants because of the kick, but in the current universe only globular clusters or the smallest dwarf galaxies could have black holes ejected because of gravitational radiation recoil.