Remnant mass, spin, and recoil from spin aligned black-hole binaries

TL;DR

This paper models the final properties of black hole mergers with aligned or counteraligned spins, providing formulas for mass, spin, and recoil, and finds that high recoil velocities are more probable than previously thought.

Contribution

It introduces new phenomenological formulas for the final mass, spin, and recoil velocity of black hole mergers with aligned spins, validated against independent results.

Findings

Maximum recoil velocity is 526 km/s for specific spin and mass ratio configurations.

Probability of recoil exceeding 400 km/s can be as high as 17%.

Maximum radiated energy is approximately 11.3% of the total mass.

Abstract

We perform a set of 36 nonprecessing black-hole binary simulations with spins either aligned or counteraligned with the orbital angular momentum in order to model the final mass, spin, and recoil of the merged black hole as a function of the individual black hole spin magnitudes and the mass ratio of the progenitors. We find that the maximum recoil for these configurations is $V_{max}=526\pm23\,km/s$, which occurs when the progenitor spins are maximal, the mass ratio is $q_{max}=m_1/m_2=0.623\pm0.038$, the smaller black-hole spin is aligned with the orbital angular momentum, and the larger black-hole spin is counteraligned ($\alpha_1=-\alpha_2=1$). This maximum recoil is about $80\,km/s$ larger than previous estimates, but most importantly, because the maximum occurs for smaller mass ratios, the probability for a merging binary to recoil faster than $400\,km/s$ can be as large as $17\%$, while the probability for recoils faster than $250\, km/s$ can be as large as $45\%$. We provide explicit phenomenological formulas for the final mass, spin, and recoil as a function of the individual BH spins and the mass difference between the two black holes. Here we include terms up through fourth-order in the initial spins and mass difference, and find excellent agreement (within a few percent) with independent results available in the literature. The maximum radiated energy is $E_{\rm rad}/m\approx11.3\%$ and final spin $\alpha_{\rm rem}^{\rm max}\approx0.952$ for equal mass, aligned maximally spinning binaries.