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

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 $V_{max}=526\pm 23km/s$, which occurs when the progenitor spins are maximal, the mass ratio is $q_{max}=m_1/m_2=0.623\pm 0.038$, 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 $80km/s$ 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 $400km/s$ can be as large as $17\%$, while the probability for recoils faster than $250km/s$ 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 $E_{\mathrm{rad}}/m\approx 11.3\%$ and final spin ${\alpha }_{\mathrm{rem}}^{\max }\approx 0.952$ for equal mass, aligned maximally spinning binaries.

19 pages, 25 figures, revtex 4

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• The second RIT binary black hole simulations catalog and its application to gravitational waves parameter estimation
• Flip-flopping binary black holes
• The Detection Rates of Merging Binary Black Holes Originating from Star Clusters and Their Mass Function
• The nonspinning binary black hole merger scenario revisited
• The antikick strikes back: recoil velocities for nearly-extremal binary black hole mergers in the test-mass limit