Recoil velocities from equal-mass binary black-hole mergers: a systematic investigation of spin-orbit aligned configurations

TL;DR

This study systematically investigates recoil velocities from equal-mass binary black-hole mergers with aligned spins, refining previous results, and providing a phenomenological model for recoil as a function of spin ratio, with implications for astrophysical evolution.

Contribution

It extends prior work by accurately quantifying recoil velocities for aligned spins and deriving a nonlinear phenomenological formula for recoil as a function of spin ratio.

Findings

Maximum recoil velocity of 448 km/s for anti-aligned spins.

Recoil velocity depends nonlinearly on spin ratio, differing from PN predictions.

Radiated energy and angular momentum increase linearly with spin ratio.

Abstract

Binary black-hole systems with spins aligned with the orbital angular momentum are of special interest, as studies indicate that this configuration is preferred in nature. If the spins of the two bodies differ, there can be a prominent beaming of the gravitational radiation during the late plunge, causing a recoil of the final merged black hole. We perform an accurate and systematic study of recoil velocities from a sequence of equal-mass black holes whose spins are aligned with the orbital angular momentum, and whose individual spins range from a = +0.584 to -0.584. In this way we extend and refine the results of a previous study and arrive at a consistent maximum recoil of 448 +- 5 km/s for anti-aligned models as well as to a phenomenological expression for the recoil velocity as a function of spin ratio. This relation highlights a nonlinear behavior, not predicted by the PN estimates, and can be readily employed in astrophysical studies on the evolution of binary black holes in massive galaxies. An essential result of our analysis is the identification of different stages in the waveform, including a transient due to lack of an initial linear momentum in the initial data. Furthermore we are able to identify a pair of terms which are largely responsible for the kick, indicating that an accurate computation can be obtained from modes up to l=3. Finally, we provide accurate measures of the radiated energy and angular momentum, finding these to increase linearly with the spin ratio, and derive simple expressions for the final spin and the radiated angular momentum which can be easily implemented in N-body simulations of compact stellar systems. Our code is calibrated with strict convergence tests and we verify the correctness of our measurements by using multiple independent methods whenever possible.