Final spin of a coalescing black-hole binary: an Effective-One-Body approach

TL;DR

This paper updates the Analytical estimate of the final spin $\hat{a}$ for unequal-mass, non-spinning black-hole binaries within the Effective-One-Body framework. By incorporating higher-order PN dynamics ($3$PN/3.5PN), two radiation-reaction prescriptions, and a physically motivated treatment of ringdown losses, the authors achieve a close convergence (within about 2%) to numerical-relativity results across the accessible mass-ratio range and extend predictions to $\nu$ values not yet simulated. They show that including ringdown losses is crucial for accurate final-spin predictions and demonstrate that the EOB approach can bracket NR results, with a simple quadratic fit providing a practical surrogate over the explored parameter space. The work underscores the EOB framework’s capacity to capture plunge-merger physics and to inform waveform modeling and parameter estimation in gravitational-wave astronomy.

Abstract

We update the analytical estimate of the final spin of a coalescing black-hole binary derived within the Effective-One-Body (EOB) approach. We consider unequal-mass non-spinning black-hole binaries. It is found that a more complete account of relevant physical effects (higher post-Newtonian accuracy, ringdown losses) allows the {\it analytical} EOB estimate to `converge towards' the recently obtained {\it numerical} results within 2%. This agreement illustrates the ability of the EOB approach to capture the essential physics of coalescing black-hole binaries. Our analytical approach allows one to estimate the final spin of the black hole formed by coalescing binaries in a mass range ($ν=m_1m_2/(m_1+m_2)^2 < 0.16 $) which is not presently covered by numerical simulations.

Figures (2)

• Figure 1: Time evolution of the orbital frequency $\Omega$ for $\nu=1/4$: the maximum occurs near the $\nu$-deformed light ring at $r_{\rm LR}(1/4)\approx 2.316$.
• Figure 2: Dimensionless spin parameter of the final black hole: convergence of Effective-One-Body estimates towards Numerical Relativity ones as one increases the post-Newtonian accuracy and takes into account the ringdown losses. See text for discussion.