On the mass radiated by coalescing black-hole binaries

TL;DR

This paper presents an analytic formula to predict the final mass of black-hole remnants after mergers, validated against numerical simulations, with applications in gravitational-wave modeling and cosmology.

Contribution

The authors derive a new phenomenological formula that accurately predicts the remnant mass for generic black-hole binaries across a wide range of separations, validated against numerical relativity results.

Findings

The formula reproduces numerical relativity results for various binary configurations.

It improves the phase accuracy of effective-one-body waveforms during ringdown.

It estimates energy radiated in gravitational waves across different cosmic models.

Abstract

We derive an analytic phenomenological expression that predicts the final mass of the black-hole remnant resulting from the merger of a generic binary system of black holes on quasi-circular orbits. Besides recovering the correct test-particle limit for extreme mass-ratio binaries, our formula reproduces well the results of all the numerical-relativity simulations published so far, both when applied at separations of a few gravitational radii, and when applied at separations of tens of thousands of gravitational radii. These validations make our formula a useful tool in a variety of contexts ranging from gravitational-wave physics to cosmology. As representative examples, we first illustrate how it can be used to decrease the phase error of the effective-one-body waveforms during the ringdown phase. Second, we show that, when combined with the recently computed self-force correction to the binding energy of nonspinning black-hole binaries, it provides an estimate of the energy emitted during the merger and ringdown. Finally, we use it to calculate the energy radiated in gravitational waves by massive black-hole binaries as a function of redshift, using different models for the seeds of the black-hole population.