Article

# On the mass radiated by coalescing black-hole binaries

The Astrophysical Journal (Impact Factor: 5.99). 06/2012; 758(1). DOI: 10.1088/0004-637X/758/1/63

Source: arXiv

**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.

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.

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