Article

# On the mass radiated by coalescing black-hole binaries

The Astrophysical Journal (Impact Factor: 6.73). 06/2012; 758(1). DOI: 10.1088/0004-637X/758/1/63

Source: arXiv

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**ABSTRACT:**The behavior of merging black holes (including the emitted gravitational waves and the properties of the remnant) can currently be computed only by numerical simulations. This paper introduces ten numerical relativity simulations of binary black holes with equal masses and equal spins aligned or anti-aligned with the orbital angular momentum. The initial spin magnitudes have $|\chi_i| \lesssim 0.95$ and are more concentrated in the aligned direction because of the greater astrophysical interest of this case. We combine this data with five previously reported simulations of the same configuration, but with different spin magnitudes, including the highest spin simulated to date, $\chi_i \approx 0.97$. This data set is sufficiently accurate to enable us to offer improved analytic fitting formulae for the final spin and for the energy radiated by gravitational waves as a function of initial spin. The improved fitting formulae can help to improve our understanding of the properties of binary black hole merger remnants and can be used to enhance future approximate waveforms for gravitational wave searches, such as Effective-One-Body waveforms.Physical review D: Particles and fields 05/2013; 88(6). - [Show abstract] [Hide abstract]

**ABSTRACT:**Accretion and merger triggered accretion episodes are thought to primarily contribute to the mass accumulation history of supermassive black holes throughout cosmic time. While this might be the dominant growth mode at high redshifts, at lower redshifts and for the most massive black holes, mergers themselves might add significantly to the mass budget. In this paper, we use merger trees derived from hydrodynamical cosmological simulations of a cluster and void region to examine the growth of SMBHs from 4 > z > 0. Mass gains from gas accretion and BH-BH mergers are tracked as are black holes that remain unmerged and "orbiting" due to insufficient dynamical friction in a merger remnant, as well as those that are ejected due to gravitational recoil. We find that gas accretion remains the dominant source of mass accumulation in almost all of the SMBHs produced; mergers contribute an average of 3.3 +/- 0.2% for all SMBHs in the cluster, and 1.3 +/- 0.2% in the void from z = 4 to 0. However, mergers are significant for massive SMBHs, with the contribution from mergers reaching a maximum of 20% in the cluster for black holes with mass around 10^9 M_sun. We also find that the total mass in orbiting SMBHs is generally negligible in the void, but significant in the cluster, with a median value of M_orbiting >~ 10^7 M_sun per galaxy for galaxies with stellar mass M_{*} > 10^11.5 M_sun. We find that 40% of SMBHs and approximately 14% of the total SMBH mass is found orbiting in the cluster region at z = 0. We estimate the correction to the Soltan argument due to such orbiting SMBHs as well as SMBHs ejected via gravitational slingshot effects to be in the range 1.6 - 15%, with a mean value of 7.4 +/- 3.7% in the estimate of the inventory of the integrated accreted mass density of SMBHs. We also calculate the total energy output and strain due to gravitational waves emitted by merging SMBHs.07/2013; - [Show abstract] [Hide abstract]

**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.The Astrophysical Journal 06/2012; 758(1). · 6.73 Impact Factor

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