Gravitational waves from scattering of stellar-mass black holes in galactic nuclei

Stellar-mass black holes (BHs) are expected to segregate and form a steep density cusp around supermassive black holes (SMBHs) in galactic nuclei. We follow the evolution of a multimass system of BHs and stars by numerically integrating the Fokker–Planck energy diffusion equations for a variety of BH mass distributions. We find that the BHs ‘self-segregate’, and that the rarest, most massive BHs dominate the scattering rate closest to the SMBH (≲10−1 pc). BH–BH binaries form out of gravitational wave emission during BH encounters. We find that the expected rate of BH coalescence events detectable by Advanced LIGO is ∼1–102 yr−1, depending on the initial mass function of stars in galactic nuclei and the mass of the most massive BHs. We find that the actual merger rate is likely ∼10 times larger than this due to the intrinsic scatter of stellar densities in many different galaxies. The BH binaries that form this way in galactic nuclei have significant eccentricities as they enter the LIGO band (90 per cent with e > 0.9), and are therefore distinguishable from other binaries, which circularize before becoming detectable. We also show that eccentric mergers can be detected to larger distances and greater BH masses than circular mergers, up to ∼700 M⊙. Future ground-based gravitational wave observatories will be able to constrain both the mass function of BHs and stars in galactic nuclei.