The role of primordial kicks on black hole merger rates

Primordial stars are likely to be very massive (≥ 30 M _⊙), form in isolation, and will likely leave black holes as remnants in the centres of their host dark matter haloes. We expect primordial stars to form in haloes in the mass range 10⁶-10¹⁰ M _⊙. Some of these early black holes, formed at redshifts z ≳ 10, could be the seed black holes for a significant fraction of the supermassive black holes (SMBHs) found in galaxies in the local Universe. If the black hole descendants of the primordial stars exist, their merger with nearby SMBHs may be a prime candidate for long wavelength gravitational wave detectors. We simulate formation and evolution of dark matter haloes in a A cold dark matter universe. We seed high-redshift dark matter haloes with early black holes, and explore the merger history of the host haloes and the implications of black hole kick velocities arising from their coalescence. The central concentration of low-mass early black holes in present-day galaxies is reduced if they experience even moderate kicks of tens of km s^-1. Even such modest kicks allow the black holes to leave their parent halo, which consequently leads to dynamical friction being less effective on the low-mass black holes that were ejected, compared to those still embedded in their parent haloes. Therefore, merger rates with central SMBHs in the largest halo may be reduced by more than an order of magnitude. Using analytical and illustrative cosmological N-body simulations, we quantify the role of kicks on the merger rates of black holes formed from massive metal-free stars with SMBHs in present-day galaxies.