Merger rate of primordial black-hole binaries

Abstract

Primordial black holes (PBHs) have long been a candidate for the elusive dark matter (DM), and remain poorly constrained in the $\ensuremath{\sim}20--100\text{ }\text{ }{M}_{\ensuremath{\bigodot}}$ mass range. PBH binaries were recently suggested as the possible source of LIGO's first detections. In this paper, we thoroughly revisit existing estimates of the merger rate of PBH binaries. We compute the probability distribution of orbital parameters for PBH binaries formed in the early Universe, accounting for tidal torquing by all other PBHs, as well as standard large-scale adiabatic perturbations. We then check whether the orbital parameters of PBH binaries formed in the early Universe can be significantly affected between formation and merger. Our analytic estimates indicate that the tidal field of halos and interactions with other PBHs, as well as dynamical friction by unbound standard DM particles, do not do significant work on nor torque PBH binaries. We estimate the torque due to baryon accretion to be much weaker than previous calculations, albeit possibly large enough to significantly affect the eccentricity of typical PBH binaries. We also revisit the PBH-binary merger rate resulting from gravitational capture in present-day halos, accounting for Poisson fluctuations. If binaries formed in the early Universe survive to the present time, as suggested by our analytic estimates, they dominate the total PBH merger rate. Moreover, this merger rate would be orders of magnitude larger than LIGO's current upper limits if PBHs make a significant fraction of the dark matter. As a consequence, LIGO would constrain $\ensuremath{\sim}10--300\text{ }\text{ }{M}_{\ensuremath{\bigodot}}$ PBHs to constitute no more than $\ensuremath{\sim}1%$ of the dark matter. To make this conclusion fully robust, though, numerical study of several complex astrophysical processes---such as the formation of the first PBH halos and how they may affect PBH binaries, as well as the accretion of gas onto an extremely eccentric binary---is needed.