Formation and evolution of primordial black hole binaries in the early universe

Abstract

The abundance of primordial black holes (PBHs) in the mass range $0.1 - 10^3\nM_\\odot$ can potentially be tested by gravitational wave observations due to\nthe large merger rate of PBH binaries formed in the early universe. To put the\nestimates of the latter on a firmer footing, we first derive analytical PBH\nmerger rate for general PBH mass functions while imposing a minimal initial\ncomoving distance between the binary and the PBH nearest to it, in order to\npick only initial configurations where the binary would not get disrupted. We\nthen study the formation and evolution of PBH binaries before recombination by\nperforming N-body simulations. We find that the analytical estimate based on\nthe tidally perturbed 2-body system strongly overestimates the present merger\nrate when PBHs comprise all dark matter, as most initial binaries are disrupted\nby the surrounding PBHs. This is mostly due to the formation of compact N-body\nsystems at matter-radiation equality. However, if PBHs make up a small fraction\nof the dark matter, $f_{\\rm PBH} \\lesssim 10\\%$, these estimates become more\nreliable. In that case, the merger rate observed by LIGO imposes the strongest\nconstraint on the PBH abundance in the mass range $2 - 160 M_\\odot$. Finally,\nwe argue that, even if most initial PBH binaries are perturbed, the present\nBH-BH merger rate of binaries formed in the early universe is larger than\n$\\mathcal{O}(10)\\,{\\rm Gpc}^{-3} {\\rm yr}^{-1}\\, f_{\\rm PBH}^3$\n