The impact on distant fly-bys on the rate of binary primordial black hole mergers

By performing Monte Carlo simulations of the evolution of binary primordial black hole (PBH) systems, we estimate the effect of distant encounters with single PBHs upon the coalescence time and merger rate of binary PBHs. We find that, for models where PBHs compose a large fraction of dark matter, integral(PBH) similar to 1, the expected fractional change in coalescence time is negligible, of order 10(-6) for most binaries. For models with significantly lower PBH abundances, integral(PBH) << 1, we find that the average change in binary lifetime due to encounters can be as large as O(10(-2)), with a small number of binaries experiencing an order unity change in lifetime. In the absence of encounters, we also compare the use of an analytic approximation for the coalescence time to numerically evolving the binary system, finding that the analytic approximation results in an order 10% error in the coalescence time. However, when these effects are taken into consideration, there is a negligible change to the calculated merger rate, placing previous constraints on the PBH abundance arising from observed gravitational wave signals from merging binary black holes on a more secure footing.