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

TL;DR

This study uses Monte Carlo simulations to assess how distant fly-bys influence the merger times of primordial black hole binaries, finding negligible effects at high PBH abundances and modest impacts at low abundances, thus supporting existing merger rate constraints.

Contribution

It provides the first detailed analysis of distant encounters' effects on PBH binary coalescence times, confirming their minimal impact on merger rate estimates.

Findings

Negligible effect on coalescence time for high PBH abundance models.

Possible order of 1% change in binary lifetime at low PBH abundances.

Analytic approximation of coalescence time has about 10% error compared to numerical evolution.

Abstract

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, $f_\mathrm{PBH}\sim 1$, the expected fractional change in coalescence time is negligible, of order $10^{-6}$ for most binaries. For models with significantly lower PBH abundances, $f_\mathrm{PBH}\ll 1$, we find that the average change in binary lifetime due to encounters can be as large as $\mathcal{O}(10^{-2})$, 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.