Lensing by primordial black holes: Constraints from gravitational wave observations

Abstract

Primordial black holes (PBHs) have been proposed to explain at least a portion of dark matter. Observations have put strong constraints on PBHs in terms of the fraction of dark matter which they can represent, ${f}_{\mathrm{PBH}}$, across a wide mass range---apart from the stellar-mass range of $20\text{ }\text{ }{M}_{\ensuremath{\bigodot}}\ensuremath{\lesssim}{M}_{\mathrm{PBH}}\ensuremath{\lesssim}100\text{ }\text{ }{M}_{\ensuremath{\bigodot}}$. In this paper, we explore the possibility that such PBHs could serve as point-mass lenses capable of altering the gravitational-wave (GW) signals observed from binary black hole (BBH) mergers along their line-of-sight. We find that careful GW data analysis could verify the existence of such PBHs based on the fitting factor and odds ratio analyses. When such a lensed GW signal is detected, we expect to be able to measure the redshifted mass of the lens with a relative error $\mathrm{\ensuremath{\Delta}}{M}_{\mathrm{PBH}}/{M}_{\mathrm{PBH}}\ensuremath{\lesssim}0.3$. If no such lensed GW events were detected despite the operation of sensitive GW detectors accumulating large numbers of BBH mergers, it would translate into a stringent constraint of ${f}_{\mathrm{PBH}}\ensuremath{\lesssim}{10}^{\ensuremath{-}2}\ensuremath{-}{10}^{\ensuremath{-}5}$ for PBHs with a mass larger than $\ensuremath{\sim}10\text{ }\text{ }{M}_{\ensuremath{\bigodot}}$ by the Einstein Telescope after one year of running, and ${f}_{\mathrm{PBH}}\ensuremath{\lesssim}0.2$ for PBHs with mass greater than $\ensuremath{\sim}50\text{ }\text{ }{M}_{\ensuremath{\bigodot}}$ for advanced LIGO after ten years of running.