Microlensing and dynamical constraints on primordial black hole dark matter with an extended mass function

Abstract

The recent discovery of gravitational waves from mergers of $\ensuremath{\sim}10\text{ }\text{ }{M}_{\ensuremath{\bigodot}}$ black hole binaries has stimulated interested in primordial black hole (PBH) dark matter in this mass range. Microlensing and dynamical constraints exclude all of the dark matter in compact objects with a delta function mass function in the range ${10}^{\ensuremath{-}7}\ensuremath{\lesssim}M/{M}_{\ensuremath{\bigodot}}\ensuremath{\lesssim}1{0}^{5}$. However it has been argued that all of the dark matter could be composed of compact objects in this range with an extended mass function. We explicitly recalculate the microlensing and dynamical constraints for compact objects with an extended mass function which replicates the PBH mass function produced by inflation models. We find that the microlensing and dynamical constraints place conflicting constraints on the width of the mass function, and do not find a mass function which satisfies both constraints.