The Impact of the Mass Spectrum of Lenses in Quasar Microlensing Studies. Constraints on a Mixed Population of Primordial Black Holes and Stars

Abstract We show that quasar microlensing magnification statistics induced by a population of point microlenses distributed according to a mass spectrum can be very well approximated by that of a single-mass, monochromatic, population. When the spatial resolution (physically defined by the source size) is small compared with the Einstein radius, the mass of the monochromatic population matches the geometric mean (GM) of the mass spectrum. Otherwise, the best-fit mass can be larger. Taking into account the degeneracy with the GM, the interpretation of quasar microlensing observations under the hypothesis of a mixed population of primordial black holes and stars makes the existence of a significant population of intermediate mass black holes (∼100 M ⊙ ) unlikely but allows, within a 2 σ confidence interval, the presence of a large population (≳40% of the total mass) of substellar black holes (∼0.01 M ⊙ ).