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

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 as compared with the Einstein radius, the mass of the monochromatic population matches the geometric mean of the mass-spectrum. Otherwise, the best-fit mass can be larger. Taking into account the degeneracy with the geometric mean, 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 ($\sim$ 100$M_\odot$) unlikely but allows, within a two-$\sigma$ confidence interval, the presence of a large population ($\gtrsim 40\%$ of the total mass) of substellar black holes ($\sim$ 0.01$M_\odot$).