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

TL;DR

This study demonstrates that quasar microlensing effects from a mixed mass spectrum of lenses can be approximated by a single effective mass, influencing constraints on primordial black holes and stellar populations.

Contribution

It introduces a method to approximate microlensing statistics for a mass spectrum with a single effective mass, aiding interpretation of mixed lens populations.

Findings

Monochromatic approximation matches mass spectrum when source size is small.

Best-fit mass is the geometric mean of the spectrum under certain conditions.

Constraints on black hole populations are affected by this approximation.

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 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$M_\odot$).