The Mass Function of Primordial Rogue Planet MACHOs in quasar nanolensing

TL;DR

This paper investigates the microlensing effects of primordial rogue planet MACHOs, using statistical theory to match observed quasar microlensing amplitudes and estimate the mass function slope, suggesting a steep distribution.

Contribution

It applies a statistical microlensing theory to quasar data to estimate the mass function slope of primordial rogue planet MACHOs, providing a novel methodology for characterizing their distribution.

Findings

Close agreement between observed and theoretical microlensing amplitudes.

Estimated power law exponent of the mass function is approximately 2.98.

Methodology enables determination of the mass function slope from microlensing data.

Abstract

The recent Sumi et al (2010, 2011) detection of free roaming planet mass MACHOs in cosmologically significant numbers recalls their original detection in quasar microlening studies (Schild 1996, Colley and Schild 2003). We consider the microlensing signature of such a population, and find that the nano-lensing (microlensing) would be well characterized by a statistical microlensing theory published previously by Refsdal and Stabel (1991). Comparison of the observed First Lens microlensing amplitudes with the theoretical prediction gives close agreement and a methodology for determining the slope of the mass function describing the population. Our provisional estimate of the power law exponent in an exponential approximation to this distribution is $2.98^{+1.0}_{-0.5}.$ where a Salpeter slope is 2.35.