The mass function of primordial rogue planet MACHOs in quasar nano-lensing

The recent Sumi et al (2010 Astrophys. J. 710 1641; 2011 Nature 473 349) detection of free roaming planet mass MACHOs in cosmologically significant numbers recalls their original detection in quasar microlening studies (Colley and Schild 2003 Astrophys. J. 594 97; Schild R E 1996 Astrophys. J. 464 125). 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 Stabell (1991 Astron. Astrophys. 250 62) 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.