On the probability distribution of cosmological microlensing optical depths

Abstract

It is conventional to calculate the probability of microlensing for a cosmologically distant source based on the Press-Gunn approximation that the lensing objects are uniformly and randomly distributed in the intervening space with a constant comoving density. We here investigate more realistic cosmological microlensing statistics by considering the strong spatial clustering of likely lensing objects with each other in galaxies and their association with the clumps of dark matter that make up the massive halos of galaxies. Both cases in which microlensing objects are distributed like the observed starlight in galaxies and ones in which the extended massive halos themselves are also composed of compact massive objects capable of acting as microlenses are investigated. The distribution of microlensing optical depth κ along randomly chosen sight lines is calculated, as is the conditional distribution of κ along sight lines near one that is strongly microlensed. Illustrative magnification biases are also considered. These distributions allow us to calculate both the probability that a high-redshift source will be microlensed in the various scenarios and the likely local κ (averaged over nearby sight lines) at which such microlensing events will occur. Our overall result is that the Press-Gunn approximation is a useful order-of-magnitude approximation if the massive halos of galaxies are made of dark compact objects, but that it fails badly and can be qualitatively misleading in the more likely case in which only the ordinary stellar populations of galaxies are the dominant source of cosmological microlensing events. In particular, we find that microlensing by stars is limited to of the order of 1% of high-redshift sources at any one time. Furthermore, even though only a small fraction of high-redshift sources are multiply imaged (by galaxies), it is these sources that are most likely to be microlensed by stars. Consequently, microlensing by stars is usually observed at κ near 1 where the simple isolated point mass lens approximation is not appropriate. However, if cold dark matter halos are composed of condensed objects, then more than 10% of high-redshift sources are microlensed at any given time. The vast majority of these sources are not multiply imaged, and have κ smaller than 0.01. Show more