On simple analytic models of microlensing amplification statistics

Gravitational microlensing is a key probe of the nature of dark matter and its distribution on the smallest scales. For many practical purposes, confronting theory to observation requires to model the probability that a light source is highly amplified by many-lens systems. This article reviews four simple analytic models of the amplification probability distribution, based on different approximations: (i) the strongest-lens model; (ii) the multiplicative model, where the total amplification is assumed to be the product of all the lenses’ individual amplifications; (iii) a hybrid version of the previous two; and (iv) an empirical fitting function. In particular, a new derivation of the multiplicative amplification distribution is proposed, thereby correcting errors in the literature. Finally, the accuracy of these models is tested against ray-shooting simulations. They all produce excellent results as long as lenses are light and rare (low optical depth); however, for larger optical depths, none of them succeeds in capturing the relevant features of the amplification distribution. This conclusion emphasizes the crucial role of lens–lens coupling at large optical depthsPF received the support of a fellowship from ‘‘la Caixa’’ Foundation, Spain (ID 100010434). The fellowship code is LCF/BQ/PI19/11690018. JGB thanks the CERN TH-Division for hospitality during his sabbatical, when this project was initiated, and acknowledges support from the Research Project FPA2015-68048-03-3P [MINECO-FEDER] and the Centro de Excelencia Severo Ochoa Program SEV-2012-0597. He also acknowledges support from the Salvador de Madariaga Program, Ref. PRX17/0005