A method for the microlensed flux variance of QSOs

Abstract

A fast and practical method is described for calculating the microlensed flux variance of an arbitrary source by uncorrelated stars. The required inputs are the mean convergence and shear due to the smoothed potential of the lensing galaxy, the stellar mass function, and the absolute square of the Fourier transform of the surface brightness in the source plane. The mathematical approach follows previous authors but has been generalized, streamlined, and implemented in publicly available code. Examples of its application are given for Dexter and Agol’s inhomogeneous-disc models as well as the usual Gaussian sources. Since the quantity calculated is a second moment of the magnification, it is only logarithmically sensitive to the sizes of very compact sources. However, for the inferred sizes of actual quasi-stellar objects (QSOs), it has some discriminatory power and may lend itself to simple statistical tests. At the very least, it should be useful for testing the convergence of microlensing simulations.