New Approximation of Magnification Statistics for Random Microlensing of
  Magnified Sources
  Gravitationally lensed extragalactic sources are often subject to statistical
microlensing by stars in the galaxy or cluster lens. Accurate models of the
flux statistics are required for inferring source and lens properties from flux
observations. We derive an accurate semi-analytic approximation for calculating
the mean and variance of the magnification factor, which are applicable to
Gaussian source profiles and arbitrary non-uniform macro lens models, and hence
can save the need to perform expensive numerical simulations. The results are
given as single and double lens-plane integrals with simple, non-oscillatory
integrands, and hence are fast computable using common Monte Carlo integrators.
Employing numerical ray-shooting experiments, we examine the case of a highly
magnified source near a macro fold caustic, and demonstrate the excellent
accuracy of this semi-analytic approximation in the regime of multiple micro
images. Additionally, we point out how the maximum persistent magnification
achievable near a macro caustic is fundamentally limited by the masses and
number density of the foreground microlenses, in addition to the source's
physical size.
