An Efficient Method for Modeling High Magnification Planetary Microlensing Events

Abstract

I present a previously unpublished method for modeling multiple lens microlensing events that is based on the image centered ray shooting approach of Bennett and Rhie. It has been used to model all a wide variety of binary and triple lens systems, but it is designed to efficiently model high-magnification planetary microlensing events, because these are, by far, the most challenging events to model. It is designed to be efficient enough to handle microlensing events with more than two lens masses and lens orbital motion. This method uses a polar coordinate integration grid with a smaller grid spacing in the radial direction than in the angular direction, and it employs an integration scheme specifically designed to handle limb darkened sources. I present tests that show that these features achieve second order accuracy for the light curves of a number of high-magnification planetary events. They improve the precision of the calculations by a factor of >100 compared to first order integration schemes with the same grid spacing in both directions (for a fixed number of grid points). This method also includes a Metropolis algorithm chi^2 minimization method that allows the jump function to vary in a way that allows quick convergence to chi^2 minima. Finally, I introduce a global parameter space search strategy that allows a blind search of parameter space for light curve models without requiring chi^2 minimization over a large grid of fixed parameters. Instead, the parameter space is explored on a grid of initial conditions for a set of chi^2 minimizations using the full parameter space. While this method may be faster than methods that find the chi^2 minima over a large grid of parameters, I argue that the main strength of this method is for events with the signals of multiple planets, where a much higher dimensional parameter space must be explored to find the correct light curve model.