Microlensing with advanced contour integration algorithm: Green's theorem to third order, error control, optimal sampling and limb darkening

TL;DR

This paper introduces an enhanced contour integration method for microlensing light curve computation, incorporating parabolic correction, error estimation, and limb darkening handling, resulting in faster and more accurate calculations.

Contribution

The paper develops an improved contour integration algorithm with error control and limb darkening treatment, advancing the computational efficiency and precision in microlensing modeling.

Findings

Significant speed-up of contour integration computations.

Accurate error estimation enables optimal sampling strategies.

Effective handling of limb-darkened sources at arbitrary accuracy.

Abstract

Microlensing light curves are typically computed either by ray-shooting maps or by contour integration via Green's theorem. We present an improved version of the second method that includes a parabolic correction in Green's line integral. In addition, we present an accurate analytical estimate of the residual errors, which allows the implementation of an optimal strategy for the contour sampling. Finally, we give a prescription for dealing with limb-darkened sources reaching arbitrary accuracy. These optimizations lead to a substantial speed-up of contour integration codes along with a full mastery of the errors.