Finite source effects in microlensing: A precise, easy to implement, fast and numerical stable formalism

TL;DR

This paper introduces a fast, stable, and easy-to-implement formalism for modeling microlensing amplification of extended sources, applicable across all amplification regimes, improving efficiency and accuracy in light-curve analysis.

Contribution

The paper presents a novel numerical method for microlensing amplification that is faster, more stable, and applicable in all regimes, including finite source and lens effects, suitable for large surveys.

Findings

Method is numerically stable and fast compared to previous approaches.

Accurately models finite source and lens effects in microlensing light curves.

Validated with real microlensing events, consistent with prior studies.

Abstract

The goal of this paper is to provide a numerically fast and stable description for the microlensing amplification of an extended source (either uniform or limb-darkened) that holds in any amplification regime. We show that our method of evaluating the amplification can be implemented into a light-curve fitting routine using the Levenberg-Marquardt algorithm. We compare the accuracy and computation times to previous methods that either work in the high-amplification regime only, or require special treatments due to the singularity of elliptic integrals. In addition, we also provide the equations including finite lens effects in microlensing light curves. We apply our methods to the MACHO-1995-BLG-30 and the OGLE-2003-BLG-262 events and obtain results consistent to former studies. We derive an upper limit for the OGLE-2003-BLG-262 event lens size. We conclude that our method allows to simultaneously search for point-source and finite-source microlensing events in future large area microlensing surveys in a fast manner.