Line Caustic Microlensing and Limb Darkening

TL;DR

This paper investigates how line caustic microlensing events can be used to measure stellar limb darkening profiles by analyzing the amplification behavior of images during caustic crossings, providing a method to determine stellar luminosity profiles with high precision.

Contribution

It derives the amplification behavior of images during line caustic crossings and assesses the accuracy needed in microlensing lightcurves to measure limb-darkening parameters.

Findings

Microlensing can measure stellar luminosity profiles during caustic crossings.

Accurate determination of limb-darkening parameters requires lightcurve precision better than 0.3-0.8%.

Analytic models for limb darkening are used to interpret microlensing data.

Abstract

In a line caustic crossing microlensing event, the caustic line moving across the surface of the source star provides a direct method to measure the integrated luminosity profile of the star. Combined with the enormous brightening at the caustic crossings, microlensing offers a promising tool for studying stellar luminosity profiles. We derive the amplification behavior of the two extra images that become partial images conjoined across the critical curve at a line caustic crossing. We identify the multiplicative factors that depend on the caustic crossing point and the relative size of the star, and the shape function that depends on the stellar luminosity profile. We examine the analytic limb-darkening models -- linear, square root, and square -- using the analytic form of the shape function. We find that the microlensing lightcurves must be determined to an accuracy of better than 0.3-0.8% in order to be able to determine the linear limb-darkening parameter $c_1$ with precision of $\delta c_1 = 0.1$. This is similar to the accuracy level required in eclipsing binaries as reported by Popper (1984).