Properties of analytic transit light curve models

TL;DR

This paper provides analytic formulas for derivatives of transit light curves with quadratic limb darkening, improving computational efficiency and aiding data modeling in exoplanet and binary star studies.

Contribution

It introduces new analytic expressions for flux derivatives during transits, enhancing modeling speed and accuracy over previous numerical methods.

Findings

Achieves approximately 8-fold speedup in light curve fitting algorithms.

Provides explicit formulas for derivatives under quadratic limb darkening.

Facilitates more efficient analysis of transit and eclipse data.

Abstract

In this paper a set of analytic formulae are presented with which the partial derivatives of the flux obscuration function can be evaluated -- for planetary transits and eclipsing binaries -- under the assumption of quadratic limb darkening. The knowledge of these partial derivatives is crucial for many of the data modeling algorithms and estimates of the light curve variations directly from the changes in the orbital elements. These derivatives can also be utilized to speed up some of the fitting methods. A gain of ~8 in computing time can be achieved in the implementation of the Levenberg-Marquardt algorithm, relative to using numerical derivatives.