Analytic approximations for transit light curve observables and uncertainties

TL;DR

This paper provides analytic formulas to estimate exoplanet transit parameters and their uncertainties, simplifying the analysis process especially for stars with uniform brightness, though less accurate with limb darkening.

Contribution

It introduces new analytic approximations for transit light curve parameters and uncertainties, applicable to uniform stellar brightness scenarios.

Findings

Formulas for planetary radius and other parameters derived analytically.

Approximate covariances and uncertainties provided for transit analysis.

Limitations noted when limb darkening effects are significant.

Abstract

The light curve of an exoplanetary transit can be used to estimate the planetary radius and other parameters of interest. Because accurate parameter estimation is a non-analytic and computationally intensive problem, it is often useful to have analytic approximations for the parameters as well as their uncertainties and covariances. Here we give such formulas, for the case of an exoplanet transiting a star with a uniform brightness distribution. When limb darkening is significant, our parameter sets are still useful, although our analytic formulas underpredict the covariances and uncertainties.