Analytic Approximations for Transit Light Curve Observables, Uncertainties, and Covariances

TL;DR

This paper provides analytic formulas to estimate exoplanet transit parameters, uncertainties, and covariances for uniform stellar brightness, aiding efficient data analysis despite some limitations with limb darkening.

Contribution

It introduces new analytic approximations for transit parameter uncertainties and covariances, improving data fitting efficiency for uniform star brightness models.

Findings

Analytic formulas accurately estimate uncertainties for uniform brightness transits.

Parameter sets reduce correlations and improve fitting efficiency.

Formulas underpredict uncertainties when limb darkening is 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. We also assess the advantages of some relatively uncorrelated parameter sets for fitting actual data. When limb darkening is significant, our parameter sets are still useful, although our analytic formulas underpredict the covariances and uncertainties.