An Empirical Bayesian Approach to Limb Darkening in Modeling WASP-121b Transit Light Curves

Abstract

We present a novel, iterative method using an empirical Bayesian approach for modeling the limb-darkened WASP-121b transit from the TESS light curve. Our method is motivated by the need to improve R_p/R_* estimates for exoplanet atmosphere modeling and is particularly effective with the limb-darkening (LD) quadratic law requiring no prior central value from stellar atmospheric models. With the nonlinear LD law, the method has all the advantages of not needing atmospheric models but does not converge. The iterative method gives a different R_p/R_* for WASP-121b at a significance level of 1σ when compared with existing noniterative methods. To assess the origins and implications of this difference, we generate and analyze light curves with known values of the LD coefficients (LDCs). We find that noniterative modeling with LDC priors from stellar atmospheric models results in an inconsistent R_p/R_* at a 1.5σ level when the known LDC values are the same as those previously found when modeling real data by the iterative method. In contrast, the LDC values from the iterative modeling yield the correct value of R_p/R_* to within 0.25σ. For more general cases with different known inputs, Monte Carlo simulations show that the iterative method obtains unbiased LDCs and correct R_p/R_* to within a significance level of 0.3σ. Biased LDC priors can cause biased LDC posteriors and lead to bias in the R_p/R_* of up to 0.82%, 2.5σ for the quadratic law and 0.32%, 1.0σ for the nonlinear law. Our improvement in R_p/R_* estimation is important when analyzing exoplanet atmospheres.