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.

LTD064402+245919: A Subgiant with a 1-3 M$_{\odot}$ Undetected Companion Identified from LAMOST-TD Data

“…The transit parameters from fixing the inclination can be many σ away from the best-fit result. This scenario relates to the model-dependent Bayesian statistics (Yang et al 2020a(Yang et al , 2021. In this work, fixing the inclination to, e.g., 75 degrees, supports a model hypothesis that the secondary component is a compact object (due to transit non-detection).…”

“…Fixing inclination to specific values can be regarded as adding model hypotheses. Combining models with different hypotheses into a global estimation is a common difficulty in Bayesian statistics (Yang et al 2020a(Yang et al , 2021.…”

“…Limb darkening is interpolated from PHOEBE's built-in tables. The limb darkening model is commonly following one of the linear, square root, quadratic, or non-linear limb darkening laws (Claret & Bloemen 2011;Yang et al 2020aYang et al , 2021. We choose a square-root limb darkening law with parameters supplied by PHOEBE (Conroy et al 2020).…”

“…Other parameter sets obtained by fixing some parameters are acceptable given the data though they might not be as favored. This is common in transit fitting and leads to the 'best-fit' parameter sets (as discussed in Yang et al 2020aYang et al , 2021. The transit parameters from fixing the inclination can be many σ away from the best-fit result.…”

Transit Timing Variation of XO-3b: Evidence for Tidal Evolution of Hot Jupiter with High Eccentricity

“…An example image of XO-3b is present in Figure 1. Highquality TESS photometry has been well utilized in exoplanet researches, e.g., the atmospheric measurement, transit timing variation (Deming et al 2009;Placek et al 2016;Kempton et al 2018;Bouma et al 2020;Yang et al 2020aYang et al , 2021bKane et al 2021;Turner et al 2021).…”