Identifying and Fitting Eclipse Maps of Exoplanets with Cross-Validation

Abstract

Eclipse mapping uses the shape of the eclipse of an exoplanet to measure its two-dimensional structure. Light curves are mostly composed of longitudinal information, with the latitudinal information only contained in the brief ingress and egress of the eclipse. This imbalance can lead to a spuriously confident map, where the longitudinal structure is constrained by out-of-eclipse data and the latitudinal structure is wrongly determined by the priors on the map. We present a new method to address this issue. The method tests for the presence of an eclipse mapping signal by using k-fold cross-validation to compare the performance of a simple mapping model to the null hypothesis of a uniform disk. If a signal is found, the method fits a map with more degrees of freedom, optimising its information content. The information content is varied by penalising the model likelihood by a factor proportional to the spatial entropy of the map, optimised by cross-validation. We demonstrate this method for simulated datasets then apply it to three observational datasets. The method identifies an eclipse mapping signal for JWST MIRI/LRS observations of WASP-43b but does not identify a signal for JWST NIRISS/SOSS observations of WASP-18b or Spitzer Space Telescope observations of HD 189733b. It is possible to fit eclipse maps to these datasets, but we suggest that these maps are overfitting the eclipse shape. We fit a new map with more spatial freedom to the WASP-43b dataset and show a flatter east-west structure than previously derived.