Bringing 2D Eclipse Mapping out of the Shadows with Leave-one-out Cross-validation

Eclipse mapping is a technique for inferring 2D brightness maps of transiting exoplanets from the shape of an eclipse light curve. With JWST's unmatched precision, eclipse mapping is now possible for a large number of exoplanets. However, eclipse mapping has only been applied to two planets and the nuances of fitting eclipse maps are not yet fully understood. Here, we use Leave-one-out Cross- Validation (LOO-CV) to investigate eclipse mapping, with application to a JWST NIRISS/SOSS observation of the ultra-hot Jupiter WASP-18b. LOO-CV is a technique that provides insight into the out-of-sample predictive power of models on a data-point-by-data-point basis. We show that constraints on planetary brightness patterns behave as expected, with large-scale variations driven by the phase-curve variation in the light curve and smaller-scale structures constrained by the eclipse ingress and egress. For WASP-18b we show that the need for higher model complexity (smaller-scale features) is driven exclusively by the shape of the eclipse ingress and egress. We use LOO-CV to investigate the relationship between planetary brightness map components when mapping under a positive-flux constraint to better understand the need for complex models. Finally, we use LOO-CV to understand the degeneracy between the competing ``hotspot'' and ``plateau'' brightness map models of WASP-18b, showing that the plateau model is driven by the ingress shape and the hotspot model is driven by the egress shape, but preference for neither model is due to outliers or unmodeled signals. Based on this analysis, we make recommendations for the use of LOO-CV in future eclipse-mapping studies.