  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.
