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High-precision exoplanet eclipse light curves, like those possible with JWST,enable flux and temperature mapping of exoplanet atmospheres. These eclipsemaps will have unprecedented precision, providing an opportunity to constraincurrent theoretical predictions of exoplanet atmospheres. However, eclipsemapping has unavoidable mathematical limitations because many map patterns areunobservable. This ``null space'' has implications for making comparisonsbetween predictions from general circulation models (GCMs) and the observedplanet maps, and, thus, affects our understanding of the physical processesdriving the observed maps. We describe the eclipse-mapping null space and showhow GCM forward models can be transformed to their observable modes for moreappropriate comparison with retrieved eclipse maps, demonstrated withapplications to synthetic data of an ultra-hot Jupiter and a cloudy warmJupiter under JWST-best-case- and extreme-precision observing scenarios. Weshow that the effects of the null space can be mitigated and manipulatedthrough observational design, and JWST exposure times are short enough to notincrease the size of the null space. Furthermore, we show the mathematicalconnection between the null space and the ``eigenmapping'' method,demonstrating how eigenmaps can be used to understand the null space in amodel-independent way. We leverage this connection to incorporate null-spaceuncertainties in retrieved maps, which increases the uncertainties to nowencompass the ground truth for synthetic data. The comparisons between observedmaps and forward models that are enabled by this work, and the improvedeclipse-mapping uncertainties, will be critical to our interpretation ofmultidimensional aspects of exoplanets in the JWST era.

The Eclipse Mapping Null Space: Comparing Theoretical Predictions with Observed Maps