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Mapping exoplanets across phases and during secondary eclipse is a powerfultechnique for characterizing Hot Jupiters in emission. Since these planets areexpected to rotate about axes normal to their orbital planes, with rotationperiods synchronized with their orbital periods, mapping provides a directcorrespondence between orbital phase and planetary longitude. We develop aframework to understand the information content of planets where their rotationstates are not well constrained, by constructing bases of light curves acrossdifferent rotation rates and obliquities that are orthogonal in integrated fluxacross secondary eclipse. These demonstrate that brightness variability duringeclipse may arise from a variety of rotation rates, obliquities, and mapstructures, requiring priors to properly disentangle each of these components.By modeling eclipse observations of the Warm Jupiter HAT-P-18 b we demonstratethat, at a signal-to-noise equivalent to $\sim 10$ orbits with JWST, confusionabout map structure is likely a concern only at the upper physical limits ofpossible rotation rates. Even without priors, one may nevertheless be able toput an order-of-magnitude constraint on rotation rate by determining at whatrates the fitted map complexity is minimized, a prescription whose efficacyincreases if out-of-eclipse data are available to isolate the effects ofrotation. Finally, in the limit of maps with longitudinal symmetry, theprojected obliquity in the plane of the sky determines the informationavailable during eclipse, ranging from non-detections of structure to a basicconstraint on hemispherical asymmetry and orientation depending on theobliquity angle.

The Sensitivity of Eclipse Mapping to Planetary Rotation