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Thermal phase curves of exoplanet atmospheres have revealed temperature mapsas a function of planetary longitude, often by sinusoidal decomposition of thephase curve. We construct a framework for describing two-dimensionaltemperature maps of exoplanets with mathematical basis functions derived for afluid layer on a rotating, heated sphere with drag/friction, which aregeneralizations of spherical harmonics. These basis functions naturally producephysically-motivated temperature maps for exoplanets with few free parameters.We investigate best practices for applying this framework to temperature mapsof hot Jupiters by splitting the problem into two parts: (1) we constrain thetemperature map as a function of latitude by tuning the basis functions toreproduce general circulation model (GCM) outputs, since disk-integrated phasecurve observations do not constrain this dimension; and (2) we infer thetemperature maps of real hot Jupiters using original reductions of severalSpitzer phase curves, which directly constrain the temperature variations withlongitude. The resulting phase curves can be described with only three freeparameters per bandpass -- an efficiency improvement over the usual five or soused to describe sinusoidal decompositions of phase curves. Upon obtaining thehemispherically averaged dayside and nightside temperatures, the standardapproach would be to use zero-dimensional box models to infer the Bond albedoand redistribution efficiency. We elucidate the limitation of these box modelsby demonstrating that negative Bond albedos may be obtained due to a choice ofboundary condition on the nightside temperature. We propose generalizeddefinitions for the Bond albedo and heat redistribution efficiency for use withtwo-dimensional (2D) temperature maps. Open-source software called kelp isprovided to efficiently compute these phase curves.

Physically-motivated basis functions for temperature maps of exoplanets