Physicallymotivated basis functions for temperature maps of exoplanets
Abstract
Thermal phase curves of exoplanet atmospheres have revealed temperature maps as a function of planetary longitude, often by sinusoidal decomposition of the phase curve. We construct a framework for describing twodimensional temperature maps of exoplanets with mathematical basis functions derived for a fluid layer on a rotating, heated sphere with drag/friction, which are generalisations of spherical harmonics. These basis functions naturally produce physicallymotivated temperature maps for exoplanets with few free parameters. We investigate best practices for applying this framework to temperature maps of hot Jupiters by splitting the problem into two parts: (1) we constrain the temperature map as a function of latitude by tuning the basis functions to reproduce general circulation model outputs, since diskintegrated phase curve observations do not constrain this dimension; and (2) we infer the temperature maps of real hot Jupiters using original reductions of several Spitzer phase curves, which directly constrain the temperature variations with longitude. The resulting phase curves can be described with only three free parameters per bandpass  an efficiency improvement over the usual five or so used to describe sinusoidal decompositions of phase curves. Upon obtaining the hemispherically averaged day side and night side temperatures, the standard approach would be to use zerodimensional box models to infer the Bond albedo and redistribution efficiency. We elucidate the limitation of these box models by demonstrating that negative Bond albedos may be obtained due to a choice of boundary condition on the night side temperature. We propose generalized definitions for the Bond albedo and heat redistribution efficiency for use with twodimensional (2D) temperature maps. Opensource software called kelp is provided to efficiently compute the 2D temperature maps, phase curves, albedos and redistribution efficiencies.
 Publication:

Astronomy and Astrophysics
 Pub Date:
 April 2022
 DOI:
 10.1051/00046361/202142135
 arXiv:
 arXiv:2110.11837
 Bibcode:
 2022A&A...660A.123M
 Keywords:

 radio continuum: planetary systems;
 planets and satellites: atmospheres;
 planets and satellites: gaseous planets;
 techniques: photometric;
 methods: analytical;
 methods: observational;
 Astrophysics  Earth and Planetary Astrophysics
 EPrint:
 Accepted in A&