Inferred tidal heating distribution and internal structure of Tethys and Enceladus

In our submitted paper, "Estimates for Tethys' Moment of Inertia, Heat Flux Distribution, and Interior Structure from its Long-Wavelength Topography" (Gyalay & Nimmo, 2023), we sought to infer the heat flux distribution at the base of Tethys' ice shell. This heat flux distribution allows us to infer whether there is a fluid or rigid layer interior to the ice shell – the latter of which would suggest a global, subsurface ocean. We calculate the heat flux distribution from the long-wavelength (spherical harmonic degrees 2 and 4) topography but require some assumptions, such as how thick the ice layer is, if the upper portion is porous, and what the moment of inertia of Tethys is. Thus we fit for the tidal heating distribution for a wide suite of varying parameters to find which combination best represents the structure and thermal state of Tethys. We also test our procedure on Enceladus, a moon for which we already know the moment of inertia and interior structure (i.e. that it has a subsurface ocean). This dataset contains the code we used to model these icy satellites and generate our data, as well as the output data.

Methods
In our paper, we establish the mathematics behind how we use assumed parameters (upper ice shell porosity, total ice shell thickness, moment of inertia, basal temperature at the base of the ice shell) to infer the average basal heat flux and fit for spatial patterns of tidal heating (Beuthe, 2013, Icarus). Using this best-fit tidal heating for each set of parameters, we forward model the topography (also described in our paper) and calculate its spherical harmonic weights as well as compare them to the originally observed topography.