Inferring Mimas' spatial distribution of tidal heating from its long-wavelength topography

In new work (Gyalay et al., 2023), we infer the interior of Mimas from its global shape (long-wavelength topography). To do so, we have to make various assumptions on how the ice shell of Mimas operates. This includes the temperature at the base of the ice shell, the thickness of the ice shell, what mode of isostasy it operates under (equal-mass vs. equal-pressure and Airy vs. Pratt), whether tidal tidal heating is due to eccentricity vs. obliquity, and how porous the region of the ice shell with a temperature <140 K may be. Further, as it has not yet been measured for Mimas, we must make an assumption on its moment of inertia. We vary through these assumptions and calculate how well an inferred heat distribution matches with a tidal heating distribution, among other physical self-consistency checks. In the associated paper, we analyze the dataset we produced to make conclusions on Mimas' interior structure and orbital dynamic history., This dataset was produced by a model using the methods described in Gyalay & Nimmo (2023a; JGR: Planets 128(2), doi: 10.1029/2022JE007550). In that paper, we established the mathematics behind how we used 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 that paper) and calculate its spherical harmonic weights as well as compare them to the originally observed topography. The code used to generate this dataset and as well as the dataset associated with Gyalay & Nimmo (2023a) are included in that paper's associated repository (Gyalay & Nimmo, 2023b; Dryad, dataset, doi: doi.org/10.7291/D11969). This repository contains only the produced model output for Mimas., The header of each data-output file should describe what each column refers to. MoI is the moment of inertia. From these data, one can compute density profiles for each model of Tethys (or Enceladus) and judge whether it is consistent with the inferred heating pattern weight. Values were not printed to file if the calculated average heat flux was NaN, if any of chi_A,B,C were not between 0 and 1, or if any of the spherical harmonic weights of forward-modeled topography were NaN. Further descriptions of parameters and their uses are described in Gyalay & Nimmo (2023a) and Gyalay et al. (2023).
We also include an input file for the solid body tidal heating code of Roberts & Nimmo (2008; Icarus 194(2), doi: 10.1016/j.icarus.2007.11.010). Usage of the input file is included in the file README.md, # Inferring Mimas' spatial distribution of tidal heating from its long-

## wavelength topography

In this repository there is a series of data files for outputs of Mimas modeled
under different assumptions. The biggest indicators of well-fitting models are
the r_sq, which is the coefficient of determination that shows how well the
inferred heating pattern beneath the ice shell can be fit by spatial
patterns of tidal heating, and the RMS, which is the root mean square
difference between the observed topography of Mimas and the topography forward
modeled from the best fit tidal heating pattern weights. In the associated
paper, we conclude there was a past epoch of strong obliquity tides in a solid
Mimas.

Additionally, there is one last file that is input for the TIRADE solid-body
tidal heating code of Roberts & Nimmo 2008. That code is not ours to provide,
but we can at least provide the input. Further, the Roberts & Nimmo code needs
to be updated to calculate the tidal dissipat...