Fig. 2: Surface heat flux after convergence of the iterative procedure for a c that describes a strong coupling strength (subplot d).

Overlain are the 343 thermal sources identified by Davies et al.¹² with the marker size indicating their thermal output. Directly flanking the map are the longitudinally and latitudinally integrated fluxes from the converged solution (subplots c and e), a spherically symmetric Io, and the fluxes for two other values of c: a weak coupling and a medium coupling. The longitudinal and latitudinal profiles of the observed volcanic heat flux and the distribution of thermal sources¹² are shown in the subplots b and f with red and black solid lines. Subplot a shows the eastward shift for binned versions of the longitudinal profiles for different bin sizes. The bins are spaced such that the westernmost bin has its center at the prime meridian. The magnitude of the shift is taken as the longitudinal location of the highest bin on each hemisphere. The melt fraction pattern causing the plotted surface heat flux pattern is shown in Supplementary Fig. 2.