Potential Melting of Extrasolar Planets by Tidal Dissipation

Tidal heating on Io due to its finite eccentricity was predicted to drive surface volcanic activity, which was subsequently confirmed by the $\textit{Voyager}$ spacecrafts. Although the volcanic activity in Io is more complex, in theory volcanism can be driven by runaway melting in which the tidal heating increases as the mantle thickness decreases. We show that this runaway melting mechanism is generic for a composite planetary body with liquid core and solid mantle, provided that (i) the mantle rigidity, $\mu$, is comparable to the central pressure, i.e. $\mu/ (\rho g R_{\rm P})\gtrsim0.1$ for a body with density $\rho$, surface gravitational acceleration $g$, and radius $R_{\rm P}$, (ii) the surface is not molten, (iii) tides deposit sufficient energy, and (iv) the planet has nonzero eccentricity. We calculate the approximate liquid core radius as a function of $\mu/ (\rho g R_{\rm P})$, and find that more than $90\%$ of the core will melt due to this runaway for $\mu/ (\rho g R_{\rm P})\gtrsim1$. From all currently confirmed exoplanets, we find that the terrestrial planets in the L98-59 system are the most promising candidates for sustaining active volcanism. However, uncertainties regarding the quality factors and the details of tidal heating and cooling mechanisms prohibit definitive claims of volcanism on any of these planets. We generate synthetic transmission spectra of these planets assuming Venus-like atmospheric compositions with an additional 5, 50, and $98\%$ SO$_2$ component, which is a tracer of volcanic activity. We find a $\gtrsim 3 \sigma$ preference for a model with SO$_2$ with 5-10 transits with $\textit{JWST}$ for L98-59bcd.
Comment: 16 pages, 8 Figures, accepted for publication in ApJ