The Equation of State of MH-III: A Possible Deep CH₄ Reservoir in Titan, Super-Titan Exoplanets, and Moons

Abstract

We investigate the thermal equation of state, bulk modulus, thermal expansion coefficient, and heat capacity of MH-III (CH 4 filled-ice Ih), needed for the study of CH 4 transport and outgassing for the case of Titan and super-Titans. We employ density functional theory and ab initio molecular dynamics simulations in the generalized-gradient approximation with a van der Waals functional. We examine the finite temperature range of 300 K-500 K and pressures between 2 GPa-7 GPa. We find that in this P-T range MH-III is less dense than liquid water.There is uncertainty in the normalized moment of inertia (MOI) of Titan; it is estimated to be in the range of 0.33 − 0.34. If Titan's MOI is 0.34, MH-III is not stable at present in Titan's interior, yielding an easier path for the outgassing of CH 4 . However, for an MOI of 0.33, MH-III is thermodynamically stable at the bottom of a ice-rock internal layer capable of storing CH 4 . For rock mass fractions 0.2 upwelling melt is likely hot enough to dissociate MH-III along its path. For super-Titans considering a mixture of MH-III and ice VII, melt is always positively buoyant if the H 2 O:CH 4 mole fraction is > 5.5. Our thermal evolution model shows that MH-III may be present today in Titan's core, confined to a thin (≈ 10 km) outer shell. We find that the heat capacity of MH-III is higher than measured values for pure water-ice, larger than heat capacity often adopted for ice-rock mixtures with implications for internal heating.

A High-pressure Filled Ice in the H2O–CO2–CH4 System, with Possible Consequences for the CO2–CH4 Biosignature Pair

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New Perspectives on the Exoplanet Radius Gap from a Mathematica Tool and Visualized Water Equation of State

“…On one hand, in order to gain a clear understanding of the physics and chemistry on the surfaces and in the deep interiors of those water worlds (Levi et al 2014(Levi et al , 2016(Levi et al , 2017Levi & Cohen 2018;Levi & Sasselov 2018;Ramirez & Levi 2018;Yang et al 2018;Mazevet et al 2019;Haldemann et al 2020;Mousis et al 2020), one needs to delve into the details of the EOSs of the cosmic ices (H 2 O, NH 3 , CH 4 , etc.) and their mixtures, in their full temperature-density-entropy-pressure parameter space, from the low-density gaseous state to the high-density condensed and compressed states, which include the fluid state and the solid state.…”

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