Convective inhibition with an ocean

Abstract

Aims. In this work we generalize the notion of convective inhibition to apply it to cases where there is an infinite reservoir of condensible species (i.e., an ocean). We propose a new model for the internal structure and thermal evolution of super-Earths with hydrogen envelopes. Methods. We derive the criterion for convective inhibition in a generalized phase mixture from first principles thermodynamics. We then investigate the global ocean case using a water-hydrogen system, for which we have data, as an example. After illustrating the relevant thermodynamics, we extend our arguments to apply to a system of hydrogen and silicate vapor. We then employ a simple atmospheric model to apply our findings to super-Earths and to make predictions about their internal structures and thermal evolution. Results. For hydrogen envelope masses roughly in the range 10 −3 − 10 −1 M ⊕ , convective contact between the envelope and core may shut down because of the compositional gradient that arises from silicate partial vaporization. For envelope hydrogen masses that cause the associated basal pressure to exceed the critical pressure of pure silicate (on the order of a couple kilobars), the base of that envelope and the top of the core lie on the critical line of the two-phase hydrogen-silicate phase diagram. The corresponding temperature is much higher than convective models would suggest. The core is then "supercritical" in the sense that the temperature exceeds the critical temperature for pure silicate. The core then cools inefficiently, with intrinsic heat fluxes potentially comparable to the Earth's internal heat flux today. Conclusions. This low heat flux may allow the core to remain in a high entropy supercritical state for billions of years, but the details of this depend on the nature of the two-component phase diagram at high pressure, something that is currently unknown. A supercritical core thermodynamically permits the dissolution of large quantities of hydrogen into the core.

Creating the Radius Gap without Mass Loss

“…Corepowered envelope mass loss can also naturally give rise to mass loss over Gyr timescale. However, the ability of the cores to cool down fast enough has recently been called into question (e.g., Markham et al 2022), and so we focus on the effect of photoevaporation.…”

The Runaway Greenhouse Effect on Hycean Worlds

“…Neglecting this effect results in an underestimation of the deep atmospheric temperature in gas giant planets (Leconte et al 2017). Recent studies have investigated convective inhibition due to condensing silicates in an H 2 -He envelope, which alters the radius and cooling times of young super-Earths and sub-Neptunes (Markham et al 2022;Misener & Schlichting 2022).…”

“…For example, how efficient is thermal conduction at transporting flux deposited in the lower atmosphere? We can compare the efficiency of thermal conduction to radiation by comparing the thermal diffusion coefficient for conduction and radiation, as in Markham et al (2022). For an ideal gas, the thermal diffusivity of conduction is:…”

“…Our models represent a "cold start," i.e., warming a planet up that initially starts with a surface water ocean. However, realistically a sub-Neptune will form hot and cool down from a state where the water is supercritical (Markham et al 2022;Misener & Schlichting 2022). Most rocky planets greater than Martian-to-Earth sized will host a magma ocean in their early history (Lichtenberg et al 2022).…”

Modeling Noncondensing Compositional Convection for Applications to Super-Earth and Sub-Neptune Atmospheres

“…Convection parameterizations for exoplanet atmospheres are challenged by the greater diversity of exoplanet atmospheric compositions compared to Earth. For many sub-Neptune and super-Earth atmospheres, the effects of vertically inhomogeneous atmospheric trace gases on convection are important (Guillot 1995;Li & Ingersoll 2015;Leconte et al 2017;Markham et al 2022). Compositional convection is a convective process in which buoyancy is significantly influenced by the compositional gradient of atmospheric tracers.…”