Impact of Subsurface Temperature Gradients on Emission Spectra of Airless Exoplanets: the Solid-state Greenhouse and Anti-Greenhouse

TL;DR

This work demonstrates that subsurface temperature gradients in airless exoplanet regoliths can create solid-state greenhouse or anti-greenhouse effects, substantially altering thermal emission and secondary eclipse signals. By deriving analytic two-stream radiative-transfer solutions and coupling them with Mie theory for mineral-specific optical depths, the authors show that gradients up to around 200 K can exist in the upper subsurface (order of 100 μm) and modify JWST-accessible spectra by up to ~50%. The study finds material-dependent behavior (basalt/granite favor greenhouse; hematite favors anti-greenhouse) and identifies degeneracies with space weathering and particle-size variations that can obscure surface composition in JWST data. These results emphasize the necessity of including subsurface regolith physics in exoplanet spectral modeling and suggest targeted observations and laboratory experiments to constrain regolith conductivity and microphysics, with testable predictions such as hematite-induced super-blackbody emission beyond ~10 μm on TRAPPIST-1b-like planets.

Abstract

An emerging goal of exoplanet science is to constrain the surface composition of airless exoplanets. Without the protection of an atmosphere, these planets are likely covered by a powder-like regolith, similar to the Moon. Laboratory studies show that, under vacuum conditions, such regoliths can develop subsurface temperature gradients, also known as the solid-state greenhouse effect. This effect can significantly modify the emission features of airless bodies, but its potential impact on exoplanets is still unexplored. Here we derive analytic solutions of the two-stream radiative transfer equations with scattering, absorption, plus emission, and combine them with Mie theory calculations to model subsurface temperature gradients and emission spectra of airless exoplanets. The results show exo-regoliths can develop strong solid-state greenhouse or anti-greenhouse effects, with temperature gradients $>200$~K in the upper-most subsurface ($\mathcal{O}(100)μ$m). These temperature gradients alter surface emission features, modify secondary eclipse depths by up to $\sim50\%$, and can produce higher-than-blackbody emission at some wavelengths. In addition, we study whether subsurface temperature gradients can be disentangled from other microscopic effects, such as changes in space weathering or particle size. At least in some cases, the co-existence of these effects makes it essentially impossible to distinguish different surface compositions within the precisions achievable by JWST. Overall, subsurface temperature gradients thus open potentially new ways to characterize surfaces of airless exoplanets, but they also complicate the interpretation of airless exoplanet spectra. In either case, their effect can be important and should be included in future modeling studies.

Figures (4)

• Figure 1: The solid-state greenhouse versus anti-greenhouse is primarily controlled by the relative extinction depth of radiation at short versus long wavelengths, $d_s\mu_0$ versus $d_l\overline{\mu}$. Insets show idealized semi-grey spectra of single-scattering albedo (SSA) and extinction depth ($d$). Left: A strong solid-state greenhouse develops for $d_s\mu_0> d_l\overline{\mu}$. Middle: Intermediate states with $d_s\mu_0 \approx d_l\overline{\mu}$. In this case temperature gradients are primarily governed by the wavelength-dependent single-scattering albedo. Right: A strong solid-state anti-greenhouse develops for $d_s\mu_0<d_l\overline{\mu}$. Here, subscripts 's' and 'l' denote properties shortward and longward of 2$\mu$m. All profiles assume an instellation equal to that of TRAPPIST-1b's substellar point.
• Figure 2: Variations in subsurface temperature gradients can modify the emission spectra of airless exoplanets by up to $\sim50\%$ at JWST wavelengths. Basalt and granite exhibit a strong solid-state greenhouse, whereas hematite exhibits a strong strong solid-state anti-greenhouse. Top row: For each material, spectra of skin depth (colored) and single-scattering albedo (grey). Middle and Bottom rows: Secondary eclipse spectra for TRAPPIST-1b and LHS 3844b. Insets shows the corresponding temperature profiles at the substellar point, for different thermal conductivity $k$. For reference, black points show Spitzer and JWST observations of TRAPPIST-1b and LHS 3844b.
• Figure 3: Grain-scale variations via space weathering and particle size changes can modify secondary eclipse spectra as strongly as large changes in subsurface temperature gradients. Top rows: Simulations with variations in space weathering, thermal conductivity, or diameter changes compared to default simulations. Grey shows the possible range in eclipse spectra due to two co-varying effects (see Appendix \ref{['appendix A']}). Bottom rows: We take the spectra from top and subtract best-fit grey blackbodies, to isolate the induced spectral effect of different grain-scale variations. Black errorbars show a photon-noise estimate for possible 1$\sigma$ JWST precision at 15$\mu$m for one eclipse of LHS 3844b.
• Figure 4: Left: If grain-scale effects are held fixed, JWST can relatively easily distinguish between different surface compositions. Shown are secondary eclipse spectra of LHS 3844 for the three materials in Fig. \ref{['Compare']} with default grain-scale conditions. Right: Allowing for co-variations in grain-scale effects can make it impossible to distinguish different surface compositions. Shown simulations were hand-picked to yield spectra that are effectively identical. Black dots are hypothetical JWST observations, based on a grey body model with 0.1 albedo. Error bars show $1\sigma$ photon noise estimate for one eclipse of LHS 3844b with 1$\mu m$ bin size.