Thermoelastic Contraction as a Suppressor of Atmospheric Escape in Close-in Exoplanets

TL;DR

This work addresses the mismatch between classical hydrodynamic escape predictions and the observed persistence of atmospheres in close-in exoplanets by introducing a fully classical, interior-driven mechanism: thermoelastic contraction of the mantle. By computing the volumetric strain $\epsilon_V$ from internal pressure and radial temperature gradients, the authors derive a corrected escape velocity $v_{esc}^*$ and a dimensionless suppression index $\Xi$ that quantify how interior elasticity raises the effective escape surface. Across a parametric grid, they show $\epsilon_V$ values of order $\sim 0.005$–$0.01$ can boost $v_{esc}^*$ by about $5$–$7\%$, producing mass-loss reductions exceeding $50\%$ in energy-limited regimes, and successfully explain atmospheres of planets like GJ $1214b$, K2-18b, and TOI-270c without invoking nonstandard stellar or chemical conditions. These results position planetary elasticity as a first-order control on atmospheric evolution and offer testable observational predictions for JWST and ARIEL, linking remote atmospheric measurements to deep interior thermomechanics.

Abstract

The long-term retention of substantial atmospheres in close-in exoplanets presents a major challenge to classical hydrodynamic escape theory, which predicts rapid mass loss under intense stellar irradiation. In this work, we propose a fully classical, interior-driven suppression mechanism based on thermoelastic contraction of the planetary mantle. By incorporating pressure- and temperature-dependent elastic deformation into the structural evolution of the planet, we demonstrate that radial contraction can lead to measurable increases in surface escape velocity. We analytically derive a modified escape condition and introduce a dimensionless suppression index Xi that quantifies the extent to which internal mechanical response inhibits atmospheric loss. Numerical simulations across a wide parameter space show that volumetric strain values in the range 0.005 to 0.01 can enhance escape velocities by up to 10 percent, leading to a reduction in energy-limited escape rates by over 50 percent. When applied to warm mini-Neptunes such as GJ 1214b, K2-18b, and TOI-270c, the model successfully accounts for their persistent atmospheres without invoking exotic stellar conditions or chemical outliers. Our results indicate that planetary elasticity, often neglected in escape models, plays a first-order role in shaping the atmospheric evolution of close-in worlds. The theory yields specific observational predictions, including suppressed outflow signatures and radius anomalies, which may be testable with JWST, ARIEL, and future spectroscopic missions.

Figures (4)

• Figure 1: Escape velocity enhancement as a function of thermoelastic volumetric strain. The normalized escape velocity $v_{\mathrm{esc}}^* / v_{\mathrm{esc}}$ increases monotonically with volumetric strain $\epsilon_V$, reflecting geometric contraction of the escape surface. Even modest strain ($\sim 1\%$) leads to measurable enhancement, validating the analytic expression $\left(1 / (1 - \epsilon_V)\right)^{1/6}$.
• Figure 2: Sensitivity of Escape Suppression to Mantle Anisotropy. The plot shows the suppression index $\Xi$ as a function of the anisotropy factor $\zeta$, defined as the ratio of shear moduli along different directions. For $\zeta = 1$, the mantle is isotropic, and $\Xi$ attains its reference value of 1.15 as obtained from the elastic model. As $\zeta$ increases, representing enhanced directional stiffness contrasts, the effective thermoelastic contraction becomes spatially fragmented, thereby reducing the net increase in escape velocity. The model assumes that anisotropic strain reduces suppression according to $\Xi(\zeta) = \Xi_\text{iso} \cdot \left(1 - \eta \left(1 - \zeta^{-2} \right) \right)$, where $\eta = 0.3$ captures the efficiency loss due to internal directional bias. This parametric visualization supports the interpretation that isotropy maximizes contraction coherence, while strong anisotropy may diminish the escape-inhibiting effect.
• Figure 3: Normalized escape velocity $v_{\mathrm{esc}}^{*} / v_{\mathrm{esc}}$ as a function of volumetric strain $\epsilon_V$ for a representative super-Earth with $M = 5~M_{\oplus}$, $R = 1.8~R_{\oplus}$. Even small thermoelastic strains produce non-negligible enhancements in escape velocity.
• Figure 4: Suppression index $\Xi$ as a function of mantle thermal gradient $\Delta T$ and bulk modulus $K$. Regions with $\Xi > 1.1$ (light-shaded) correspond to $>10\%$ enhancements in escape velocity, indicating strong thermoelastic suppression of atmospheric loss.