Estimation of the tidal heating in the TRAPPIST-1 planets. Influence of the internal structure

TL;DR

The paper addresses how tidal heating shapes the heat budgets of the TRAPPIST-1 rocky planets and how this heating depends on uncertain interior structures. It develops a BurnerMan-based layered interior model combined with an Andrade viscoelastic rheology to compute the frequency-dependent Love number $k_2$ and the volumetric heating $h_{ m tide}$, deriving total tidal power for synchronous, low-obliquity cases across a range of core sizes and surface temperatures. The results indicate that TRAPPIST-1b and c can exhibit tidal flux comparable to or exceeding Io, while d and e likely experience dominant tidal heating; f, g, and h show much smaller contributions, with uncertainties largely driven by eccentricity and interior structure degeneracy. The study also proposes a scalable method to obtain heating profiles for generic rotation and eccentricity states by constraining the global tidal flux with observational limits, outlining a path toward self-consistent evolution models that couple interior heat, melting, and orbital dynamics. These findings have implications for interpreting JWST observations, exploring planetary habitability, and guiding future interior-evolution modeling of tidally active rocky exoplanets.

Abstract

With the arrival of JWST observations of the TRAPPIST-1 planets, it is timely to reassess the contribution of tidal heating to their heat budget. JWST thermal phase curves could reveal endogenic heating through an anomalously high nightside temperature, providing an opportunity to estimate tidal heating. In this study, we revisit the tidal heating of these planets and propose a simple method to compute the tidal heating profile across a broad range of parameters. Our approach leverages a known formulation for synchronously rotating planets on low-eccentricity orbits and the fact that the profile shape depends solely on internal structure. We calculate the tidal heating contributions for all T-1 planets, with a particular focus on the impact of internal structure and eccentricity uncertainties on their total heat budget. Although the masses and radii of these planets are well constrained, degeneracies remain in their internal structure and composition. For volatile-poor planets of silicate-rock compositions, we investigate the role of core iron content by exploring a range of core sizes. For each structure, we compute the degree-two gravitational Love number, $k_2$, and the corresponding tidal heating profiles. We assume sub-solidus temperatures profiles that are decoupled from interior heat production, which means our estimates are conservative and likely represent minimum values. We find that the tidal heat flux for T-1b and c can exceed Io's heat flux, with uncertainties primarily driven by eccentricity. These high fluxes may be detectable with JWST. For T-1f to g, the tidal flux remains below Earth's geothermal flux, suggesting that tidal heating is unlikely to be the dominant energy source. For planets d and e, however, tidal heating likely dominates their heat budget, potentially driving intense volcanic and tectonic activity, which could enhance their habitability prospects.

Figures (6)

• Figure 1: Density, shear modulus, viscosity and temperature profiles of TRAPPIST-1b computed with the BurnMan code for different compositions (listed in Table \ref{['tab:table1']}). Top panel shows the influence of the temperature on the profile. Bottom panel shows the influence of the composition on the profile. The black curve shows the same composition in all panels (Earth-like composition and a surface temperature of 800 K). The gray curve in the top panels shows the curve corresponding to the reference temperature (here 670 K). The right most panels also show the temperature of the solidus (red dashed line).
• Figure 2: Frequency dependence of the imaginary part of the Love number for T-1b, for different compositions and temperatures (listed in Table \ref{['tab:table1']}). Top panel shows the influence of the temperature. Bottom panel shows the influence of the composition. The black curve shows the same composition in both panels (Earth-like composition and a surface temperature of 300 K). The gray curve in the top panels shows the curve corresponding to the reference temperature (here 670 K). The excitation frequency of T-1b is shown as the vertical black dashed line, it corresponds to its orbital frequency. The shaded region illustrate the dependence of the imaginary part on $\alpha$ (bracketed between 0.20 and 0.30). At the frequency of the planet, the dissipation for $\alpha=0.20$ is higher than for $\alpha=0.30$.
• Figure 3: Volumetric tidal heating profile for T1-b for different surface temperatures (and thus viscosity profiles): a) 300 K, b) 600 K, c) 670 K, d) 800 K. The different colors represent the different structures listed in Table \ref{['tab:table1']}. The areas delimited by the full/dashed lines correspond to the minimum/maximum eccentricities given in Table \ref{['tab:table2']}. The extent of the areas represents the sensitivity of the profile to $\alpha$, with the lower (left) limit corresponding to $\alpha=0.30$ and the upper (right) limit corresponding to $\alpha=0.20$. These profiles were obtained with Eq. \ref{['htide']}. The tidal heating profile of the Earth is shown in a dashed black line as in 2020AA...644A.165B. Additionally, we represent areas delimited by faint dotted lines. These profiles are compatible with JWST observational constraints on the nightside temperature of the T1-b (291 K at 2$\sigma$, 322 K at 3$\sigma$ from 2025arXiv250902128G), which are here hypothesized to be equal to a tidal temperature. The lower left limit thus corresponds to 291 K, and the upper right to 322 K.
• Figure 4: Total heat flux for all planets. Left panel: calculated for a surface temperature of 300 K (or a high viscosity). The transparency of the colored areas represents the dependency on $\alpha$, with the more transparent (lower values of tidal heating) corresponding to $\alpha=0.30$. Right panel: calculated for an $\alpha=0.25$. The lighter shaded region (lower values of tidal heating) corresponds to a surface temperature of 300 K (high viscosities). The darker shaded region (higher values of tidal heating) corresponds to a surface temperature of 800 K (low viscosities). The hatched region corresponds to the reference temperatures (670 K for b and c, 650 K for d, 300 K for e, 250 K for f, 210 K for g and 170 K for h). The colored area delimited by triangles represents the uncertainty we have on the internal structure, for a given assumption of the eccentricity (blue: minimum eccentricity, green: maximum eccentricity). These values are compared to the tidal heat flux of Io (full red triangle), Earth's heat flux (full black triangle), and the Earth's tidal heat flux (black triangle). The Top Of the Atmosphere (TOA) fluxes coming from 2020AA...640A.112D are shown as full black circles. Finally, we show as red squares recent observational constraints from the JWST 2025arXiv250902128G for the maximum nightside temperature of T1-b which we assume is a tidal temperature (see Section \ref{['generic']}).
• Figure 5: Profiles of density, temperature and pressure of the TRAPPIST-1 planets computed with the BurnMan code, assuming an Earth-like composition for the core and mantle. The solidus is shown in dashed lines.