The Persistent Thermal Anomalies in Rocky Worlds

TL;DR

This work investigates puzzling thermal emission excesses in rocky exoplanets, particularly M-Earths, to determine whether internal heating (residual, tidal, induction) can account for dayside temperatures that exceed the irradiation-only limit $T_{\rm day,max}$. It assembles emission data, defines $\mathcal{R} = T_{\rm day} / T_{\rm day,max}$, analyzes a large rocky-planet sample, and applies three internal-heating models via CMAPPER and fixed-$\mathcal{Q}$ tidal theory to compute $\Delta\mathcal{R}$, culminating in a combined metric $\Delta\mathcal{R}_{\rm total}$. The main finding is that internal processes generally fail to produce significant thermal excess or the observed positive $\mathcal{R}$ trend with irradiation, implying that stellar contamination or surface/atmospheric effects are more plausible explanations. The results guide future observations, including the Roman Space Telescope, which will vastly expand the sample of rocky exoplanets and refine constraints on their thermal emissions and interior evolution.

Abstract

Observing the dayside thermal emissions of rocky exoplanets provides essential insights into their compositions and the presence of atmospheres. Even though no conclusive evidence has been found for atmospheres on small rocky exoplanets orbiting M dwarfs, recent JWST observations identified puzzling thermal emission excesses: some rocky exoplanets orbiting M dwarfs have dayside emission temperatures higher than the theoretical maximum. Theoretical maximum temperatures assume stellar irradiation as the sole energy source, implying that these planets may have internal heat sources. In this work, we simulate three possible planetary internal processes that may generate excessive heat in addition to stellar irradiation: residual heating from formation, tidal heating, and induction heating due to interactions with the stellar magnetic field. We found that these mechanisms, even when combined, cannot explain the observed thermal emission excesses, nor can they explain a tentative positive trend in the brightness temperature scaling factor as a function of irradiation temperature. Our results imply that planetary internal processes are unlikely to generate remotely detectable heat, so the observed thermal excesses, if astrophysical, are likely caused by stellar contamination, surface processes, or other internal processes not considered in this study. The ongoing JWST-HST Rocky Worlds Director's Discretionary Time Program and the upcoming Nancy Grace Roman Space Telescope will provide more insights into the thermal emission of rocky exoplanets.

Figures (11)

• Figure 1: Mass-radius plot for exoplanets studied in this work. Rocky ($p_{\rm rocky}\geq32\%$) planets are shown in black, while non-rocky planets are shown in gray. Observed rocky exoplanets (Table \ref{['tab:obs_planets_data']}) are highlighted in red. Constant composition curves calculated using zeng_massradius_2016 rock (MgSiO$_3$) and iron equations of state, as well as the AQUA water equation of state haldemann_aqua_2020, are plotted for comparison.
• Figure 2: (a) Irradiation temperature $T_{\rm irr}$ and (b) ratio of $T_{\rm irr}$ to the maximum irradiation limited by the Roche distance, $T_{\rm irr}/T_{\rm irr,\,Roche}$, as functions of stellar effective temperature. In (a), two different $T_{\rm irr,\,Roche}$ limits assuming Earth-like (red) and super-Earth (green) compositions are shown. Temperatures at which silicates begin to melt (850 K) and are fully molten (1473 K) are shown for comparison lutgens_essentials_2015. In (b), Mercury is shown as a red triangle for reference, and exoplanets closest to Roche limits are annotated. Planets near the Roche limit are ideal targets for the search for thermal emission excesses.
• Figure 3: Dayside temperature scaling factor, $\mathcal{R}=T_{\rm day}/T_{\rm day,max}$, as a function of irradiation temperature, $T_{\rm irr}$, for (a) all observed rocky exoplanets and (b) planets with $T_{\rm irr}>1500$ K, which may have rock vapor atmospheres. Observed exoplanets (Table \ref{['tab:obs_planets_data']}), excluding LHS 1478 b, are shown as black error bars. Two fits are shown: (cyan) linear fit for M-Earths shows a positive trend, while (blue) BPL fit shows a positive trend for M-Earths with $T_{\rm irr}<T_b=1790$ K and a negative trend for five extremely hot planets with $T_{\rm irr}>T_b$. Both fits are better than the null hypothesis (red line in panel a), suggesting an underlying physical mechanism that produces both thermal emission excess and deficit. In (a), the melting temperatures of silicates (orange and magenta vertical lines) are annotated. In (b), $\mathcal{R}$ of exoplanets with rock vapor atmospheres derived from a scaling relation koll_scaling_2022 are shown in red, green, and orange for surface Bond albedo of 0, 0.3, and 0.5, respectively. Thick atmospheres with $P_s$ much greater than the equilibrium pressure $P_{\rm eq}$ are required to explain the observed thermal deficit.
• Figure 4: (a) Atmospheric loss timescale $\tau_{\rm loss}$ as a function of $T_{\rm irr}$ for rocky exoplanets. Planets simulated with CMAPPER are highlighted in orange. (b) Residual thermal excess $\Delta\mathcal{R}_{\rm residual}$ due to surface heat flux after total atmospheric loss as a function of $T_{\rm irr}$, at four stages in the planet's evolutionary history: (red) 0.01 Myr after atmospheric loss, (blue) 0.1 Myr, (green) 1 Myr, and (purple) 10 Myr. Note that $\Delta\mathcal{R}_{\rm residual}$ is negatively correlated with $T_{\rm irr}$, as opposed to the positive trend observed in Figure \ref{['fig:tirr_vs_r_fits']}. (c) The time at which $\Delta\mathcal{R}_{\rm residual}=0.1$, considering (orange) only surface cooling and (brown) atmospheric loss plus surface cooling.
• Figure 5: Upper limit on tidal heat flux, $F_{\rm tidal}$, as a function of irradiation temperature, $T_{\rm irr}$, assuming Earth-like tidal ${\rm Im}(k_2)$. Rocky exoplanets ($p_{\rm rocky}\geq32\%$) are color-coded by their eccentricities, while non-rocky exoplanets are shown in gray. Observed rocky exoplanets (Table \ref{['tab:obs_planets_data']}) are highlighted with red edges. Planets with $F_{\rm tidal}$ greater than the irradiation of GJ 3929 b ($17.3\times S_\oplus$) are annotated. $F_{\rm tidal}$ are shown as upper limits for clarity because many exoplanets have $e$ within error with, or very close to, zero.