The Effect of Tidal Heating and Volatile Budgets on the Outgassed Atmosphere of 55 Cancri e

55 Cancri e is a $\sim$8 Gyr rocky world (1.95 $R_\oplus$, 8.8 $M_\oplus$) orbiting a K-type star. JWST observations suggest a carbon-dominated atmosphere (CO$_2$/CO) over a global magma ocean ($>$3000 K). We suggest that any CO$_2$-dominated atmosphere, with trace H$_2$O/O$2$, likely arises from outgassing of its initial volatile reservoir. As solidification drives the magma ocean and atmosphere away from solution-equilibrium, tidal and greenhouse heating can prolong outgassing. Early atmosphere outgassing reflects rapid degassing of the volatile-saturated melt during post-formation cooling. Without tidal heating, an initial 5 wt% water mass fraction ($F{\text{H}_2\text{O}}$) or 3 wt% $\text{CO}2$ mass fraction ($F{\text{CO}_2}$) can sustain outgassing for at least $\sim$10 Myr. With both at 10 wt%, greenhouse warming alone can prolong outgassing up to $\sim$30 Myr. Our model shows that tidal heating can reduce the volatile threshold required to maintain a high surface temperature ($\sim$3200 K at $e = 0.005$) and delay outgassing of additional volatiles to the present-day. However, higher tidal heating presents a tradeoff between prolonging tenuous outgassing and enlarging the overall size of the secondary atmosphere. Tidally-enhanced outgassing may produce minor pressure variations that could contribute to the observed phase-curve variability. Additionally, our model shows that tidal heating strongly controls outgassing in the planet’s young-to-midlife stage, then shifts toward a volatile inventory dependence at mature ages. Using 55 Cnc e, we present a framework to prioritize atmosphere detections on rocky ultra short period (USP) magma ocean planets, linking age-dependent tidal heating and volatile inventory to the formation and size of secondary atmospheres.

💡 Research Summary

The paper presents a comprehensive coupled model of interior evolution, atmospheric physics, and orbital dynamics to investigate how tidal heating and volatile inventories shape the outgassed secondary atmosphere of the ultra‑short‑period (USP) super‑Earth 55 Cancri e. The authors begin by summarizing the observational context: JWST NIRCam/MIRI data indicate a hot (dayside > 3000 K) magma‑ocean world with a carbon‑dominated atmosphere (CO/CO₂) and possible trace H₂O/O₂. The planet’s mass (8.8 M⊕) and radius (1.95 R⊕) imply a bulk density consistent with a rocky composition, while its 0.74‑day orbit around a K‑type star yields an insolation‑only equilibrium temperature of ~1400 K.

To assess the role of tidal dissipation, the authors adopt a nominal eccentricity e = 0.005, which produces a tidal heating flux of ~8400 W m⁻². This additional heat raises the effective equilibrium temperature to ~3200 K, sufficient to maintain a global magma ocean of peridotite melt (> 3000 K). The interior model is adapted from Schaefer et al. (2016) and tracks the cooling of the magma ocean, the partitioning of volatiles (H₂O, CO₂) between melt and atmosphere, and the rate of degassing as the melt solidifies.

The atmospheric component uses a gray‑radiator scheme to compute the outgoing long‑wave radiation (OLR) as a function of surface temperature, atmospheric optical depth, and composition. Optical depth is calculated from the mass of each species and their absorption coefficients (k₀,CO₂ = 0.001 m² kg⁻¹, k₀,H₂O = 0.01 m² kg⁻¹). The model also includes a simple energy‑limited XUV‑driven hydrodynamic escape formulation, with an XUV saturation fraction f₀ = 10⁻³, saturation time t_sat = 100 Myr, and decay exponent β_XUV = −1.23. Hydrogen produced by water photolysis is assumed to dominate the escape flow, dragging heavier species (CO₂, O₂) via cross‑over mass diffusion (Hunten et al. 1987).

A key result is the identification of volatile‑mass thresholds required to sustain outgassing for given heating scenarios. Without tidal heating, an initial water mass fraction of 5 wt % or a CO₂ mass fraction of 3 wt % can keep the atmosphere outgassing for ≳10 Myr. If both volatiles are present at 10 wt % each, greenhouse warming alone can extend outgassing to ~30 Myr. Introducing tidal heating dramatically lowers these thresholds: at e = 0.005, only ~2 wt % of each volatile is sufficient to maintain a high‑temperature surface and continuous outgassing for tens of Myr. However, higher tidal flux also enlarges the total atmospheric pressure, which can accelerate escape once the atmosphere becomes massive—a trade‑off between prolonging a tenuous outgassed envelope and inflating the secondary atmosphere to a point where loss rates increase.

Temporal analysis shows that tidal heating dominates the early (first few hundred Myr) evolution, controlling the rate at which melt‑derived gases are released. As the planet ages, the remaining volatile inventory becomes the primary determinant of atmospheric size and composition. This shift explains how 55 Cancri e could retain a CO/CO₂‑rich atmosphere today despite intense stellar XUV irradiation: the early tidal boost allowed a modest volatile reservoir to be released gradually, while later reduced tidal input limited further loss, preserving a thin but detectable carbon‑dominated envelope.

The authors also connect their findings to observed phase‑curve variability. Small pressure fluctuations (0.1–1 % of the total atmospheric pressure) induced by episodic outgassing events under tidal stress could modulate the infrared phase curve, offering a potential diagnostic for future JWST or ELT observations.

Finally, the paper proposes a framework for prioritizing atmospheric searches on USP magma‑ocean planets. Planets with strong tidal heating require lower volatile budgets to sustain observable atmospheres, making CO₂/CO detection more feasible. Conversely, planets with weak tidal dissipation need higher initial volatile contents, suggesting that water‑rich systems are better targets for detecting secondary atmospheres. By applying this framework to the known USP population, the authors identify a subset of candidates where JWST’s spectroscopic capabilities are most likely to reveal secondary atmospheres.

In summary, the study demonstrates that tidal heating is a critical, age‑dependent driver of volatile outgassing on ultra‑short‑period rocky worlds, and that the interplay between tidal energy input and the planet’s volatile inventory determines both the longevity and the observable characteristics of their secondary atmospheres. This work provides a quantitative tool for interpreting current observations of 55 Cancri e and for guiding future atmospheric characterizations of similar exoplanets.