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

TL;DR

The study investigates how tidal heating and initial volatile inventories shape the formation and persistence of a secondary atmosphere on the rocky ultra-short-period planet 55 Cnc e. It extends magma-ocean evolution modeling to include $CO_2$ and couples it to an atmosphere–climate framework to track outgassing and greenhouse feedback. Without tides, an initial volatile mass fraction of $F_{\mathrm{H_2O}} = 5\ \mathrm{wt\%}$ or $F_{\mathrm{CO_2}} = 3\ \mathrm{wt\%}$ can sustain outgassing for roughly $10\ \mathrm{Myr}$; with $F_{\mathrm{H_2O}} = F_{\mathrm{CO_2}} = 10\ \mathrm{wt\%}$, greenhouse warming can extend up to $\sim 30\ \mathrm{Myr}$. Tidal heating lowers the volatile threshold needed to maintain a surface temperature of about $T_{\mathrm{surf}} \sim 3200\ \mathrm{K}$ at $e = 0.005$, but strong tides can enlarge the secondary atmosphere and delay outgassing of additional volatiles to the present day. The results indicate tides dominate the early-to-mid evolution and then shift to a volatile/inventory dependence at mature ages, providing a framework to prioritize atmosphere detections on USP magma-ocean planets by linking age, tides, and volatiles.

Abstract

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.

Figures (1)

• Figure 1: Left: Mass-radius diagram of 75 ultra-short period planets (USPs) below 10 $M_{\oplus}$ and 2 $R_{\oplus}$ with both measured and constrained mass and radius, including 55 Cnc e which is marked with a star symbol. A USP planet is defined as a planet with an orbital period $P_{\text{orb}}$ < 1 day. The planetary mass and radii data are taken from the NASA Exoplanet Archive. Bulk planetary density curves from zeng_growth_2019 are overlaid, showing 100% iron composition (dotted black), 100% rocky composition (dashed black), Earth-like rocky composition (dot-dashed black), 50% water vapor atmosphere with 50% rocky composition (solid black), 5% $\text{H}_2$ atmosphere with 95% rocky composition at 1000 K (dotted gray), and 5% $\text{H}_2$ atmosphere with 95% rocky composition at 2000 K (dashed gray). The insolation-only equilibrium temperature $T_{\text{eq}}$ of each planet in K is plotted on a color scale, which is on the same scale as the tidally-enhanced equilibrium temperature $T_{\text{eq}}$ on the right. Right: Tidal-insolation heat curve plot for planets included in our 75 USP dataset in which respective nominal tidal heating flux potentials were also calculated by mcintyre_s_r_n_tidally_2022. The predicted effective $T_{\text{eq}}$ of planets with a tidal heating contribution, from Eq. (\ref{['eqn:tidal_Teq']}) as $T_{\text{eq}}^{\text{tidal}}$, are shown on the same scale as the insolation-only equilibrium temperature. From this work, we evaluate the nominal value of tidal heating for 55 Cnc e as 8400 $\text{W m}^{-2}$, assuming the nominal eccentricity $e = 0.005$, and no atmosphere-derived greenhouse warming effect ($P_{\text{atm}} =0)$. Red and blue parameter spaces denote the effective equilibrium temperatures $T_{\text{eq}}$ that represent magma ocean worlds and water worlds respectively.