Bistability, Oscillations, and Multistability on Hycean Planets

TL;DR

This work addresses the climate dynamics of Hycean planets, where moist convective inhibition can create a multi-layer atmosphere that challenges conventional 1D models. The authors develop pen-and-paper theory for the onset and breakdown of inhibition and validate it with a 1D radiative-convective model, revealing regimes of bistability, oscillations, and multistability that depend on instellation, surface pressure, and water-vapor diffusivity. Key contributions include a thought-experiment-based transition framework around the Guillot threshold $T_c$, a grey-radiation regime diagram with thresholds $F_1$, $F_{3a}$, and $F_{3b}$, and a suite of 1D experiments that map where each regime occurs and how diffusivity through the inhibition layer drives multiple equilibria and hysteresis. The findings imply that Hycean climates can be far more dynamic and history-dependent than previously recognized, with significant implications for interpreting observations (e.g., K2-18b and JWST-derived atmospheric signatures) and for habitable-zone definitions, underscoring the need for self-consistent 1D and 3D modeling of these worlds.

Abstract

Hycean planets are hypothetical exoplanets characterized by $H_2O$ oceans and $H_2$-rich atmospheres. These planets are high-priority targets for biosignature searches, as they combine abundant surface liquid water with easy-to-characterize $H_2$-rich atmospheres. Perhaps their most unusual climate feature is convective inhibition, which can dramatically alter a planet's temperature structure. However, so far hycean planets have mostly been investigated using 1D models that do not account for convective inhibition, and its effects are still poorly understood. This work develops pen-and-paper theory to analyze the effects of moist convective inhibition on hycean planets. The theory is tested and verified against a 1D radiative-convective model. We show that hycean planets near the onset of convective inhibition can exhibit either bistability or oscillations, due to the inhibition layer's trapping of heat and moisture. Meanwhile, hot hycean planets exhibit multistability, in which the inhibition layer and surface climate show multiple stable equilibria due to the lack of constraints on the water cycle inside the inhibition layer. The water cycle inside the inhibition layer is influenced by numerous processes that are challenging to resolve in 1D, including turbulent diffusion, convective overshoot and large-scale circulations. Our results demonstrate that hycean planets have unexpectedly rich climate dynamics. Meanwhile, previous claims about hycean planets should be treated with caution until confirmed with more self-consistent 1D and 3D models; this includes the claim that K2-18b might be habitable, and the proposal to infer $H_2O$ oceans on sub-Neptunes from JWST measurements of chemical species in their upper atmospheres.

Figures (9)

• Figure 1: Hycean atmospheres become inhibited from the bottom-up; as the planet warms, the inhibition layer first forms right above the surface. Solid line shows the Guillot threshold temperature $T_c$. Dashed lines are moist adiabats with surface temperature equal to $300\,\mathrm{K}$, $325\,\mathrm{K}$, and $350\,\mathrm{K}$, from left to right, respectively. The intersection $T=T_c$ represents the approximate inhibition level, below which moist convection will be inhibited. The assumed parameters are $p_s=10\,\mathrm{bar}$, and $\mathrm{H_2O}$ convection in background air with $M_d=2.3\,\mathrm{g/mol}$.
• Figure 2: Schematic plots of convective and inhibited states and the transitions between them. (a) Atmospheric temperature profile with or without inhibition. Point A represents the air above the inhibition level; point B represents the inhibition layer. The transition at the inhibition level is approximated as a discontinuity, and the thickness of the inhibition layer is exaggerated. (b)-(d) The evolution of points A and B on the $T$-$T_v$ plot for $\mathrm{H_2O}$ in a background air with $M_d=2.3\,\mathrm{g/mol}$. The virtual temperature $T_v=\frac{TM_d}{\mu}$ ($\mu$ is the average molecular weight that depends on the vapor concentration) is proportional to $1/\rho$ when the pressure is fixed. In these plots, a parcel of air gets hotter going to the right and less dense going up. The two solid lines show $T_v$ under constant relative humidity (RH). The vertical dashed line shows the Guillot threshold temperature $T_c$, which is also the point at which a saturated air parcel reaches its lowest density (peak of the green curve). The horizontal line is a reference for comparing the virtual temperatures of A" and B". (b) The onset of inhibition by warming. (c) Pathway A: The inhibition breaks once the near-surface air becomes cooler than the Guillot threshold. This pathway is more likely when the upper atmosphere is dry. (d) Pathway B: The inhibition breaks once near-surface air becomes less dense than the air at the top of inversion layer. This pathway is more likely when the upper atmosphere is close to saturation, and is always preferred over Pathway A when assuming 100% relative humidity.
• Figure 3: Bistability or oscillations arise because there are three possible relationships between the OLR above which convection breaks down ($F_1$) versus the OLRs below which inhibition breaks down (Pathway A $F_{3a}$, Pathway B $F_{3b}$). If $\max(F_{3a}, F_{3b})<F_1$, both convective and inhibited states are stable, leading to bistability for intermediate values of the instellation $S$, namely $\max(F_{3a}, F_{3b}) < S < F_1$ (yellow shaded region in a,b). (a) When $F_{3b} < F_{3a} < F_1$, Pathway A is favored. Both edges of the bistable regime satisfy the condition that surface temperature equals the Guillot threshold, $T_s=T_c$, leading to a large bistable regime. (b) When $F_{3a} < F_{3b} < F_1$, Pathway B is favored. In this case inhibition can break even when the surface temperature is still higher than the Guillot threshold, leading to a smaller bistable regime. This scenario is more likely when the upper atmosphere is close to saturated. (c) When $F_{3a} < F_{1} < F_{3b}$, neither convective nor inhibited states are stable (represented by dotted lines), so the climate must oscillate between them.
• Figure 4: Regime diagram showing four distinct climate regimes, according to our semi-analytical model. The solid blue line represents the instellation above which an atmosphere enters an inhibited state, dashed lines represent the instellation below which an atmosphere becomes fully convective (green versus brown assumes the atmosphere above the inhibition layer follows a moist versus dry adiabat). Arrows indicate the direction of transition. In the lower left of parameter space, atmospheres are convective (blue), in the upper right they are inhibited (red); note, atmospheres in the inhibited regime additionally show multistability (see Section \ref{['sec:sim_rslt']}). Between the convective and the inhibited regimes, thicker atmospheres are bistable (light and dark yellow) and thinner atmospheres oscillate (light and dark green). All parameters used in the semi-analytical model are listed in Table \ref{['tab:Ana']}.
• Figure 5: Numerical simulations confirm hycean planets can occupy four different climate regimes. Here we show time series from typical cases in each regime. Dashed black lines show the Guillot threshold temperature $T_c$. Simulation parameters are: $K_{zz}=10^{-4}\,\mathrm{m^2/s}$; $p_s=2\,\mathrm{bar}$ (a-c) or $p_s=0.1\,\mathrm{bar}$ (d); $S=44\,\mathrm{W/m^2}$ (a), $S=58\,\mathrm{W/m^2}$ (b), $S=48\,\mathrm{W/m^2}$ (c), $S=189\,\mathrm{W/m^2}$ (d). Because the surface layer is always saturated in these cases, whether the atmosphere convective or inhibited is determined by whether the surface air temperature exceeds $T_c(p_s)$. (a): Both hot-start and cool-start initial conditions lead to a convective state. (b): Both initial conditions lead to an inhibited state. (c): Hot-start leads to an inhibited state, while cool-start leads to a convective state. (d): Both initial conditions lead to an oscillating state.