Not Earth-like Yet Temperate? More Generic Climate Feedback Configurations Still Allow Temperate Climates in Habitable Zone Exo-Earth Candidates

TL;DR

To assess whether temperate climates in the habitable zone can arise under non-Earth-like feedback configurations, the paper develops a minimal four-feedback climate model and analyzes 20k+ simulations under fixed-luminosity and stellar-evolution scenarios. The fourth feedback can yield runaway and chaotic regimes, and its sign strongly modulates long-term temperate habitability: negative or weak fourth feedbacks preserve temperate climates, while strong positive ones shrink the habitable fraction and shift HZ boundaries. Stellar evolution further broadens climate diversity, enabling transitions and chaotic trajectories that can intermittently sustain temperate conditions. The results imply that Earth-like temperate climates may be rarer than classical HZ estimates and have implications for exoplanet survey design and interpretation, while serving as a dynamical framework for interpreting a broader range of Earth-like exoplanet climates.

Abstract

Earth's climate is influenced by over a dozen feedbacks, but only three dominate its long-term climate behavior. Models of the exoplanet habitable zone (HZ) assume that this is similar for other Earth-like planets. We used dynamical simulations to study Earth-like planets with a fourth, (potentially strong) generalized climate feedback. Across over 20,000 climate simulations, we find that the addition of the fourth feedback produces novel behaviors, including runaway and chaotic climate trajectories, that are more diverse than one would expect based on Earth's climate configuration. Non-negligible fourth feedbacks -- if negative -- would not lessen the probability of planets with temperate climates. However, positive fourth feedbacks decrease the fraction of exo-Earth candidates that are long-term habitable. Therefore, strong fourth feedbacks will alter (and mostly shrink) the boundaries of the classical habitable zone. When combined with occurrence rates of Earth-sized planets around sun-like stars, our results imply that the fraction of stars hosting rocky planets with temperate climates may be substantially lower than classical estimates under Earth-like climate assumptions. Our results are subject to the validity of the model assumptions and not intended to represent conclusive predictions about exoplanet populations but rather to demonstrate the potential climate diversity that emerges from non-Earth-like model configurations. Our conclusions provide context on sample sizes and science questions for next-generation exoplanet surveys.

Figures (9)

• Figure 1: Strength of key long-term feedbacks governing Earth's climate system Forster20212020RSPSA.47600303A2016ApJ...827..117A2018PNAS..11510293K. Each bar represents the feedback parameter in W m$^{-2}$ K$^{-1}$, estimated from Earth system model assessments and paleoclimate constraints. The upper axis shows the approximate feedback strength associated with a 50 K climate perturbation, representative of transitions between major states (e.g., snowball to temperate). Feedbacks are sorted by magnitude. Negative values (blue) represent stabilizing feedbacks that damp temperature changes, while positive values (orange) indicate destabilizing feedbacks that amplify them. Outgoing longwave radiation and the carbonate–silicate cycle are among the strongest stabilizing processes, while the ice–albedo feedback exerts a strong destabilizing influence. Models incorporating the three dominant feedbacks explain the general behavior of Earth's long-term mean climate.
• Figure 2: Dynamics of the planetary climate system with coupled ice-albedo and carbonate-silicate feedback mechanisms without a fourth feedback, consistent with 2020RSPSA.47600303A. Left: Feedback configuration showing the relationship between equilibrium temperature (K) and the timescale (years) for the three canonical feedbacks. Middle: T (green solid) and pCO$_2$ (purple dashed) time series. Right: Phase plane illustrating the trajectory of the system (black) in the T-pCO$_2$ phase space. The blue curve represents the temperature nullcline, while the red curve corresponds to the pCO$_2$ nullcline. The intersection of these nullclines denotes potential steady states, but with this particular configuration of $S = 1000$ W/m$^{2}$ and $V = 10 W_0$ we observe a limit cycle.
• Figure 3: Representative examples of climate trajectory behaviors in a four-feedback Earth-like model, consistent with possible states of Earth but excluding the role of stellar evolution. Each row shows a different behavior: Out-of-Bounds, Fixed Point, Limit Cycle, and Non-Periodic/Chaotic. Left column: Feedback timescales and effective temperatures, with the fourth feedback shown in purple. Middle columns: Time evolution of temperature (blue) and pCO$_2$ (red, log scale) with zoomed-in series insets. Right column: Phase space plots of pCO$_2$ vs. temperature. Out-of-bounds runs leave the temperate regime before the end of the simulation; fixed points collapse to a single state; limit cycles trace loops; non-periodic/chaotic states show irregular structure.
• Figure 4: Climate behaviors emerge in distinct regions of planetary parameter space from a generalized Earth-motivated climate model that excludes stellar evolution. Each point represents the outcome of a single climate simulation sampled across stellar flux ($S$), fourth-feedback strength ($c$), and the feedback’s equilibrium temperature ($T_f$). Colors and marker shapes denote long-term climate behaviors, including warm and snowball fixed points, limit cycles, non-periodic/chaotic states, transient chaos, and out-of-bounds trajectories. The diagonal panels show the one-dimensional distributions of outcomes along each parameter, while the off-diagonal panels display pairwise projections of the sampled parameter space. Earth’s present-day parameters are shown for reference. Dynamical behaviors cluster cleanly within the parameter space, highlighting the substantial diversity of climate states produced by the four-feedback configuration.
• Figure 5: Representative examples of climate trajectory behaviors in a four-feedback Earth-like model under increasing stellar luminosity. Each row shows a different behavior: Snowball$\rightarrow$Warm transition, Warm$\rightarrow$Snowball transition, Transient Chaos, and Non-Periodic/Chaotic. Left column: Feedback timescales and equilibrium temperatures, with the fourth feedback shown in purple. Middle columns: Time evolution of temperature (blue) and pCO$_2$ (red, log scale) over the stellar evolution window, with insets highlighting oscillatory structure where present. Right column: Phase space plots of pCO$_2$ vs. temperature, colored by time. Snowball$\rightarrow$Warm runs cross from glaciated to temperate states; Warm$\rightarrow$Snowball runs collapse into permanent glaciation; transiently chaotic runs exhibit irregular excursions before settling; non-periodic/chaotic runs maintain sustained irregular variability.