Potential long-term habitable conditions on planets with primordial H-He atmospheres

The study explores whether rocky and super-Earth exoplanets that retain primordial hydrogen–helium (H–He) envelopes can host long-lasting surface liquid water. While classical habitability focuses on Earth-like atmospheres with greenhouse gases such as CO2 and CH4, sufficiently massive H2-rich atmospheres can warm planetary surfaces via collision-induced absorption. Prior work established static conditions under which liquid water could exist under such envelopes, but the duration and stability of these conditions considering stellar evolution and atmospheric escape remained unclear. The research question is how long planets with primordial H–He atmospheres can maintain pressure–temperature conditions permitting liquid water, across a range of core masses, envelope masses, orbital distances, and including atmospheric escape. This has importance for broadening the concept of habitability beyond the classical habitable zone and considering alternative biospheres under high-pressure, low-light conditions.

The paper situates itself within findings that super-Earths are common and may retain primordial H–He envelopes beyond several AU, where stellar irradiation is insufficient to strip them. Hydrogen collision-induced absorption can provide strong greenhouse warming at high pressures, potentially enabling liquid water even far beyond the traditional habitable zone and for unbound planets (Stevenson 1999; Pierrehumbert & Gaidos 2011). Recent work on Hycean worlds (Madhusudhan et al. 2021) suggested broad parameter spaces for liquid water beneath H–He atmospheres. However, prior studies largely examined static or equilibrium states and did not quantify the longevity of liquid water phases, nor fully incorporate atmospheric escape processes, which can be critical for close-in, low-mass planets. The authors also reference exoplanet demographics, showing super-Earths are prevalent, and planet formation models suggesting envelopes can be retained at large separations, with additional processes (e.g., core-powered mass loss, collisions) modulating envelope masses.

The authors compute time-dependent thermal and structural evolution for planets with rocky/iron cores plus H–He envelopes, spanning core masses ~1–10 M⊕, envelope masses 10−6–10−1 M⊕, and semi-major axes 1–100 AU, with an additional unbound case (effectively 105 AU). For a given core mass they run 1,144 models over 8 Gyr using a Sun-like stellar luminosity evolution. Key components: 1) Interior/envelope structure: a 1D spherically symmetric hydrostatic model solving standard structure equations for mass, pressure, luminosity, and temperature profiles. Energy transport switches between radiative and convective gradients via the Schwarzschild criterion. At low optical depth, a double-grey atmosphere with greenhouse parameter γ (ratio of infrared to optical opacity) is used, transitioning to diffusive radiative transport at higher optical depths. Opacities are Rosseland mean, grain-free, from literature tables including collision-induced absorption, extrapolated at low temperatures as needed; EOS is non-ideal for H–He; water uses AQUA EOS. 2) Core: a solid silicate–iron core (2:1 ratio) without ices in the nominal setup, modeled via a modified polytropic EOS. External pressure from the envelope is included. 3) Intrinsic luminosity: initial intrinsic luminosity shortly after formation (starting age 20 Myr) is set via an analytical fit to formation models; long-term luminosity includes radiogenic heating from 40K, 232Th, 238U scaled with mantle mass (assumed 2/3 of core mass). The total intrinsic luminosity evolves by energy conservation, with radiogenics dominating at late times; sensitivity to ±10× radiogenic power is explored. 4) Boundary conditions and irradiation: planetary equilibrium temperature uses a Sun-like star with evolving luminosity and a fixed Bond albedo (0.343). The atmospheric temperature profile at low optical depth depends on both intrinsic and stellar flux; for cold, distant, or young planets, intrinsic flux dominates, reducing sensitivity to γ. 5) Atmospheric escape: two thermal escape regimes are implemented. Jeans escape assumes hydrostatic equilibrium at the exobase with a fixed exosphere temperature Texo in the range 300–2000 K (upper-limit rates using H-only), affecting mostly small, low-gravity planets. Hydrodynamic escape includes energy-limited X-ray-driven loss transitioning to XUV-driven loss, with energy-limited and radiation/recombination-limited formulations; the model uses solar X-ray/XUV luminosity evolution and accounts for planetary mass and radius at relevant optical depths. 6) Liquid water criterion: at each timestep, pressure and temperature at the bottom of the modeled atmosphere (interface with potential water layer) are compared with the H2O phase diagram to determine whether water would be liquid. The duration of uninterrupted liquid water conditions is recorded as t_w (also denoted τ_liq); an optional biological constraint requires surface temperatures between 270 and 400 K. 7) Parameter studies and validation: large grids across a, M_env, and M_core; a control unbound case; sensitivity tests for γ, opacities (+10× IR), initial luminosity, radiogenic luminosity (×0.1, ×10), core ice fraction (0.5); and cross-checks against Pierrehumbert & Gaidos via PETITcode and the authors’ own model to match atmosphere masses needed for 280 K surfaces under static conditions.

• Planets with Earth to super-Earth cores (~1–10 M⊕) and primordial H–He envelopes can maintain temperate surface conditions for 5–8 Gyr at orbital distances beyond approximately 2 AU, provided suitable envelope masses. Typical required envelope masses near a few AU are ~10−4 M⊕ (about two orders of magnitude above Earth’s present atmosphere), varying by roughly an order of magnitude smaller at closer distances and larger at farther distances. - Within ~10 AU, long-term liquid water durations (≥5 Gyr in many cases) emerge across a wide span of envelope masses (10−6–10−1 M⊕), with a scaling between received stellar flux and envelope mass for achieving temperate conditions. For envelopes ≲10−5 M⊕ near several AU, surface temperatures are Earth-like and stellar irradiation dominates the energy budget; beyond ~10 AU, interior cooling and radiogenic heat dominate, with smaller envelopes yielding earlier liquid water phases and larger envelopes reaching liquid conditions later. - Imposing a biological upper temperature constraint of 400 K reduces allowed parameter space near the star but still permits multi-Gyr durations in certain cases (demonstrated for 3 M⊕ cores). - Atmospheric escape: Jeans escape has negligible impact for most cases (even at Texo = 2000 K), modestly affecting only the smallest cores (~1.5 M⊕). In contrast, X-ray/XUV-driven hydrodynamic photoevaporation can substantially erode envelopes of close-in low-mass planets. When included, it eliminates the possibility of long-term liquid water on primordial-atmosphere planets within ~2 AU around Sun-like stars. - Unbound planets: Many ejected planets begin too hot but cool into prolonged liquid water conditions powered by intrinsic heat. τ_liq can greatly exceed stellar lifetimes; cores ≥5 M⊕ with ~0.01 M⊕ envelopes can sustain liquid water for >50 Gyr. The maximum found is 84 Gyr for a 10 M⊕ core with a 0.01 M⊕ envelope. Many such τ_liq values exceed the current age of the universe, though they may only be realized after ~10 Gyr of cooling. - Surface environments under H–He envelopes exhibit high pressures (~100–1000 bar). Despite extreme conditions (darkness, high pressure), analogues exist in Earth’s biosphere, suggesting potential for chemoautotrophic life, though the emergence of life under these conditions remains uncertain. - Sensitivity analyses show long-term results are robust to variations in initial luminosity and moderate changes in γ and opacities, with larger dependence on radiogenic heat at large semi-major axes.

The results demonstrate that, under realistic thermal evolution and stellar irradiation, many rocky to super-Earth planets with retained primordial H–He envelopes can sustain multi-gigayear windows of liquid surface water beneath their atmospheres. This directly addresses the longevity question absent from prior static analyses and shows that the habitable zone concept should be broadened to include H2-rich greenhouse mechanisms. The findings also clarify the role of atmospheric escape: close-in planets (<~2 AU) around Sun-like stars are unlikely to maintain the required pressures due to hydrodynamic photoevaporation, whereas planets beyond ~2 AU or unbound are less vulnerable and can exploit interior heat to maintain habitability over Gyr to tens of Gyr timescales. The dependence of τ_liq on core mass and envelope mass highlights formation and evolutionary pathways as key determinants of habitability, not solely orbital distance. While photosynthesis-based biosignatures may be scarce under thick H–He envelopes, the potential for chemoautotrophic ecosystems suggests alternative biosignature frameworks are needed. Overall, the study indicates that persistently temperate conditions can arise from initial conditions alone, without requiring Earth-like climate feedbacks, thereby expanding the inventory of potentially habitable worlds.

The paper establishes that terrestrial and super-Earth planets (≈1–10 M⊕) with modest primordial H–He envelopes can maintain liquid water at their surfaces for billions of years, especially beyond ~2 AU, and for unbound planets far exceeding stellar lifetimes (up to 84 Gyr in simulations). Hydrodynamic escape precludes such long-term conditions inside ~2 AU around Sun-like stars, while Jeans escape is generally unimportant. These insights argue for a more inclusive definition of habitability that encompasses H2-rich greenhouse planets and unbound worlds. Future work should quantify formation likelihoods for the requisite initial conditions, incorporate more realistic compositions (metallicity, greenhouse species), water inventories (avoiding high-pressure ice barriers), and magnetic field generation, assess planets around M dwarfs with their elevated early UV/XUV histories, and develop detection strategies and biosignature frameworks suited to H–He atmospheres using facilities like JWST, Ariel, ELT, PLATO (for ages), and Roman (for cold and unbound planets).

Key limitations and assumptions include: (1) Nominal cores are dry silicate–iron (2:1) without ices; ice-rich compositions alter mass–radius, heat capacity, and radiogenic scaling. (2) The atmosphere model employs double-grey radiative transfer and tabulated mean opacities with low-temperature extrapolations; specific greenhouse species and wavelength-dependent effects are simplified. (3) The greenhouse parameter γ and opacities are uncertain at low Teq; composition changes (e.g., increased metallicity) could modify the greenhouse effect. (4) Intrinsic luminosity relies on an analytical post-formation fit and chondritic radiogenic inventories that scale with mantle mass; true abundances and half-lives could differ. (5) Atmospheric escape models adopt simplified hydrodynamic prescriptions and an assumed exosphere temperature range for Jeans escape; composition-dependent and non-thermal losses are not treated. (6) Fixed Bond albedo and Sun-like stellar evolution; no late-stage migration is included. (7) The biological temperature cap (400 K) is Earth-derived and may not generalize. (8) Simulations for bound planets span 8 Gyr; longer-term behavior is assessed primarily for unbound cases. These factors may affect quantitative τ_liq estimates and generalizability.