Narrow Loophole for H₂-Dominated Atmospheres on Habitable Rocky Planets around M Dwarfs

Rocky planets with H₂-dominated atmospheres would be ideal targets for atmospheric characterization via transmission spectroscopy because of their large atmospheric scale height that causes large expected spectral features (e.g., Miller-Ricci et al. 2008; Seager & Deming 2010; Greene et al. 2016). A moderately irradiated rocky planet with a H₂-dominated atmosphere may have surface pressure and temperature consistent with liquid water (Pierrehumbert & Gaidos 2011; Wordsworth 2012; Ramirez & Kaltenegger 2017; Koll & Cronin 2019). Such potentially habitable worlds sustained by H₂-dominated atmospheres, if they exist around M dwarfs, would unlock the opportunity to study extrasolar habitability with spectroscopy (e.g., Seager et al. 2013), as TESS and ground-based surveys find temperate rocky planets around M dwarfs (e.g., Sebastian et al. 2021; Kunimoto et al. 2022), and JWST provides the sensitivity to analyze any H₂-dominated atmospheres on them with a wide spectral coverage (e.g., Batalha et al. 2018). Here we ask: Are such worlds likely?

To have surface liquid water, the H₂-dominated atmosphere cannot be much larger than ∼10 bar because the surface temperature is primarily a function of the size of the atmosphere (this is valid for the stellar irradiation of 200–1400 W m⁻²; Koll & Cronin 2019). The exact size and irradiation limit depends on the cloud albedo effect (e.g., Popp et al. 2015). This moderate-sized atmosphere is much smaller than the massive H₂-dominated atmospheres proposed to explain the sub-Neptune-sized low-density planet population, which are typically 1% planet mass or >10⁴ bar (e.g., Rogers et al. 2023). A 10 bar H₂ atmosphere would only add < ∼ 0.1 R_⊕ to the planetary radius, which can be accommodated by typical uncertainties in planetary mass, radius, and Fe content (Luque & Pallé 2022). Also, the temperate rocky planets will have a solid surface, as opposed to the sub-Neptunes that may have a permanent magma ocean (Kite & Barnett 2020). Because the permeability of the crust decreases dramatically with increasing depth (Manning & Ingebritsen 1999), any post-formation source of H₂ must come from shallow fresh crust via either volcanic outgassing or crustal alteration processes such as serpentinization.

Meanwhile, temperate planets around M dwarfs receive intense high-energy irradiation from host stars because of their close-in orbits, and this intense irradiation can drive hydrodynamic escape from a H₂-dominated atmosphere (e.g., Salz et al. 2016; Kubyshkina et al. 2018a, 2018b). The high-energy irradiation will be measured by a bevy of new spacecraft (Ardila et al. 2022; France et al. 2023). We are thus motivated to determine the lifetime of a moderate-sized H₂ atmosphere—permitting surface liquid water—on a large rocky planet orbiting an M dwarf against the hydrodynamic escape and evaluate the geologic processes that could resupply the H₂ atmosphere.

The hydrodynamic escape rate, f_es (kg s⁻¹), can be approximated by the energy-limited escape rate formula,

$$\begin{eqnarray}&&{f}_{\mathrm{es}}=\displaystyle \frac{{\eta }_{\mathrm{es}}({F}_{{\rm{X}}}+{F}_{\mathrm{EUV}})\pi {R}_{{\rm{p}}}^{3}{a}^{2}}{{{KGM}}_{{\rm{p}}}},\end{eqnarray} \tag{ 1 }$$

where F_X and F_EUV are the stellar fluxes in X-ray (5–100 Å) and extreme ultraviolet (EUV; 100–1240 Å), a ≥ 1 is the ratio between the X-ray/EUV absorbing radius and the (optical) planetary radius, K ≤ 1 is a factor that accounts for the Roche lobe effect (Erkaev et al. 2007), and η_es is the escape efficiency. Recent hydrodynamic escape models find the escape efficiency to be in a range of 0.1–0.25 for solar-abundance atmospheres (Salz et al. 2016), and Equation (1) is a good approximation of the full hydrodynamic calculations in the Jeans escape parameter regime for temperate rocky planets (Jeans escape parameter = 25–60; Kubyshkina et al. 2018a, 2018b). For a conservative estimate of the escape rate, we adopt η_es = 0.1, a = 1, and K = 1.

As shown in Table 1, we pick GJ 832, GJ 436, and TRAPPIST-1 as the representative stars for early-, mid-, and late-type M dwarfs. Their emission spectra in X-ray, Lyα, far-ultraviolet (FUV), and near-ultraviolet (NUV) bands have been measured, and their emission spectra and fluxes in the EUV band can be inferred from these measurements (Peacock et al. 2019b, 2019a). We find that the lifetime of a 10 bar H₂ atmosphere on a rocky planet that receives Earth-like insolation from these stars would be uniformly <0.1 Ga. Thus, a source of H₂ would be needed to maintain such an atmosphere.

We first consider volcanic outgassing as the source of H₂ (e.g., Liggins et al. 2020). The volcanic outgassing rate, f_og (kg s⁻¹), can be modeled by the following equation,

$$\begin{eqnarray}&&{f}_{\mathrm{og}}={\eta }_{\mathrm{og}}{{Vx}}_{{\rm{H}}},\end{eqnarray} \tag{ 2 }$$

where V is the rate of magma generation, x_H is the hydrogen content (wt%) of magma that degasses, and η_og is the outgassing efficiency. We do not expect the outgassing efficiency to be close to unity because, even though extrusive volcanism (magma that reaches and degases at the planetary surface) can probably degas effectively (but often not completely), intrusive volcanism (magma that does not reach the surface) probably degases poorly, especially for H₂ (to be detailed later in this section). For Earth, the extrusive:intrusive ratio is typically 3:1 to 10:1 (White et al. 2006), and so as a fiducial value, we assume η_og = 0.1.

The rate of volcanism can be estimated for a rocky planet by modeling its thermal evolution history. We adopt the geodynamics model of Kite et al. (2009) for the rate of volcanism, which used a melting model from pMELTS (Ghiorso et al. 2002) for the plate tectonic mode and Katz et al. (2003) for the stagnant-lid mode (Table 2). Focusing first on the planets around field M dwarfs, we take the 4 Gyr age values for the rate of volcanism. The values for the plate tectonic and stagnant-lid modes are similar. Detailed models of mantle convection in the stagnant-lid regime predict that volcanism would cease much sooner than what Table 2 indicates (Noack et al. 2017; Dorn et al. 2018), but this model uncertainty does not impact the conclusion of this paper. For volcanic outgassing to sustain the atmosphere, it is required that f_es = f_og. With f_es and V, we derive the required x_H and list the values in Table 1.

Arc volcanoes on Earth, which are formed by flux melting caused by release of water from subduction of plates rich in hydrated materials, have magmas that contain 1–7 wt% water (e.g., Rasmussen et al. 2022). The water content in the mid-ocean ridge basalt (MORB) and the ocean island basalt (OIB) is lower by 1–2 orders of magnitude (Dixon et al. 2002). Complete outgassing of 1–7 wt% water in the form of H₂ would provide an x_H of 0.1–0.8 wt%. We consider this to be a very generous upper limit; comparing it with Table 1 shows that it is very unlikely for volcanic outgassing to sustain the H₂ atmosphere.

The hydrogen content of the magma for degassing depends on the oxygen fugacity of the magma and the pressure at which degassing takes place. We use the magma degassing and speciation model of Gaillard & Scaillet (2014) to calculate x_H for the typical volatile content of terrestrial magmas and a wide range of oxygen fugacities (Figure 1). The H₂ content is higher for a more reducing magma and when degassing at a lower pressure. In addition to counting the H₂ degassing, one may also include the potential for atmospheric photochemistry to postprocess CO to form H₂, via CO + H₂O → CO₂ + H₂. The complete postprocessing means that degassing 1 mole CO would be equivalent to degassing 1 mole H₂, and this situation is shown as dashed lines in Figure 1. However, x_H predicted by the geochemical model, even when including the CO conversion, is at least 1 order of magnitude lower than the minimum required x_H for a 7M_⊕ planet around an early M dwarf (Table 1). This again indicates that volcanic outgassing is unlikely to sustain a H₂ atmosphere.

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We turn to serpentinization as an alternative source of H₂. Serpentinization is water–rock reactions between warm water and mafic and ultramafic rocks (usually olivine-rich) in the fresh crust. This process probably occurs on all rocky planets with liquid water, and it may have produced H₂-rich water on early Earth (Sleep et al. 2004) and H₂ and CH₄ on early Mars and on modern Enceladus (Oze & Sharma 2005; Chassefière & Leblanc 2011; Batalha et al. 2015; Zandanel et al. 2021).

For an upper bound of the H₂ production rate from serpentinization, we assume that 1 mole H₂ is produced for every 3 moles Fe²⁺ oxidized, as the process can be written as H₂O + 3FeO → H₂ + Fe₃O₄. We also assume that the fresh crust is entirely composed of olivine, (Mg_0.9Fe_0.1)₂SiO₄, and all Fe²⁺ is used by serpentinization to produce H₂. The olivine has a molar mass of 146.9 g, and it contains 0.2 moles Fe²⁺, corresponding to 0.067 moles H₂, or a mass of 0.13 g. The corresponding x_H is thus 0.13/146.9 = 0.09 wt%. In reality, the fresh crust may not be entirely composed of olivine, and the rate of serpentinization is limited by the rate of dissolution of olivine in water (Oze & Sharma 2007), which is a function of temperature, pH, water/rock ratio, and the Fe/Mg composition of olivine (Wogelius & Walther 1992; Allen & Seyfried 2003), as well as by the extent of fracturing of the crust (Vance et al. 2007). We thus expect the actual x_H provided by serpentinization to be much smaller than 0.09 wt%. However, even this generous upper bound falls short of the required x_H by at least a factor of 4 (Table 1). It is thus also unlikely that serpentinization would sustain a moderate-sized H₂ atmosphere on rocky planets around M dwarfs.

So far we have assumed 4 Gyr for the planet age, which broadly corresponds to the field M dwarfs. Now we consider the age dependency of the sources and sinks of H₂ and see if a steady-state H₂ atmosphere would be possible on younger planets. Richey-Yowell et al. (2019) recently presented the NUV, FUV, and X-ray fluxes of M dwarfs in their habitable zones as a function of age, and meanwhile, the EUV fluxes follow a similar age dependency as their FUV fluxes (Peacock et al. 2020). We adopt an age dependency of t^−0.9 for the X-ray fluxes and t^−1.3 for the EUV fluxes. Meanwhile, the rate of volcanism can be much higher for young planets, when the heat flux from the planetary interior is higher. We explore an age dependency that varies between t⁻¹ (based on the model for Earth in Schubert et al. 2001) and t⁻² (based on the model for large rocky planets of Kite et al. 2009). We consider an age as young as 1 Gyr. Before that, the planet could have a residual primordial H₂ atmosphere (Kite & Barnett 2020), and the stellar high-energy output may have different age dependencies (Richey-Yowell et al. 2019). As shown in Figure 2, it remains unlikely for volcanic outgassing or serpentinization to compensate for the intense atmospheric escape of H₂ experienced by rocky planets of M dwarfs from 1 to 5 Gyr.

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How about a planet that is located further away from the star than the 1 au equivalent distance? Moving the planets 2.6 times further away (or receiving 7 times less irradiation, or ∼200 W m⁻²) would still produce a potentially habitable climate (Koll & Cronin 2019), and this would reduce the escape rate by a factor of 7. In this case, the escape rate is comparable to the upper limit of serpentinization (Figure 2). However, the upper limit assumes complete oxidization of Fe²⁺ in the fresh crust and is thus unlikely. The utility of these distant habitable worlds for observations is probably limited, as they are less likely to transit and harder to find than the closer-in planets.

The estimates above show that it is unlikely to sustain moderate-sized H₂-dominated atmospheres on rocky planets around M dwarfs through volcanic outgassing or serpentinization. Here we explore alternative mechanisms that could result in large source fluxes of H₂.

First, the rate of hydrogen generation during serpentinization is controlled by the Fe content of olivine (Klein et al. 2013). In Section 4, we have assumed an Fe:Mg ratio of 1:9, corresponding to the terrestrial value. On Mars, however, the Fe:Mg ratio of crustal olivine can be ∼1:1 (Koeppen & Hamilton 2008; Morrison et al. 2018). Such Fe-rich olivine could result in higher fluxes of H₂ from serpentinization than our estimates by a factor of ∼5, making it more likely for serpentinization to meet the H₂ escape flux.

Second, on a planet with plate tectonics but amagmatic spreading, water–rock interaction near the ridge axis could produce H₂. Our discussion of serpentinization so far assumes that water interacts with the products of volcanism/partial melting. However, water could interact directly with the mantle if it is exposed by amagmatic spreading. This mechanism occurs on Earth today at Gakkel Ridge and Southwest Indian Ridge and has the potential to generate more H₂ because the Fe content of mantle rock is greater than that of the crustal basalt. This mechanism would decouple serpentinization from volcanism and allow serpentinization to continue even after volcanism has shut down. The upper limit of H₂ production from this mechanism is then given by assuming (unrealistically) a 100% fayalite (Fe₂SiO₄), which would give an equivalent x_H of 0.6 wt%. Suppose fractures, and therefore hot-water alteration, penetrate as far down into the subsurface on this amagmatic planet as the base of the oceanic crust on our planet, which is probably unrealistic because fractures should self-seal at shallower depths (Vance et al. 2007). Then the present-day terrestrial production of 20 km³ yr⁻¹ of MORB, with full serpentinization, would correspond to 1 × 10⁴ kg s⁻¹ of H₂ output. This is on the same order of magnitude as the lower end of the escape rate (Table 1) and could be higher for younger or larger rocky planets.

Third, Earth's heat flux of ∼0.1 W m⁻² is ∼10% in the form of advective cooling (magma moves upward and cools) and ∼90% conductive cooling. This implies that the rates of volcanism could be 10 × higher without excessively cooling Earth's mantle. Indeed, it has been hypothesized that heat-pipe tectonics occurred early in Earth's history (e.g., Moore & Webb 2013). Small variations in exoplanet mantle composition or exoplanet mantle volatile content, among other factors, could make melting easier at a given mantle temperature (Spaargaren et al. 2020), perhaps enabling heat-pipe mode of planetary cooling even for planets that are as old as the Earth. If heat-pipe volcanism occurs, then the amount of outgassing and serpentinization could be ∼10 × greater than for an Earth-scaled plate-tectonics model because ∼10 × more eruptions would occur.

Fourth, N-, O-, and C-bearing molecules mixed in the H₂-dominated atmosphere may substantially reduce the escape rate. The escape rate and efficiency calculations have been based on solar-abundance atmospheres (Kubyshkina et al. 2018a, 2018b). However, H₂-dominated atmospheres sustained by volcanism should also have H₂O, CO/CH₄, and N₂/NH₃ at the levels that exceed the solar abundance (Liggins et al. 2022). Recently, Nakayama et al. (2022) show that with an N₂–O₂ atmosphere, cooling from atomic line emissions (of N, N⁺, O, O⁺) and radiative recombination can prevent rapid hydrodynamic escapes for XUV irradiation fluxes that are up to 1000 × the modern Earth value. It is thus conceivable that an H₂-dominated atmosphere richer in N, O, and C would be more stable. The challenge is that the N-, O-, and C-bearing molecules are separated from H₂ by diffusion (typically at ∼1 Pa) and can be largely depleted in the upper atmosphere. It is thus unclear whether 10% non-H₂ species (which would still allow for a low molecular weight atmosphere for transmission spectroscopy) would slow down the hydrodynamic escape sufficiently to achieve long-term stability.

Lastly, there could be transient episodes of high volcanism and serpentinization that support H₂-dominated atmospheres. A leading hypothesis for why early Mars sometimes had lakes is that a lot of H₂ was emitted transiently from the subsurface by volcanism or serpentinization (Wordsworth et al. 2021). The amount of H₂ needed to warm up Mars by H₂–CO₂ collision-induced absorption is now well understood (Turbet et al. 2020), and the H₂ flux needed is approximately 10⁴ kg s⁻¹. A large rocky planet could have 10 × the surface area of Mars and thus plausibly 10 × the amount of serpentinization. This process-agnostic (but model-dependent) scaling hints at short-term source fluxes sufficient for H₂-dominated atmospheres on a 7M_⊕ planet (Figure 2).

From the analyses presented above, we conclude that rocky planets around M dwarfs rarely have potentially habitable conditions accompanied by H₂-dominated atmospheres. This is because forming a potentially habitable environment will require a moderate-sized (∼10 bar) atmosphere, but such an atmosphere is removed quickly by stellar X-ray and EUV irradiation and could only exist on the planet as a steady-state atmosphere with replenishment. However, neither volcanic outgassing nor serpentinization provides the required H₂ source that would maintain such a steady-state atmosphere. Small planets around M dwarfs could have massive H₂ atmospheres, but to have a stable and moderate-sized H₂ atmosphere consistent with habitability would require special circumstances such as direct interaction between liquid water and mantle (e.g., near a ridge axis undergoing amagmatic spreading), heat-pipe volcanism from a highly reduced mantle, or hydrodynamic escape quenched by efficient atomic line cooling. These special mechanisms to sustain the moderate-sized H₂ atmosphere are generally more effective on large rocky planets (e.g., ∼7M_⊕ planets exemplified by LHS 1140b) than on Earth-sized planets.

The finding here is consistent with the nondetection to date of clear H₂-dominated atmospheres on rocky planets of M dwarfs via transmission spectroscopy (e.g., De Wit et al. 2018; Lustig-Yaeger et al. 2023) although these results could also be interpreted as widely occurring photochemical haze that mutes transmission spectral features of H₂-dominated atmospheres. Swain et al. (2021) suggested a H₂-dominated atmosphere on the rocky planet GJ 1132 b based on Hubble Space Telescope (HST) data, but independent data analyses could not confirm their result (Mugnai et al. 2021; Libby-Roberts et al. 2022). The ongoing HST and JWST transmission spectroscopy of small exoplanets of M dwarfs will further test our findings and, potentially, discover exceptional cases. Meanwhile, N₂–CO₂ or other high mean molecular weight atmospheres should probably be considered as the default assumption when planning for future spectroscopic observations of rocky planets around M dwarfs. This would require planning more repeated visits of preferred targets for transmission spectroscopy (e.g., Batalha et al. 2018) or turning to thermal emission spectroscopy and phase-curve mapping (e.g., Angelo & Hu 2017; Koll et al. 2019; Kreidberg et al. 2019; Mansfield et al. 2019; Whittaker et al. 2022).

We thank Evgenya Shkolnik and Tyler Richey-Yowell for helpful discussion of stellar evolution. This work was supported in part by the NASA Exoplanets Research Program grant #80NM0018F0612. E.S.K. acknowledges support from a Scialog grant, Heising-Simons Foundation 2021–3119. Part of this research was carried out at the Jet Propulsion Laboratory, California Institute of Technology, under a contract with the National Aeronautics and Space Administration.