The Volatile Evolution of GJ 1132 b

GJ 1132 b is an approximately Earth-sized planet transiting a nearby 0.2 solar mass star on a 1.6 day orbit. This configuration is favorable for atmospheric detection with JWST, but the first observations have generated ambiguous results (May et al., 2023; Xue et al., 2024). Thus, we explored if a theoretical model of the evolution carbon dioxide, hydrogen, oxygen, and water that includes the major geochemical, thermal, and escape processes while the planet transitions through hydrogen envelope, magma ocean, and stagnant lid phases can provide any insight into the current distribution of volatiles on GJ 1132 b. Our treatment is fully probabilistic and is observationally constraints.

Our model includes self-consistent treatments of the star (Baraffe et al., 2015; Ribas et al., 2005; Engle & Guinan, 2023; Engle, 2024), hydrogen envelope loss (do Amaral et al., 2022), magma ocean evolution (Carone et al. 2025), stagnant lid evolution (Garcia et al. submitted), and orbital/rotational/tidal evolution (Barnes et al. 2025). These models have all been calibrated to stellar and Solar System observations and their coupling creates a self-consistent “whole planet” model for GJ 1132 b that includes perturbations from GJ 1132 c.

We first employed a machine learning algorithm (Birky et al., in prep.) to quickly infer posteriors for the star’s age and quiescent XUV evolution conditioned on stellar rotation and X-ray luminosity, employing empirical models for the evolution of both (Baraffe et al., 2015; Ribas et al., 2005; Engle & Guinan, 2023; Engle, 2024). Example posteriors for the Ribas et al. (2005) model are shown in Fig. 1.

Figure 1: Corner plot for the Ribas et al. (2005) stellar XUV evolutionary model parameters. Blue curves are from emcee Foreman-Mackey et al. (2013), red from dynesty (Speagle, 2020), and grey are priors. In practice, both posteriors were generated by alabi (Birky et al., in prep.), which employs Gaussian processes to generate a surrogate model for VPLanet (Barnes et al., 2020) simulations of GJ 1132.

 

We estimated the flaring history from the TESS lightcurve and models of M dwarf activity, see Fig. 2, to calculate the flares’ contribution to the overall XUV luminosity. We use the Feinstein et al. (2020) model and inferred distributions of their 4 model parameters for their flare frequency distribution (FFD) model. By combining the quiescent and flaring models, we found that GJ 1132 b has likely intercepted 100 – 3000 times more XUV radiation than Earth, as shown in Fig. 3. These uncertainties suggest planet b may lie closer to the “Cosmic Shoreline” (Zahnle & Casting 2017)  than previously thought, see Fig. 4.

Figure 2: GJ 1132’s FFD as derived from TESS lightcurves. The GJ 1243 FFD is from Hawley et al. (2014); GJ 4083 is from Davenport et al. (2014).

Figure 3: Distributions of cumulative XUV fluxes planet b has received, with quiescent only in gray and the sum of queiscence and flaring in black.

Figure 4: 95% confidence intervals of GJ 1132 b with relation to the so-called Cosmic Shoreline (Zahnle & Catling, 2017) for both the quiescent (gray) and quiescent+flares (black). The horizontal position of the planet is slightly offset for clarity.

We construct a model for CMEs based on our Sun due to poor constraints for M dwarfs. We assume that CMEs are associated with X-class flares and higher, have opening angles of 120◦, and proton fluences that scale with the Carrington Event (Cliver & Dietrich, 2013; Youngblood et al., 2017). We then assume that protons remove all atmospheric constituents equally well, including carbon dioxide.

We considered initial hydrogen masses up to 10 Earth masses and find for all cases that the envelope evaporated in < 10⁹ years.

We considered magma ocean phases that were either primordial or emerged after the envelope evaporated. Our initial conditions allowed water masses up to 1000 times Earth’s modern ocean mass, and carbon dioxide masses in between 10 and 90% of the water mass. Once the mantle solidifies, the planet transitioned to the stagnant lid model and evolved to an age permitted by the XUV modeling (see Fig. 1).

We find that permanent atmospheric loss is most likely for initial water + carbon dioxide masses less than 10 times Earth’s modern ocean mass. For volatile contents over 100x Earth’s ocean mass, the planet can remain in a magma ocean today (8+ Gyr). We found that significant fractions of our simulations produce a planet that has a) permanently lost all its volatiles, b) a transient atmosphere in which the outgassing flux is smaller than the escape flux, or c) a permanent secondary atmosphere. We thus conclude that the current uncertainties in the initial conditions and planetary evolution are too large to offer strong theoretical constraints on the current volatile state of GJ 1132 b.

 

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