Using observations of escaping H/He to constrain the atmospheric composition of sub-Neptunes

TL;DR

This work introduces a simple analytic timescale framework that links atmospheric escape to the mean molecular weight of sub‑Neptune envelopes, yielding upper bounds on μ from observed hydrogen or helium loss. A Bayesian inference approach combines mass‑loss constraints with an interior-structure model to recover core mass, envelope fraction, and μ from M_p, R_p, and escape data for planets like GJ‑436 b, TOI‑776 b, and TOI‑776 c. The study extends to JWST spectroscopy, showing that for TOI‑776 c the spectrum is consistent with a low-μ atmosphere muted by high-altitude aerosols, and demonstrates that joint mass‑loss and transit spectroscopy analyses can tighten μ constraints (e.g., μ ≤ 12.4 g mol⁻¹ for TOI‑776 c). The method is also applied to hycean candidates (K2‑18 b) and helium escape scenarios, highlighting potential tests of planetary interiors and atmospheric chemistry, while noting significant model and prior choices that require further refinement and observational follow‑up.

Abstract

The internal composition of sub-Neptunes remains a prominent unresolved question in exoplanetary science. We present a technique to place constraints on envelope mean molecular weight that utilises observations of escaping hydrogen or helium exospheres. This method is based on a simple timescale argument, which states that sub-Neptunes require a sufficiently large hydrogen or helium reservoir to explain on-going escape at their observed rates. This then naturally leads to an upper limit on atmospheric mean molecular weight. We apply this technique to archetypal sub-Neptunes, namely GJ-436 b, TOI-776 b and TOI-776 c, which have all been observed to be losing significant hydrogen content as well as relatively featureless transit spectra when observed with JWST. Combining constraints from atmospheric escape and transit spectroscopy in the case of TOI-776 c allows us to tentatively rule out the high mean molecular weight scenario, pointing towards a low mean molecular weight atmosphere with high-altitude aerosols muting spectral features in the infra-red. Finally, we reframe our analysis to the hycean candidate K2-18 b, which has also been shown to host a tentative escaping hydrogen exosphere. If such a detection is robust, we infer a hydrogen-rich envelope mass fraction of $\log f_\text{env} = -1.67\pm0.78$, which is inconsistent with the hycean scenario at the $\sim 4σ$ level. This latter result requires further observational follow-up to confirm.

Figures (7)

• Figure 1: The upper limit on envelope mean molecular weight is shown as a function of observed hydrogen mass loss rate for various envelope mass fractions. This applies to a $5$ Gyr old sub-Neptune with a core mass of $5$ M$_\oplus$ and assuming a Solar hydrogen-to-helium mass fraction following Equations \ref{['eq:X-inequality']} and \ref{['eq:mmw-inequality']}. Dashed grey lines denote upper limits on mean molecular weight that are below Solar values. The higher the observed mass loss rate and the smaller the envelope mass, the lower the mean molecular weight needs be in order to explain the escaping hydrogen observations.
• Figure 2: Marginalised posteriors are shown for the composition of TOI-776 b, TOI-776 c and GJ-436 b in the top, middle and bottom rows, respectively. The constraints come from observed masses, radii and escaping hydrogen mass loss rates from Schreyer2024Loyd2025. Here we show results for a selection of inferred parameters, including planetary core masses, $M_\text{c}$, core radii, $R_\text{c}$, envelope mass fractions $f_\text{env} \equiv M_\text{env} / M_\text{c}$, and envelope mean molecular weights $\mu$. Inferred values are quoted with their associated $1\sigma$ uncertainties (upper limits in the case of $1$-tailed posteriors). Grey histograms represent the prior probability distributions for each model parameter.
• Figure 3: Three choices in prior parameterisation of atmospheric metallicity when applied to transmission spectroscopy in the case of a relatively featureless spectrum due to a high mean molecular weight atmosphere. If one wishes to place constraints on mean molecular weight, $\mu$, then we recommend a prior that is uniform with atmospheric scale height, or equivalently $\mu^{-1}$ (top row). Other options, including uniform in composition parameter Benneke2012 or log-scaled mass or molar abundance (bottom row) place an unnecessarily heavy posterior bias to low mean molecular weight.
• Figure 4: Left: JWST NIRSpec/G395H spectrum for TOI-776 c from Teske2025 with our best-fit H$_2$-He-H$_2$O atmospheric model in orange. The shaded regions correspond to $1\sigma$ and $2\sigma$ confidence intervals. Right: marginalised posterior for atmospheric mean molecular weight and opaque pressure level. Contours represent increasing posterior probability (in $20\%$ intervals).
• Figure 5: Marginalised posteriors for envelope mean molecular weights for TOI-776 c. In the left-hand panel we show the constraints from Section \ref{['sec:partI']}, namely Ly-$\alpha$ escaping exosphere observations from HST (see Figure \ref{['fig:Structure_posteriors']}). In the central panel, we show the results from JWST atmospheric transit spectroscopy from Section \ref{['sec:PartII']} (see Figure \ref{['fig:TOI-776c_JWST']}). In the right-hand panel, we combine these results to produce the joint posterior from HST and JWST.