Modelling helium in exoplanet atmospheres. A revised network with photoelectron-driven processes

Antonio Garc\'ia Mu\~noz

REVIEW 4 major objections 6 minor 1 cited by

Modelling helium in exoplanet atmospheres. A revised network with photoelectron-driven processes

T0 review · 4 major / 6 minor · reviewed 2026-08-15 · deepseek-v4-flash

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Pith's one-line read Penning ionization of H atoms and a weaker stellar spectrum explain the missing helium 1.08 μm absorption at GJ 436 b.

desk verdict A substantive update to the He 1.08 micron network—new H2/photoelectron chemistry and a careful Penning rate—but the GJ 436 b match hinges on an unvalidated SED, so the observational claim is provisional. read the letter →

arxiv 2505.12148 v1 pith:QBWYHYFJ submitted 2025-05-17 astro-ph.EP

Antonio García Muñoz This is my paper · ORCID

classification astro-ph.EP

keywords helium1083nmlinemetastableHe(2^3S)exoplanetatmosphericescapeGJ436bPenningionizationphotoelectronschemical-collisional-radiativenetworkstellarspectralenergydistribution

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

This paper argues that the helium 1.08 μm line in exoplanet outflows cannot be interpreted with the standard recombination-only network: H2, molecular ions, and photoelectrons must be included. Applying an expanded chemical-collisional-radiative network to GJ 436 b, the author finds that Penning ionization of H atoms is the main destroyer of the metastable He($2^{3}$S) absorber at the altitudes that set the line core, and updates the rate coefficient from published cross sections. For this planet, photoelectron-driven excitation and ionization change He($2^{3}$S) mainly deep in the atmosphere, so they barely affect the in-transit spectrum. The paper further shows that the reported non-detections of the line are consistent with a solar-metallicity outflow if the star's ultraviolet-X-ray spectrum follows the weaker of two commonly used reconstructions, whereas the stronger reconstruction overpredicts the signal. The result matters because it offers a way to reconcile a puzzling null detection and shows that line-strength inferences hinge on the assumed stellar spectrum and on collision rates that are often extrapolated.

What carries the argument

The central machinery is a five-state helium atom model (ground, two metastables, two P states) embedded in a network of about 200 chemical-collisional-radiative processes that also tracks H2 and the H2+, H3+, and HeH+ ions, coupled to a Monte Carlo model that follows the energy degradation of photoelectrons. Its linchpin is the revised rate coefficient for Penning ionization, He($2^{3}$S)+H -> He($1^{1}$S)+H+ + e-, with a small branch to HeH+ + e-, computed from published cross sections and extrapolated with $E^{-0.2}$ and $E^{-1}$ laws. The competing electron-impact channels He($2^{3}$S)+e- -> He($2^{1}$S), He($2^{3}$P) make the line core sensitive to temperature, H density, and electron density.

What would settle it

A high-quality empirical spectrum of GJ 436 in the extreme-ultraviolet and far-ultraviolet would settle the SED question: if its fluxes match the stronger of the two reconstructions, the paper's solar-metallicity model would predict a 1.08 μm excess absorption clearly above the published upper limits, falsifying the claimed consistency.

Watch

Extended reading notes

Core claim

The central claim is that the strength of the He I 1.08 μm signal at GJ 436 b is governed by competition between Penning ionization of H atoms and electron-impact excitation out of He($2^{3}$S), with radiative recombination feeding the metastable state; once the Penning rate coefficient is updated to the most recent experimental and theoretical cross sections, and once the stellar spectrum is represented by the weaker of two tested SED reconstructions, the predicted in-transit excess absorption falls close to the published upper limits. The paper argues that earlier models overpredicted the line because they omitted Penning ionization (or used an older rate coefficient) and adopted a stronger stellar SED. It also claims that photoelectrons alter the He($2^{3}$S) population mainly deep in the atmosphere at this planet, and that in H2-rich outflows with deep molecule-to-atom transitions photoelectron effects may be stronger for transit spectra.

Load-bearing premise

The reconciliation with the non-detections assumes that GJ 436's true ultraviolet-X-ray spectrum is the weaker of the two reconstructions tested—the one stitched beyond 2800 Å with a blackbody discontinuity the author calls unphysical—and that the lower boundary has solar composition with a somewhat arbitrary H mixing ratio of $10^{-3}$.

Editorial extensions

If this is right

For H2-rich outflows like GJ 436 b, radiative recombination is the main source of the He(2^3S) that absorbs during transit, while Penning ionization with H and electron-impact excitation keep its lifetime below one second in the line-forming layers.
Using the older Penning rate coefficient biases the predicted core strength of the 1.08 μm line by more than typical measurement errors, so model-observation comparisons should adopt the updated rate.
Photoelectron-driven chemistry changes the He(2^3S) population only in layers deeper than those probed in transit for GJ 436 b, implying that ignoring photoelectrons is acceptable for this target but not necessarily elsewhere.
The predicted in-transit excess absorption changes substantially between the two tested stellar SEDs, so SED choice, not just chemistry, controls whether a non-detection is considered consistent with escape.
If the weaker SED is correct, the published upper limits do not require a high-metallicity, small-scale-height atmosphere; a solar-metallicity H2-dominated outflow can hide the helium line.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

Should the result transfer to hotter or more strongly irradiated H2-rich planets, the deep-layer-only caveat for photoelectrons might invert: in an atomic-gas region photoelectrons ionize more than recombine, which can change the ion balance in the line-forming layers.
A dedicated retrieval or atmospheric model that treats the SED as a free parameter, anchored to an empirical spectrum, would convert the reported 'consistent with non-detection' into a sharper constraint on metallicity and escape.
The $E^{-0.2}$ and $E^{-1}$ extrapolations of the Penning cross sections are a testable weak point; new measurements of He(2^3S)+H ionization below 1 eV would either validate the rate or force a revision with direct transit-spectrum consequences.
For the growing sample of He I detections, the revised network implies that reported abundance constraints should be re-derived with the updated Penning rate before drawing conclusions about H/He ratios.

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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Desk Editor's Note

read the letter

Two things to know. The paper is a genuine step forward for the He 1.08 micron modelling community: it expands the standard Oklopcic-Hirata network with H2 and molecular-ion chemistry, couples photoelectron energy degradation to the He(2^3S) population for the first time, and re-derives the Penning ionization rate for He(2^3S)+H from the original published cross sections rather than quoting older compilations. It also shows, usefully, that photoelectrons change the metastable population mainly in layers too deep to affect the in-transit spectrum for GJ 436 b. That negative result is worth having.

The chemistry work is careful. The author tracks the factor-of-six discrepancy among Penning rate prescriptions back to the primary sources, provides fits and an appendix with explicit rate coefficients, and demonstrates that the choice matters for the line core. The paper is also honest: it flags the unphysical blackbody splice in the X-Exoplanets SED extension and the 'somewhat arbitrary' lower-boundary H mixing ratio.

The soft spot is the observational comparison. The claim that GJ 436 b's non-detections are consistent with a solar-metallicity model rides on adopting the X-Exoplanets SED; with MUSCLES the same model clearly overpredicts. The X-Exoplanets SED is a recent reconstruction, and the decisive 0-500 angstrom flux that drives He+ production and the outflow is not independently checked. I think the blackbody splice above 2800 angstrom is a red herring—the paper correctly notes those photons cannot ionize He(2^3S)—but the EUV difference between the two SEDs is exactly what the match hinges on. On top of that, the 'consistency' is qualitative: no error bars on the synthetic spectra, and the upper limits come from three different groups with different analyses. The H mixing ratio at the lower boundary is not varied even though it controls where H2 hands over to H and thus where Penning loss acts. These are real gaps, but they are gaps in confidence, not signs the model is wrong.

Who this is for: anyone modeling escape tracers or interpreting He 1.08 micron observations. It deserves serious peer review—the network work is substantial and the author is appropriately cautious. A revision that adds an SED sensitivity analysis with a broader set of reconstructions and propagates some uncertainty into the spectra would make it a standard reference. I would send it to review, and I would cite it for the rate coefficients and the photoelectron finding. Take the GJ 436 b non-detection match as provisional until the SED question is settled.

Referee Report

4 major / 6 minor

Summary. The paper presents a revised chemical-collisional-radiative network for modelling the He(2^3S) metastable population that sets the He I 1.08 micron in-transit absorption. It adds processes involving H2 and molecular ions, and couples a Monte Carlo photoelectron energy-degradation model to a hydrodynamic escape model. The network is applied to GJ 436 b. The main findings are that Penning ionization of H is a key He(2^3S) loss channel near the line-forming region, that the rate coefficient for this process should be updated from published cross sections, and that photoelectron-driven processes affect only deep atmospheric layers for this planet. The predicted in-transit signal is strongly dependent on the adopted stellar SED: models with the MUSCLES SED clearly overpredict the published non-detections, while models with the X-Exoplanets SED are described as notably closer to, and reasonably consistent with, those upper limits.

Significance. If the conclusions hold, the paper offers a more complete and explicitly documented framework for interpreting He I 1.08 micron observations, particularly for atmospheres where H2 remains abundant to high altitudes. The strengths of the work are the transparent appendix tables of rate coefficients, the forward-modeling approach in which no parameter is fitted to the He observations, the Monte Carlo treatment of photoelectrons, and the explicit sensitivity analysis of the Penning ionization rate. These qualities make the paper a useful reference for the community. The quantitative value is, however, limited by the qualitative comparison to the GJ 436 b non-detections and by the strong sensitivity of the main observational claim to a single, partly unvalidated SED reconstruction and to an arbitrary lower-boundary H abundance.

major comments (4)

[Sec. 5, Fig. 6] The central observational claim that the GJ 436 b non-detections are reasonably consistent with the X-Exoplanets models is supported only qualitatively. The text states that the MUSCLES-based spectra are clearly inconsistent while the X-Exoplanets-based spectra are notably closer to the upper limits, but it does not report whether the modelled line-core excess absorption lies below the limits of Nortmann et al. (2018), Guilluy et al. (2024), and Masson et al. (2024), nor by what margin. Because this comparison is the basis for the abstract's main conclusion, please provide a quantitative comparison, for example the model EA at line center versus each upper limit together with a defined consistency metric.
[Sec. 2, Fig. 1] The X-Exoplanets SED is extended above 2,800 A with an unphysical blackbody splice, and the decisive EUV flux is not independently validated. Since it is the X-Exoplanets SED, not the MUSCLES SED, that brings the model into agreement with the non-detections, the agreement is only as credible as the SED reconstruction. The paper's argument that the blackbody extension does not matter for He(2^1S) photoionization does not validate the EUV portion that sets the He+ production and outflow. Please either validate the 0-500 A flux against an independent empirical reconstruction, or treat the SED as an explicitly varied input and show the range of predictions across plausible EUV fluxes.
[Sec. 2, lower boundary conditions] The lower boundary H mixing ratio is described as somewhat arbitrary and set to 1e-3, with solar metallicity assumed. Penning ionization of H is identified as a key He(2^3S) loss process near the line-forming peak, and the H density there depends on the location of the H2-to-H transition, which in turn depends on the boundary H abundance and metallicity. Please add a sensitivity run that varies the boundary H mixing ratio and/or the metallicity, or justify the adopted value from photochemistry timescales; without this, the central Penning-loss conclusion is not fully pinned down.
[Appendix A, Tables A.1-A.2] The effective recombination coefficients, which dominate He(2^3S) production near the line-forming peak (Fig. 4), are built on an assumed 1:3 singlet-to-triplet partitioning for recombinations into n>10 states and on assigning all such recombinations to n=10. This assumption is not tested, yet recombination is a central production channel for the metastable state. Please include a sensitivity test (e.g., extreme 0:1 or 1:0 partitionings, or an alternative cascade treatment) or provide a quantitative argument for why the 1:3 choice is conservative and does not materially affect the predicted spectra.

minor comments (6)

[Throughout] Several inline expressions appear garbled in the typeset text, such as p/greaterorsimilar10^-2 dyn cm^-2 and i,i/nequal1; these should be cleaned before publication.
[Table A.4] Some entries in Table A.4 are written with a space instead of a multiplication sign, e.g., 2.31 -20 instead of 2.31E-20; please make the scientific notation consistent throughout the table.
[Fig. 6] The Nortmann et al. (2018) and Guilluy et al. (2024) upper limits are only mentioned in the text and caption; plotting all three upper limits in Fig. 6 would make the comparison with the model spectra more transparent.
[Data Availability] The text promises that fits to the rate coefficients can be found through a link, but no URL or DOI appears in the arXiv version; please provide a persistent identifier or repository reference.
[Sec. 5] The suggestion that Roberge & Dalgarno (1982) may have mistakenly adopted the cross sections for He(2^3S)+D is speculative; it would be better phrased as one of several possible explanations for the discrepancy.
[Sec. 2] The statement that photoexcitation between bound states is omitted would benefit from a clarification of whether this includes stellar pumping of He(2^3S) to higher triplet states, since such pumping could affect line formation and is only briefly deferred to future work.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the Penning rate update and the GJ 436 b non-detection comparison are forward calculations from independent inputs, not fits to the target observations.

full rationale

The paper's central results are not restatements of its inputs. The revised He(2^3S) network is assembled from externally published cross sections and rate data (NORAD, Wiese & Fuhr, Berrington & Kingston, Bray et al., Movre & Meyer, etc.), and the Penning-ionization rate coefficient is explicitly calculated from published cross sections rather than adjusted to reproduce any spectrum. The in-transit spectra for GJ 436 b are forward predictions from a coupled hydrodynamic/Monte Carlo model with fixed boundary conditions; the comparison to the Masson et al. (2024) non-detection upper limit uses no fitted parameter. The two SEDs (MUSCLES and X-Exoplanets) are independent external inputs, and the paper reports both outcomes, including that the MUSCLES predictions are inconsistent with the upper limits; selecting the X-Exoplanets SED as a better match is a model-comparison statement, not a parameter fit disguised as a prediction. The 'somewhat arbitrary' H mixing ratio and the acknowledged unphysical blackbody splice above 2800 Å are stated limitations, but neither is tuned to the He I non-detections, and the paper's own sensitivity discussion shows the main SED dependence lies in the EUV flux. Self-citations to García Muñoz (2023a), García Muñoz & Bataille (2024), and García Muñoz & Schneider (2019) are methodological references (Monte Carlo photoelectron treatment and spectral synthesis routines); they are not invoked as external proof of the present conclusions, and the load-bearing physics is grounded in the cited atomic data and cross sections. No equation in the paper is defined in terms of the quantity it purports to predict, and no fitted parameter is renamed as a prediction. The acknowledged gaps (low-temperature electron-collision data, neutral-collision rate coefficients, empirical SED verification) are uncertainty caveats, not circularity.

Assumptions & free parameters 3 free parameters · 5 assumptions · 0 invented entities

The model rests on several unverified choices: an arbitrary H mixing ratio at the lower boundary, an ad hoc SED extension, a hand-chosen branching ratio, and extrapolated rate coefficients. None of these are fitted to the target observations, so they do not make the comparison circular, but they widen the uncertainty of the predictions.

free parameters (3)

Lower boundary H mixing ratio = 10^-3
Set at the lower boundary in Section 2 and described as "somewhat arbitrary"; it affects the H2-to-H transition altitude and the Penning ionization loss of He(2^3S).
Penning versus associative ionization branching ratio = 0.9:0.1
Partitioning of He(2^3S)+H collisions between ionization and HeH+ formation, adopted as an average in Section 2 without an uncertainty estimate.
Choice of stellar SED = X-Exoplanets (extended with blackbody above 2800 Å)
A discrete modeling choice in Section 5, not fitted to target data, that strongly affects the predicted in-transit signal. The extension above 2800 Å is acknowledged as introducing an unphysical discontinuity.

assumptions (5)

domain assumption Line opacity prevents radiative decay of He states into the ground state, so cascade probabilities p_ji exclude transitions to the ground state.
Used in Section 2 to compute effective recombination coefficients alpha_i,eef; if line opacity is partial, the cascade contributions change.
ad hoc to paper The He atom model is truncated at i<=5 and He^2+ is omitted, with recombination from n>10 assigned to n=10 using a 1:3 singlet to triplet partitioning.
The truncation is a pragmatic choice stated in Section 2, and the 1:3 partitioning is an assumption because NORAD reports only joint singlet and triplet contributions above n=10.
ad hoc to paper Cross sections for Penning ionization are extrapolated with an E^-0.2 law at low energies and an E^-1 law at high energies.
Used in Figure 5 to compute the updated rate coefficient from published cross sections; the extrapolation laws are not derived from theory.
domain assumption The coupled Monte Carlo photoelectron model and hydrodynamic model converge to steady state with only a few Monte Carlo calculations.
Stated in Section 2; the convergence criterion is not quantified in the paper.
ad hoc to paper Charge-exchange rate coefficients from Loreau et al. (2018) are extrapolated to temperatures below 3,000 K using private communication.
Used in Section 2 and Table A.7 for the loss of He metastables in collisions with H+; the low-temperature extrapolation is not independently published.

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Cite this review

Pith. "Pith review of Modelling helium in exoplanet atmospheres. A revised network with photoelectron-driven processes." pith.science (2026). https://pith.science/paper/QBWYHYFJ

@misc{pith2026250512148,
  author       = {Pith},
  title        = {Pith review of: Modelling helium in exoplanet atmospheres. A revised network with photoelectron-driven processes},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/QBWYHYFJ}},
  note         = {Machine review of arXiv:2505.12148}
}

abstract

The He I line at 1.08 $\mu$m is a valuable tracer of atmospheric escape in exoplanet atmospheres. We expand past networks used to predict the absorbing He(2$^3S$) by including, firstly, processes that involve H$_2$ and some molecular ions and, secondly, the interaction of photoelectrons with the atmosphere. We survey the literature on the chemical-collisional-radiative processes that govern the production-loss of He(2$^3S$). We simulate the atmospheric outflow from the Neptune-sized GJ 436 b by coupling a hydrodynamic model that solves the bulk properties of the gas and a Monte Carlo model that tracks the energy degradation of the photoelectrons. We identify Penning ionization of H as a key He(2$^3S$) loss process at GJ 436 b and update its rate coefficient to a value consistent with the most recent available cross sections. The update affects notably the predicted strength of the He I line. For GJ 436 b, photoelectron-driven processes (mainly ionization and excitation) modify the He(2$^3S$) population in layers too deep to affect the in-transit spectrum. The situation might be different for other atmospheres though. The spectral energy distribution of GJ 436 has a strong effect on the predicted in-transit signal. The published non-detections of the He I line for GJ 436 b are reasonably consistent with our model predictions for a solar-metallicity atmosphere when the model adopts a recently proposed spectral energy distribution. The interpretation of the He I line at 1.08 $\mu$m is model-dependent. Our revised network provides a general framework to extract more robust conclusions from measurements of this line, especially in atmospheres where H$_2$ remains abundant to high altitudes. We will explore additional, previously-ignored processes in future work.

Figures

Figures reproduced from arXiv: 2505.12148 by the authors.

**Figure 1.** MUSCLES SED (black) and X-Exoplanets SED (grey) at 1 AU and the spectral resolution adopted here. The quoted numbers refer, from left to right, to the integration over the intervals 0→100 Å; 0→503 Å; 0→911 Å; 0→2,600 Å, in units of erg cm−2 s −1 . relatively minor because for a temperate planet such as GJ 436 b the geometric size of the region between 100 and 1 dyn cm−2 is notably less than that of the layer masked… view at source ↗

**Figure 2.** Top. From the MUS-a and -b models, production rates of primary (dashed lines) and secondary (dotted lines) electrons. Colors separate the contributions by donor. The dashed black line refers to the primaries summed over all donors. The solid black line refers to the total of primaries and secondaries summed over all donors. Bottom. Number densities. Dashed and solid lines refer to MUS-a and -b, respectively. Each pa… view at source ↗

**Figure 3.** From the MUS-b and X-Exo-b models, temperature and velocity profiles. to the in-transit spectra. In contrast, the He(23S ) produced by radiative recombination forms at higher altitudes and effectively sets the stellar area masked by the He i line during transit. It is difficult to anticipate how general this finding is, and whether the He(23S ) formed from photoelectron-driven excitation makes a bigger difference at… view at source ↗

Figures from the paper (2 more)

**Figure 4.** Figure 4: From the MUS-b model. Rates of the dominant He(23S ) production (top) and destruction (bottom) processes; e− refers to thermal electrons, and e ∗ to photoelectrons. 6. Summary We propose a revised network of chemical-collisional-radiative processes for modelling He(23S…

**Figure 5.** Figure 5: Rate coefficients for total ionization through the processes He(23S )+H→He(11S )+H ++e − , →HeH++e − . We calculated them from the (scanned) cross sections reported in the quoted references over a range of temperatures commensurate with the range of energies at which…

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