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The Effect of Weak Cosmic Ray Heating Events on the Desorption of $\rm H_2$

T0 review · 0 major / 4 minor · reviewed 2026-08-06 · deepseek-v4-flash

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Pith's one-line read Frequent weak cosmic-ray heating events do not desorb H2 from interstellar grains fast enough to prevent its accumulation on 0.1 µm dust.

desk verdict A solid, clearly-scoped negative result: weak cosmic-ray heating events do not solve the H2 freeze-out problem for 0.1 micron grains, and the paper's new treatment of the full Tmax distribution is worth engaging with. read the letter →

arxiv 2507.01612 v1 pith:ROFKW6H7 submitted 2025-07-02 astro-ph.GA

O. Sipilä , K. Silsbee , N. Carbajal , P. Caselli , M. Padovani This is my paper
classification astro-ph.GA
keywords cosmic-rayinduceddesorptionweakheatingeventsH2freeze-outinterstellaricesgas-grainchemistrymolecularhydrogendustastrochemistry
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

Molecular hydrogen is by far the most abundant molecule in space, but secure detections of H2 in interstellar ices are missing, while standard chemical models routinely predict huge H2 freeze-out on dust. This paper asks whether the frequent but weak cosmic-ray hits that transiently warm grains to a few tens of kelvin can remove H2 quickly enough to resolve that mismatch. Using a gas-grain model that sums cosmic-ray desorption over a full distribution of peak grain temperatures rather than a single hot spike, the authors conclude that the weak events do not occur often enough: H2 adsorbs faster than the strikes can desorb it, at least for the canonical 0.1 µm spherical grain. If correct, cosmic-ray desorption is not the mechanism that keeps H2 out of interstellar ices, and other processes—such as coverage-dependent binding energies—remain necessary; the weak events do, however, affect lightly bound species like N2 at low column densities.

What carries the argument

The central object is the discretized cosmic-ray desorption rate coefficient of Eq. (5), $$k_{\rm CRD}(i)=\sum_j \min\!\left[f(a,$T_j^{{\max}}$)\,k_{\rm therm}(i,$T_j^{{\max}}$),\;(\tau_{\rm heat}^j)^{-1}\right],$$ which replaces the single fixed $T_{\max}=70$ K value of earlier models with a sum over a spectrum of peak temperatures. The minimum enforces the physical constraint that desorption cannot occur more often than the grain is struck by a cosmic ray. The load-bearing comparison is that for $T_{\max} \gtrsim 14$ K the uncapped H2 coefficient exceeds $\tau_{\rm heat}^{-1}$, so every potentially effective strike is capped, while strikes with $T_{\max}<14$ K are too cold to matter. The grain cooling time that enters through $f(a,T_j^{\max})$ is itself time-dependent, being set by the evolving ice composition via Eq. (2).

What would settle it

Extend the sum in Eq. (5) over a realistic grain size distribution that includes sub-0.1 µm grains; if the size-averaged H2 desorption rate then exceeds the adsorption rate at 10 K, the null result rests on the monodisperse assumption rather than on the physics of weak heating events.

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Extended reading notes

Core claim

This paper's central claim is that weak cosmic-ray heating events—the frequent hits that warm a grain only to a few tens of kelvin—do not desorb H2 from interstellar grains often enough to keep it from accumulating, at least for the canonical grain radius of 0.1 µm. The reason is the cap built into Eq. (5): for peak temperatures above roughly 14 K the uncapped H2 desorption coefficient $k_{\rm H_2}$ is already larger than the grain heating frequency $\tau_{\rm heat}^{-1}$, so the physical rate is pinned at $\tau_{\rm heat}^{-1}$; for temperatures below 14 K the strikes are too cold to desorb H2 efficiently. Summing over the full distribution of $T_{\max}$ therefore leaves the total H2 desorption rate below the adsorption rate, so including weak events changes the predicted H2 ice abundance very little compared with earlier strong-event-only models. The cap is shown to be the controlling factor: removing it lets the model destroy H2 ice rapidly, but those solutions are unphysical because a molecule cannot desorb more often than the grain is struck.

Load-bearing premise

The load-bearing premise is that the grain population is monodisperse spherical dust with radius 0.1 µm; if smaller grains dominate the population and reach desorbing temperatures often enough, the conclusion that weak cosmic-ray events cannot desorb H2 would break down.

Editorial extensions

If this is right

  • The paper's result implies that cosmic-ray desorption cannot resolve the longstanding H2 freeze-out problem for 0.1 µm dust, so the H2 ice population must be controlled by other physics, such as coverage-dependent binding energies.
  • Chemical models that omit the strike-frequency cap overestimate cosmic-ray desorption for weakly bound species, with the error growing as binding energy decreases; the cap should be included even in treatments that use a single fixed peak temperature of 70 K.
  • Weak heating events still matter for other lightly bound ice species: at low column densities they reduce N2 and CO ice abundances, and at high densities they produce small gas-phase abundance shifts, so cloud chemistry models may need the full temperature spectrum.
  • If H2 is allowed to act as a grain coolant, the grain cooling time shortens dramatically and N2 (and hence N2H+) is heavily depleted, which conflicts with observations; the authors take this as evidence that the real H2 ice content must be low.
  • Using a higher cosmic-ray flux raises H2 desorption somewhat, but the effect remains small and decreases with density, so a stronger CR flux alone does not overturn the central conclusion.

Reading between the lines

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

  • A natural next step the authors leave open is to run Eq. (5) over a grain size distribution: sub-0.1 µm grains reach a given peak temperature with less deposited energy and are more numerous, so size-averaged H2 desorption could beat adsorption even though monodisperse 0.1 µm grains fail; this is the most direct way to test whether the null result generalizes.
  • Because the crossover near 14 K is set by the assumed H2 binding energy of about 500 K on water ice, a laboratory measurement of that binding energy on realistic amorphous ice would directly constrain whether weak events can ever be effective.
  • Applied to neighboring problems, the same machinery suggests that isotopic or spin-state variants of H2, whose binding energies differ slightly, could be desorbed at different rates by weak heating events; gas-phase ortho/para or HD abundance patterns might then carry a signature of the desorption mechanism.
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Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

0 major / 4 minor

Summary. This paper presents an updated cosmic-ray desorption (CRD) treatment for gas-grain chemical models in which the maximum grain temperature Tmax after a CR hit is drawn from a distribution of deposited energies, rather than fixed at 70 K as in the classic HH93 model. The authors apply the new treatment to three cloud environments (E1-E3) using heating frequencies from Kalvāns & Kalnin (2022) and the P18 low and high CR spectra. The central finding is that for the adopted monodisperse 0.1 μm grains, weak CR heating events (Tmax of a few tens of K) do not significantly enhance H2 desorption: for Tmax ≳ 14 K, the uncapped H2 desorption coefficient exceeds the CR strike frequency, so the rate is capped at the strike frequency, and the summed CRD rate remains below the adsorption rate. Weak events do affect other weakly bound species, mainly at low column densities. The paper also stresses the necessity of the physical cap in Eq. (5) and demonstrates that removing it yields unphysical results.

Significance. The paper makes a useful and falsifiable contribution: it generalizes the CRD formalism beyond the single-Tmax HH93 model, independently verifies the KK22 input data (Appendix A), and shows that the frequency cap, not the thermal desorption formula, controls H2 CRD for canonical 0.1 μm grains. The negative result is internally consistent and clearly demonstrated via Fig. 3 and Eq. (5). The authors are transparent about the main limitation — the monodisperse grain-size assumption — and explicitly defer size-distribution simulations to future work. Taken as a statement about 0.1 μm monodisperse grains, the result is solid; the abstract and conclusions would benefit from stating this qualifier more prominently so that readers do not overgeneralize the finding to interstellar grain populations.

minor comments (4)
  1. [Abstract and Section 5] The sentences "even the weak heating events do not occur often enough to lead to significant H2 desorption" (Abstract) and "Other ways of keeping the H2 ice population in check remain necessary" (Section 5) should carry the qualifier "for the adopted 0.1 μm monodisperse grains" in the same sentence. Section 4 and Appendix B state that smaller grains may overturn this conclusion, so placing the qualifier after the claim invites overgeneralization by readers.
  2. [Section 2.1, Eq. (5)] Please clarify that (τ^j_heat)^-1 in each term of Eq. (5) is the per-bin strike frequency for the discrete bin j, not the cumulative frequency of all events with Tmax above the bin value. The surrounding text in Section 3.1 is consistent with per-bin frequencies, but a one-sentence definition would remove ambiguity relative to the cumulative-looking curve in Fig. 3.
  3. [Reproducibility] The pyRate code and the processed KK22 tables underlying the simulations are not provided. Because the abundance curves in Figs. 2, 4, 6, 7, and 9 depend on a large chemical network, a data-availability statement or supplementary material for the input tables would improve reproducibility; the rate-cap argument itself is transparent enough to be checked independently.
  4. [Figure 8] The caption contains typographical errors: "T emperature" should be "Temperature" and "Kelvins" should be "Kelvin".

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the central claim is a simulation outcome bounded by a physically motivated strike-frequency cap, not a restatement of the model inputs.

full rationale

The paper's derivation chain is self-contained in the relevant sense. The input Tmax distributions and deposited energies are taken from Kalvāns & Kalnin (2022) and independently checked in Appendix A; the CRD rate in Eq. (5) is a sum over Tmax bins of the min of the nonlimited desorption coefficient and the strike frequency tau_heat^-1; and the conclusion that weak heating events do not significantly desorb H2 follows from comparing the capped, summed rate with the independently computed adsorption rate in the chemical model. The cap itself is not equivalent to the conclusion: it merely imposes the physical upper bound that desorption cannot occur more often than strikes, and the paper shows (Fig. 4) that removing it yields unphysical results. The self-citations to Sipilä et al. (2021) and Padovani et al. (2018) supply model components and CR spectra, but the target result is not asserted by those citations; the strike-frequency cap is justified by explicit physical reasoning in the text. The paper also explicitly flags its scope limitation: Section 4 states 'It is conceivable that in the case of a grain size distribution, weak heating events could provide a boost to H2 desorption coming off small grains,' and Appendix B restricts the conclusion to 'monodisperse and relatively large' grains. That is an admitted conditional scope, not a circular definition. No equation is fitted to the quantity it later predicts, and no load-bearing claim reduces by construction to its inputs.

Assumptions & free parameters 2 free parameters · 6 assumptions · 0 invented entities

The central claim rests on three pillars: the KK22 heating-frequency spectra, the S21 frequency cap, and the monodisperse 0.1 μm grain assumption. The first is externally sourced and independently checked in Appendix A; the second is physically motivated and stress-tested by the unphysical no-cap run (Fig. 4); the third is canonical but untested and is the paper's own stated caveat. These are the main liabilities, and the paper introduces no new entities.

free parameters (2)
  • Cosmic-ray ionization rate zeta = 1.3e-17 s^-1 (P18 Low); 1.0e-16 s^-1 (P18 High)
    Chosen for simplicity and held constant across environments; the paper notes a realistic treatment would be attenuation-dependent (Section 2.4).
  • Ice mantle thickness per environment = 0 μm (E1); 0.01 μm (E2); 0.025 μm (E3)
    Picked by hand from the KK22 data as appropriate for each extinction value; not derived from a self-consistent ice growth model (Section 2.2, Table 1).
assumptions (6)
  • domain assumption Monodisperse spherical grains with radius 0.1 μm
    Canonical grain size adopted to match S21; the authors flag that small grains could overturn the H2 conclusion (Section 4).
  • domain assumption CRD rate coefficient capped by the CR strike frequency (Eq. 4 and Eq. 5)
    Physical constraint introduced in S21: desorption cannot occur more often than grains are struck. Removing it yields unphysical depletion (Fig. 4).
  • domain assumption KK22 heating frequencies and deposited energies as functions of Tmax for the P18 Low and High CR spectra
    External input data from Kalvans and Kalnin (2022); independently recomputed in Appendix A with very similar results.
  • domain assumption Binding energies: H2 on water ice 500 K; CO 1150 K; N2 1000 K
    From Katz et al. (1999) and Garrod and Herbst (2006). The Fig. 3 crossing point depends on the H2 value; a dynamic-binding test down to about 420 K leaves the conclusion unchanged.
  • standard math Rate-equation chemistry through pyRate with the KIDA 2014 network
    Modeling framework described in Sipila et al. (2015) and S21; the network contains over 70,000 gas-phase and about 2000 grain-surface reactions (Section 2.4).
  • domain assumption CRD proportionality k_CRD = f(a, Tmax) k_therm(i, Tmax)
    The HH93/S21 formalism (Eq. 1) relating desorption efficiency to the thermal desorption rate at peak temperature, with f = tau_cool / tau_heat.

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Pith. "Pith review of The Effect of Weak Cosmic Ray Heating Events on the Desorption of $\rm H_2$." pith.science (2026). https://pith.science/paper/ROFKW6H7

@misc{pith2026250701612,
  author       = {Pith},
  title        = {Pith review of: The Effect of Weak Cosmic Ray Heating Events on the Desorption of $\rm H_2$},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/ROFKW6H7}},
  note         = {Machine review of arXiv:2507.01612}
}
abstract

The typical amount of molecular hydrogen (${\rm H_2}$) in interstellar ices is not known, but significant freeze-out of ${\rm H_2}$ on dust grains is not expected. However, chemical models ubiquitously predict large amounts of $\rm H_2$ freeze-out in dense cloud conditions, and specialized treatments are needed to control the $\rm H_2$ population on grains. Here we present a numerical desorption model where the effect of weak heating events induced by cosmic rays (CRs) that heat grains to temperatures of a few tens of Kelvin at high frequencies is included, improving upon earlier desorption models that only consider strong heating events (maximum grain temperature close to 100 K) that occur at a low frequency. A temperature of a few tens of Kelvin is high enough to induce efficient desorption of $\rm H_2$, but we find that even the weak heating events do not occur often enough to lead to significant $\rm H_2$ desorption. Taking the weak heating events into account does affect the predicted abundances of other lightly-bound species, but the effect is restricted to low column densities. We make here the canonical assumption that the grains are spherical with a radius of 0.1 $\mu$m. It is conceivable that in the case of a grain size distribution, weak heating events could provide a boost to $\rm H_2$ desorption coming off small grains, which are the most numerous. Further studies are still required to better quantify the role of CRs in the desorption of $\rm H_2$ and other weakly bound species.

Figures

Figures reproduced from arXiv: 2507.01612 by the authors.

Figure 1
Figure 1. Heating frequencies per unit temperature (νheat/T) and deposited energies (∆E) as a function of Tmax for 0.1 µm bare grains (simulation E1, top left), 0.1 µm grains coated with a 0.01 µm ice mantle (E2, top right), or 0.1 µm grains coated with a 0.025 µm ice mantle (E3, bottom left). Solid lines reproduce the data from Kalv¯ans & Kalnin (2022) assuming either the P18 Low (red) or High (blue) CR spectrum. Pink, orang… view at source ↗
Figure 2
Figure 2. Abundances with respect to H2 of selected gas phase (top) and grain-surface (bottom; labeled as “ice”) species as a function of time in physical conditions E1 to E3 (columns from left to right), assuming the P18 Low CR spectrum. Solid lines indicate results of simulations using the variable Tmax CRD model, while dashed lines indicate results of simulations using the S21 CRD model. weakly bound species like H2 [PITH… view at source ↗
Figure 3
Figure 3. Nonlimited CRD rate coefficient of H2 (kH2 ; see text) and the grain heating frequency (inverse of the heating time; τ −1 heat) as a function of Tmax in the E2 model. The evolutionary time, which affects the grain cooling time and hence the value of f(0.1µm, Tmax) at each Tmax, is set to t = 105 yr. is so small so as to be only very slightly visible in the plot; this is because of the low amount of N2 in the ice at … view at source ↗
Figures from the paper (6 more)
Figure 4
Figure 4. Figure 4: Abundances with respect to H2 of selected gas phase (top) and grain-surface (bottom; labeled as “ice”) species as a function of time in physical conditions E2, as￾suming the P18 Low CR spectrum. Solid lines indicate re￾sults of simulations using the variable Tmax CRD m…
Figure 5
Figure 5. Figure 5: Time-dependent desorption rate coefficients (kCRD) of H2, N2, and CO in physical conditions E3. Solid lines show results calculated with the variable Tmax model, while dashed lines show results calculated using the S21 CRD model. 103 104 105 106 t [yr] 10−10 10−9 10−8 …
Figure 6
Figure 6. Figure 6: Abundances with respect to H2 of selected gas phase (top) and grain-surface (bottom; labeled as “ice”) species as a function of time in physical conditions E2, as￾suming the P18 Low CR spectrum. Solid lines indicate re￾sults of simulations using the variable Tmax CRD m…
Figure 7
Figure 7. Figure 7: Abundances with respect to H2 of selected gas phase (top) and grain-surface (bottom; labeled as “ice”) species as a function of time in physical conditions E1 to E3 (columns from left to right), assuming the P18 Low CR spectrum. Solid lines indicate results of simulati…
Figure 8
Figure 8. Figure 8: Comparison of the heating frequencies given in Kalv¯ans & Kalnin (2022) with those we calculated. The three panels correspond to the environments (mantle thickness and composition, and amount of shielding material) E1 to E3 as described in the main text. In the legend,…
Figure 9
Figure 9. Figure 9: As [PITH_FULL_IMAGE:figures/full_fig_p014_9.png]

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