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The Astrochemical Impact of Cosmic Rays in Protoclusters II: CI-to-H$_2$ and CO-to-H$_2$ Conversion Factors

T0 review · 3 major / 4 minor · reviewed 2026-08-14 · deepseek-v4-flash

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Pith's one-line read Cosmic rays from newborn stars may hold the Milky Way's CO-to-H2 conversion factor steady.

desk verdict A useful modeling study of how embedded protostellar CRs affect X_CO and X_CI, but the headline 'regulation' result holds only for one of two unconstrained transport models. read the letter →

arxiv 1908.06999 v1 pith:UWMO6RSL submitted 2019-08-19 astro-ph.GA

Brandt A.L. Gaches , Stella S.R. Offner , Thomas G. Bisbas This is my paper · ORCID
classification astro-ph.GA
keywords cosmicraysCO-to-H2conversionfactorX_COX_CIprotostellaraccretionshocksmolecularcloudchemistrystarformationefficiencycosmic-rayionizationrate
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 asks whether cosmic rays produced by accreting newborn stars inside a forming cluster change how astronomers convert carbon-monoxide or neutral-carbon emission into a molecular gas mass. Using one-dimensional cloud models whose chemistry computes cosmic-ray attenuation throughout the gas, it argues that embedded protostellar cosmic rays can regulate the conversion factors. The main result is that clouds with more than about 2% star formation efficiency have $X_{\rm CO} = (2.5 \pm 1)\times 10^{20}$ cm$^{-2}$ (K km s$^{-1}$)$^{-1}$, matching the Milky Way average, even as cloud surface density and efficiency vary widely. A reader should care because this suggests the Galaxy's nearly constant CO-to-H2 conversion factor is partly a consequence of the star formation process itself, not just a fixed property of molecular gas.

What carries the argument

The load-bearing object is the model of protostellar cosmic rays built from accretion-shock acceleration: each protostar produces a power-law momentum spectrum via diffuse shock acceleration, normalized by the shock energy, with maximum proton energies typically between 1 and 10 GeV. Those spectra are attenuated through the protostellar core column and then transported into the surrounding cloud either diffusively, with intensity falling as $1/r$, or rectilinearly, falling as $1/r^2$, combined with one of two external cosmic-ray spectra. Feeding these spectra into a modified photodissociation-region astrochemistry code that computes cosmic-ray attenuation in situ, together with the chemical network and CO and CI line emissivities, is what turns the cosmic-ray prescription into specific $X_{\rm CO}$ and $X_{\rm CI}$ predictions. The diffusive $1/r$ case is the one that lets embedded sources dominate the ionization rate and regulate the conversion factors.

What would settle it

Map the radial falloff of the cosmic-ray ionization rate around an embedded protostar using ${\rm H}_3^+$ or OH$^+$ absorption toward multiple sightlines: a $1/r$ profile supports the claim, while a $1/r^2$ profile would remove the predicted regulation of $X_{\rm CO}$.

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Extended reading notes

Core claim

The paper's central claim is that cosmic rays accelerated at protostellar accretion shocks, if they diffuse through the surrounding cloud, act as an internal source that regulates the CO-to-H2 conversion factor. Once the star formation efficiency exceeds roughly 2%, these embedded cosmic rays lower $X_{\rm CO}$ and flatten its dependence on cloud surface density and star formation efficiency, producing $X_{\rm CO} = (2.5 \pm 1)\times 10^{20}$ cm$^{-2}$ (K km s$^{-1}$)$^{-1}$, consistent with the Milky Way value and its scatter. The same mechanism lowers $X_{\rm CI}$ by over an order of magnitude and leaves a 1.2 dex dispersion, from $2\times 10^{20}$ to $4\times 10^{21}$ cm$^{-2}$ (K km s$^{-1}$)$^{-1}$, so the neutral-carbon conversion factor is far more sensitive to the assumed cosmic-ray model than $X_{\rm CO}$ is.

Load-bearing premise

The result stands on the premise that cosmic rays from embedded protostars diffuse through the cloud with a $1/r$ intensity profile, so internal sources dominate the ionization rate; if transport were rectilinear instead, declining as $1/r^2$, the paper finds essentially no effect on $X_{\rm CO}$.

Editorial extensions

If this is right

  • If the diffusive-transport model is right, $X_{\rm CO}$ should be nearly flat across clouds with star formation efficiency above roughly 2%, matching the observed Milky Way scatter.
  • Raising the assumed external cosmic-ray ionization rate to the observationally preferred $\zeta \approx 10^{-16}$ s$^{-1}$ lowers $X_{\rm CO}$ by 0.2 dex in low-surface-density clusters with $\Sigma_{\rm cl} < 3$ g cm$^{-2}$, which would trim typical molecular-gas mass estimates.
  • Embedded cosmic rays reduce $X_{\rm CO}$ by up to about 0.5 dex and $X_{\rm CI}$ by up to about 1.2 dex relative to models with no internal sources, so CI-based gas masses depend strongly on the assumed cosmic-ray environment.
  • The models reproduce the observed tendency for $X_{\rm CO}$ to decrease in extreme cosmic-ray environments such as starburst galaxies and the Galactic Center, implying that applying a single Milky Way conversion factor there would misestimate gas mass.

Reading between the lines

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

  • If this is right, $X_{\rm CO}$ may be partly self-regulating: more star formation makes more cosmic rays, which lowers $X_{\rm CO}$ and trims the inferred gas mass, so the conversion factor could buffer against environmental changes.
  • A direct test would be to measure $X_{\rm CO}$ in clouds with matched surface density but different star formation efficiencies; the model predicts a systematic drop in $X_{\rm CO}$ with efficiency only under diffusive cosmic-ray transport.
  • Because $X_{\rm CI}$ is so sensitive to the cosmic-ray model, comparing CI and CO maps in starbursts could constrain how cosmic rays actually travel through dense gas, which the paper identifies as an open question.
  • At high redshift, where galaxies form stars efficiently, CO-based gas masses computed with the Milky Way $X_{\rm CO}$ could be systematically too high if embedded cosmic rays matter as modeled here.
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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

3 major / 4 minor

Summary. The paper uses the modified 3d-pdr astrochemistry code from Paper I, which includes in-situ cosmic-ray attenuation, to compute the CO-to-H2 and CI-to-H2 conversion factors X_CO and X_CI for one-dimensional models of protoclusters embedded in molecular clouds. The models vary the external cosmic-ray spectrum (low and high), the presence of embedded protostellar cosmic rays, and the cosmic-ray transport law (diffusive 1/r vs rectilinear 1/r^2). The paper reports that for the diffusive-transport model with a low external spectrum, clouds with star formation efficiencies above 2% have X_CO = (2.5 +/- 1) x 10^20 cm^-2 (K km s^-1)^-1, consistent with Milky Way observations; that embedded sources reduce X_CO and X_CI and lower their variance; and that X_CI is highly sensitive to the assumed cosmic-ray model.

Significance. If the central mechanism holds, the paper offers a physically motivated explanation for the near-constancy of X_CO in the Milky Way and Local Group, and it predicts systematically lower X_CO in extreme cosmic-ray environments such as starbursts and galactic centers. The study is a forward-modeling calculation rather than a fit to the Milky Way value: it uses explicit cosmic-ray spectra, a public astrochemistry code, realistic protostellar mass sampling, and treats the observed Milky Way X_CO as an external benchmark. These are genuine strengths. However, the headline regulator claim is realized only in the 1/r diffusive transport branch, and the paper itself states that the transport law is unknown; this is the main load-bearing weakness addressed below.

major comments (3)
  1. [Section 2; Section 3.3; Abstract] The abstract-level claim that embedded protostellar cosmic rays "regulate X_CO and decrease its variance" is only true for the diffusive (1/r) transport branch. Section 2 states that it is not known how cosmic rays transport through molecular clouds and therefore considers both 1/r and 1/r^2 regimes, while Section 3.3 reports that if embedded cosmic rays transport as r^-2 "there is no impact on X_CO because the CRIR is lower and dominated by the CRs originating from external sources rather than internal." The quoted value X_CO = (2.5 +/- 1) x 10^20 cm^-2 (K km s^-1)^-1 for clouds with SFE > 2% and the Milky Way consistency shading in Figure 1 are properties of the LDI branch only. Because the transport exponent determines whether the mechanism operates at all, the central astrophysical claim has a binary sensitivity to an assumption the authors explicitly identify as unknown. I request that the abstract and Section 3.4 be rephrased to make the LDI/diffusive-transport condition explicit, and that the paper either provide an independent physical or observational reason to prefer 1/r transport or present both branches as equally viable and report the resulting range of X_CO and X_CI.
  2. [Section 2 (chemistry network)] The UMIST12 network used here excludes freeze-out, desorption, and gas-grain reactions. Freeze-out can strongly reduce gas-phase CO in the cold, dense gas that dominates the H2 column in these models, and CO depletion is a first-order effect for the absolute value of X_CO. The sensitivity test reported for grain-assisted recombination of C+ and He+ does not constrain the freeze-out/desorption uncertainty. Since the paper's headline is a specific numerical agreement with the Milky Way value to within ~0.3 dex, the authors should either include a freeze-out/desorption sensitivity test or give a quantitative argument for why its omission does not bias X_CO and X_CI at that level.
  3. [Section 2, Eq. (4)] The text says that the integrated flux defined by Eq. (4) assumes the interstellar medium is entirely optically thin, immediately after stating that 3d-pdr uses an escape probability method to account for line opacity. These two statements are in tension. If the emissivity epsilon in Eq. (4) already includes the escape probability, then the integrated flux is not optically thin and the sentence is misleading; if it does not, the CO(1-0) flux from optically thick lines will be overestimated and X_CO underestimated. Please clarify which is the case and, if necessary, quantify the effect on the reported X_CO values.
minor comments (4)
  1. [Figure 3] The y-axis labels appear to render as "log X_CI,i X_CI,LNA" and "log X_CO,i X_CO,LNA" without a division sign; please correct the typesetting so the ratio is clear.
  2. [Section 3.5] The word "efficiences" should be "efficiencies".
  3. [Section 2] The reference to "Offner et al. 2019, sub." is to an unpublished manuscript; please update it or mark it as in preparation consistently.
  4. [Title and throughout] The notation "CI" is conventionally written as "C I" for neutral atomic carbon; consider using "C I" to avoid confusion with the cyanogen molecule CI or with the abbreviation for confidence interval.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: X_CO and X_CI values are computed from astrochemical models and benchmarked externally against Milky Way observations.

full rationale

The paper's X_CO and X_CI are direct outputs of the astrochemical models: Equations (1)-(2) define the conversion factors from computed H2 column densities and line fluxes, and the cloud grid over Sigma_cl and epsilon_g is an input grid, not a fit to X_CO. The Section 3.4 comparison to the Milky Way value X_CO,MW = 2e20 cm-2 (K km s-1)-1 (Bolatto et al. 2013) is an external benchmark, so the agreement for LDI clouds with epsilon_g > 2% is a prediction, not a fitted target. Self-citations to Paper I and Gaches & Offner 2018b supply the modified code and CR acceleration prescription, but those papers do not contain the X_CO result and the code is public, so the citation is independent support rather than load-bearing. The transport uncertainty is explicitly stated ('It is not known exactly how CRs transport through molecular clouds', Section 2) and both diffusive (1/r) and rectilinear (1/r^2) branches are tested; Section 3.3's admission that r^-2 transport gives no impact is a model-sensitivity caveat, not a definitional reduction. No equation or fitted parameter is identical to the claimed result by construction.

Assumptions & free parameters 8 free parameters · 7 assumptions · 0 invented entities

The central claim rests on a heavily parameterized model: a DSA prescription, an assumed core attenuation factor, a binary transport law, a chosen density profile, and external CR spectra. Most parameters are adopted from the authors' prior work or the literature, not fit to the Milky Way X_CO. The strongest sensitivity is the transport law: the 'regulation' result only holds for diffusive transport. No new physical entities are introduced.

free parameters (8)
  • CR power-law index a in j(p) = not specified in text; set by shock compression factor
    Equation 3 defines the accelerated proton spectrum; the value controls the hardness of the spectrum and hence the depth of ionization, but is not varied or constrained in this work.
  • CR normalization j0 = not specified; computed from shock energy and acceleration efficiency
    Sets the absolute CR flux from each protostar; depends on an assumed acceleration efficiency carried from previous work.
  • Injection momentum p_inj = not specified; tied to shock gas temperature
    Low-energy cutoff of the DSA spectrum in Equation 3; affects the ionization rate in dense gas.
  • Maximum CR proton energy = 1-10 GeV
    Constrained by collisional losses and upstream diffusion (Gaches & Offner 2018b); determines penetration depth and heating.
  • Core attenuation column ratio Sigma_core / Sigma_cl = 1.22
    Assumed relation between core and cloud column density following Padovani et al. 2009; controls how many CRs escape the core.
  • CR transport law exponent = binary: r^-1 (DI) vs r^-2 (RI)
    Unknown transport physics; the central result depends on the r^-1 choice.
  • Outer cloud density n0 = 100 cm^-3
    Edge density of the 1D cloud model; sets the density profile normalization independently of surface density.
  • Protostellar CR acceleration efficiency = not stated explicitly
    Hidden inside j0; the fraction of shock energy going into cosmic rays is a free parameter carried from Paper I.
assumptions (7)
  • domain assumption DSA accelerates protons at the protostellar accretion shock with a power-law spectrum (Equation 3).
    Standard diffusive shock acceleration theory for non-relativistic shocks; invoked in Section 2.
  • ad hoc to paper CRs free-stream out of the protostellar core with attenuation set by Sigma_core = 1.22 Sigma_cl.
    Section 2 states shallower attenuation produces too much CR heating, so the choice is tuned to avoid that.
  • ad hoc to paper Two transport laws for CRs in the cloud, 1/r and 1/r^2, bracket the unknown real transport.
    Section 2 says the transport is not known; these are assumed models, not derived.
  • domain assumption The line-integrated flux assumes optically thin emission (Equations 4-5).
    Used for both CO and CI; for CO this is questionable since CO J=1-0 is typically optically thick, but the paper uses it for all models.
  • domain assumption The UMIST12 gas-phase network with no freeze-out or gas-grain reactions is sufficient for CO and CI abundances.
    Section 2 lists this limitation; they tested grain-assisted recombination and found no significant effect on the conversion factors.
  • domain assumption One-dimensional spherical clouds with n(r) = n0 (R/r)^2 represent protocluster environments.
    Geometry and density profile chosen in Section 2; 1D approximations of real clumpy clouds.
  • domain assumption External CR spectra L and H from Ivlev et al. 2015 bracket the interstellar flux.
    Input spectra from prior literature; used as the external boundary condition.

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Cite this review

Pith. "Pith review of The Astrochemical Impact of Cosmic Rays in Protoclusters II: CI-to-H$_2$ and CO-to-H$_2$ Conversion Factors." pith.science (2026). https://pith.science/paper/UWMO6RSL

@misc{pith2026190806999,
  author       = {Pith},
  title        = {Pith review of: The Astrochemical Impact of Cosmic Rays in Protoclusters II: CI-to-H$_2$ and CO-to-H$_2$ Conversion Factors},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/UWMO6RSL}},
  note         = {Machine review of arXiv:1908.06999}
}
abstract

We utilize a modified astrochemistry code which includes cosmic ray attenuation in-situ to quantify the impact of different cosmic-ray models on the CO-to-H$_2$ and CI-to-H$_2$ conversion factors, $X_{\rm CO}$ and $X_{\rm CI}$, respectively. We consider the impact of cosmic rays accelerated by accretion shocks, and show that clouds with star formation efficiencies greater than 2\% have $X_{\rm CO} = (2.5 \pm 1)\times10^{20}$ cm$^{-2}$(K km s$^{-1}$)$^{-1}$, consistent with Milky Way observations. We find that changing the cosmic ray ionization rate from external sources from the canonical $\zeta \approx 10^{-17}$ to $\zeta \approx 10^{-16}$ s$^{-1}$, which better represents observations in diffuse gas, reduces $X_{\rm CO}$ by 0.2 dex for clusters with surface densities below 3 g cm$^{-2}$. We show that embedded sources regulate $X_{\rm CO}$ and decrease its variance across a wide range of surface densities and star formation efficiencies. Our models reproduce the trends of a decreased $X_{\rm CO}$ in extreme cosmic ray environments. $X_{\rm CI}$ has been proposed as an alternative to $X_{\rm CO}$ due to its brightness at high redshifts. The inclusion of internal cosmic ray sources leads to 1.2 dex dispersion in $X_{\rm CI}$ ranging from $2\times10^{20} < X_{\rm CI} < 4\times10^{21}$ cm$^{-2}$ (K km s$^{-1}$)$^{-1}$. We show that $X_{\rm CI}$ is highly sensitive to the underlying cosmic ray model.

Figures

Figures reproduced from arXiv: 1908.06999 by the authors.

Figure 1
Figure 1. Color shows log XCO/XMW where XMW = 2 × 1020 cm−2 (K km s−1 ) −1 as a function of gas surface density, Σcl, and star formation efficiency, εg. White shaded cells show regions where XCO is consistent with Milky Way observations, −0.3 ≥ log XCO/XMW ≤ 0.3. The hatched regions indicate different cosmic-ray environments, where we define hζix, the spatially-averaged CRIR, hζix < 10−16 as “quiescent”, 10−16 < hζix < 10−15 … view at source ↗
Figure 2
Figure 2. Same as [PITH_FULL_IMAGE:figures/full_fig_p007_2.png] view at source ↗
Figure 3
Figure 3. Logarithm of the ratio of XCO and XCI for a given cosmic-ray model i ⊂ (LNI, HNI, LRI, LDI, HDI) compared to model LNA (low, external spectrum and no attenuation). Black line indicates the mean. Magenta line indicates the median. XCO only by 0.2 dex, within the measured spread of XCO in the MW (Bolatto et al. 2013). The difference in XCI is more pronounced: it declines by an order of magnitude for the lowest surface… view at source ↗

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