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REVIEW 4 major objections 4 minor 57 references

High sensitivity molecular line observations towards the L1544 pre-stellar core challenge current models

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

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Pith's one-line read High-sensitivity spectra of L1544 show sulphur abundances that differ from chemical models by up to a factor of 20, and single-line fits are degenerate.

desk verdict Valuable data and an honest account of fitting degeneracy, but the sulphur-chemistry 'challenge' rests on abundance profiles the authors themselves show are not unique. read the letter →

arxiv 2508.20355 v1 pith:6UHADFXO submitted 2025-08-28 astro-ph.GA

J. Ferrer Asensio , S. S. Jensen , S. Spezzano , P. Caselli , F. O. Alves , O. Sipilä , E. Redaelli This is my paper · ORCID
classification astro-ph.GA
keywords ISM:moleculescloudsradiolines:ISMstars:formationradiativetransferpre-stellarcoressulphurchemistryL1544
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 current chemical models can reproduce the molecular emission from the pre-stellar core L1544 when confronted with unusually sensitive, high-resolution spectra. Using a non-local-thermodynamic-equilibrium radiative transfer code coupled to a Markov Chain Monte Carlo fit of simple step abundance profiles, the authors find that no single-transition fit converges to a unique solution. They also find that the best-fitting abundances for the sulphur-bearing species CS, C$^{34}$S, SO and $^{34}$SO deviate from the pyRate chemical network predictions by factors of 2 to 20, with the depletion radius shifted outward for CS, C$^{34}$S and $^{34}$SO, while SO is overproduced by the model by about a factor of 2. Because L1544 is a benchmark pre-stellar core, this matters: it suggests current sulphur networks are missing an important depletion process, and that high-sensitivity single lines alone cannot pin down the core's abundance structure.

What carries the argument

The machinery is the combination of a non-LTE radiative transfer solver and a Monte Carlo sampler over a deliberately simple abundance model. The LOC code solves the statistical equilibrium equations with an accelerated $\lambda$ iteration and computes 1D line radiative transfer through the contracting Bonnor-Ebert sphere model of L1544; the MCMC sampler then explores five parameters: inner abundance $a_\mathrm{in}$, outer abundance $a_\mathrm{out}$, depletion radius $r$, velocity scaling $f_v$, and turbulent velocity dispersion $\sigma_\mathrm{turb}$, with the prior constraint $a_\mathrm{in} < a_\mathrm{out}$. The 'extended' variant adds a constant-abundance envelope between 0.32 and 1 pc. The abundance profiles that emerge are compared with pyRate, a pseudo-time-dependent chemical model run in concentric shells of the same physical model; this comparison is what carries the paper's challenge to sulphur chemistry.

What would settle it

Fit several rotational lines of CS, C$^{34}$S, SO and $^{34}$SO (for example J = 1-0, 2-1 and 3-2 for CS and SO) jointly toward the L1544 dust peak with the same LOC + MCMC machinery. If the joint fit converges to outer abundances within a factor of 2 of the pyRate predictions, the single-line sulphur discrepancy is an artefact of degeneracy rather than a chemical-network failure.

Watch

Extended reading notes

Core claim

On the authors' own terms, the central discovery is a mismatch between what the observations require and what the chemistry predicts. The observed C$^{34}$S and CS lines toward the L1544 dust peak are best matched by step abundance profiles whose outer abundances are roughly 9 and 20 times higher, respectively, than the peak abundances produced by the pyRate chemical model; for $^{34}$SO the fitted outer abundance is about 3 times higher, though within errors, and for SO it is about 2 times lower. In all sulphur-bearing species the depletion radius is shifted outward relative to the model's abundance drop, though with large uncertainties for the SO species. For C$^{34}$S and CS, the fitted abundances are so high that the inferred optical depths reach $\tau \sim 4$ and $\tau \sim 10^5$, unusually large for a rare isotopologue and for a supposedly optically thinner line. The paper also establishes that fitting a single transition per isotopologue leaves most parameters unconstrained, with flat or multi-peaked posteriors, so the fitted profiles are degenerate; Appendix A explicitly cautions that the result 'may not be the correct or a physically accurate result.' These findings are interpreted as a challenge to current chemical networks, specifically their sulphur depletion treatment, which typically begins from a reduced elemental sulphur abundance to solve the so-called sulphur depletion problem.

Load-bearing premise

The load-bearing premise is that the MCMC-fitted step abundance profiles are a faithful empirical benchmark; the paper itself notes the fits can be degenerate, with flat or multi-peaked corner plots and parameters sitting at prior boundaries, and that the result may not be physically accurate.

Editorial extensions

If this is right

  • Sulphur chemical networks for dense cores need to be revisited: the paper argues that starting from the elemental cosmic abundance of sulphur with a consistent S-depletion process would reproduce the observed CS, C$^{34}$S, SO and $^{34}$SO abundances better than the currently 'depleted' initial-S assumption.
  • Single-line fits to pre-stellar core spectra should not be used to claim a unique abundance structure; multi-line fits per species are necessary to break the degeneracies the corner plots reveal, and combined fits of isotopologue pairs do not by themselves add enough constraints.
  • H$_{2}$CO, like HCO$^{+}$, must be present in the diffuse envelope beyond 0.32 pc to reproduce deep self-absorption, so radiative transfer models of such lines cannot stop at the traditional core boundary.
  • The layering inferred from line morphologies — HCO$^{+}$/H$_{2}$CO outermost, CS and c-C$_{3}$H$_{2}$ in a static middle layer, SO in a contracting intermediate layer, C$^{34}$S and HC$^{17}$O$^{+}$ deepest — is a concrete prediction that mapping the core in these lines can test.
  • The high fitted optical depths for C$^{34}$S ($\tau\sim4$) and CS ($\tau\sim10^5$) imply that even rare-isotopologue lines toward L1544 may be optically thick, complicating simple column-density estimates.

Reading between the lines

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

  • Editorial inference: if the pyRate under-prediction is caused by the 'depleted' initial sulphur abundance assumption, then a testable fix is to rerun the same radiative transfer comparison with a network that begins from cosmic sulphur and follows freeze-out self-consistently; that would distinguish a missing reaction set from a wrong boundary condition.
  • Editorial inference: the degeneracy seen here implies that published abundance profiles of pre-stellar cores derived from single molecular transitions may carry systematic uncertainties of order the factors quoted, and comparisons between species should treat them as correlated rather than independent constraints.
  • Editorial inference: the newly measured $^{34}$SO rest frequency (97715.395 MHz) shifts the line velocity by 0.23 km/s relative to the old value; re-observing the 6.9 km/s blue shoulder at higher angular resolution could reveal whether it is an unresolved second component or a genuinely new kinematic feature.
  • Editorial inference: if sulphur is indeed more abundant in the outer core than chemical models predict, the standard 'sulphur depletion problem' may be at least partly a network completeness problem; the same comparison could be applied to other cores such as L183, where SO emission is extended, to see whether the mismatch is generic.
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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

4 major / 4 minor

Summary. The paper presents new high-sensitivity, high-spectral-resolution IRAM 30m observations of HCO+, CS, C34S, H2CO, c-C3H2, SO, and 34SO toward the L1544 pre-stellar core, together with the HC17O+ line from an earlier work. The authors couple the LOC non-LTE radiative transfer code with an MCMC sampler and fit simple two-step abundance profiles (ain, aout, r, fv, sigma_turb) to each transition. They then compare the fitted abundance profiles with the pyRate chemical model and conclude that current chemical models, particularly for sulphur chemistry, poorly reproduce the observations. They also argue that single-transition fits cannot find a unique global minimum, that the lines trace distinct layers with different kinematics, and that an extended envelope is needed for HCO+ and H2CO. The paper includes optical depth estimates, corner plots, and combined isotopologue fits in the appendices.

Significance. If the fitted abundance profiles were robust, the reported factor-of-2 to factor-of-20 discrepancies for CS and C34S and the outward-shifted depletion radii would be an important challenge to sulphur chemical networks and would motivate a more consistent treatment of sulphur depletion. The observational dataset is genuinely valuable, and the paper is commendably transparent about degeneracies: it explicitly states that single-line fits cannot locate a global minimum, shows flat and multi-peaked posteriors, and warns in Appendix A that the LOC+MCMC result 'may not be the correct or a physically accurate result.' This honesty is a strength. However, for the reasons developed in the major comments, the empirical benchmark used to evaluate pyRate is not robust enough to carry the central sulphur-chemistry conclusion as stated. The paper is best viewed as a careful presentation of new data and a demonstration of the limitations of single-line abundance fitting, rather than as a definitive falsification of current sulphur chemistry models.

major comments (4)
  1. [Section 5 and Appendix A] The central claim that pyRate poorly reproduces sulphur chemistry depends on using the LOC+MCMC step-abundance fits as the empirical benchmark, but the paper itself establishes that these fits are non-unique. Section 5 states that high-resolution single lines do not provide enough information to converge to one solution, and Appendix A concedes that the fit may not be physically accurate. This is the load-bearing logical gap: the abundance profiles are then compared quantitatively with pyRate (e.g., the factor-of-9 and factor-of-20 excesses for C34S and CS), despite the fact that the profiles themselves are admitted to be underconstrained. The conclusion 'poor reproduction of sulphur chemistry' therefore needs either multi-line constraints for the relevant species or a substantial softening of the claim.
  2. [Section 4.2.1 and Appendix A, Figs. 16 and 20] The CS fit, which provides the largest abundance discrepancy (a factor of about 20) and the highest optical depth (about 10^5), is the least trustworthy of the fits. The MCMC drives fv to 1.99 and sigma_turb to 0.01, both at the edges of the priors, and the authors themselves call the resulting optical depth 'unexpectedly high.' A fit that only succeeds by pinning two parameters to the prior boundaries and producing a pathological optical depth cannot alone support the conclusion that pyRate underestimates the outer CS abundance by two orders of magnitude. This point needs to be addressed with additional transitions or with an explicit demonstration that the inferred aout is insensitive to the prior boundaries.
  3. [Section 4.1.2 and Fig. 18] The 34SO fit has a flat inner-abundance posterior and only weak constraints on r, fv, and sigma_turb. Despite these broad uncertainties, Section 5.1 describes the depletion radius as 'significantly displaced' from the pyRate prediction. The paper's own criterion in Section 3.1 is that flat histograms indicate that the parameter is not constrained; under that criterion, the 34SO depletion-radius shift is not statistically established. The qualitative discussion of a sulphur-chemistry problem should be separated from the parts of the analysis that are actually constrained, such as the better-determined aout value.
  4. [Sections 4.2.2 and 5.2, Fig. 8] The abundance comparison is not uniformly in one direction: for SO the fitted aout is a factor of about 2 lower than the pyRate maximum, while for CS and C34S the fitted values are higher than pyRate, and for 34SO the values agree within errors. The abstract and conclusions frame the result as 'a poor reproduction of sulphur chemistry,' but the heterogeneous pattern of over- and underproduction does not point to a single missing depletion process without a more specific mechanistic test. The discussion of SO + C+ destruction and the initial sulphur abundance assumption in Section 5.2 is plausible, but it is not quantitatively connected to the fitted profiles. The conclusions should be reframed as a demonstration that current models fail to match the shape and normalization of the sulphur-bearing profiles in a species-dependent way, rather than as a global sulphur-chemistry failure.
minor comments (4)
  1. [Section 2, Table 1] The rest frequency of 34SO is given as a private communication from the CAS laboratory; for reproducibility, this measurement should be published in a refereed context or documented in an accessible form before the paper is final.
  2. [Section 1] There is a typo in the introduction: 'the the ionization fraction' should read 'the ionization fraction.'
  3. [Section 5.3, Figure 14] The layered schematic of L1544 is based on line-profile morphology and fits with several poorly constrained radii; it would be helpful to label the figure explicitly as an illustrative stack rather than a quantitatively determined radial stratification.
  4. [Appendix C, Table 3] The combined isotopologue fits report sigma_turb = 0.00 with zero uncertainty in some cases, which likely indicates a poor exploration or a prior-boundary issue rather than a precise constraint; a brief comment on this would prevent readers from misinterpreting the reported precision.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the LOC+MCMC abundance fits are constrained by observed spectra, and the pyRate comparison is an external model benchmark.

full rationale

The paper's derivation chain is empirical rather than circular. The step-abundance parameters (ain, aout, r, fv, sigma_turb) are fitted by MCMC directly to IRAM 30m observed line profiles through the LOC non-LTE radiative transfer code; no quantity is fitted to a subset of data and then renamed as a prediction of the same quantity. The pyRate fractional abundance profiles compared in Section 4 are produced by an independent astrochemical network (Sipilä et al. 2015) under stated elemental-abundance assumptions, so the comparison is a genuine model-vs-data test. The authors' Appendix A caveat that 'with the lack of enough constraints, the result found by LOC + MCMC may not be the "correct" or a physically accurate result' is a robustness limitation, not evidence that a result reduces by construction to its inputs. Self-citations to Keto et al. (2015) for the 1D physical model and to Sipilä et al. (2015) for pyRate involve overlapping authors, but these models are used as the framework and benchmark and are checked against external observed spectra; no load-bearing argument depends on an unverified self-citation. The paper's own warning that single-transition fits cannot find a unique global minimum weakens the strength of the model comparison, but that is a correctness and robustness concern rather than circularity.

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

The central comparison rests on the MCMC-fitted step abundance profiles, which are free parameters, and on the adopted 1D spherical physical model and pyRate chemical network from prior work. No new physical entities are invented; the 'external layer' is a modelling component, not a new entity.

free parameters (6)
  • ain (inner fractional abundance, per species fit) = 1e-14 to 1e-9 (median values per species, Table 2)
    Inner constant abundance from 0 to r pc; fitted by MCMC for each molecule.
  • aout (outer fractional abundance, per species fit) = 1e-11 to 1e-7 (Table 2)
    Outer constant abundance from r to 0.32 pc (or edge of core); fitted by MCMC; often the only well-constrained parameter.
  • r (depletion radius, per species fit) = 884 to 19876 au (Table 2)
    Radius separating inner and outer abundance regions; fitted by MCMC; unconstrained for several species.
  • fv (velocity profile scaling, per species fit) = 0.56 to 1.99 (Table 2)
    Scaling factor for the Keto et al. (2015) radial velocity profile; reached the prior boundary for CS.
  • sigma_turb (turbulent velocity dispersion, per species fit) = 0.01 to 0.12 km/s (Table 2)
    Assumed constant across the core; fitted by MCMC; reached the prior boundary (0.01 approximately 0) for CS.
  • aext (external layer abundance) = 3.7e-9 (H2CO), 6.4e-10 (c-C3H2), pyRate value at 0.32 pc (HCO+)
    Fixed from diffuse cloud observations (Snow & McCall 2006) or from pyRate, not fitted.
assumptions (6)
  • domain assumption 1D spherically symmetric Bonnor-Ebert physical model of L1544 from Keto et al. (2015)
    Adopted without refitting; if density, temperature, or velocity profiles are wrong, abundance inferences change. Invoked in Section 3.1.
  • domain assumption Step abundance profile parameterization with ain <= aout
    Imposed depletion toward the center; structure of abundance profile defined in Section 3.2.
  • domain assumption External layer beyond 0.32 pc has constant physical properties equal to edge values
    Used for HCO+, H2CO, and c-C3H2 extended models; described in Section 3.1 and Figure 2.
  • domain assumption Collisional rate coefficients of main isotopologues apply to C34S and 34SO
    Stated in Table 1 note c; needed for radiative transfer of rare isotopologues.
  • domain assumption pyRate chemical network with depleted initial sulphur abundance
    Used as the chemistry benchmark; the depleted-S assumption is discussed in Section 5.2 as a possible cause of the discrepancy.
  • ad hoc to paper Uniform priors and parameter bounds for MCMC
    Bounds in Section 3.2 come from previous knowledge; CS fit ends at the boundary, affecting the derived solution.

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Cite this review

Pith. "Pith review of High sensitivity molecular line observations towards the L1544 pre-stellar core challenge current models." pith.science (2026). https://pith.science/paper/6UHADFXO

@misc{pith2026250820355,
  author       = {Pith},
  title        = {Pith review of: High sensitivity molecular line observations towards the L1544 pre-stellar core challenge current models},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/6UHADFXO}},
  note         = {Machine review of arXiv:2508.20355}
}
read the original abstract

The increased sensitivity and spectral resolution of observed spectra towards the pre-stellar core L1544 are challenging the current physical and chemical models. With the aim of further constraining the structure of L1544 as well as assessing the completeness of chemical networks, we turn to radiative transfer modelling of observed molecular lines towards this source. We obtained high-sensitivity and high-spectral resolution observations of HCO+ (J = 1 - 0), CS (J = 2 - 1), C34S (J = 2 - 1), H2CO (J ,Ka,Kc = 2,1,2 - 1,1,1), c-C3H2 (J,Ka,Kc = 2,1,2 - 1,0,1), SO (N,J = 2,3 - 1,2) and 34SO (N,J = 2,3 - 1,2) with the IRAM 30m telescope towards the dust peak of L1544. A non-Local Thermodynamic Equilibrium radiative transfer code is coupled to the Markov Chain Monte Carlo method to model the observations. We find that with just one transition for each isotope, the modelling cannot find a global minimum that fits the observations. The derived fractional abundance profiles are compared to those computed with chemical models. The observed transitions trace gas components with distinct dynamics at different distances along the radius of the core. Moreover, the results evidence a poor reproduction of sulphur chemistry by chemical modelling and stresses the need to include a more consistent S-depletion process to accurately reproduce the S-chemistry towards dense cores.

Figures

Figures reproduced from arXiv: 2508.20355 by the authors.

Figure 1
Figure 1. Spectra of the molecular lines observed towards the dust peak of L1544. HC17O + is included from previous work (Ferrer Asensio et al. 2022). The vertical dotted grey line represents the LSR velocity of L1544 (7.2 km s−1 ). The misalignment between the SO (2,3 - 1,2) and c-C3H2 (21,2 - 10,1) line centres and the LSR of L1544 lays within the laboratory measured transition frequency uncertainties. 3. RADIATIVE TRANSFER… view at source ↗
Figure 2
Figure 2. 1D pre-stellar core physical model profiles used for the radiative transfer modelling. The model described in Keto et al. (2015) is plotted between 0 and 0.32 pc. The vertical dotted black line marks the radius at 0.32 pc. The physical profiles between 0.32 and 1 pc correspond to an ”external layer” used for some of the transition modelling. The physical parameters in this external layer are constant profiles with v… view at source ↗
Figure 3
Figure 3. Schematics of the abundance profiles used for the radiative transfer modelling. The vertical axis repre￾sents the abundance, and the horizontal axis the radius in units of parsec. From the centre of the core (left) to the parameter r, we have the inner fractional abundance ain and from r to 0.32 pc, there is the outer fractional abundance aout. This constitutes the spatial extent of the ”non-extended” model, as indi… view at source ↗
Figures from the paper (22 more)
Figure 4
Figure 4. Figure 4: Top panel: Comparison of the C34S (2 - 1) spectra computed with different models. The spectrum computed with the LOC + MCMC approach is plotted in a red solid line ( Model 0). The spectrum computed with the pyRate abundance profile and the resulting LOC + MCMC fv and σ…
Figure 5
Figure 5. Figure 5: Same as [PITH_FULL_IMAGE:figures/full_fig_p009_5.png]
Figure 6
Figure 6. Figure 6: Same as [PITH_FULL_IMAGE:figures/full_fig_p010_6.png]
Figure 7
Figure 7. Figure 7: Same as [PITH_FULL_IMAGE:figures/full_fig_p011_7.png]
Figure 9
Figure 9. Figure 9: Same as [PITH_FULL_IMAGE:figures/full_fig_p012_9.png]
Figure 10
Figure 10. Figure 10: Same as for [PITH_FULL_IMAGE:figures/full_fig_p013_10.png]
Figure 11
Figure 11. Figure 11: Same as for [PITH_FULL_IMAGE:figures/full_fig_p014_11.png]
Figure 12
Figure 12. Figure 12: Same as for [PITH_FULL_IMAGE:figures/full_fig_p015_12.png]
Figure 14
Figure 14. Figure 14: Schematics of the L1544 layers traced by the different molecular transitions presented in the previous sections. 5.3. Spatial Distribution of Molecular Emission in L1544 All of the transitions presented in this manuscript trace different parts of the L1544 core, which…
Figure 16
Figure 16. Figure 16: Same as [PITH_FULL_IMAGE:figures/full_fig_p021_16.png]
Figure 15
Figure 15. Figure 15: The observed C34S (2 - 1) transition is plotted in black, the LOC + MCMC spectra is plotted in red and the optical depth (τ ) is plotted with a grey dashed line. An additional y axis (right) indicating the optical depth is included [PITH_FULL_IMAGE:figures/full_fig_p…
Figure 18
Figure 18. Figure 18: Corner plot of the 34SO (2,3 - 1,2) parameters used for the LOC + MCMC in [PITH_FULL_IMAGE:figures/full_fig_p022_18.png]
Figure 17
Figure 17. Figure 17: Corner plot of the parameters used for the C 34S (2 - 1) LOC + MCMC in [PITH_FULL_IMAGE:figures/full_fig_p022_17.png]
Figure 19
Figure 19. Figure 19: Corner plot of the HC17O + (1 - 0) parameters used for the LOC + MCMC in [PITH_FULL_IMAGE:figures/full_fig_p022_19.png]
Figure 20
Figure 20. Figure 20: Corner plot of the CS (2 - 1) parameters used for the LOC + MCMC in [PITH_FULL_IMAGE:figures/full_fig_p023_20.png]
Figure 21
Figure 21. Figure 21: Corner plot of the SO (2,3 - 1,2) parameters used for the LOC + MCMC in [PITH_FULL_IMAGE:figures/full_fig_p023_21.png]
Figure 24
Figure 24. Figure 24: Corner plot of the extended H2CO (21,2 - 11,1) parameters used for the LOC + MCMC in [PITH_FULL_IMAGE:figures/full_fig_p024_24.png]
Figure 25
Figure 25. Figure 25: Corner plot of the c-C3H2 (21,2 - 10,1) param￾eters used for the LOC + MCMC in [PITH_FULL_IMAGE:figures/full_fig_p024_25.png]
Figure 27
Figure 27. Figure 27: Top panel: CS (2 - 1) observations towards the L1544 dust peak in black and modelling results in red. Middle panel: as the top panel but for C34S (2 - 1). Bottom panel: Corner plot for the CS + C34S non-extended model [PITH_FULL_IMAGE:figures/full_fig_p025_27.png]
Figure 29
Figure 29. Figure 29: The model using the approach of Redaelli et al. (2022) is shown in a dash-dotted blue line. Observations towards the L1544 dust peak are shown in black [PITH_FULL_IMAGE:figures/full_fig_p027_29.png]
Figure 28
Figure 28. Figure 28: Top panel: SO (2,3 - 1,2) observations towards the L1544 dust peak in black and combined modelling re￾sults in red. Middle panel: 34SO (2,3 - 1,2) observations towards the L1544 dust peak in black and combined mod￾elling results in red. Bottom panel: Corner plot of th…
Figure 30
Figure 30. Figure 30: Top panel: HCO+ (1 - 0) observations to￾wards the L1544 dust peak in black and HCO+ + HC17O + extended modelling results in a dash-dotted blue line. Mid￾dle panel: HC17O + (1 - 0) observations towards the L1544 dust peak in black and combined modelling results in a da…

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Pith tools

Reviewed August 15, 2026 · model on record in the stance chip above.