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REVIEW 4 major objections 6 minor 46 references

Considerations with stacking absorption spectra: cold HI gas in cirrus region of the Milky Way

T0 review · 4 major / 6 minor · reviewed 2026-08-10 · deepseek-v4-flash

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Pith's one-line read Stacking HI spectral pairs keeps spin temperatures true while making off-centre components' peak optical depths strict lower limits — a bias used to detect 1320 K unstable gas and stable cold gas over about 100 pc.

desk verdict A careful stacking analysis that convincingly shows spin temperatures survive velocity-offset biases, with an untested but plausible alignment assumption for non-detection sightlines. read the letter →

arxiv 2501.11910 v1 pith:EPLH3XOC submitted 2025-01-21 astro-ph.GA

Callum Lynn , Antoine Marchal , N. M. McClure-Griffiths , Marc-Antoine Miville-Deschênes , Claire E. Murray , Hiep Nguyen , James Dempsey , Enrico Di Teodoro
show 10 more authors
Jacco Th. van Loon John M. Dickey Min-Young Lee Gilles Joncas Yik Ki Ma Nickolas M. Pingel Snežana Stanimirović Ian Kemp Steven Gibson Helga Dénes
This is my paper · ORCID
classification astro-ph.GA
keywords ISM:structuresolarneighbourhoodgalaxies:ISMradiolines:spintemperaturespectralstackingcoldneutralmediumGASKAPsurvey
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 establishes what spectral stacking does to measurements when thousands of Milky Way HI absorption–emission pairs are averaged together to reveal gas too faint for any single sightline. Shifting each spectrum by its emission peak centres the dominant cold component correctly, but every additional component keeps its own velocity offset, and averaging those misaligned features produces a broad, shallow 'secondary' component whose peak optical depth and brightness temperature are mathematically guaranteed lower limits of the true average, because total flux is conserved and the offsets broaden the stack. The spin temperature escapes this bias: the velocity offset moves the emission and absorption spectra equally, so it cancels in the ratio $T_s = T_{\rm B,peak}/(1-e^{-\tau_{\rm peak}})$ that defines the temperature, a property the paper verifies with toy models and then exploits on real data. Stacking 462 detection sightlines after subtracting the known cold components yields a $1320 \pm 263$ K component, gas of the unstable neutral medium; stacking 2240 non-detections uncovers cold neutral medium gas at $98 \pm 12$ K (narrow primary component) and $255 \pm 106$ K (broad secondary component), whose optical depth falls with distance from known cold-gas regions while its temperature stays constant over about 100 pc.

What carries the argument

The load-bearing mechanism is the ratio symmetry of the spin-temperature formula, $T_s = T_{\rm B,peak}/(1 - e^{-\tau_{\rm peak}})$, combined with flux conservation in the average. When a Gaussian component sits at a different velocity on each sightline, the stack broadens by an amount set by the spread of central velocities; with the integrated flux fixed, a wider component must have a lower peak, which makes the stacked $\tau_{\rm peak}$ and $T_{\rm B,peak}$ strict lower limits of the true noise-weighted averages and the FWHM a strict upper limit. Because the velocity offset of a given component is the same in emission and in absorption, the same broadening factor enters the numerator and the denominator of the $T_s$ ratio and cancels, leaving a spin temperature linearly correlated with the true average — a property the paper verifies for both primary and secondary components. The alignment choice that makes this split clean is shifting each spectrum by the peak of the emission profile rather than by the first velocity moment: the primary component, tied to the emission peak, is centred correctly, while all remaining components are relegated to the secondary component of the stack.

What would settle it

On the 462 detection sightlines the true average is already known component by component, so the claim is directly testable: stack the secondary components after emission-peak shifting exactly as the paper does, then bin the sightlines by the measured size of the emission–absorption velocity offset and compare the recovered $T_s$ against the noise-weighted mean of the individually measured components. If the recovered spin temperature drifts with the offset or deviates beyond the bootstrap uncertainties, the claimed cancellation fails; a toy-model version with offsets deliberately correlated with component temperature rather than drawn at random would show whether the unbiasedness is a general property or only holds for the assumed symmetry.

Watch

Extended reading notes

Core claim

The paper's central claim is a pair of statements about stacking HI emission–absorption spectral pairs after aligning each spectrum by the peak of its emission. First, the component that follows the emission peak — the 'primary' component — is correctly centred, and its stacked peak optical depth, width, and spin temperature reproduce the noise-weighted average of the individual sightlines. Second, every additional component on a sightline — the 'secondary' component — keeps a non-zero, sightline-dependent velocity offset after this shifting; when stacked, those offsets broaden the feature, and because total flux is conserved, a broader Gaussian must have a lower peak, so the measured peak optical depth and brightness temperature of the secondary component are mathematically guaranteed lower limits of their true averages, while its FWHM is an upper limit. The spin temperature remains well correlated with the truth because the velocity offset affects emission and absorption equally and therefore cancels in the ratio that sets $T_s$; the paper demonstrates this cancellation both by comparing the stacked values with the individually measured components on the same 462 sightlines and with toy models of 2000-component ensembles. It then exploits the sensitivity gain: stacking the 462 detection spectra after subtracting the modelled cold gas reveals a broad component with $T_s = 1320 \pm 263$ K, attributed to the unstable neutral medium; stacking 2240 non-detections reveals narrow and broad cold neutral medium components at $98 \pm 12$ K and $255 \pm 106$ K; and spatially binning the non-detections shows the primary component's optical depth decreasing by almost an order of magnitude with distance from known cold gas while both components' spin temperatures stay constant over roughly 100 pc of sky. The stacked spectra reach optical-depth noise near $10^{-3}$ yet do not detect the warm neutral medium, setting an upper limit $\tau_{\rm peak,WNM} \lesssim 3.3 \times 10^{-3}$ for this survey field.

Load-bearing premise

The whole method assumes the brightest feature of each emission spectrum is the cold gas that produces the absorption, with only a small random offset between the two; if the emission peak instead comes from warm gas, or if the emission and absorption probe different gas because they are taken on slightly different sightlines, even the main component is misaligned and the spin temperatures the stacking recovers would no longer be trustworthy (Section 3.1).

Editorial extensions

If this is right

  • Peak optical depths and brightness temperatures of secondary components in any emission-peak-aligned stack are rigorous lower limits of the true averages, and their FWHMs are upper limits; quantities derived from those peaks, such as turbulent Mach numbers, column densities, and mass fractions, become unreliable and should not be reported from stacked spectra alone.
  • Stacked spin temperatures remain trustworthy: for the 462 detection sightlines the stacked values ($68 \pm 7$ K primary, $159 \pm 58$ K secondary) agree with the noise-weighted means of the same components measured individually, and the toy models show the cancellation holds for any spread of central velocities.
  • Gas of the thermally unstable neutral medium is present in this cirrus region at an average $T_s = 1320 \pm 263$ K, detected in absorption only after subtracting the cold components and stacking; this is the highest-temperature component found so far with GASKAP in this region.
  • Cold neutral medium exists even along the 2240 sightlines where no single absorption detection was possible, at $98 \pm 12$ K (narrow) and $255 \pm 106$ K (broad) — the broad component sitting at the CNM/UNM boundary and likely mixing warmer CNM with cooler unstable gas.
  • Over roughly 100 pc of sky the amount of cold gas varies strongly — the primary component's peak optical depth falls from about $187 \times 10^{-3}$ to $46 \times 10^{-3}$ with distance from known cold-gas regions — while the spin temperature of cold gas stays constant within about $1\sigma$ across all bins.

Reading between the lines

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

  • The lower-limit theorem is generic, not HI-specific: any stacking or averaging procedure that aligns spectra by a proxy feature will under-estimate peaks and over-estimate widths of components not tied to that proxy, while any ratio diagnostic whose two quantities share the same misalignment stays protected; the same caveat should attach to molecular-line stacks, background-absorption surveys, and
  • Because the observed secondary optical depth is a lower limit that scales linearly with the true average, the plateau of the secondary component across the spatial bins is evidence that the warm-cold gas column responsible for it is roughly uniform over the ~100 pc field, even though the dense cold gas traced by the primary component is not — a distinction the current data cannot fully resolve.
  • The constancy of CNM spin temperature alongside a changing optical depth points to local pressure balance, not proximity to the large filaments, as the controller of cold-gas temperature; comparing the measured $T_s$ with pressure-regulated two-phase model predictions along the same sightlines would test this directly.
  • The claimed cancellation assumes emission–absorption velocity offsets are random; if deeper surveys find offsets correlated with optical depth or gas temperature — for example in denser, more turbulent regions — the stacked spin temperature would carry a residual bias, so the current result is best read as holding for gas with genuinely random offsets.
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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 / 6 minor

Summary. This paper studies biases in stacking HI absorption-emission spectra, using toy models and 2702 GASKAP Phase II Pilot sightlines toward the Magellanic system. The authors argue that shifting spectra by the emission brightness-temperature peak correctly aligns the dominant 'primary' cold component, while offset 'secondary' components combine into a broader, shallower Gaussian whose peak optical depth is a lower limit and whose FWHM is an upper limit, but whose spin temperature remains a good estimator of the average because the offset affects emission and absorption equally. They apply this to stacking 462 detected absorption sightlines after subtracting Nguyen et al. (2024) Gaussian models, detecting a broad residual component with Ts = 1320 +/- 263 K, and to stacking 2240 non-detection sightlines, finding primary and secondary components with Ts = 98 +/- 12 K and 255 +/- 106 K. Spatial binning of the non-detections shows an increase in primary optical depth toward regions of high detection density and a primary spin temperature consistent with no spatial variation over roughly 100 pc.

Significance. The paper's main methodological point is useful and largely correct: flux conservation makes the stacked peak optical depth of velocity-offset secondary components a lower limit, while the Ts estimate is more robust because the velocity offset enters emission and absorption together. The toy model in Appendix A, the comparison with individual sightline properties in Section 3.4, and the bootstrap and half-inverted controls in Sections 4.2 and 5.2 are carefully done and go beyond what is common in stacking papers. If the observational results stand, the detection of an average UNM component at 1320 K in residual spectra and the apparent stability of CNM Ts across roughly 100 pc are interesting additions to the GASKAP pilot analysis. However, the strongest observational claims rest on assumptions about the emission-peak alignment of non-detection sightlines and on Gaussian decomposition systematics, both of which need stronger support.

major comments (4)
  1. [Section 3.1 / Section 5.1] The alignment rule, shifting by the emission peak so that the 'primary' component sits at 0 km/s, is established on the detection sample, where the cold absorber can be identified in absorption, but it is applied to the 2240 non-detection sightlines without independent verification. If in even a fraction of those sightlines the emission peak is produced by warm or blended gas rather than by the dominant cold absorber, the primary component is not centred at zero and the cold gas is partly redistributed into the broad secondary component, so the quoted Ts values in Section 5.2 and Table 2 and the ~100 pc stability claim in Section 6.2 would be affected. I request a validation on the non-detection spectra themselves, for example by generating synthetic absorption spectra from the non-detection emission profiles with assumed spin temperatures and checking whether the emission-peak-aligned stack recovers the injected primary Ts and tau.
  2. [Section 3.3 / Section 4.2] The spin temperatures are derived from a decomposition in which a single broad component is added to the emission to complete the fit, and the manuscript explicitly notes that this choice can under-represent the spin temperature of the absorption feature. The 1320 +/- 263 K UNM result in Section 4.2 and the 98/255 K CNM values in Section 5.2 therefore carry a systematic error from the number and shape of the emission-only components that is not included in the bootstrap uncertainties, which only resample sightlines. Please quantify this systematic by varying the decomposition configuration, for example the number of emission-only Gaussians and the allowed parameter ranges, and report the resulting range of Ts for each component.
  3. [Section 4.1 / Section 4.2] The residual stack is formed by subtracting Nguyen et al. (2024) Gaussian fits from individual detection spectra. Errors in the fitted velocities, widths, or amplitudes of those cold components enter the residual spectra coherently, so the half-inverted bootstrap in Section 4.2, which tests only sign-symmetric random noise, cannot exclude a spurious broad absorption feature produced by systematic model-subtraction residuals. Please propagate the published fit uncertainties through the subtraction and re-stacking procedure, or otherwise demonstrate that the 1320 K component is not produced by residual cold-gas signal.
  4. [Abstract / Section 5.3.1 / Table 2] The claim that the spin temperature 'remains stable in both components' over ~100 pc is not supported by Table 2 and the caption of Fig. 12: a secondary component is detected in only two of the six spatial bins (bins 2 and 4), and bin 4 has Ts = 135 +/- 215 K. The spatial stability claim is therefore established only for the primary component; the abstract and summary should be revised to state this limitation, unless additional bins with detected secondary components can be provided.
minor comments (6)
  1. [Section 3.1] The statement that 'the peak in emission typically traces cold gas' is an assertion that should be supported by a quantitative check within the detection sample, for example the fraction of sightlines where the nearest absorption component is within half a FWHM of the emission peak.
  2. [Section 3.2] The weighting is described as 'weights tau_res / sigma_tau^2' and then said to simplify to 1/sigma_tau; please write the actual weight used for the stacks explicitly and define tau_res in that context, since the same symbol is used later for model-subtracted residuals.
  3. [Section 3.3] The phrase 'allowing for a +/-1 km/s deviation in their central velocities and 10 per cent deviation in their widths' should clarify whether this allowance is a fitting constraint or an acceptance criterion for the Gaussian decomposition.
  4. [Table 2] The notation '>20 +/- 10' for the secondary optical depth lower limits is confusing as printed; a footnote explaining that the quoted values are the observed stacked values and the inequality indicates the relation to the true average would help.
  5. [Section 6.2 / Eq. (1)] The conversion n_H = C x A'_ZGR23 with C = 1653 cm^-3 needs the units of A'_ZGR23 stated and a reference to O'Neill et al. (2024) for the conversion constant; as written the units on the two sides do not visibly match.
  6. [Fig. 5] The vertical dotted lines representing stacked values are not labelled in the legend; please add labels or a caption note identifying which colour and dash style corresponds to the primary and secondary stack values.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the stacking-bias results follow from flux conservation and explicit toy-model assumptions; the observational claims are new averages of spectra not used to fit the subtracted models.

full rationale

The paper's derivation chain is not circular. The stacking-bias results (secondary-component peak optical depths are lower limits, FWHMs are upper limits, and spin temperatures remain correlated) follow from flux conservation and are verified with toy models whose assumptions, including the same central velocity for emission and absorption within a component, are stated explicitly and then cross-checked against the GASKAP detection sample in Section 3.4. The UNM detection in Section 4 is obtained by subtracting the published Nguyen et al. (2024) Gaussian component models from individual detection spectra and stacking the residuals; the residual equivalent width and spin temperature are new quantities measured from leftover data, not quantities used to construct the subtracted models. The non-detection stacks and spatial bins in Section 5 are fresh averages of 2240 sightlines not included in the detection catalogue, and the binning variable (detection source density) is independent of the measured optical depth and temperature. The main caveats are explicitly acknowledged by the authors: the emission-peak alignment assumption for non-detections (Section 3.1) and the single emission-only component fitting bias (Section 3.3). These are correctness risks rather than circular reductions. Reliance on the same-team Nguyen et al. catalogue is a normal use of an external, published, falsifiable data product and does not smuggle in the target conclusions.

Assumptions & free parameters 2 free parameters · 4 assumptions · 0 invented entities

The analysis adds no new physical entities. The free parameters are the warm-gas background fraction and Gaussian fit parameters. The main assumptions are astrophysical: emission peak traces cold gas, and emission and absorption share velocities.

free parameters (2)
  • Fraction of background warm gas in radiative transfer = 0, 0.5, 1 (three values, averaged)
    The paper treats the fraction of warm gas behind the absorbing cold gas as a parameter and averages over three values. This affects the derived spin temperatures.
  • Gaussian decomposition parameters = Reported per component for each stack
    The central velocities, widths, and amplitudes of the Gaussian components are fitted to the stacked spectra. The values are derived from the data, and the reported uncertainties come from bootstrap resampling.
assumptions (4)
  • domain assumption The peak in HI emission traces the primary cold gas component along each sightline.
    Used to justify shifting all spectra by the emission peak (Section 3.1). If false, even the primary component would be misaligned.
  • domain assumption Emission and absorption spectra probe the same gas with comparable velocity structure.
    The cancellation of velocity-offset bias in spin temperature relies on the same velocity offsets affecting emission and absorption equally (Section 3.4, Appendix A2).
  • domain assumption The cold gas components subtracted from detection spectra using Nguyen et al. (2024) Gaussian fits are accurate.
    The residual stacking in Section 4.1 subtracts these fits; any error biasing the fits propagates into the reported UNM temperature.
  • domain assumption The fitted Gaussian decomposition of stacked spectra correctly separates the primary and secondary components.
    The method assumes the stacked absorption profile is well-described by two Gaussian components plus an emission-only component (Section 3.3).

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Cite this review

Pith. "Pith review of Considerations with stacking absorption spectra: cold HI gas in cirrus region of the Milky Way." pith.science (2026). https://pith.science/paper/EPLH3XOC

@misc{pith2026250111910,
  author       = {Pith},
  title        = {Pith review of: Considerations with stacking absorption spectra: cold HI gas in cirrus region of the Milky Way},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/EPLH3XOC}},
  note         = {Machine review of arXiv:2501.11910}
}
abstract

We use the Milky Way neutral hydrogen (HI) absorption and emission spectra from the Galactic Australian Square Kilometre Array Pathfinder (GASKAP) Phase II Pilot survey along with toy models to investigate the effects of stacking multicomponent spectra on measurements of peak optical depth and spin temperature. Shifting spectra by the peak in emission, 'primary' components shifted to 0 km s$^{-1}$ are correctly averaged. Additional components on individual sightlines are averaged with non-centred velocities, producing a broader and shallower 'secondary' component in the resulting stack. Peak optical depths and brightness temperatures of the secondary components from stacks are lower limits of their true average values due to the velocity offset of each component. The spin temperature however is well correlated with the truth since the velocity offset of components affects the emission and absorption spectra equally. Stacking 462 GASKAP absorption-emission spectral pairs, we detect a component with a spin temperature of 1320 $\pm$ 263 K, consistent with gas from the unstable neutral medium and higher than any previous GASKAP detection in this region. We also stack 2240 pilot survey spectra containing no Milky Way absorption, revealing a primary narrow and secondary broad component, with spin temperatures belonging to the cold neutral medium (CNM). Spatially binning and stacking the non-detections across the plane-of-sky by their distance from CNM absorption detections, the primary component's optical depth decreases with distance from known locations of cold gas. The spin temperature however remains stable in both components, over an approximate physical plane-of-sky distance of $\sim$ 100 pc.

Figures

Figures reproduced from arXiv: 2501.11910 by the authors.

Figure 2
Figure 2. Scatter plot of the background source flux, 𝑆cont, versus the optical depth noise, 𝜎𝜏, for each source of the 2240 non-detections (blue) and the 462 detections (orange) of Milky Way H i absorption. All sources, regardless of detection, have a background flux higher than the cut-off of 15 mJy (Dempsey et al. 2022). to them as the non-detection sample. An example of an absorption￾emission pair selected randomly from t… view at source ↗
Figure 1
Figure 1. Top panels: Brightness temperature 𝑇𝐵 in units of kelvin of the absorption source J040848-750719 from the detection catalogue (top), and its corresponding absorption profile 𝑒 −𝜏 (bottom). The coloured lines show the Gaussian decomposition as documented in Nguyen et al. (2024), with the fit of the Gaussian components found in absorption (dashed blue lines) along with their total contribution in emission (solid blue)… view at source ↗
Figure 3
Figure 3. Spatial distribution of background sources from the GASKAP-HI absorption survey overlaid on a grey-scale map of the column density of H i gas computed in the optically thin limit from the GASS survey (McClure-Griffiths et al. 2009; Kalberla et al. 2010; Kalberla & Haud 2015). Detections of cold gas in the velocity range −50 < 𝑣 < 50 km s−1 are annotated with white circles. Sightlines with non-detections of cold gas … view at source ↗
Figures from the paper (10 more)
Figure 4
Figure 4. Figure 4: Top: Weighted-mean emission profile of the stacked GASKAP detection spectra. The original stacked spectrum is shown in black and the model of the joint Gaussian decomposition in green. The model is made by the addition of the emission produced by the narrow and broad c…
Figure 5
Figure 5. Figure 5: Distributions of the peak optical depth (top), FWHM (middle), and spin temperature (bottom) of individual absorption components found by Nguyen et al. (2024). The components are separated into primary components (blue), which are aligned with the peak in their correspo…
Figure 6
Figure 6. Figure 6: Top: Weighted-mean emission profile of the stacked GASKAP detection spectra after subtracting the cold gas models in individual sight￾lines from Nguyen et al. (2024). The original stacked spectrum is shown in black and the model of the joint Gaussian decomposition in g…
Figure 7
Figure 7. Figure 7: Histograms of the EW distribution from 105 trials of bootstrap￾ping, randomly sampling 462 spectra from the model-subtracted detection sample derived in Section 4.1, with possibility of replacement. The blue his￾togram displays the distribution of EW values from the tr…
Figure 10
Figure 10. Figure 10: A 2-dimensional contour plot of the source density of Milky Way H i detections found through the GASKAP Pilot II survey towards the Magellanic system (Nguyen et al. 2024). The contours are created based on a kernel density PDF using the spatial location of the detecte…
Figure 11
Figure 11. Figure 11: Spatial distribution of the non-detection sources coloured based on their respective contour level from the contour regions shown in [PITH_FULL_IMAGE:figures/full_fig_p009_11.png]
Figure 12
Figure 12. Figure 12: H i emission and absorption stacked profiles of the spatially binned groups of spectra from [PITH_FULL_IMAGE:figures/full_fig_p011_12.png]
Figure 13
Figure 13. Figure 13: Properties of the Gaussian decompositions of the stacked profiles binned in Section 5.3 (bin 1 not shown). Left: Plot of the peak 𝜏 values for the primary components (blue circles) and secondary (red squares) components from each of the stacked absorption profiles. Th…
Figure 14
Figure 14. Figure 14: Variation of the spin temperature values for the primary (blue circles) and secondary (red squares) components from each of the stacked profiles binned in Section 5.3 (bin 1 not shown). The black line denotes the cutoff between CNM and UNM used in this work of ∼ 250 K…
Figure 15
Figure 15. Figure 15: Weighted-mean of 𝑛H along the sightlines of each of the 6 bins de￾scribed in Section 5.3. The dust densities were converted from the Edenhofer et al. (2024) 3D dust map to total hydrogen densities using a conversion factor of 1653 cm−3 (O’Neill et al. 2024). Note as t…

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Pith tools

Reviewed August 10, 2026 · model on record in the stance chip above.