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REVIEW 3 major objections 5 minor 85 references

Joint Analysis of HI Absorption Zeeman Measurements and the Morphology of Filamentary HI Emission

T0 review · 3 major / 5 minor · reviewed 2026-08-05 · deepseek-v4-flash

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Pith's one-line read The disorder of hydrogen filaments in radio maps carries a measurable imprint of the magnetic field along the line of sight: Zeeman field strength and filament orientation scatter correlate in 42 absorption components (rho = 0.3, p = 0.01).

desk verdict A careful, interesting observational study whose headline correlation is plausible but whose p=0.01 rests on an independence assumption the paper itself undercuts; worth refereeing, but the significance needs to be re-derived. read the letter →

arxiv 2508.20065 v1 pith:44NIFT7U submitted 2025-08-27 astro-ph.GA

Marta Nowotka , Susan E. Clark , Blakesley Burkhart , Laura Fissel , Tao-Chung Ching , Timothy Robishaw , Carl Heiles This is my paper · ORCID
classification astro-ph.GA
keywords ZeemaneffectHIabsorptionfilamentaryemissionRollingHoughTransformmagneticfieldinclinationinterstellarmediumGALFA-HILocalBubble
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

The paper tries to establish that the shapes of hydrogen filaments seen in narrow radio velocity channels encode information about the three-dimensional magnetic field of the diffuse gas between the stars—specifically about the field's projection along our line of sight. Zeeman splitting in 21-cm absorption is the only direct measurement of magnetic field strength in this gas, but it sees only the line-of-sight component; filaments, which trace the plane-of-sky field direction, could supply the missing orientation information. Analyzing 42 spectrally distinct absorption components from the Arecibo Millennium Survey plus new Five-hundred-meter Aperture Spherical Telescope (FAST) data, the paper finds a weak but statistically significant correlation (Spearman rho = 0.3, p = 0.01) between the magnitude of the line-of-sight field and the circular variance of filament orientations: the more disordered the filaments, the stronger the line-of-sight field tends to be. If true, filament morphology becomes a practical tracer of magnetic field inclination, able to break the long-standing degeneracy that keeps Zeeman measurements from directly yielding the total field strength. The paper presents the result as a first statistical link, attributes it to large-scale variations in field strength or inclination across different Galactic environments, and leaves total-field recovery as an open problem.

What carries the argument

The load-bearing pair is the Zeeman Stokes V fit and the Rolling Hough Transform (RHT), an algorithm that detects coherent linear filaments in maps and assigns each pixel a distribution of orientation angles. From the RHT output the paper constructs Q_HI and U_HI maps, then a circular mean and the circular variance Var(theta_HI), a unitless disorder measure in [0,1] computed over a 2.5-degree patch centered on each background radio source at the absorber's velocity. A 70% emission-dominance criterion (Equation 19) keeps only absorption components that produce most of the cold-neutral-medium emission in the 1.7 km/s channel, so the degree-scale filament statistics can be attributed to gas rel

What would settle it

One test: measure filament orientation dispersion at the absorber's own angular scale (arcminutes rather than degrees) with next-generation HI surveys. The paper finds the correlation only appears at patch sizes of 2.5 degrees and larger; if the trend vanishes at scales matched to the Zeeman pencil beam and to the parsec-scale coherence the paper itself infers, the degree-scale correlation would be a scale-mismatch artifact. A cheaper companion test: re-observe the strongest Zeeman detections (notably the 3C 409 component at B_LOS = 9.1 ± 1.9 microgauss) with doubled integration time and check

Watch

Extended reading notes

Core claim

Across 42 spectrally distinct HI absorption components drawn from the Arecibo Millennium Survey and new FAST observations, the magnitude of the line-of-sight magnetic field inferred from Zeeman splitting correlates positively with the circular variance of HI filament orientation angles measured in narrow-channel GALFA-HI emission maps (Spearman rho = 0.3, p = 0.01). The significance is tested against one million null-hypothesis samples that preserve each measurement's uncertainty, with only 1.0–1.4% of simulated samples producing a correlation at least as positive. The signal strengthens when blended components are excluded more aggressively (rho = 0.40, p = 0.004 at an 80% emission-dominanc

Load-bearing premise

The degree-scale filament dispersion (measured over 2.5 degrees, i.e., roughly 4–22 parsecs at the inferred distances) is a faithful statistical picture of the magnetic field seen by the pencil-beam Zeeman absorber at the same velocity; if the filaments trace unrelated gas or a different field-coherence scale, the correlation would be an artifact of line-of-sight structure.

Editorial extensions

If this is right

  • If the correlation is real, narrow-channel HI emission morphology becomes a usable statistical tracer of the line-of-sight component of the magnetic field, complementing Zeeman measurements that alone cannot separate field strength from orientation.
  • Sight lines dominated by Local Bubble gas show both low |B_LOS| and orderly filaments, implying a field oriented mainly in the plane of the sky there—so inclination effects are already visible in existing data.
  • Zeeman absorption components trace fields coherent on parsec scales: co-spectral components within about 7.5 degrees agree in strength and direction (K-S p = 0.002 versus widely separated pairs), with physical separations of a few parsecs inferred from 3D dust maps.
  • Sight lines with higher dust extinction and HI column density carry higher average |B_LOS| (Spearman rho = 0.48, p about 0.005), pointing to systematic environmental differences in total field strength or orientation.
  • Recovering the total field strength B_TOT from the combination of Zeeman and filament statistics is not yet achieved; the paper identifies larger high-signal-to-noise samples and sharper HI maps as the path forward.

Reading between the lines

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

  • An implication the paper leaves implicit: once calibrated on this sample, the |B_LOS|-versus-disorder slope could be applied across the full GALFA-HI footprint, turning filament statistics in every velocity channel into a map of the field's line-of-sight geometry in regions with no background radio source for Zeeman observations.
  • The sharp velocity dependence (weaker at ±6 km/s offsets, gone at ±9 km/s) functions as a built-in consistency check; the editor's reading predicts that spectrally matched, higher-resolution HI data will sharpen the correlation rather than dilute it, because the signal lives in velocity-coherent gas.
  • The rise of sight-line-averaged |B_LOS| with dust extinction combined with the absence of a component-level density trend suggests environment, not local cloud density, sets the total field strength; an unstated corollary is that future Zeeman measurements toward CO-dark, low-extinction clouds should come out systematically low.
  • The sign disagreement between HI and OH Zeeman measurements toward 3C 133 has an either-or consequence the paper does not pursue: a convention or calibration error would affect cross-tracer Zeeman comparisons broadly, while a real reversal would imply sub-parsec field structure invisible to the paper's few-parsec coherence analysis.
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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 / 5 minor

Summary. The paper combines Zeeman measurements of HI absorption from the Arecibo Millennium Survey with new FAST observations toward 3C 75, 3C 207, and 3C 409, and uses GALFA-HI narrow-channel emission maps processed with the Rolling Hough Transform to quantify the circular variance of filament orientation angles at the positions and velocities of Zeeman absorbers. In a subsample of 42 spectrally distinct, non-blended components, the authors report a weak positive correlation between |B_LOS| and Var(theta_HI) (Spearman rho = 0.3, p = 0.01), and argue this correlation is robust to RHT parameter choices and angular scale. They also examine the environments probed by the Zeeman measurements using dust extinction, 3D dust maps, OH absorption, and CO emission, and find evidence for parsec-scale coherence of the magnetic field, with most components tracing gas at 100--500 pc, often associated with the Local Bubble wall. The paper interprets the correlation as arising from large-scale variations in magnetic field strength and/or inclination angle across different Galactic environments.

Significance. If the reported correlation is real, it would establish a new velocity-resolved observational link between HI filament morphology and the line-of-sight projection of the magnetic field, with implications for recovering the total magnetic field strength from combined Zeeman and filament measurements. The paper is careful in several respects: it tests RHT parameter choices (Section 5.4), checks robustness to the blending threshold and angular scale, uses null simulations with three different B_TOT distributions, provides new FAST Zeeman data consistent with Arecibo, and combines multi-wavelength environmental diagnostics. These strengths make the central hypothesis worth investigating. However, the headline statistical significance is not yet established because the null model treats the 42 components as independent despite the clustering and coherence demonstrated in the same paper, and because the correlation may be driven by environmental confounders such as A_V and Galactic latitude.

major comments (3)
  1. [Section 5.3, with Section 7.1] The reported p = 0.01 is computed against a null model (Equations 22--23) that draws 42 independent B_LOS values from the fitted PDF(B_TOT). This independence assumption is inconsistent with the paper's own demonstration in Section 7.1 that Zeeman measurements are coherent within angular separations <= 7.5 deg and velocity separations < 3 km/s. The sample is also strongly clustered, with multiple components per sight line (e.g., five toward 3C 409). Under the null, B_LOS values from the same sight line or nearby sight lines would still be spatially/velocity coherent, so the effective number of independent samples is smaller than 42. The p-value should be recomputed with a cluster-robust permutation or block bootstrap that resamples at the level of sight lines (or coherent angular/velocity neighborhoods) while preserving the pairing of B_LOS with Var(theta_HI). Without this, the central c
  2. [Section 8.2 and Figure 16] The paper does not test whether the |B_LOS|-Var(theta_HI) correlation survives controlling for environmental variables. Figure 16 shows that the sample splits by A_V and Galactic latitude occupy different regions of the correlation plot, and Section 6.1 reports a significant correlation between A_V (and N_HI) and sight-line averaged |B_LOS|. It is therefore possible that both |B_LOS| and Var(theta_HI) are correlated with a third variable and not directly with each other. A partial Spearman correlation controlling for A_V, N_HI, Galactic latitude, and possibly distance or molecular tracers should be reported. This is important for the physical interpretation: the title and abstract suggest HI filament morphology carries information about B_LOS, but the current analysis does not exclude the possibility that the apparent relationship is an environmental projection.
  3. [Section 5.1 and 5.3] The selection of the 42 non-blended components uses a 70% dominance threshold in Equation 19, and the paper also reports results for a 0.80 threshold (38 components, rho = 0.40, p = 0.004) and for all 62 usable components (rho = 0.21, p = 0.04). The headline p-value is therefore one of several selection-dependent values, and no correction for this selection or for the multiple tested thresholds is applied. The selection criterion is physically motivated, but the statistical significance should be assessed in a way that accounts for the choice of threshold, or the paper should clearly state that the reported p-values are not adjusted for post-hoc selection. A sensitivity analysis that treats the threshold as a tuning parameter and reports the distribution of p-values across thresholds would be more convincing.
minor comments (5)
  1. [Section 2.3.3, Eq. (4)] The leakage terms C_on T_on(v) - C_off T_off(v) are not explicitly defined in the text; please define the units and whether C_on/C_off are fitted constants, and briefly explain why the leakage subtraction appears as a difference of two terms.
  2. [Section 4.3] The definition of circular variance in Eq. (16) uses doubled angles, but the range [0,1] and interpretation as 'disorder' would benefit from a one-sentence clarification that this is the standard axial circular variance.
  3. [Section 5.4, Figure 8] The text says 'no significant correlation is found at dPOS < 2 deg' while the figure caption says 'dPOS < 2.5 deg'; please unify the notation and the exact angular scale used in the analysis.
  4. [Section 5.4] The reference to 'Putman et al. (2025, in prep)' should be updated or, if not yet available, flagged as a personal communication with details of the analysis.
  5. [Section 6.2, Figure 11] The text mentions 'OH 1667 Hz line' in the figure caption; the correct unit is MHz, not Hz. Please correct.

Circularity Check

0 steps flagged · score 1.0 of 10

No significant circularity: the central |BLOS|–Var(θHI) correlation is an empirical result computed from independent datasets, and the fitted null model affects only the conditioning of the p-value, not the correlation itself.

full rationale

The central claim is an empirical Spearman correlation between |BLOS| from HI absorption Zeeman measurements and Var(θHI) from GALFA-HI RHT maps. These two quantities are measured from independent datasets (Stokes V absorption spectra vs. 21-cm emission maps), and the correlation coefficient is computed directly from the observed pairs; it is not generated by any fitted model. The null-hypothesis significance test in §5.3 does fit parameters of PDF(BTOT) (B0=6.2 μG, 9.6 μG; lognormal 1.7/0.2) by maximum likelihood to the same 42 |BLOS| values, but this fit is to the marginal distribution of |BLOS| alone; null samples are then drawn independently of Var(θHI), so the observed ρ is not forced by the fit. The paper also checks three different PDF forms and obtains similar p-values (1.0–1.4%), so the significance is not an artifact of a single fitted ansatz. The more substantive statistical caveat, explicitly acknowledged in §5.2, is that components clustered within one sight line or between nearby sight lines are treated as independent in the null, even though §7.1 demonstrates coherence on scales ≲7.5° and ≲3 km/s. That is a robustness/correctness limitation, not circularity: the correlation coefficient is not defined in terms of the null model, and the null model is not fitted to the joint |BLOS|–Var(θHI) relation. The RHT formalism and the 'HI filaments trace B⊥' premise are cited from prior work including co-author papers (Clark et al. 2014; Clark & Hensley 2019; Halal et al. 2024a), but these are supported by independent starlight-polarization and Planck dust-polarization comparisons and are further tested for parameter sensitivity in this paper; they are not assumed as the target result. No step in the paper reduces by construction to its inputs, and the correlation is not renamed from a known result.

Assumptions & free parameters 7 free parameters · 5 assumptions · 0 invented entities

The central claim rests on standard observational assumptions about filament-field alignment and on a set of hand-chosen or fitted parameters: RHT settings, masking radii, the blending threshold, and the parameters of the null BTOT distributions. The paper does not introduce any new physical entity. The weakest part of the ledger is the domain assumption that a 2.5 degree filament dispersion statistic captures the magnetic field orientation relevant to a pencil-beam Zeeman absorption measurement.

free parameters (7)
  • B0 (Delta PDF null model) = 6.2 uG
    Fitted to the 42 non-blended Zeeman measurements in Section 5.3 to generate null-hypothesis samples.
  • B0 (Uniform PDF null model) = 9.6 uG
    Fitted to the same 42 measurements in Section 5.3 for the uniform BTOT null model.
  • B0 and sigma (lognormal null model) = B0=1.7, sigma=0.2
    Fitted to the same 42 measurements in Section 5.3 for the lognormal BTOT null model.
  • RHT parameters (DW, theta_FWHM, ZRHT) = 105 arcmin, 5 arcmin, 0.75
    Chosen from Ade et al. 2023, tested for robustness in Section 5.4; not fitted to the Zeeman data.
  • Absorption mask radius per sight line = 3 to 10 arcmin
    Chosen by visual inspection for each GALFA-HI map in Section 4.1.
  • Blending threshold = 0.70
    Hand-selected in Section 5.1 to define the non-blended subsample of 42 components; threshold of 0.80 is also tested.
  • Angular scale dPOS = 2.5 degrees
    Chosen as the smallest scale with sufficient filament statistics; the dependence on scale is explored in Section 5.4.
assumptions (5)
  • domain assumption HI filaments trace the plane-of-sky magnetic field orientation
    The paper relies on established correlations between HI filaments and starlight polarization / polarized dust emission, cited in Section 1. This is the foundation for interpreting circular variance as a magnetic field statistic.
  • domain assumption Narrow-channel HI emission near the absorber velocity represents the same cold neutral medium as the absorption component
    Invoked in Section 5.1, especially the selection criterion in Equation 19, which assumes the dominant CNM component contributes at least 70% of the emission in the velocity channel.
  • domain assumption Magnetic field coherence over the 2.5 degree RHT region
    The correlation analysis assumes that the filament dispersion in the extended region is relevant to the pencil-beam absorption measurement. The paper explicitly discusses scale matching in Section 8.1.
  • domain assumption The chosen parametric forms of PDF(BTOT) are representative of the underlying population
    The null hypothesis tests in Section 5.3 use Delta, Uniform, and lognormal distributions, following prior literature, but the true distribution is unknown.
  • domain assumption Stokes V gradients in the off-source emission are negligible
    In Section 2.3.2 the authors adopt the HT04 assumption that spatial gradients in polarized HI emission are undetectable, which is needed to separate absorption Zeeman signal from emission.

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Cite this review

Pith. "Pith review of Joint Analysis of HI Absorption Zeeman Measurements and the Morphology of Filamentary HI Emission." pith.science (2026). https://pith.science/paper/44NIFT7U

@misc{pith2026250820065,
  author       = {Pith},
  title        = {Pith review of: Joint Analysis of HI Absorption Zeeman Measurements and the Morphology of Filamentary HI Emission},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/44NIFT7U}},
  note         = {Machine review of arXiv:2508.20065}
}
abstract

We present a joint analysis of HI absorption Zeeman measurements and the morphology of filamentary HI emission to investigate the three-dimensional structure of the magnetic field in the diffuse neutral interstellar medium (ISM). Our analysis is based on the Arecibo Millennium Survey and new data from the Five-hundred-meter Aperture Spherical radio Telescope (FAST) toward radio sources 3C 75, 3C 207, and 3C 409. Toward 3C 409, we make a 4$\sigma$ Zeeman detection and infer $B_{LOS}$ = 9.1 +/- 1.9$\mu$G, in agreement with Arecibo results. We quantify the dispersion of HI filaments at the locations and velocities of Zeeman components using GALFA-HI narrow-channel emission maps. Focusing on a subsample of 42 spectrally distinct components, we find a weak but statistically significant positive correlation (Spearman r = 0.3, $p = 0.01$) between $|B_{LOS}|$ and the circular variance of HI filament orientation angles. To examine its origin, we characterize the environments probed by HI absorption using dust emission, 3D dust maps, OH absorption, and CO emission. We find evidence that existing HI absorption Zeeman measurements trace magnetic fields that are coherent on parsec scales, probe primarily local gas ($100$-$500$ pc, often at distances consistent with the Local Bubble wall), and exhibit systematic differences in the magnitude of $B_{LOS}$. We attribute the correlation between Zeeman measurements and filamentary HI morphology to large-scale variations in magnetic field strength and/or inclination angle across different Galactic environments, which could arise due to the Local Bubble geometry or enhanced total field strength in denser regions.

Figures

Figures reproduced from arXiv: 2508.20065 by the authors.

Figure 1
Figure 1. 66 Zeeman measurements from the Millennium Survey plotted over the GALFA-HI column density map obtained for velocity range |v| ≤ 90 km s−1 . Locations of the background radio sources are marked with stars, white for Arecibo measurements and green for targets where new data was collected with FAST. Zeeman measurements represented by squares are color-coded by BLOS inferred by HT04 and stacked in increasing radial vel… view at source ↗
Figure 2
Figure 2. On-Off Stokes V = IEEE RCP - IEEE LCP spectra from FAST toward sources 3C 409, 3C 98, and 3C 207 with the Zeeman splitting fit in purple. For comparison, the Zeeman splitting fit to Millennium Survey data from the Arecibo Observatory obtained by HT04 is plotted in orange. For visual clarity, the leakage of Stokes I into Stokes V has been subtracted and the spectra are binned by 4 spectral channels using the unweight… view at source ↗
Figure 3
Figure 3. Difference between BLOS from FAST and Mil￾lennium Survey for absorption components with Millennium uncertainties < 10 µG. The error bars represent 1σ uncer￾tainties computed as (σ(BLOS,FAST) 2 + σ(BLOS,Arecibo) 2 ) 1/2 . The Zeeman measurements from FAST and Arecibo agree within 2σ in all absorption components. 0.184km s−1 , respectively. In this work, we use GALFA￾HI to study the morphology of HI emission in narrow… view at source ↗
Figures from the paper (13 more)
Figure 4
Figure 4. Figure 4: 28 Millennium lines of sight with Zeeman measurements plotted over a velocity-integrated map of CO emission intensity from T. M. Dame & P. Thaddeus (2022) centered at (l, b) = (120◦ , 0 ◦ ). Circles indicate CO emission line detections (yellow) and non-detections (pink…
Figure 5
Figure 5. Figure 5: Top: GALFA-HI narrow-channel emission maps centered on the radio source 3C 409 and on the radial velocities of absorption components with existing Zeeman measurements. Each map has a dimension of 2.5 ◦ × 2.5 ◦ and a channel width of 1.7 km s−1 . Bottom: Gaussian compon…
Figure 6
Figure 6. Figure 6: Top row: Examples of two 2.5 ◦ ×2.5 ◦ GALFA-HI emission maps with 1.7 km s−1 channel width representative of high (Var(θHI) = 0.82, left) and low (Var(θHI) = 0.15, right) variance of θHI angles constructed using the Rolling Hough Transform. Middle row: Corresponding RH…
Figure 7
Figure 7. Figure 7: Zeeman measurements plotted against the circu￾lar variance of HI filament orientations Var(θRHT) computed in a dPOS < 2.5 ◦ region around each radio source. Top: We plot the mean and 1σ errors of a normal distribution centered at |BLOS| with uncertainties of the direct…
Figure 8
Figure 8. Figure 8: Spearman correlation between |BLOS| and Var(θHI) as a function of the plane-of-sky diameter dPOS of the region where Var(θHI) is computed and as a function of RHT parameters: the window length DW and the smooth￾ing radius θFWHM, at a fixed RHT threshold ZRHT = 0.75. We…
Figure 9
Figure 9. Figure 9: Spatially averaged RHT output R(θ) centered around the mean orientation and stacked in quartiles of Zeeman field strength. HI emission maps corresponding to lower Zeeman field strengths show more sharply peaked distributions of filament orientations (dark blue), and vi…
Figure 10
Figure 10. Figure 10: Inverse variance-weighted mean |BLOS| along the line of sight plotted against integrated density tracers: dust visual extinction AV (left) and the total HI column density (right). In the top row, points are color-coded by the integrated column density of CO; the botto…
Figure 11
Figure 11. Figure 11: Zeeman field strength measured in HI absorp￾tion as a function of velocity offset between HI absorption component and the nearest OH 1667 Hz absorption compo￾nent, for sight lines where OH is detected. and BLOS(vHI = 8.0 km s−1 ) = 5.8 ± 1.1 µG, but not in direction. …
Figure 12
Figure 12. Figure 12: Zeeman measurements toward background sources with the smallest angular separations in the survey. Each panel shows Zeeman measurements toward two sight lines, and panels are ordered by the angular separation of the background sources. We find a general agreement, bot…
Figure 13
Figure 13. Figure 13: For each component pair i, j in the Millennium sample, we plot the statistical significance of the Zeeman measurement difference, |BLOS,i−BLOS,j |/σi,j , as a function of their radial velocity separation. We show pairs that lie along the same line of sight in blue squ…
Figure 14
Figure 14. Figure 14: Dust extinction per parsec toward Millennium Zeeman targets extracted from G. Edenhofer et al. (2024) 3D dust maps. The dust profiles have been averaged over the 12 posterior samples. In dotted orange, we marked the boundaries of the Local Bubble from the model of T. …
Figure 15
Figure 15. Figure 15: The number of dust peaks in G. Edenhofer et al. (2024) extinction profiles against the number of Gaussian components in the HI optical depth spectrum. The purple histogram includes all 80 Millennium sight lines, while the 28 Millennium sight lines with Zeeman measurem…
Figure 16
Figure 16. Figure 16: As in [PITH_FULL_IMAGE:figures/full_fig_p022_16.png]

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Works this paper leans on

85 extracted references · 15 canonical work pages

  1. [1]

    Ade, P. A. R., Ahmed, Z., Amiri, M., et al. 2023, ApJ, 945, 72, doi: 10.3847/1538-4357/acb64c

    work page doi:10.3847/1538-4357/acb64c 2023

  2. [2]

    Alves, M. I. R., Boulanger, F., Ferri` ere, K., & Montier, L. 2018, A&A, 611, L5, doi: 10.1051/0004-6361/201832637

    doi:10.1051/0004-6361/201832637 2018

  3. [3]

    Angarita, Y., Versteeg, M. J. F., Haverkorn, M., et al. 2024, AJ, 168, 47, doi: 10.3847/1538-3881/ad4b14 Astropy Collaboration, Robitaille, T. P., Tollerud, E. J., et al. 2013, A&A, 558, A33, doi: 10.1051/0004-6361/201322068

    doi:10.3847/1538-3881/ad4b14 2024

  4. [4]

    N., Offner, S

    Beaumont, C. N., Offner, S. S. R., Shetty, R., Glover, S. C. O., & Goodman, A. A. 2013, ApJ, 777, 173, doi: 10.1088/0004-637X/777/2/173

    doi:10.1088/0004-637x/777/2/173 2013

  5. [5]

    E., Bialy, S., et al

    Burkhart, B., Dharmawardena, T. E., Bialy, S., et al. 2025, Nature Astronomy, 9, 1064, doi: 10.1038/s41550-025-02541-7

    work page doi:10.1038/s41550-025-02541-7 2025

  6. [6]

    A., Clayton, G

    Cardelli, J. A., Clayton, G. C., & Mathis, J. S. 1989, ApJ, 345, 245, doi: 10.1086/167900

    doi:10.1086/167900 1989

  7. [7]

    2025, AJ, 169, 158, doi: 10.3847/1538-3881/ada8aa

    Chen, X., Ching, T.-C., Li, D., et al. 2025, AJ, 169, 158, doi: 10.3847/1538-3881/ada8aa

    doi:10.3847/1538-3881/ada8aa 2025

  8. [8]

    C., Li, D., Heiles, C., et al

    Ching, T. C., Li, D., Heiles, C., et al. 2022, Nature, 601, 49, doi: 10.1038/s41586-021-04159-x

    doi:10.1038/s41586-021-04159-x 2022

Show all 85 references
  1. [9]

    2025, AJ, 170, 116, doi: 10.3847/1538-3881/ade144

    Ching, T.-C., Heiles, C., Li, D., et al. 2025, AJ, 170, 116, doi: 10.3847/1538-3881/ade144

    2025 doi

  2. [10]

    Clark, S. E. 2018, ApJL, 857, L10, doi: 10.3847/2041-8213/aabb54

    2018 doi

  3. [11]

    E., & Hensley, B

    Clark, S. E., & Hensley, B. S. 2019, ApJ, 887, 136, doi: 10.3847/1538-4357/ab5803

    2019 doi

  4. [12]

    Babler, B. L. 2015, PhRvL, 115, 241302, doi: 10.1103/PhysRevLett.115.241302

    2015 doi

  5. [13]

    E., Peek, J

    Clark, S. E., Peek, J. E. G., & Miville-Deschˆ enes, M. A. 2019, ApJ, 874, 171, doi: 10.3847/1538-4357/ab0b3b

    2019 doi

  6. [14]

    E., Peek, J

    Clark, S. E., Peek, J. E. G., & Putman, M. E. 2014, ApJ, 789, 82, doi: 10.1088/0004-637X/789/1/82

    2014 doi

  7. [15]

    M., & Kemball, A

    Crutcher, R. M., & Kemball, A. J. 2019, Frontiers in Astronomy and Space Sciences, 6, 66, doi: 10.3389/fspas.2019.00066

    2019

  8. [16]

    Troland, T. H. 2010, ApJ, 725, 466, doi: 10.1088/0004-637X/725/1/466

    2010 doi

  9. [17]

    M., & Thaddeus, P

    Dame, T. M., & Thaddeus, P. 2022, ApJS, 262, 5, doi: 10.3847/1538-4365/ac7e53

    2022 doi

  10. [18]

    2024, A&A, 685, A82, doi: 10.1051/0004-6361/202347628

    Edenhofer, G., Zucker, C., Frank, P., et al. 2024, A&A, 685, A82, doi: 10.1051/0004-6361/202347628

    2024 doi

  11. [19]

    1991, An Introduction to Probability Theory and Its Applications, Volume 2 (John Wiley & Sons)

    Feller, W. 1991, An Introduction to Probability Theory and Its Applications, Volume 2 (John Wiley & Sons)

    1991

  12. [20]

    Field, G. B. 1958, Proceedings of the IRE, 46, 240, doi: 10.1109/JRPROC.1958.286741

    1958

  13. [21]

    M., Ade, P

    Fissel, L. M., Ade, P. A. R., Angil` e, F. E., et al. 2019, ApJ, 878, 110, doi: 10.3847/1538-4357/ab1eb0

    2019 doi

  14. [22]

    Garrett, J. D. 2021, None, doi: 10.5281/zenodo.4106649

    2021 doi

  15. [23]

    A., & Heiles, C

    Goodman, A. A., & Heiles, C. 1994, ApJ, 424, 208, doi: 10.1086/173884

    1994 doi

  16. [24]

    Green, G. M. 2018, The Journal of Open Source Software, 3, 695, doi: 10.21105/joss.00695

    2018 doi

  17. [25]

    E., Cukierman, A., Beck, D., & Kuo, C.-L

    Halal, G., Clark, S. E., Cukierman, A., Beck, D., & Kuo, C.-L. 2024a, ApJ, 961, 29, doi: 10.3847/1538-4357/ad06aa

    doi

  18. [26]

    E., & Tahani, M

    Halal, G., Clark, S. E., & Tahani, M. 2024b, ApJ, 973, 54, doi: 10.3847/1538-4357/ad61e0

    doi

  19. [27]

    Han, J. L. 2017, ARA&A, 55, 111, doi: 10.1146/annurev-astro-091916-055221

    2017 doi

  20. [28]

    R., Millman, K

    Harris, C. R., Millman, K. J., van der Walt, S. J., et al. 2020, Nature, 585, 357, doi: 10.1038/s41586-020-2649-2

    2020 doi

  21. [29]

    1989, ApJ, 336, 808, doi: 10.1086/167051

    Heiles, C. 1989, ApJ, 336, 808, doi: 10.1086/167051

    1989 doi

  22. [30]

    A., McKee, C

    Heiles, C., Goodman, A. A., McKee, C. F., & Zweibel, E. G. 1993, in Protostars and Planets III, ed. E. H. Levy & J. I. Lunine, 279

    1993

  23. [31]

    Heiles, C., & Troland, T. H. 2003, ApJS, 145, 329, doi: 10.1086/367785

    2003 doi

  24. [32]

    Heiles, C., & Troland, T. H. 2004, ApJS, 151, 271, doi: 10.1086/381753

    2004 doi

  25. [33]

    Heiles, C., & Troland, T. H. 2005, ApJ, 624, 773, doi: 10.1086/428896

    2005 doi

  26. [34]

    2001, PASP, 113, 1247, doi: 10.1086/323290

    Heiles, C., Perillat, P., Nolan, M., et al. 2001, PASP, 113, 1247, doi: 10.1086/323290

    2001 doi

  27. [35]

    S., Zhang, C., & Bock, J

    Hensley, B. S., Zhang, C., & Bock, J. J. 2019, ApJ, 887, 159, doi: 10.3847/1538-4357/ab5183 HI4PI Collaboration, Ben Bekhti, N., Fl¨ oer, L., et al. 2016, A&A, 594, A116, doi: 10.1051/0004-6361/201629178

    2019 doi

  28. [36]

    D., & Krumholz, M

    Hu, Z., Wibking, B. D., & Krumholz, M. R. 2023, MNRAS, 521, 5604, doi: 10.1093/mnras/stad931

    2023 doi

  29. [37]

    Hunter, J. D. 2007, Computing in Science & Engineering, 9, 90, doi: 10.1109/MCSE.2007.55

    2007 doi

  30. [38]

    2020, ApJ, 890, 153, doi: 10.3847/1538-4357/ab672b

    Jiang, H., Li, H.-b., & Fan, X. 2020, ApJ, 890, 153, doi: 10.3847/1538-4357/ab672b

    2020 doi

  31. [39]

    2019, Science China

    Jiang, P., Yue, Y., Gan, H., et al. 2019, Science China

    2019

  32. [40]

    Physics, Mechanics, and Astronomy, 62, 959502, doi: 10.1007/s11433-018-9376-1

    doi

  33. [41]

    2020, Research in Astronomy and Astrophysics, 20, 064, doi: 10.1088/1674-4527/20/5/64

    Jiang, P., Tang, N.-Y., Hou, L.-G., et al. 2020, Research in Astronomy and Astrophysics, 20, 064, doi: 10.1088/1674-4527/20/5/64

    2020 doi

  34. [42]

    Kalberla, P. M. W., Kerp, J., & Haud, U. 2020, A&A, 639, A26, doi: 10.1051/0004-6361/202037602

    2020 doi

  35. [43]

    Kalberla, P. M. W., Kerp, J., Haud, U., et al. 2016, ApJ, 821, 117, doi: 10.3847/0004-637X/821/2/117 Nowotka et al. 25

    2016 doi

  36. [44]

    M., & Draine, B

    Lee, H. M., & Draine, B. T. 1985, ApJ, 290, 211, doi: 10.1086/162974

    1985 doi

  37. [45]

    A., et al

    Lee, M.-Y., Stanimirovi´ c, S., Douglas, K. A., et al. 2012, ApJ, 748, 75, doi: 10.1088/0004-637X/748/2/75

    2012 doi

  38. [46]

    Lei, M., & Clark, S. E. 2023, ApJ, 947, 74, doi: 10.3847/1538-4357/acc02a

    2023 doi

  39. [47]

    S., & Dor´ e, O

    Lenz, D., Hensley, B. S., & Dor´ e, O. 2017, ApJ, 846, 38, doi: 10.3847/1538-4357/aa84af

    2017 doi

  40. [48]

    2018a, IEEE Microwave Magazine, 19, 112, doi: 10.1109/MMM.2018.2802178

    Li, D., Wang, P., Qian, L., et al. 2018a, IEEE Microwave Magazine, 19, 112, doi: 10.1109/MMM.2018.2802178

    2018

  41. [49]

    2018b, ApJS, 235, 1, doi: 10.3847/1538-4365/aaa762

    Li, D., Tang, N., Nguyen, H., et al. 2018b, ApJS, 235, 1, doi: 10.3847/1538-4365/aaa762

    doi

  42. [50]

    R., Vera-Ciro, C., Murray, C

    Lindner, R. R., Vera-Ciro, C., Murray, C. E., et al. 2015, AJ, 149, 138, doi: 10.1088/0004-6256/149/4/138

    2015 doi

  43. [51]

    2001, A&A, 371, 698, doi: 10.1051/0004-6361:20010395

    Liszt, H. 2001, A&A, 371, 698, doi: 10.1051/0004-6361:20010395

    2001 doi

  44. [52]

    2016, MNRAS, 460, 1934, doi: 10.1093/mnras/stw1061

    Malinen, J., Montier, L., Montillaud, J., et al. 2016, MNRAS, 460, 1934, doi: 10.1093/mnras/stw1061

    2016 doi

  45. [53]

    G., Blagrave, K

    Martin, P. G., Blagrave, K. P. M., Lockman, F. J., et al. 2015, ApJ, 809, 153, doi: 10.1088/0004-637X/809/2/153

    2015 doi

  46. [54]

    A., & Troland, T

    Mayo, E. A., & Troland, T. H. 2012, AJ, 143, 32, doi: 10.1088/0004-6256/143/2/32

    2012 doi

  47. [55]

    J., & Haverkorn, M

    Green, A. J., & Haverkorn, M. 2006, ApJ, 652, 1339, doi: 10.1086/508706

    2006 doi

  48. [56]

    F., & Ostriker, J

    McKee, C. F., & Ostriker, J. P. 1977, ApJ, 218, 148, doi: 10.1086/155667

    1977 doi

  49. [57]

    E., Peek, J

    Murray, C. E., Peek, J. E. G., & Kim, C.-G. 2020, ApJ, 899, 15, doi: 10.3847/1538-4357/aba19b

    2020 doi

  50. [58]

    E., Stanimirovi´ c, S., Goss, W

    Murray, C. E., Stanimirovi´ c, S., Goss, W. M., et al. 2018, ApJS, 238, 14, doi: 10.3847/1538-4365/aad81a

    2018 doi

  51. [59]

    C., Goodman, A

    Myers, P. C., Goodman, A. A., Gusten, R., & Heiles, C. 1995, ApJ, 442, 177, doi: 10.1086/175433

    1995 doi

  52. [60]

    R., Miville-Deschˆ enes, M

    Nguyen, H., Dawson, J. R., Miville-Deschˆ enes, M. A., et al. 2018, ApJ, 862, 49, doi: 10.3847/1538-4357/aac82b O’Neill, T. J., Goodman, A. A., Soler, J. D., Zucker, C., &

    2018 doi

  53. [61]

    Han, J. J. 2025, ApJ, 988, 191, doi: 10.3847/1538-4357/ade306 O’Neill, T. J., Zucker, C., Goodman, A. A., & Edenhofer, G. 2024, ApJ, 973, 136, doi: 10.3847/1538-4357/ad61de OpenAI. 2022, Introducing ChatGPT,, https://openai.com/blog/chatgpt Pandas Development Team. 2020, None,...

    2025 doi

  54. [62]

    Peek, J. E. G., & Clark, S. E. 2019, ApJL, 886, L13, doi: 10.3847/2041-8213/ab53de

    2019 doi

  55. [63]

    Peek, J. E. G., Babler, B. L., Zheng, Y., et al. 2018, ApJS, 234, 2, doi: 10.3847/1538-4365/aa91d3 Planck Collaboration, Ade, P. A. R., Aghanim, N., et al. 2015, A&A, 576, A105, doi: 10.1051/0004-6361/201424086 Planck Collaboration, Ade, P. A. R., Aghanim, N., et al. 2016a, A&...

    2018 doi

  56. [64]

    2020, The Innovation, 1, 100053, doi: 10.1016/j.xinn.2020.100053

    Qian, L., Yao, R., Sun, J., et al. 2020, The Innovation, 1, 100053, doi: 10.1016/j.xinn.2020.100053

    2020

  57. [65]

    2011, MNRAS, 418, 467, doi: 10.1111/j.1365-2966.2011.19497.x

    Remazeilles, M., Delabrouille, J., & Cardoso, J.-F. 2011, MNRAS, 418, 467, doi: 10.1111/j.1365-2966.2011.19497.x

    2011

  58. [66]

    2008, PhD thesis, University of California, Berkeley

    Robishaw, T. 2008, PhD thesis, University of California, Berkeley

    2008

  59. [67]

    2021, in The WSPC Handbook of Astronomical Instrumentation, Volume 1: Radio Astronomical Instrumentation, ed

    Robishaw, T., & Heiles, C. 2021, in The WSPC Handbook of Astronomical Instrumentation, Volume 1: Radio Astronomical Instrumentation, ed. A. Wolszczan, 127–158, doi: 10.1142/9789811203770 0006

    2021 doi

  60. [68]

    P., Troland, T

    Sarma, A. P., Troland, T. H., Roberts, D. A., & Crutcher, R. M. 2000, ApJ, 533, 271, doi: 10.1086/308667

    2000 doi

  61. [69]

    P., Troland, T

    Sarma, A. P., Troland, T. H., & Rupen, M. P. 2002, ApJ, 564, 696, doi: 10.1086/324234

    2002 doi

  62. [70]

    J., Killeen, N

    Sault, R. J., Killeen, N. E. B., Zmuidzinas, J., & Loushin, R. 1990, ApJS, 74, 437, doi: 10.1086/191505

    1990 doi

  63. [71]

    J., Burkhart, B., et al

    Saxena, S., Haworth, T. J., Burkhart, B., et al. 2025, MNRAS, 540, L109, doi: 10.1093/mnrasl/slaf044

    2025 doi

  64. [72]

    Seta, A., & McClure-Griffiths, N. M. 2025, MNRAS, 539, 1024, doi: 10.1093/mnras/staf520

    2025 doi

  65. [73]

    D., Bracco, A., & Pon, A

    Soler, J. D., Bracco, A., & Pon, A. 2018, A&A, 609, L3, doi: 10.1051/0004-6361/201732203

    2018 doi

  66. [74]

    D., Beuther, H., Rugel, M., et al

    Soler, J. D., Beuther, H., Rugel, M., et al. 2019, A&A, 622, A166, doi: 10.1051/0004-6361/201834300

    2019 doi

  67. [75]

    R., Moran, J

    Thompson, A. R., Moran, J. M., & Swenson, Jr., G. W. 2017, Interferometry and Synthesis in Radio Astronomy, 3rd Edition, doi: 10.1007/978-3-319-44431-4

    2017 doi

  68. [76]

    L., Troland, T

    Thompson, K. L., Troland, T. H., & Heiles, C. 2019, ApJ, 884, 49, doi: 10.3847/1538-4357/ab364e

    2019 doi

  69. [77]

    V., Mouschovias, T

    Tritsis, A., Panopoulou, G. V., Mouschovias, T. C., Tassis, K., & Pavlidou, V. 2015, MNRAS, 451, 4384, doi: 10.1093/mnras/stv1133

    2015 doi

  70. [78]

    H., & Heiles, C

    Troland, T. H., & Heiles, C. 1982, ApJ, 252, 179, doi: 10.1086/159544 van der Velden, E. 2020, The Journal of Open Source Software, 5, 2004, doi: 10.21105/joss.02004

    1982 doi

  71. [79]

    Verschuur, G. L. 1968, PhRvL, 21, 775, doi: 10.1103/PhysRevLett.21.775

    1968 doi

  72. [80]

    E., et al

    Virtanen, P., Gommers, R., Oliphant, T. E., et al. 2020, Nature Methods, 17, 261, doi: 10.1038/s41592-019-0686-2 26 Nowotka et al

    2020 doi

  73. [81]

    Waskom, M. L. 2021, Journal of Open Source Software, 6, 3021, doi: 10.21105/joss.03021

    2021 doi

  74. [82]

    J., Srinivasan, S., Pudritz, R

    Whitworth, D. J., Srinivasan, S., Pudritz, R. E., et al. 2025, MNRAS, 540, 2762, doi: 10.1093/mnras/staf901

    2025 doi

  75. [83]

    W., Jefferts, K

    Wilson, R. W., Jefferts, K. B., & Penzias, A. A. 1970, ApJL, 161, L43, doi: 10.1086/180567

    1970 doi

  76. [84]

    M., & Rix, H.-W

    Zhang, X., Green, G. M., & Rix, H.-W. 2023, MNRAS, 524, 1855, doi: 10.1093/mnras/stad1941

    2023 doi

  77. [85]

    2019, The Journal of Open Source Software, 4, 1298, doi: 10.21105/joss.01298

    Zonca, A., Singer, L., Lenz, D., et al. 2019, The Journal of Open Source Software, 4, 1298, doi: 10.21105/joss.01298

    2019 doi

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