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REVIEW 3 major objections 8 minor 66 references

Reviewed by Pith at T0; open to challenge.

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First 3D map of nearby atomic hydrogen with velocities

2026-07-09 10:21 UTC pith:6GLTOQT2

load-bearing objection First velocity-resolved 3D HI map within 1.25 kpc via IFT forward modeling; synthetic validation is prior-informed but real-data checks are encouraging. the 3 major comments →

arxiv 2607.07451 v1 pith:6GLTOQT2 submitted 2026-07-08 astro-ph.GA

Milky Way Atlas: A radial-velocity-resolved, three-dimensional map of H I within 1.25 kpc

Lewis McCallum , Laurin S\"oding , Mareike Berkner , Philipp Frank , Matteo Guardiani , Jakob Roth , Juan D. Soler , Robert Benjamin
show 4 more authors
Torsten En{\ss}lin Philipp Mertsch Konstantinos Tassis Vasiliki Pavlidou
This is my paper
classification astro-ph.GA PACS 98.38.-j98.38.Dq98.35.Bd95.75.Mn
keywords atomic hydrogen3D ISM mappingkinetic tomographyInformation Field Theorydust extinctionGalactic kinematicsHI4PIlocal interstellar medium
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper claims to have produced the first velocity-resolved three-dimensional map of atomic hydrogen (HI) within 1.25 kiloparsecs of the Sun, solving the long-standing problem of converting 21-cm radio emission — which is observed in position-position-velocity space — into true 3D physical positions. The method works by combining the HI4PI all-sky hydrogen survey with the Edenhofer et al. (2024) 3D dust map in a Bayesian inference framework called Information Field Theory. The key idea is morphological matching: where dust structures and hydrogen emission shapes align on the sky, the method assigns the gas to that 3D location and infers its density, line-of-sight velocity, and line width simultaneously. A flexible remainder component absorbs emission from beyond the mapped volume, breaking the degeneracy between nearby and distant gas. The reconstruction fits the HI4PI data with a reduced chi-squared of 1.3, recovers the expected transition from atomic to molecular hydrogen at dust column densities consistent with theoretical predictions, and produces velocities that agree with independent maser and young stellar cluster measurements.

Core claim

The central object is a jointly inferred set of three 3D fields — HI density, line-of-sight velocity, and effective line width — within 1.25 kpc of the Sun, reconstructed by forward-modeling how these fields would produce the observed HI4PI emission when combined with the Edenhofer et al. (2024) dust map as a spatial anchor. The paper validates this reconstruction through synthetic data tests showing accurate recovery of ground-truth density and velocity structure even with substantial distant-emission contamination, and through comparisons with 11 maser sources (reduced chi-squared of 2.4) and 123 young stellar clusters. The map reveals that local HI is smoother and more diffuse than the粉尘,

What carries the argument

The inference uses Metric Gaussian Variational Inference to handle approximately 25 million free parameters across three 3D correlated Gaussian random fields (HI-to-dust ratio, velocity, line width) plus a 2D remainder-sky component. A forward model computes synthetic 21-cm emission from each voxel including optical-depth self-absorption along the line of sight. The HI-to-dust ratio is modeled as a smooth spatially correlated field rather than a constant, allowing local departures from a fixed gas-to-dust conversion. A velocity-seeding pre-step identifies regions where dust-HI morphological correlation exceeds 0.75 to initialize velocities for kinematically anomalous high-latitude clouds (IV

Load-bearing premise

The reconstruction assumes the HI-to-dust ratio can be modeled as a smooth 3D correlated Gaussian random field, which means HI structures lacking a dust morphological counterpart can only be recovered where the data alone is strong enough to overcome the prior — a limitation demonstrated by the erroneous local placement of the distant Magellanic Stream.

What would settle it

If the velocity field were not physically meaningful, the reconstructed line-of-sight velocities at the positions of independent maser sources (which directly trace gas motion) would show no correlation with observed maser velocities. The paper reports a reduced chi-squared of 2.4 for 11 masers, dominated by two outliers in low-density regions, suggesting the velocities are broadly correct but degrade where HI density is low.

Watch this falsifier — get emailed when new claim-graph text bears on it.

If this is right

  • The 3D velocity field can serve as a lookup table: any emission line observed in position-position-velocity space within 1.25 kpc can be localized in true 3D position by matching its velocity to the reconstructed field along the line of sight.
  • The recovered HI-to-dust ratio field, which varies significantly in 3D, can replace the constant gas-to-dust conversions assumed in existing 3D models of ionized gas or extinction, improving those reconstructions.
  • The local/distant sky decomposition (approximately 50% of emission within |V_LSR| < 75 km/s is local) can inform and constrain larger-scale Galactic gas reconstructions by providing a well-characterized local foreground model.
  • Extending the framework to include CO-traced molecular hydrogen would close the hydrogen budget and enable a complete 3D map of all neutral gas phases in the solar neighborhood.
  • The velocity field's power spectrum (turnover at 157 pc, slope of -4.0) provides a new observational constraint on the turbulent cascade in the local ISM, though the paper notes this is complicated by the fact that only radial velocity is measured.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The Magellanic Stream contamination — where a known distant structure is erroneously placed locally — demonstrates that the method's reliance on dust morphology as a spatial prior creates a systematic blind spot for gas structures that have no dust counterpart. This suggests the map should be used with caution for high-latitude or high-velocity gas where dust is sparse.
  • The steeper-than-expected decline in the circular rotation profile compared to Reid et al. (2019) could reflect real non-circular motions from local features (Local Bubble expansion, spiral arm perturbations) rather than a true change in the underlying rotation curve, given the limited radial range sampled.
  • The velocity-seeding step's correlation threshold of 0.75 could bias the reconstruction toward gas that follows dust morphology, potentially missing kinematically distinct HI features that are genuinely uncorrelated with dust — a selection effect that would be invisible in the synthetic data tests if those tests draw from the same prior assumptions.
  • The fixed spin temperature of 200 K likely causes systematic density underestimation in cold dense regions and overestimation in diffuse regions, which would affect the HI-to-dust ratio measurements precisely where the atomic-to-molecular transition is occurring.

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

3 major / 8 minor

Summary. This paper presents a velocity-resolved 3D map of atomic hydrogen within 1.25 kpc of the Sun, constructed by combining the HI4PI 21-cm survey with the Edenhofer et al. (2024) 3D dust map within an Information Field Theory framework. The authors jointly infer three 3D fields — HI-to-dust ratio, LOS velocity, and effective line width — using Metric Gaussian Variational Inference (MGVI), while simultaneously fitting a flexible 'remainder' component that absorbs emission from beyond the mapped volume. The method is validated through synthetic data tests and comparisons with independent kinematic tracers (masers and young stellar clusters). The resulting map shows a smoother HI distribution than dust, a declining HI-to-dust ratio at high dust columns consistent with the atomic-to-molecular transition (matching Krumholz et al. 2009 predictions), and a velocity field capturing both Galactic rotation and local non-circular motions. The data products are publicly available.

Significance. The paper makes a valuable contribution to Galactic ISM studies by producing the first IFT-based, velocity-resolved 3D HI reconstruction tied to the newest generation of parsec-scale dust maps. The approach of jointly modeling local and distant emission via a remainder component is methodologically interesting and addresses a real obstacle in local ISM studies. The HI-to-dust transition matching Krumholz et al. (2009) at the expected column densities is a physically meaningful, falsifiable check that lends credibility to the density reconstruction. The public release of posterior mean grids and samples on Zenodo is a strength. The comparison to the independent Soler et al. (2025) HOG-based velocity field, showing broad agreement on high-confidence structures, is a useful cross-validation. The maser comparison (reduced chi-squared = 2.4 for 11 sources) provides an external kinematic check, though the sample is small.

major comments (3)
  1. §2.2.6: The synthetic data test draws ground truth from the same Matérn GRF prior family used in the reconstruction. The authors acknowledge this implicitly by noting that IVCs require a manual velocity-seeding workaround (§2.2.7) because they are 'hard to find in parameter space' under the GRF prior, yet the synthetic test does not include such non-Gaussian structures. This means the synthetic test likely overestimates real-data fidelity for structures that depart from the prior's support (sharp filamentary transitions, multiple velocity components along a single sightline, phase boundaries). The paper should explicitly discuss this limitation — ideally quantifying how the velocity-seeding step affects the synthetic test recovery rates, or at minimum adding a caveat that the synthetic test validates recovery within the prior's support and may not represent performance on the full range
  2. §2.2.7: The velocity seeding step pre-selects regions where dust-HI morphological correlation exceeds 0.75 before the main inference runs. This could bias the reconstruction toward structures that follow dust morphology and against genuinely independent gas features. The threshold of 0.75 and the 70%-of-peak contiguous-range criterion appear to be chosen empirically but no sensitivity analysis is provided. Since the central claim is that the method 'reliably reconstructs 3D HI density, velocity, and line width,' the dependence of the final product on this pre-processing step is load-bearing. The authors should either (a) demonstrate that the reconstruction is insensitive to reasonable variations of these thresholds, or (b) clearly state which structures in the final map owe their placement to the seeding step and would be absent without it.
  3. §3.3, Fig. 13: The combined maser+cluster reduced chi-squared of 4.85 (or 2.4 for masers alone) is somewhat high for a validation. The authors note that the maser value is 'dominated by only two poorly explained maser velocities, both of which exist in regions of the map with little-to-no HI emission.' This is an important caveat: the velocity field is unreliable in low-density regions. The paper should more prominently flag which regions of the published map have velocity fields that are data-driven versus prior-driven, perhaps by providing a companion map of velocity uncertainty or data-constraint quality. Without this, users of the data product may over-interpret velocities in poorly constrained regions.
minor comments (8)
  1. §2.1.2, Eq. (7): The conversion factor of 4.5e-23 g cm^-3 per dust map unit is noted as 'somewhat higher than in previous works.' The factor of ~1.6 increase relative to Zucker et al. (2021) is explained by the Draine (2009) to Hensley & Draine (2023) model update. This is clearly stated, but the impact on downstream comparisons (e.g., the HI-to-dust ratio analysis in §3.2/§4.2) should be noted — specifically, whether the Krumholz et al. (2009) transition column comparison is affected.
  2. §2.2.3, Eq. (8): The forward model assumes a single Gaussian velocity component per voxel. The authors note this limitation in the text, but it would help to state the typical velocity separation below which two components would be unresolved given the grid resolution and spectral resolution.
  3. §3.2, Fig. 7: The comparison to the Dickey & Lockman (1990) profile shows systematically higher densities at |z| > 500 pc. The authors attribute this partly to IVCs recovered via the velocity-seeding step and partly to Magellanic Stream contamination. Given the small number of voxels at extreme |z|, a simple error bar or shaded region on the reconstructed profile would help readers assess the significance of this difference.
  4. §3.3, Fig. 12: The circularly averaged rotation profile appears to decline more steeply than the Reid et al. (2019) curve. The authors caution against over-interpretation, but the figure as presented could invite unwarranted claims. A note that this is not a measurement of the Galactic rotation curve but rather a byproduct of the local velocity field reconstruction, affected by non-circular motions, would be useful. The switch from 230 to 237 km/s normalization between reconstruction and post-hoc analysis is mentioned but could be clearer.
  5. Table C1: The prior table is comprehensive but some entries could benefit from brief physical motivation. For instance, the Matérn lengthscale prior for the velocity field (mean 0.15 kpc) vs. the HI-to-dust field (mean 0.3 kpc) — is the shorter velocity lengthscale motivated by expected velocity coherence scales?
  6. §4.4, Table 2: The comparison to Soler et al. (2025) notes that quantities depend on the adopted grid and averaging scheme. The velocity dispersion ratio (6.0 vs 10.8 km/s) is a factor of ~1.8 difference; a brief discussion of whether this is physically expected (given the different methods' smoothing properties) or merely a systematic effect of gridding would strengthen the comparison.
  7. Figures: Several figures (e.g., Fig. 2, Fig. 4) use color bars that could be more clearly labeled with units. The central circular artifact (unmapped d < 69 pc) in face-on views should be masked or noted more prominently in captions.
  8. §4.6: The discussion of future possibilities is lengthy. While the individual points are reasonable, this section could be condensed to improve focus on the present results.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for a careful and constructive report. The referee identifies three main areas for improvement: (1) the synthetic data test draws from the same prior family as the reconstruction, potentially overestimating fidelity for non-Gaussian structures; (2) the velocity-seeding pre-processing step lacks a sensitivity analysis and could bias the reconstruction toward dust-morphology-following structures; and (3) the validation chi-squared values are somewhat high and the map should more prominently flag which regions have data-driven versus prior-driven velocity fields. We agree with all three points and will revise the manuscript accordingly.

read point-by-point responses

  1. Referee: §2.2.6: The synthetic data test draws ground truth from the same Matérn GRF prior family used in the reconstruction. The authors acknowledge this implicitly by noting that IVCs require a manual velocity-seeding workaround (§2.2.7) because they are 'hard to find in parameter space' under the GRF prior, yet the synthetic test does not include such non-Gaussian structures. This means the synthetic test likely overestimates real-data fidelity for structures that depart from the prior's support (sharp filamentary transitions, multiple velocity components along a single sightline, phase boundaries). The paper should explicitly discuss this limitation — ideally quantifying how the velocity-seeding step affects the synthetic test recovery rates, or at minimum adding a caveat that the synthetic test validates recovery within the prior's support and may not represent performance on the full range.

    Authors: The referee is correct that the synthetic data test draws ground truth from the same Matérn GRF prior family used in the reconstruction, and that this means the test validates recovery within the prior's support rather than for the full range of structures present in the real ISM. We agree that this limitation should be stated explicitly. We will add a caveat to §2.2.6 noting that the synthetic test validates recovery for structures consistent with the GRF prior and may overestimate real-data fidelity for structures that depart from this prior's support, including sharp filamentary transitions, multiple velocity components along a single sightline, and phase boundaries. We will also note that the velocity-seeding step (§2.2.7) was introduced precisely because IVCs — which are non-Gaussian in the sense that they are kinematically anomalous relative to their surroundings — are not well recovered under the GRF prior alone, which itself illustrates the limitation the referee identifies. We will cross-reference §2.2.7 in the synthetic data discussion to make this connection explicit. Regarding the suggestion to quantify how the velocity-seeding step affects synthetic test recovery rates: the synthetic test as currently designed does not include IVC-like structures, so the seeding step is not activated in the synthetic pipeline. Running a synthetic test with manually injected IVC-like structures and comparing recovery with and without seeding would be a valuable additional test, but it requires non-trivial development of a non-Gaussian ground-truth generator that is beyond the scope of this revision. We will state this as a direction for future work. revision: yes

  2. Referee: §2.2.7: The velocity seeding step pre-selects regions where dust-HI morphological correlation exceeds 0.75 before the main inference runs. This could bias the reconstruction toward structures that follow dust morphology and against genuinely independent gas features. The threshold of 0.75 and the 70%-of-peak contiguous-range criterion appear to be chosen empirically but no sensitivity analysis is provided. Since the central claim is that the method 'reliably reconstructs 3D HI density, velocity, and line width,' the dependence of the final product on this pre-processing step is load-bearing. The authors should either (a) demonstrate that the reconstruction is insensitive to reasonable variations of these thresholds, or (b) clearly state which structures in the final map owe their placement to the seeding step and would be absent without it.

    Authors: The referee raises a valid concern. The velocity-seeding step is indeed load-bearing for the placement of certain structures — specifically the kinematically anomalous high-latitude clouds (IVCs) that are not well recovered by the GRF prior alone. We can address this comment through option (b): we will add a clear statement identifying which structures in the final map owe their placement to the seeding step. In particular, we will note that the high-altitude HI clouds discussed in §4.1 and §4.5 (including IVC 135) are the primary structures whose placement depends on the seeding step, and that without seeding these clouds are absorbed into the distant remainder. We will also note that the seeding step provides only an initial velocity guess that is subsequently refined by the full inference, so the final velocity of these structures is not solely determined by the seed. Regarding option (a), we agree that a sensitivity analysis on the 0.75 threshold and the 70%-of-peak criterion would strengthen the paper. We will run the reconstruction with varied thresholds (e.g., 0.65 and 0.85) and report whether the set of seeded structures and their final reconstructed velocities change significantly. If the sensitivity analysis is not complete in time for the revision, we will at minimum add a discussion of the expected effects of threshold variation and flag the empirical nature of the threshold choice. We acknowledge that the seeding step could in principle bias against genuinely independent gas features that do not correlate with dust morphology; we will add this as an explicit caveat. revision: partial

  3. Referee: §3.3, Fig. 13: The combined maser+cluster reduced chi-squared of 4.85 (or 2.4 for masers alone) is somewhat high for a validation. The authors note that the maser value is 'dominated by only two poorly explained maser velocities, both of which exist in regions of the map with little-to-no HI emission.' This is an important caveat: the velocity field is unreliable in low-density regions. The paper should more prominently flag which regions of the published map have velocity fields that are data-driven versus prior-driven, perhaps by providing a companion map of velocity uncertainty or data-constraint quality. Without this, users of the data product may over-interpret velocities in poorly constrained regions.

    Authors: We agree that the velocity field reliability is density-dependent and that this should be more prominently communicated to users of the data product. The manuscript already includes uncertainty maps in Figure 4 (bottom row), showing the projected velocity uncertainty from the posterior samples. However, these are somewhat buried in the figure set and the connection between HI density, data-constraint quality, and velocity reliability is not stated prominently enough. We will make the following changes: (1) We will add explicit text in §3.3 and §4.3 stating that velocity reliability is strongly linked to reconstructed HI density, and that velocities in low-density regions should be treated as prior-driven rather than data-driven. (2) We will add a note to the data release documentation on Zenodo flagging this limitation. (3) We will consider adding a companion figure or panel showing a mask or quality flag based on HI column density, though we note that the posterior uncertainty maps already partially serve this purpose. Regarding the chi-squared values: we agree these are somewhat high, and we will add a more prominent discussion of the two outlier masers and the fact that they fall in regions with little HI emission. We will also note that the cluster chi-squared is likely inflated by overconfident error bars on cluster mean velocities, as we already discuss but will make more prominent. revision: yes

Circularity Check

0 steps flagged

No significant circularity. The synthetic data test draws ground truth from the same Matérn GRF prior family used in reconstruction, which is a mild self-consistency concern, but the central scientific claims are independently validated by external data (masers, clusters, Krumholz et al. 2009).

full rationale

I walked the paper's derivation chain and found no step where a prediction or result reduces to its inputs by construction. (1) The synthetic data test (§2.2.6) does generate ground truth as 'draws from our prior' using the same Matérn GRF family as the reconstruction prior. This is a known limitation of Bayesian synthetic tests — it validates the inverse-problem solution for signals in the prior's support but cannot quantify failures for non-Gaussian ISM structure. However, this is not strictly circular: the forward model (Eq. 8–9) adds non-trivial radiative transfer and optical-depth physics, the test includes independent distant contamination from Söding et al. (2025), and the paper explicitly acknowledges the limitation for IVCs (§2.2.7). The test validates that MGVI can invert the forward model, not that the prior equals the posterior. (2) The real-data validations are independent: maser velocities from Reid et al. (2019) and cluster velocities from Hunt & Reffert (2023) are external datasets not used in the reconstruction. The HI-to-dust transition at dust column densities consistent with Krumholz et al. (2009) is compared against an independent theoretical prediction. The χ² = 1.3 against HI4PI is a goodness-of-fit measure, not claimed as a prediction. (3) Self-citations (Söding et al. 2025 for distant-sky priors and opacity treatment; Edenhofer et al. 2024b for the dust map; McCallum et al. 2025 for prior Hα work) are methodological and do not form a load-bearing chain for the central claims. The remainder-sky scale-height priors are fitted from Söding et al. (2025), but this governs a nuisance component, not the scientific result. Overall, the derivation is self-contained against external benchmarks, and the mild prior-informedness of the synthetic test is a correctness-risk concern rather than a circularity.

Axiom & Free-Parameter Ledger

17 free parameters · 6 axioms · 1 invented entities

The remainder is validated by synthetic data tests (Fig. 3) showing clean local/distant decomposition, and by the reconstructed total sky matching HI4PI data (χ²=1.3). Its limitations are tested (Magellanic Stream failure).

free parameters (17)
  • Mean log(HI/dust) offset = inferred (prior mean 4.7)
    Sets the overall HI-to-dust ratio; learned by VI optimiser
  • Matérn variance (HI/dust field) = inferred (prior mean 0.5)
    Controls fluctuation amplitude of HI-to-dust ratio field
  • Matérn lengthscale (HI/dust field) = inferred (prior mean 0.3 kpc)
    Sets spatial correlation length of HI-to-dust variations
  • Matérn slope (HI/dust field) = inferred (prior mean 3.5)
    Power spectrum slope of HI-to-dust field
  • Mean velocity offset = inferred (prior mean 0.01 km/s)
    Additive offset to the approximate rotation curve
  • Matérn variance (velocity field) = inferred (prior mean 5.0 km²/s²)
    Fluctuation amplitude of non-circular velocity field
  • Matérn lengthscale (velocity field) = inferred (prior mean 0.15 kpc)
    Spatial correlation length of velocity field
  • Matérn slope (velocity field) = inferred (prior mean 3.5)
    Power spectrum slope of velocity field
  • Mean log line-width offset = inferred (prior mean 1.1 log(km/s))
    Sets overall effective line width
  • Matérn variance (line-width field) = inferred (prior mean 0.05)
    Fluctuation amplitude of line-width field
  • Matérn lengthscale (line-width field) = inferred (prior mean 0.3 kpc)
    Spatial correlation length of line-width field
  • Matérn slope (line-width field) = inferred (prior mean 3.5)
    Power spectrum slope of line-width field
  • Remainder sky parameters (20+ parameters) = inferred
    Scale heights, longitude modulations, velocity smoothing, intensity offsets for the distant emission model (Table C1)
  • T_spin = 200 K (fixed)
    Fixed spin temperature for 21cm radiative transfer; not inferred
  • R_V = 3.1 (fixed)
    Fixed extinction curve parameter for dust-to-mass conversion
  • Rotation curve normalization (reconstruction) = 230 km/s (fixed)
    Approximate rotation speed used in forward model
  • Rotation curve normalization (post-hoc analysis) = 237 km/s
    Post-hoc normalization from Reid et al. (2019) for Fig. 12
axioms (6)
  • domain assumption HI and dust morphology are sufficiently correlated that the dust map provides a valid spatial prior for HI density structure
    §2.2.3: HI density is derived by multiplying the dust map by an inferred HI-to-dust ratio field. If dust and HI are morphologically uncorrelated in a region, the reconstruction cannot recover HI structures there.
  • domain assumption The HI-to-dust ratio, velocity, and line-width fields are well-described by Matérn covariance Gaussian processes
    §2.2.5: All three 3D fields are modeled as correlated Gaussian random fields with Matérn kernels. This imposes smoothness and statistical homogeneity assumptions.
  • domain assumption A single Gaussian line profile per voxel adequately represents the HI emission
    §2.2.3: Each voxel produces one Gaussian emission line with one central velocity and one line width. Multiple velocity components in the same voxel cannot be resolved.
  • domain assumption T_spin = 200 K is a reasonable approximation for the 21cm spin temperature throughout the local volume
    §2.2.3: Fixed spin temperature used for radiative transfer. Authors acknowledge this is too high in dense cold regions and too low in diffuse media (§4.2).
  • domain assumption The remainder-sky model (2-disc latitude profile + correlated PPV field) can adequately represent all non-local emission
    §2.2.4: The remainder model uses exponential disc latitude profiles. The Magellanic Stream contamination (§4) shows this fails for non-disc structures at extreme latitudes.
  • domain assumption Metric Gaussian Variational Inference provides an adequate approximation to the true posterior
    §2.2.2: MGVI approximates the posterior as a high-dimensional Gaussian. The authors tested geoVI and found little impact, but non-Gaussian posterior features would be missed.
invented entities (1)
  • Remainder sky component independent evidence
    purpose: Absorbs HI emission originating beyond 1.25 kpc to break local/distant degeneracy
    The remainder is validated by synthetic data tests (Fig. 3) showing clean local/distant decomposition, and by the reconstructed total sky matching HI4PI data (χ²=1.3). Its limitations are tested (Magellanic Stream failure).

pith-pipeline@v1.1.0-glm · 34508 in / 5441 out tokens · 283584 ms · 2026-07-09T10:21:14.012792+00:00 · methodology

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read the original abstract

We present a velocity-resolved three-dimensional map of local atomic hydrogen (HI) within 1.25 kpc of the Sun, tackling the challenge of converting emission from position-position-velocity space into true 3D structure. Our method combines the HI4PI full-sky survey with the Edenhofer et al. (2024) 3D dust map in the framework of Information Field Theory, enabling a joint reconstruction of the local HI density, radial velocity field, and effective line width while also separating emission arising inside the mapped local volume from more distant Galactic HI. The inference is driven by morphological matching between dust and HI structures together with kinematic coherence in 3D space. Synthetic data tests show that the method recovers the local density and velocity structure, even in the presence of substantial contamination from distant emission. The resulting map reveals a smoother, more diffuse local HI distribution than the dust, a declining HI-to-dust ratio toward high dust column densities consistent with the atomic-to-molecular transition, and a velocity field that captures both large-scale Galactic rotation and local non-circular velocities. Independent comparisons with maser and young stellar cluster velocities agree with the recovered kinematics. This HI map provides a new three-dimensional, kinematically resolved view of the nearby atomic interstellar medium and a foundation for localising other velocity-resolved Galactic emission in physical space.

Figures

Figures reproduced from arXiv: 2607.07451 by Jakob Roth, Juan D. Soler, Konstantinos Tassis, Laurin S\"oding, Lewis McCallum, Mareike Berkner, Matteo Guardiani, Philipp Frank, Philipp Mertsch, Robert Benjamin, Torsten En{\ss}lin, Vasiliki Pavlidou.

Figure 1
Figure 1. Figure 1: Comparison between our synthetic data test ground truth and re￾constructed values. These 2D histograms count Cartesian voxels and show the 1:1 perfect match line. The top left panel shows the H i density, the top right panel shows the radial velocity, the bottom left panel shows the line width, and the bottom right panel shows the H i-to-dust mass ratio. beyond 0.3 kpc to 13.9 pc at the outer edge. The HI4… view at source ↗
Figure 2
Figure 2. Figure 2: Top-down maps comparing our ground truth and posterior mean reconstructed maps from synthetic data. In all maps the Galactic centre is to the right (+𝑥), and the direction of Galactic rotation is up (+𝑦). Left columns are the truth maps, middle columns are the reconstructed maps and the right column is the difference. For all but the velocity, the difference map is a ratio between reconstructed and truth. … view at source ↗
Figure 3
Figure 3. Figure 3: Comparison of ground truth to reconstruction showing total intensities on the plane of the sky, with each panel centred on the Galactic centre (ℓ = 0 ◦ ). The left column is ground truth, middle is reconstructed posterior mean, and right is the ratio between reconstructed and truth. Top row is the local only sky, middle row is the distant only sky, and the bottom row is the total reconstructed data. The de… view at source ↗
Figure 4
Figure 4. Figure 4: Visualisation of the three grids which make up our posterior mean reconstruction of the local H i. The top row shows the mean value through the z-axis of the grids, with the bottom row showing the uncertainty in each image. The uncertainty maps are calculated by taking the standard deviation of projected map samples, rather than being a projection of the voxel-wise variance. The left column shows the H i-t… view at source ↗
Figure 5
Figure 5. Figure 5: Left: Top-down view of linearly scaled H i column density derived from our posterior mean H i density grid. Axes are in heliocentric Galactic Cartesian coordinates, with the Galactic centre to the right. As this is a 𝑍-integrated column density through a spherical reconstructed volume, pixels towards the edge of the mapped area are integrated through a smaller range of 𝑍-values. This view of local H i is o… view at source ↗
Figure 6
Figure 6. Figure 6: Decomposition between local and distant sky from our posterior mean grids, with all panels centred on the Galactic centre (ℓ = 0 ◦ ). Top left panel shows the total reconstructed sky, which matches the HI4PI dataset at |𝑉LOS | < 75 km s−1 within a reduced 𝜒 2 𝐻𝐼4𝑃𝐼 of 1.3. The top right panel shows the Edenhofer et al. (2024b) dust map projected on the sky and converted to a total mass column density using… view at source ↗
Figure 7
Figure 7. Figure 7: Comparison between our reconstructed vertical H i profile and the expected H i profile from Dickey & Lockman (1990). Also shown is the profile extracted from the underlying Edenhofer et al. (2024b) dust map, where the density has been scaled up to match the gas density in the midplane (a factor of 45). Note that the number of voxels included in this plot changes as a function of height due to the shape of … view at source ↗
Figure 8
Figure 8. Figure 8: Probability distribution functions of H i density, as a function of reconstructed line width. We find that voxels of higher line width tend to be occupied by lower H i densities. region for our method for two reasons. Firstly, the stream crosses zero velocity in this region, meaning it is kinematically coherent with local structures. Secondly, our remainder object was built with the shape of an exponential… view at source ↗
Figure 10
Figure 10. Figure 10: The same view of our reconstructed volume as in figure 5, but showing the H i-density weighted LOS velocity of the gas. The quadrupole expected from galactic rotation can clearly be seen, as well as a number of regions of high velocity relative to the underlying rotational velocity structure. Axes are in heliocentric Galactic Cartesian coordinates, with the Galactic centre to the right. dominate the verti… view at source ↗
Figure 11
Figure 11. Figure 11: Left: the H i density weighted mean 𝑉LSR for all non-zero voxels from the local bubble definition of O’Neill et al. (2024). Colourbar is on a linear scale. Right: the total H i column density from this same selected 3D region. Both maps are centred on the Galactic centre (ℓ = 0 ◦ ). Colourbar is on a logarithmic scale. 7.0 7.5 8.0 8.5 9.0 Galactocentric radius R [kpc] 180 200 220 240 260 Cir c ula r s p e… view at source ↗
Figure 12
Figure 12. Figure 12: Radially averaged circular-rotation profile inferred from the recon￾structed LOS velocity field, assuming an axisymmetric circular component and averaging in regions of constant of Galactocentric radius. To convert the reconstructed 𝑉LSR field into an absolute circular speed, we adopt a local nor￾malisation of Θ0 = 237 km s−1 at the Solar radius. Points show the annular mean circular component, while the … view at source ↗
Figure 13
Figure 13. Figure 13: The left panel shows the LOS velocity of the dataset of masers and young stellar clusters (see section 2.1.3), versus the LOS velocity which is predicted by our velocity reconstruction. Errors in the 𝑥-axis are the measurement uncertainties on the observed data points, while errors in the 𝑦-axis come from the parallax uncertainties, and the variance between our distinct posterior samples. The right panel … view at source ↗
Figure 14
Figure 14. Figure 14: Top down view of our posterior mean reconstructed velocity field with the Reid et al. (2019) A5 Galactic rotation curve subtracted. This plot only contains cells of |𝑧 | < 150 pc, and is a volume weighted average through the 𝑧-axis. Also included are the nine masers which fall below this 𝑧-ceiling, coloured by their observed velocities, also having subtracted the Reid et al. (2019) rotation curve. Axes ar… view at source ↗
Figure 15
Figure 15. Figure 15: Top row shows the comparison in velocities from this work and Soler et al. (2025). Our velocity structure has been volume-averaged through the z-axis, including only voxels at |𝑏| < 5 ◦ . Over-plotted are the six observed maser velocities within this volume and with |𝑏| < 5 ◦ . Two of these six are further then 10 pc from the nearest valid Soler cell, and appear in diamond shape. The five square masers on… view at source ↗
Figure 16
Figure 16. Figure 16 [PITH_FULL_IMAGE:figures/full_fig_p017_16.png] view at source ↗
Figure 17
Figure 17. Figure 17: IVC 135 as seen in dust (top left) and H i data in the velocity channel at 𝑉LSR = −46.2 km s−1 . Bottom panel shows the full line of sight profile of the reconstructed velocity, reconstructed gas density, and Edenhofer et al. (2024b) derived dust density. map, while being systematically smoother and less sharply struc￾tured, as expected for the atomic phase of the ISM. The recovered vertical density profi… view at source ↗

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