pith. sign in

arxiv: 2605.22739 · v1 · pith:W4M54U4Jnew · submitted 2026-05-21 · 🌌 astro-ph.HE · astro-ph.GA

A Three-Dimensional Tomographic Reconstruction of the Galactic Cosmic-Ray Proton Density

Hanieh Zandinejad , Jakob Roth , Vo Hong Minh Phan , Gordian Edenhofer , Philipp Frank , Philipp Mertsch , Ralf Kissmann , Andr\'es Ram\'irez
show 2 more authors
Laurin S\"oding Torsten A. En{\ss}lin
This is my paper

Pith reviewed 2026-05-22 03:31 UTC · model grok-4.3

classification 🌌 astro-ph.HE astro-ph.GA
keywords cosmic raysgamma raysgalactic structuretomographic reconstructioninterstellar mediumproton densityFermi LAT3D mapping
0
0 comments X

The pith

A three-dimensional map of cosmic-ray proton density shows a smooth distribution with moderate enhancement toward the inner Galaxy.

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

This work reconstructs the three-dimensional distribution of cosmic-ray protons throughout the Milky Way disk. The authors start from ten years of Fermi-LAT gamma-ray observations that trace interactions between protons and gas. They combine this with a three-dimensional model of the gas to solve for the proton density via morphological matching. A Gaussian process on a spherical-radial grid captures the variations, and advanced inference techniques determine both the map and its spatial correlations. The outcome is a proton density field that varies smoothly with only limited contrast, rising moderately inward, and matching direct measurements near the Sun. This map provides an empirical foundation for studying how cosmic rays are accelerated and propagate without relying on specific theoretical assumptions about transport.

Core claim

The central discovery is the reconstructed three-dimensional cosmic-ray proton density field obtained by assuming that diffuse gamma-ray emission arises from hadronic interactions with interstellar gas. Using a dust-correlated gamma-ray map and a 3D gas model, the logarithmic density is modeled as a Gaussian process on a spherical-times-radial grid. The field and its correlation structure are inferred jointly with Iterative Charted Refinement, and the posterior is approximated by geometric variational inference. The result exhibits a smooth yet structured distribution across the Galactic disk with a limited dynamical range, a moderate enhancement toward the inner Galaxy, and a normalization,

What carries the argument

Morphological matching of observed gamma-ray emission to a three-dimensional gas density model, implemented through a Gaussian process on a spherical-radial grid whose parameters and correlations are inferred simultaneously via Iterative Charted Refinement and geometric variational inference.

If this is right

  • The reconstructed density can be used to compute expected gamma-ray intensities from pion decay in any direction.
  • Cosmic-ray source distributions must be such that they produce only moderate radial density gradients after propagation.
  • The agreement with local data suggests that measurements at the Sun are representative of conditions in a sizable portion of the disk.
  • Variations in the map can be compared against predictions from different cosmic-ray transport scenarios to identify the best-fitting physics.

Where Pith is reading between the lines

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

  • If applied to other wavebands or particles, similar tomographic techniques could map additional components of the interstellar medium.
  • Discrepancies between this map and hydrodynamic simulations of the Galaxy could point to missing physics in cosmic-ray feedback models.
  • Extending the grid to include the Galactic halo might reveal how protons escape the disk into the surrounding environment.
  • The limited dynamical range supports the idea of rapid diffusion or convection that homogenizes the proton population on large scales.

Load-bearing premise

The diffuse gamma-ray emission must come entirely from cosmic-ray proton collisions with gas, with no major contributions from electrons or uncertainties in the gas distribution itself.

What would settle it

Observing a region where the gamma-ray intensity does not scale with the gas column density according to the reconstructed proton map, or finding a direct cosmic-ray measurement far from the Solar position that deviates significantly from the inferred value.

Figures

Figures reproduced from arXiv: 2605.22739 by Andr\'es Ram\'irez, Gordian Edenhofer, Hanieh Zandinejad, Jakob Roth, Laurin S\"oding, Philipp Frank, Philipp Mertsch, Ralf Kissmann, Torsten A. En{\ss}lin, Vo Hong Minh Phan.

Figure 1
Figure 1. Figure 1: Masked dust-correlated diffuse gamma-ray emission map in the energy range between 1.78 and 3.16 GeV used as input data for the inference. The map –as well as any other all sky map in this publication– is shown in a Mollweide projection and downgraded to an angular resolution corresponding to Nside = 32 [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Top-down view of the total Hydrogen density [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Synthetic data validation. Top row: CR truth and synthetic gamma-ray data. Bottom row: reconstructed CR field and recon [PITH_FULL_IMAGE:figures/full_fig_p008_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Synthetic data validation. Top-down view of the reconstructed cosmic-ray proton density in the Galactic mid-plane ( [PITH_FULL_IMAGE:figures/full_fig_p009_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Mid-plane (z = 0) maps of the reconstructed cosmic-ray density. Left: posterior mean nCR,mean(30 GeV). Right: posterior standard deviation σCR(30 GeV). The two panels use independent color scales to reflect their different dynamic ranges. dynamical range. The distribution remains spatially extended, without sharp discontinuities. A localized enhancement is vis￾ible in the lower-left quadrant, while the cen… view at source ↗
Figure 6
Figure 6. Figure 6: Axis-integrated views of the reconstructed CRp distribution along the Cartesian axes. From left to right, the panels show the [PITH_FULL_IMAGE:figures/full_fig_p011_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Zoomed-in z-integrated CRp density maps restricted to x, y ∈ [−1.5, 1.5] kpc in the vicinity of Earth. The panels show the posterior mean, posterior standard deviation, and the corresponding significance. The reconstructed local structure is primarily constrained by the 3D dust map of Edenhofer et al. (2024), which extends to distances of approximately 1.25 kpc around the Sun. Article number, page 11 of 18… view at source ↗
Figure 8
Figure 8. Figure 8: Plane-of-sky maps of the reconstructed CRp distribution obtained by integrating the three-dimensional CRp density along [PITH_FULL_IMAGE:figures/full_fig_p012_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: Vertically integrated CRp density at 30 GeV in the [PITH_FULL_IMAGE:figures/full_fig_p013_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: Comparison between projections of the hadronic gamma-ray source density [PITH_FULL_IMAGE:figures/full_fig_p014_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: Normalisation of the CRp spectrum at 30 GeV as a [PITH_FULL_IMAGE:figures/full_fig_p015_11.png] view at source ↗
Figure 12
Figure 12. Figure 12: Vertical profile of the CRp density at 30 GeV in the [PITH_FULL_IMAGE:figures/full_fig_p015_12.png] view at source ↗
read the original abstract

Cosmic rays (CRs) are a ubiquitous non-thermal component of the interstellar medium (ISM). A data-driven three-dimensional (3D) map of their distribution is essential for understanding CR transport and constraining the spatial distribution of their sources. In this work, we reconstructed the 3D spatial distribution of the Galactic cosmic-ray proton (CRp) density. We model the diffuse gamma-ray emission arising from inelastic hadronic interactions between CRps and interstellar gas. Using a map of dust-correlated diffuse gamma-ray emission based on ten years of Fermi-LAT observations together with a three-dimensional gas density model, we infer the spatial CRp distribution through a morphological matching approach. The logarithmic CRp density field is described by a Gaussian process defined on a spherical-times-radial grid, while both the field and its correlation structure are inferred simultaneously using Iterative Charted Refinement. The posterior distribution of the reconstructed 3D CRp density field is approximated using geometric variational inference. The reconstructed CRp density exhibits a smooth but spatially structured distribution with a limited dynamical range across the Galactic disk. We find a moderate enhancement of the CRp density toward the inner Galaxy. The inferred normalization at the Solar position is consistent with local CR measurements by the AMS-02 instrument.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The paper presents a data-driven tomographic reconstruction of the three-dimensional Galactic cosmic-ray proton (CRp) density. It models the diffuse gamma-ray emission as arising solely from inelastic hadronic interactions between CRps and interstellar gas, using a dust-correlated Fermi-LAT gamma-ray map and an independent 3D gas density model. The log-CRp density field is represented as a Gaussian process on a spherical-radial grid whose hyperparameters and realization are inferred simultaneously via Iterative Charted Refinement; the posterior is approximated with geometric variational inference. The resulting map is reported to be smooth yet spatially structured, with limited dynamical range across the Galactic disk, a moderate enhancement toward the inner Galaxy, and a normalization at the Solar position consistent with AMS-02 local measurements.

Significance. If the central assumptions hold, the work supplies a novel, observationally anchored 3D CRp density field that can directly inform studies of cosmic-ray transport, source distributions, and Galactic propagation models. The simultaneous inference of the field and its correlation structure via Gaussian processes and geometric variational inference is a methodological strength that enables principled uncertainty quantification in a high-dimensional setting. The reported consistency with independent local CR data adds a useful cross-check. The significance is nevertheless limited by the absence of quantitative validation, which leaves the robustness of the reported morphological features uncertain.

major comments (2)
  1. [Abstract] Abstract, second paragraph: the reconstruction rests on the assumption that 'the diffuse gamma-ray emission arising from inelastic hadronic interactions' accounts for the entire dust-correlated Fermi-LAT map. This is load-bearing for the claimed spatial structure and inner-Galaxy enhancement; any non-negligible leptonic (inverse-Compton or bremsstrahlung) contribution or residual mismatch from the 3D gas model would be absorbed into the inferred CRp field. Explicit residual maps, sensitivity tests to alternative gamma-ray production channels, or synthetic-data injections of known leptonic components are required to demonstrate that the reported limited dynamical range and moderate inner enhancement are not artifacts of this assumption.
  2. [Abstract] Abstract and method description: no quantitative validation metrics, error budgets, or recovery tests on synthetic data are presented. The central claims (smooth structured distribution, limited dynamical range, Solar normalization matching AMS-02) therefore rest on an unvalidated implementation of the Gaussian-process prior, Iterative Charted Refinement, and geometric variational inference. Without such tests it is impossible to assess whether the posterior approximation faithfully recovers injected structures or whether the reported properties are robust to the choice of grid or hyperparameter priors.
minor comments (2)
  1. The spherical-radial grid on which the Gaussian process is defined should be described with explicit coordinate ranges, resolution, and boundary conditions; a schematic figure would improve clarity.
  2. [Abstract] The specific Fermi-LAT data product (e.g., which diffuse-emission template or energy range) and the reference for the adopted 3D gas density model should be cited explicitly.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their careful and constructive review of our manuscript. We address each major comment in turn below, indicating where revisions will be made to improve clarity and robustness.

read point-by-point responses

  1. Referee: [Abstract] Abstract, second paragraph: the reconstruction rests on the assumption that 'the diffuse gamma-ray emission arising from inelastic hadronic interactions' accounts for the entire dust-correlated Fermi-LAT map. This is load-bearing for the claimed spatial structure and inner-Galaxy enhancement; any non-negligible leptonic (inverse-Compton or bremsstrahlung) contribution or residual mismatch from the 3D gas model would be absorbed into the inferred CRp field. Explicit residual maps, sensitivity tests to alternative gamma-ray production channels, or synthetic-data injections of known leptonic components are required to demonstrate that the reported limited dynamical range and moderate inner enhancement are not artifacts of this assumption.

    Authors: We agree that the assumption of a purely hadronic origin for the dust-correlated gamma-ray map is central and that unaccounted leptonic contributions or gas-model residuals could bias the inferred CRp field. The dust-correlated map was chosen specifically to emphasize gas-traced emission and suppress less-correlated leptonic components, but we acknowledge that this does not eliminate the possibility of residual contamination. In the revised manuscript we will add a dedicated systematics section that includes (i) residual maps between the observed dust-correlated emission and the forward-modeled hadronic emission from the reconstructed CRp density, and (ii) sensitivity tests in which a spatially varying leptonic template is injected at varying amplitudes before re-running the inference. These tests will quantify any impact on the reported limited dynamical range and inner-Galaxy enhancement. revision: yes

  2. Referee: [Abstract] Abstract and method description: no quantitative validation metrics, error budgets, or recovery tests on synthetic data are presented. The central claims (smooth structured distribution, limited dynamical range, Solar normalization matching AMS-02) therefore rest on an unvalidated implementation of the Gaussian-process prior, Iterative Charted Refinement, and geometric variational inference. Without such tests it is impossible to assess whether the posterior approximation faithfully recovers injected structures or whether the reported properties are robust to the choice of grid or hyperparameter priors.

    Authors: We accept that the current manuscript lacks explicit synthetic-data recovery tests and quantitative validation metrics for the specific application presented. Although the underlying Iterative Charted Refinement and geometric variational inference framework has been validated in earlier methodological papers, we agree that end-to-end recovery tests tailored to this CRp tomography problem are necessary to support the central claims. We will therefore add a new validation subsection that presents (i) recovery experiments on synthetic gamma-ray maps generated from known input CRp fields (including both smooth and moderately enhanced inner-Galaxy distributions), (ii) quantitative metrics such as mean fractional error, correlation coefficient, and recovery of the limited dynamical range, and (iii) an error budget derived from the posterior covariance. These additions will directly address concerns about robustness to grid choice and hyperparameter priors. revision: yes

Circularity Check

0 steps flagged

No significant circularity; reconstruction is data-driven from external inputs

full rationale

The paper reconstructs the 3D CRp density field by morphological matching of an external Fermi-LAT dust-correlated gamma-ray map to an independent 3D gas density model under the hadronic-interaction assumption. The log-CRp field is represented as a Gaussian process on a spherical-radial grid whose values and correlation hyperparameters are inferred jointly from the data via Iterative Charted Refinement and geometric variational inference. The reported properties (smooth structured distribution, limited dynamical range, moderate inner-Galaxy enhancement, and Solar-position normalization) are direct posterior outputs of this inference rather than quantities defined by or fitted to the target result itself. No self-definitional steps, fitted inputs renamed as predictions, or load-bearing self-citations appear in the derivation chain. The method remains self-contained against the cited external observations and gas model.

Axiom & Free-Parameter Ledger

1 free parameters · 2 axioms · 0 invented entities

The central claim rests on the assumption that gamma-ray morphology directly traces CRp density via hadronic interactions, plus the accuracy of the supplied 3D gas model. No new particles or forces are introduced. The Gaussian-process correlation length and variance are inferred rather than fixed a priori, but still constitute free parameters of the statistical model.

free parameters (1)
  • Gaussian-process hyperparameters (length scale and variance)
    These control the smoothness and amplitude of the reconstructed CRp density field and are inferred simultaneously with the field itself.
axioms (2)
  • domain assumption Diffuse gamma-ray emission arises solely from inelastic hadronic interactions between CR protons and interstellar gas
    Invoked in the first paragraph of the abstract to justify morphological matching.
  • domain assumption The supplied three-dimensional gas density model is sufficiently accurate for morphological matching
    Required to convert observed gamma-ray intensity into CRp density.

pith-pipeline@v0.9.0 · 5803 in / 1542 out tokens · 44190 ms · 2026-05-22T03:31:03.974855+00:00 · methodology

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

What do these tags mean?
matches
The paper's claim is directly supported by a theorem in the formal canon.
supports
The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends
The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
uses
The paper appears to rely on the theorem as machinery.
contradicts
The paper's claim conflicts with a theorem or certificate in the canon.
unclear
Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.

Reference graph

Works this paper leans on

56 extracted references · 56 canonical work pages

  1. [1]

    2016, Astrophys

    Acero, F., Ackermann, M., Ajello, M., et al. 2016, Astrophys. J. Suppl. Ser., 223, 26

    work page 2016

  2. [2]

    Ackermann, M. et al. 2012, ApJ, 750, 3

    work page 2012

  3. [3]

    2015, Physical Review Letters, 114, 171103

    Aguilar, M., Aisa, D., Alvino, A., et al. 2015, Physical Review Letters, 114, 171103

    work page 2015

  4. [4]

    2020, Phys

    Aharonian, F., Peron, G., Yang, R., Casanova, S., & Zanin, R. 2020, Phys. Rev. D, 101, 083018

    work page 2020

  5. [5]

    Aharonian, F. A. & Atoyan, A. M. 2000, A&A, 362, 937

    work page 2000

  6. [6]

    Albert, A. et al. 2021, ApJ, 907, 105

    work page 2021

  7. [7]

    Amiranoff, F., Laberge, M., Marques, J., et al. 2011

    work page 2011

  8. [8]

    H., Westermann, R., & Enßlin, T

    Arras, P., Frank, P., Leike, R. H., Westermann, R., & Enßlin, T. A. 2019, Astron- omy & Astrophysics, 627, A134

    work page 2019

  9. [9]

    B., Abdo, A

    Atwood, W. B., Abdo, A. A., Ackermann, M., et al. 2009, ApJ, 697, 1071

    work page 2009

  10. [10]

    D., Wolfire, M., & Leroy, A

    Bolatto, A. D., Wolfire, M., & Leroy, A. K. 2013, ARA&A, 51, 207

    work page 2013

  11. [11]

    2018, JAX: composable transforma- tions of Python+NumPy programs,https://github.com/google/jax, version 0.2.5

    Bradbury, J., Frostig, R., Hawkins, P., et al. 2018, JAX: composable transforma- tions of Python+NumPy programs,https://github.com/google/jax, version 0.2.5

    work page 2018

  12. [12]

    L., Safdi, B

    Buschmann, M., Rodd, N. L., Safdi, B. R., et al. 2020, Physical Review D, 102, 023023

    work page 2020

  13. [13]

    S., Gaggero, D., Vittino, A., & Grasso, D

    Cerri, S. S., Gaggero, D., Vittino, A., & Grasso, D. 2017, JCAP, 10, 019

    work page 2017

  14. [14]

    Dermer, C. D. 1986b, Astrophysical Journal, Part 1 (ISSN 0004-637X), vol. 307, Aug. 1, 1986, p. 47-59., 307, 47

    work page 1986

  15. [15]

    D., Pendleton, B

    Duane, S., Kennedy, A. D., Pendleton, B. J., & Roweth, D. 1987, Physics Letters B, 195, 216

    work page 1987

  16. [16]

    2024, Journal of Open Source Software, 9, 6593

    Edenhofer, G., Frank, P., Roth, J., et al. 2024, Journal of Open Source Software, 9, 6593

    work page 2024

  17. [17]

    H., Frank, P., & Enßlin, T

    Edenhofer, G., Leike, R. H., Frank, P., & Enßlin, T. A. 2022, arXiv e-prints, arXiv:2206.10634

    work page arXiv 2022

  18. [18]

    2024, A&A, 685, A82 Enßlin, T

    Edenhofer, G., Zucker, C., Frank, P., et al. 2024, A&A, 685, A82 Enßlin, T. A., Pfrommer, C., Springel, V ., & Jubelgas, M. 2007, A&A, 473, 41

    work page 2024

  19. [19]

    2020, Monthly Notices of the Royal Astronomical Society, 493, 4295

    Evoli, C., Gaggero, D., Vittino, A., et al. 2020, Monthly Notices of the Royal Astronomical Society, 493, 4295

    work page 2020

  20. [20]

    1950, Prog

    Fermi, E. 1950, Prog. Theor. Phys., 5, 570

    work page 1950

  21. [21]

    Frank, P., Leike, R., & Enßlin, T. A. 2021, Entropy, 23, 853

    work page 2021

  22. [22]

    2022, Astronomy and Astrophysics Review, 30, 4

    Gabici, S. 2022, Astronomy and Astrophysics Review, 30, 4

    work page 2022

  23. [23]

    2019, IJMPD, 28, 1930022

    Gabici, S., Evoli, C., Gaggero, D., et al. 2019, IJMPD, 28, 1930022

    work page 2019

  24. [24]

    M., Schlafly, E., Zucker, C., Speagle, J

    Green, G. M., Schlafly, E., Zucker, C., Speagle, J. S., & Finkbeiner, D. 2019, ApJ, 887, 93

    work page 2019

  25. [25]

    A., Black, J

    Grenier, I. A., Black, J. H., & Strong, A. W. 2015, ARA&A, 53, 199

    work page 2015

  26. [26]

    M., & Vila, G

    Kafexhiu, E., Aharonian, F., Taylor, A. M., & Vila, G. S. 2014, Phys. Rev. D, 90, 123014

    work page 2014

  27. [27]

    M., Broughton, A., Murgia, S., et al

    Karwin, C. M., Broughton, A., Murgia, S., et al. 2023, Physical Review D, 107, 123032

    work page 2023

  28. [28]

    2014, APh, 55, 37 Knollmüller, J

    Kissmann, R. 2014, APh, 55, 37 Knollmüller, J. & Enßlin, T. A. 2019, arXiv e-prints, arXiv:1901.11033

    work page arXiv 2014

  29. [29]

    & Leibler, R

    Kullback, S. & Leibler, R. A. 1951, The Annals of Mathematical Statistics, 22, 79

    work page 1951

  30. [30]

    H., Glatzle, M., & Enßlin, T

    Leike, R. H., Glatzle, M., & Enßlin, T. A. 2020, A&A, 639, A138

    work page 2020

  31. [31]

    & Phan, V

    Mertsch, P. & Phan, V . H. M. 2023, A&A, 671, A54

    work page 2023

  32. [32]

    & Vittino, A

    Mertsch, P. & Vittino, A. 2021, A&A, 655, A64

    work page 2021

  33. [33]

    2011, in Handbook of Markov Chain Monte Carlo, 113–162

    Neal, R. 2011, in Handbook of Markov Chain Monte Carlo, 113–162

    work page 2011

  34. [34]

    & Semikoz, D

    Neronov, A. & Semikoz, D. V . 2011, APh, 34, 639

    work page 2011

  35. [35]

    2021, The Astro- physical Journal Letters, 907, L11

    Peron, G., Aharonian, F., Casanova, S., Yang, R., & Zanin, R. 2021, The Astro- physical Journal Letters, 907, L11

    work page 2021

  36. [36]

    & Enßlin, T

    Pfrommer, C. & Enßlin, T. A. 2004, A&A, 426, 777

    work page 2004

  37. [37]

    2018, Astron

    Pothast, M., Storm, E., Weniger, C., & Linden, T. 2018, Astron. Astrophys., 618, A30

    work page 2018

  38. [38]

    Prokhorov, D. A. & Moraghan, A. 2018, MNRAS, 478, 3564

    work page 2018

  39. [39]

    Rasmussen, C. E. & Williams, C. K. I. 2006, Gaussian Processes for Machine Learning

    work page 2006

  40. [40]

    2016, MNRAS, 462, 4227

    Recchia, S., Blasi, P., & Morlino, G. 2016, MNRAS, 462, 4227

    work page 2016

  41. [41]

    Roy, A. et al. 2024, A&A, 684, A87

    work page 2024

  42. [42]

    K., & Zweibel, E

    Ruszkowski, M., Yang, H.-Y . K., & Zweibel, E. G. 2023, Nature Astronomy, 7, 1441

    work page 2023

  43. [43]

    I., Knollmüller, J., Arras, P., et al

    Scheel-Platz, L. I., Knollmüller, J., Arras, P., et al. 2023, A&A, 680, A2

    work page 2023

  44. [44]

    R., Junklewitz, H., et al

    Selig, M., Bell, M. R., Junklewitz, H., et al. 2013, Astronomy & Astrophysics, 554, A26

    work page 2013

  45. [45]

    Sinha, A. et al. 2021, PoS ICRC2021, 837

    work page 2021

  46. [46]

    1970, Astrophysics and Space science, 6, 377

    Stecker, F. 1970, Astrophysics and Space science, 6, 377

    work page 1970

  47. [47]

    2019, Annalen der Physik, 531, 1800290

    Steininger, T., Dixit, J., Frank, P., et al. 2019, Annalen der Physik, 531, 1800290

    work page 2019

  48. [48]

    & Badhwar, G

    Stephens, S. & Badhwar, G. 1981, Astrophysics and Space Science, 76, 213

    work page 1981

  49. [49]

    W., Moskalenko, I

    Strong, A. W., Moskalenko, I. V ., & Ptuskin, V . S. 2007, ARNPS, 57, 285

    work page 2007

  50. [50]

    R., & Finkbeiner, D

    Su, M., Slatyer, T. R., & Finkbeiner, D. P. 2010, The Astrophysical Journal, 724, 1044 Söding, L., Edenhofer, G., Enßlin, T. A., et al. 2025, A&A, 693, A139

    work page 2010

  51. [51]

    2021, JCAP, 07, 036

    Vecchiotti, V ., Di Mauro, M., Manconi, S., & Donato, F. 2021, JCAP, 07, 036

    work page 2021

  52. [52]

    Vecchiotti, V . et al. 2025, JCAP, 01, 022

    work page 2025

  53. [53]

    L., Lallement, R., & Cox, N

    Vergely, J. L., Lallement, R., & Cox, N. L. J. 2022, A&A, 664, A174

    work page 2022

  54. [54]

    & Aharonian, F

    Yang, R.-z. & Aharonian, F. 2013, PRD, 87, 103005

    work page 2013

  55. [55]

    2016, Phys

    Yang, R.-z., Aharonian, F., & Evoli, C. 2016, Phys. Rev. D, 93, 123007

    work page 2016

  56. [56]

    Zweibel, E. G. 2013, Physics of Plasmas, 20, 055501 Article number, page 16 of 18 Hanieh Zandinejad et al.: A Three-Dimensional Tomographic Reconstruction of the Galactic Cosmic-Ray Proton Density Appendix A: Reconstruction using only the LMC/SMC mask In the main analysis (Sect. 2.1), we apply a composite mask that excludes the LMC and SMC, regions associ...

    work page 2013