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arxiv: 2605.22913 · v1 · pith:QMN4VIQVnew · submitted 2026-05-21 · 🌌 astro-ph.HE · hep-ph

A Precise Measurement of the Fermi-LAT Galactic Center Excess Morphology and Spectrum

Pith reviewed 2026-05-25 05:35 UTC · model grok-4.3

classification 🌌 astro-ph.HE hep-ph
keywords Galactic Center ExcessFermi-LATdark matterinterstellar emission modelsgamma-ray morphologygamma-ray spectrumNavarro-Frenk-White profile
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The pith

The Galactic Center Excess is described by a spherical dark-matter-like profile that remains significant even when bulge templates are included.

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

This paper introduces an improved Fermi-LAT analysis of the Galactic Center Excess that minimizes systematic uncertainties from interstellar emission and source modeling. It shows that the excess has a centrally concentrated, approximately spherical shape best matched by a generalized Navarro-Frenk-White profile with inner slope near 1.15, rather than templates tracing the stellar bulge. The dark matter component stays statistically prominent in fits using various interstellar emission models, even when bulge components are fitted at the same time. The spectrum of the excess is measured from 0.5 to 1000 GeV, peaking at a few GeV with upper limits set at higher energies.

Core claim

The analysis employs an optimized multi-step fitting procedure and iterative source-finding pipeline with multiple GALPROP-based interstellar-emission models to achieve residuals below 10 percent over a large region around the Galactic center. The reconstructed excess follows a generalized Navarro-Frenk-White morphology with inner slope gamma approximately 1.15 and is not fully reproduced by nuclear and boxy bulge templates, which fail particularly at certain angular scales. The dark-matter-motivated component provides a good fit across the full range and remains highly significant in all tested scenarios, including simultaneous fits with bulge templates. The spectrum peaks at a few GeV and

What carries the argument

The optimized multi-step fitting procedure and iterative source-finding pipeline applied to a suite of GALPROP-based interstellar-emission models, used to isolate the excess morphology and spectrum.

Load-bearing premise

The GALPROP-based interstellar-emission models and the multi-step fitting pipeline together capture the main uncertainties in the inner Galaxy without introducing bias into the excess measurement.

What would settle it

A new interstellar emission model derived independently that, when used in the same fitting framework, causes the excess to lose significance or be fully absorbed by bulge templates.

Figures

Figures reproduced from arXiv: 2605.22913 by Mattia Di Mauro.

Figure 1
Figure 1. Figure 1: FIG. 1. Normalized histogram of the fractional residuals [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. Profiled log-likelihood difference ∆ log [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. GCE SED obtained with our analysis compared with [PITH_FULL_IMAGE:figures/full_fig_p006_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. Weight maps for the weighted-likelihood analysis at [PITH_FULL_IMAGE:figures/full_fig_p009_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6. Fractional-residual maps in the 40 [PITH_FULL_IMAGE:figures/full_fig_p010_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7. Normalized histograms of the fractional residuals [PITH_FULL_IMAGE:figures/full_fig_p011_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: FIG. 8. Evolution of ∆ log [PITH_FULL_IMAGE:figures/full_fig_p012_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: FIG. 9. Surface brightness, [PITH_FULL_IMAGE:figures/full_fig_p015_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: FIG. 10. GCE SED obtained with our analysis and the different IEM models. We also display the envelope of all the spectra [PITH_FULL_IMAGE:figures/full_fig_p015_10.png] view at source ↗
read the original abstract

We present a new Fermi-LAT analysis of the Galactic-center excess (GCE) designed to substantially reduce the dominant systematic uncertainties associated with interstellar-emission and source modeling in the inner Galaxy. Using an optimized multi-step fitting procedure together with an iterative source-finding pipeline, we achieve a markedly improved agreement between data and model, reducing fractional residuals to $\lesssim 10\%$ over a $40^\circ\times 40^\circ$ region centered on the Galactic center. We analyze a suite of GALPROP-based interstellar-emission models (IEMs) and complementary analysis variants (Galactic-plane masking, fits restricted to $1$-$10$ GeV, and weighted-likelihood fits) to quantify robustness. The reconstructed surface-brightness profile is strongly centrally concentrated and is well described by an approximately spherical generalized Navarro-Frenk-White morphology with inner slope $\gamma \simeq 1.15$. Bulge-tracing templates (nuclear bulge plus boxy bulge) fail to reproduce the full radial morphology, most notably for line-of-sight angles around $\theta\simeq 1^\circ$-$2^\circ$ and at $\theta \gtrsim 8^\circ$, whereas the DM-motivated component provides a good description over the full angular range. Moreover, the DM component remains highly significant across all IEMs and analysis choices, including fits that simultaneously include the bulge templates. We also provide an updated measurement of the GCE spectrum from $0.5$ to $1000$ GeV, confirming a peak at a few GeV and setting stringent constraints above tens of GeV, where we obtain only upper limits at the level $E^2\Phi \lesssim 10^{-8}$ GeV cm$^{-2}$ s$^{-1}$ sr$^{-1}$. These results deliver a sharpened and systematically controlled characterization of the GCE morphology and spectrum, enabling more incisive tests of astrophysical and dark-matter interpretations.

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

3 major / 1 minor

Summary. This paper presents a new Fermi-LAT analysis of the Galactic Center Excess (GCE) that uses an optimized multi-step fitting procedure and iterative source-finding pipeline to reduce systematic uncertainties from interstellar emission and source modeling. The authors analyze a suite of GALPROP-based IEMs and various analysis variants, claiming residuals reduced to ≲10% over a 40°×40° region, a centrally concentrated morphology well fit by a generalized NFW profile with inner slope γ ≃ 1.15 that outperforms bulge templates, and high significance of the DM-like component even in joint fits. They also provide an updated GCE spectrum from 0.5 to 1000 GeV with a peak at a few GeV and upper limits at higher energies.

Significance. If the central claim holds, this work offers a more robust and precise characterization of the GCE morphology and spectrum, which would enable stronger discrimination between dark matter annihilation and astrophysical explanations such as millisecond pulsars or other bulge-related emission. The multi-variant approach and iterative pipeline are positive aspects that enhance the reliability of the results.

major comments (3)
  1. [IEM suite description] The suite consists exclusively of GALPROP-based models sharing the same propagation framework, gas maps, and source distributions. This may not adequately span dominant inner-Galaxy systematics such as radially varying cosmic-ray spectral indices or gas not traced by standard HI/CO maps, potentially biasing residuals toward a spherical gNFW component. A test for correlation between post-fit residuals and the gNFW template is needed to support the robustness claim.
  2. [Morphology results section] The assertion that the DM component remains highly significant in fits including bulge templates requires explicit reporting of the change in test statistic or likelihood when the gNFW template is added to the model containing the bulge templates, for each IEM variant.
  3. [Residual analysis] While fractional residuals are reported as ≲10%, the paper should quantify whether the spatial structure of these residuals is consistent with statistical fluctuations or shows patterns that could be absorbed by the gNFW template.
minor comments (1)
  1. [Abstract] The abstract mentions 'complementary analysis variants (Galactic-plane masking, fits restricted to 1-10 GeV, and weighted-likelihood fits)' but the main text should clarify how these variants are combined or selected in the primary results.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for the thoughtful comments, which will help strengthen the paper. We address each major comment below and plan to revise the manuscript accordingly.

read point-by-point responses
  1. Referee: The suite consists exclusively of GALPROP-based models sharing the same propagation framework, gas maps, and source distributions. This may not adequately span dominant inner-Galaxy systematics such as radially varying cosmic-ray spectral indices or gas not traced by standard HI/CO maps, potentially biasing residuals toward a spherical gNFW component. A test for correlation between post-fit residuals and the gNFW template is needed to support the robustness claim.

    Authors: We acknowledge the limitation of our IEM suite being based on GALPROP models. While we varied propagation parameters, gas maps, and source distributions within this framework, it does not fully cover all possible systematics like radially dependent CR indices. We will add a correlation analysis between the post-fit residuals and the gNFW template to the revised manuscript to further support the robustness of our results. revision: yes

  2. Referee: The assertion that the DM component remains highly significant in fits including bulge templates requires explicit reporting of the change in test statistic or likelihood when the gNFW template is added to the model containing the bulge templates, for each IEM variant.

    Authors: We agree that providing the explicit Delta TS values would strengthen the claim. In the revised manuscript, we will report the change in test statistic for each IEM variant when the gNFW template is added to the model that already includes the bulge templates. revision: yes

  3. Referee: While fractional residuals are reported as ≲10%, the paper should quantify whether the spatial structure of these residuals is consistent with statistical fluctuations or shows patterns that could be absorbed by the gNFW template.

    Authors: To address this, we will include in the revision a quantitative assessment of the residual spatial structure, such as by examining the power spectrum of residuals or testing if they correlate with the gNFW template beyond statistical expectations. revision: yes

Circularity Check

0 steps flagged

No circularity: morphology and significance are fit outputs from data

full rationale

The paper derives the GCE morphology parameters (e.g., inner slope γ ≃ 1.15) and the significance of the DM-like component directly from template fits to Fermi-LAT data across multiple GALPROP IEM variants and analysis choices. These quantities are outputs of the multi-step fitting and iterative source-finding pipeline rather than inputs by construction. No self-definitional steps, fitted parameters renamed as predictions, or load-bearing self-citations that reduce the central claim to its own assumptions appear in the text. The analysis is self-contained against external data benchmarks.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

The central claim rests on the accuracy of the interstellar-emission models and the assumption that the fitting pipeline isolates the excess without introducing morphology biases; no new entities are postulated.

free parameters (1)
  • inner slope gamma = ~1.15
    Fitted parameter describing the surface-brightness profile of the excess component
axioms (1)
  • domain assumption GALPROP-based IEMs span the dominant systematic uncertainties in the inner Galaxy
    Invoked when claiming robustness across the suite of models

pith-pipeline@v0.9.0 · 5885 in / 1372 out tokens · 28361 ms · 2026-05-25T05:35:44.366678+00:00 · methodology

discussion (0)

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Reference graph

Works this paper leans on

69 extracted references · 65 canonical work pages · 34 internal anchors

  1. [1]

    Common framework and components All IEMs used in this work are based on theGALPROPformalism [57], which predicts diffuseγ-ray emission by numerically solving the CR transport equation for specified inputs (CR source distribution and injection spectra, propagation setup, and interstellar target fields). In all cases, the diffuse emission is decomposed into...

  2. [2]

    fine-tune

    IEM sets adopted in this work •DiMauro21[50]. We adopt the baseline IEM used in Ref. [50], constructed within theGALPROPframework and based on the Yusifov pulsar source distribution [58]. In our implementation this is a compact template set, consisting of one bremsstrahlung and oneπ 0-decay map, three IC templates (CMB, starlight, IR), and two bubble temp...

  3. [3]

    Silket al.,Particle Dark Matter: Observations, Models and Searches, edited by G

    J. Silket al.,Particle Dark Matter: Observations, Models and Searches, edited by G. Bertone (Cambridge Univ. Press, Cambridge, 2010)

  4. [4]

    A History of Dark Matter

    G. Bertone and D. Hooper, Rev. Mod. Phys.90, 045002 (2018), arXiv:1605.04909 [astro-ph.CO]

  5. [5]

    Dark Matter

    M. Cirelli, A. Strumia, and J. Zupan, (2024), arXiv:2406.01705 [hep-ph]

  6. [6]

    Planck 2018 results. VI. Cosmological parameters

    N. Aghanimet al.(Planck), (2018), arXiv:1807.06209 [astro-ph.CO]

  7. [7]

    Schumann, J

    M. Schumann, J. Phys. G46, 103003 (2019), arXiv:1903.03026 [astro-ph.CO]

  8. [8]

    Dark Matter Searches at Colliders

    A. Boveia and C. Doglioni, Ann. Rev. Nucl. Part. Sci.68, 429 (2018), arXiv:1810.12238 [hep-ex]

  9. [9]

    J. M. Gaskins, Contemp. Phys.57, 496 (2016), arXiv:1604.00014 [astro-ph.HE]

  10. [10]

    Implications of High-Resolution Simulations on Indirect Dark Matter Searches

    L. Pieri, J. Lavalle, G. Bertone, and E. Branchini, Phys. Rev. D83, 023518 (2011), arXiv:0908.0195 [astro-ph.HE]

  11. [11]
  12. [12]

    Dark Matter Annihilation in The Galactic Center As Seen by the Fermi Gamma Ray Space Telescope

    D. Hooper and L. Goodenough, Phys. Lett.B697, 412 (2011), arXiv:1010.2752 [hep-ph]

  13. [13]

    A comment on the emission from the Galactic Center as seen by the Fermi telescope

    A. Boyarsky, D. Malyshev, and O. Ruchayskiy, Phys. Lett.B705, 165 (2011), arXiv:1012.5839 [hep-ph]

  14. [14]

    On The Origin Of The Gamma Rays From The Galactic Center

    D. Hooper and T. Linden, Phys. Rev.D84, 123005 (2011), arXiv:1110.0006 [astro-ph.HE]

  15. [15]

    K. N. Abazajian and M. Kaplinghat, Phys. Rev.D86, 083511 (2012), [Erratum: Phys. Rev.D87,129902(2013)], arXiv:1207.6047 [astro-ph.HE]

  16. [16]

    Dark Matter and Pulsar Model Constraints from Galactic Center Fermi-LAT Gamma Ray Observations

    C. Gordon and O. Macias, Phys. Rev.D88, 083521 (2013), [Erratum: Phys. Rev.D89,no.4,049901(2014)], arXiv:1306.5725 [astro-ph.HE]

  17. [17]

    K. N. Abazajian, N. Canac, S. Horiuchi, and M. Kaplinghat, Phys. Rev.D90, 023526 (2014), arXiv:1402.4090 [astro- ph.HE]

  18. [18]

    The Characterization of the Gamma-Ray Signal from the Central Milky Way: A Compelling Case for Annihilating Dark Matter

    T. Daylan, D. P. Finkbeiner, D. Hooper, T. Linden, S. K. N. Portillo, N. L. Rodd, and T. R. Slatyer, Phys. Dark Univ. 12, 1 (2016), arXiv:1402.6703 [astro-ph.HE]

  19. [19]

    A Tale of Tails: Dark Matter Interpretations of the Fermi GeV Excess in Light of Background Model Systematics

    F. Calore, I. Cholis, C. McCabe, and C. Weniger, Phys. Rev. D91, 063003 (2015), arXiv:1411.4647 [hep-ph]

  20. [20]

    Background model systematics for the Fermi GeV excess

    F. Calore, I. Cholis, and C. Weniger, JCAP1503, 038, arXiv:1409.0042 [astro-ph.CO]

  21. [21]

    Fermi-LAT Observations of High-Energy Gamma-Ray Emission Toward the Galactic Center

    M. Ajelloet al.(Fermi-LAT), Astrophys. J.819, 44 (2016), arXiv:1511.02938 [astro-ph.HE]

  22. [23]

    Search for $\gamma$-ray emission from dark matter particle interactions from Andromeda and Triangulum Galaxies with the Fermi Large Area Telescope

    M. Di Mauro, X. Hou, C. Eckner, G. Zaharijas, and E. Charles, Phys. Rev. D99, 123027 (2019), arXiv:1904.10977 [astro-ph.HE]

  23. [24]

    Di Mauro, Phys

    M. Di Mauro, Phys. Rev. D103, 063029 (2021), arXiv:2101.04694 [astro-ph.HE]

  24. [25]

    Cholis, Y.-M

    I. Cholis, Y.-M. Zhong, S. D. McDermott, and J. P. Surdutovich, Phys. Rev. D105, 103023 (2022), arXiv:2112.09706 [astro-ph.HE]

  25. [26]

    Di Mauro and M

    M. Di Mauro and M. W. Winkler, Phys. Rev. D103, 123005 (2021), arXiv:2101.11027 [astro-ph.HE]

  26. [27]

    A Comprehensive Study of WIMP Models Explaining the Fermi-LAT Galactic Center Excess

    C. Kong and M. Di Mauro, Phys. Rev. D113, 043031 (2026), arXiv:2511.21808 [hep-ph]

  27. [28]

    Koechler and M

    J. Koechler and M. Di Mauro, (2025), arXiv:2508.02775 [hep-ph]

  28. [29]

    Strong support for the millisecond pulsar origin of the Galactic center GeV excess

    R. Bartels, S. Krishnamurthy, and C. Weniger, Phys. Rev. Lett.116, 051102 (2016), arXiv:1506.05104 [astro-ph.HE]

  29. [30]

    S. K. Lee, M. Lisanti, B. R. Safdi, T. R. Slatyer, and W. Xue, Phys. Rev. Lett.116, 051103 (2016), arXiv:1506.05124 [astro-ph.HE]

  30. [31]

    Macias, C

    O. Macias, C. Gordon, R. M. Crocker, B. Coleman, D. Paterson, S. Horiuchi, and M. Pohl, Nat. Astron.2, 387 (2018), 17 Model ∆ logL DM TSDM ∆ logL NB TSB/N ∆ logL DNB TSDNB DM TSDNB B/N ∆ logL NDM TSNDM DM TSNDM N Benchmark setup1−10GeV Cholis21 8l -2148 12772 -513 4143/3677 18 11749 15/124 15 11997 123 Cholis21 ch -1664 14091 -500 5400/4203 82 8850 632/32...

  31. [32]

    The Fermi-LAT GeV Excess Traces Stellar Mass in the Galactic Bulge

    R. Bartels, E. Storm, C. Weniger, and F. Calore, Nat. Astron.2, 819 (2018), arXiv:1711.04778 [astro-ph.HE]

  32. [33]

    Manconi, F

    S. Manconi, F. Calore, and F. Donato, Phys. Rev. D109, 123042 (2024), arXiv:2402.04733 [astro-ph.HE]

  33. [34]

    Coleman, D

    B. Coleman, D. Paterson, C. Gordon, O. Macias, and H. Ploeg, (2019), arXiv:1911.04714 [astro-ph.GA]

  34. [35]

    K. N. Abazajian, S. Horiuchi, M. Kaplinghat, R. E. Keeley, and O. Macias, Phys. Rev. D102, 043012 (2020), arXiv:2003.10416 [hep-ph]

  35. [36]

    Calore, F

    F. Calore, F. Donato, and S. Manconi, Phys. Rev. Lett.127, 161102 (2021), arXiv:2102.12497 [astro-ph.HE]

  36. [37]

    M. Pohl, O. Macias, P. Coleman, and C. Gordon, Astrophys. J.929, 136 (2022), arXiv:2203.11626 [astro-ph.HE]

  37. [38]

    Manconi, C

    S. Manconi, C. Eckner, F. Calore, and F. Donato, (2025), arXiv:2511.03350 [hep-ph]

  38. [39]

    The Waning of the WIMP? A Review of Models, Searches, and Constraints

    G. Arcadi, M. Dutra, P. Ghosh, M. Lindner, Y. Mambrini, M. Pierre, S. Profumo, and F. S. Queiroz, Eur. Phys. J. C78, 203 (2018), arXiv:1703.07364 [hep-ph]. 18

  39. [40]

    Arcadi, A

    G. Arcadi, A. Djouadi, and M. Raidal, Phys. Rept.842, 1 (2020), arXiv:1903.03616 [hep-ph]

  40. [41]

    Di Mauro, C

    M. Di Mauro, C. Arina, N. Fornengo, J. Heisig, and D. Massaro, Phys. Rev. D108, 095008 (2023), arXiv:2305.11937 [hep-ph]

  41. [42]

    Arcadi, D

    G. Arcadi, D. Cabo-Almeida, M. Dutra, P. Ghosh, M. Lindner, Y. Mambrini, J. P. Neto, M. Pierre, S. Profumo, and F. S. Queiroz, (2024), arXiv:2403.15860 [hep-ph]

  42. [43]

    Di Mauro and B

    M. Di Mauro and B. Xie, (2025), arXiv:2510.08677 [hep-ph]

  43. [44]

    Secluded WIMP Dark Matter

    M. Pospelov, A. Ritz, and M. B. Voloshin, Phys. Lett. B662, 53 (2008), arXiv:0711.4866 [hep-ph]

  44. [45]

    Astrophysical Signatures of Secluded Dark Matter

    M. Pospelov and A. Ritz, Phys. Lett. B671, 391 (2009), arXiv:0810.1502 [hep-ph]

  45. [46]

    WIMP Shadows: Phenomenology of Secluded Dark Matter in Three Minimal BSM Scenarios,

    M. Di Mauro and Y. Wang, (2025), arXiv:2510.23771 [hep-ph]

  46. [47]

    Di Mauro, (2025), arXiv:2511.19622 [hep-ph]

    M. Di Mauro, (2025), arXiv:2511.19622 [hep-ph]

  47. [48]

    R. K. Leane and T. R. Slatyer, Phys. Rev. Lett.123, 241101 (2019), arXiv:1904.08430 [astro-ph.HE]

  48. [49]

    L. J. Chang, S. Mishra-Sharma, M. Lisanti, M. Buschmann, N. L. Rodd, and B. R. Safdi, (2019), arXiv:1908.10874 [astro-ph.CO]

  49. [50]

    Zhong, S

    Y.-M. Zhong, S. D. McDermott, I. Cholis, and P. J. Fox, (2019), arXiv:1911.12369 [astro-ph.HE]

  50. [51]

    F. List, Y. Park, N. L. Rodd, E. Schoen, and F. Wolf, (2025), arXiv:2507.17804 [astro-ph.HE]

  51. [52]

    Di Mauro, Phys

    M. Di Mauro, Phys. Rev. D103, 063029 (2021)

  52. [53]

    Fermi-LAT improved Pass~8 event selection

    P. Bruel, T. H. Burnett, S. W. Digel, G. Johannesson, N. Omodei, and M. Wood, arXiv e-prints , arXiv:1810.11394 (2018), arXiv:1810.11394 [astro-ph.IM]

  53. [54]

    M. Wood, R. Caputo, E. Charles, M. Di Mauro, J. Magill, J. S. Perkins, and Fermi-LAT Collaboration, in35th International Cosmic Ray Conference (ICRC2017), International Cosmic Ray Conference, Vol. 301 (2017) p. 824, arXiv:1707.09551 [astro-ph.IM]

  54. [55]

    Abdollahiet al.(Fermi-LAT), Astrophys

    S. Abdollahiet al.(Fermi-LAT), Astrophys. J. Supp.260, 53 (2022), arXiv:2201.11184 [astro-ph.HE]

  55. [56]

    Fermi Large Area Telescope Fourth Source Catalog Data Release 4 (4FGL-DR4)

    J. Ballet, P. Bruel, T. H. Burnett, and B. Lott (Fermi-LAT), (2023), arXiv:2307.12546 [astro-ph.HE]

  56. [57]

    Bruel, Astron

    P. Bruel, Astron. Astrophys.656, A81 (2021), arXiv:2109.07443 [astro-ph.HE]

  57. [58]

    Abdollahiet al.(Fermi-LAT), Astrophys

    S. Abdollahiet al.(Fermi-LAT), Astrophys. J. Suppl.247, 33 (2020), arXiv:1902.10045 [astro-ph.HE]

  58. [59]

    T. A. Porter, G. Johannesson, and V. I. Moskalenko, Astrophys. J. Supp.262, 30 (2022), arXiv:2112.12745 [astro-ph.HE]

  59. [60]

    Revisiting the radial distribution of pulsars in the Galaxy

    I. Yusifov and I. Kucuk, Astron. Astrophys.422, 545 (2004), arXiv:astro-ph/0405559

  60. [61]

    T. P. Robitaille, E. Churchwell, R. A. Benjamin, B. A. Whitney, K. Wood, B. L. Babler, and M. R. Meade, A&A545, A39 (2012), arXiv:1208.4606 [astro-ph.GA]

  61. [62]

    S. D. McDermott, Y.-M. Zhong, and I. Cholis, Mon. Not. Roy. Astron. Soc.522, L21 (2023), arXiv:2209.00006 [astro- ph.HE]

  62. [63]

    R. J. J. Grand and S. D. M. White, Mon. Not. Roy. Astron. Soc.511, L55 (2022), arXiv:2201.03567 [astro-ph.CO]

  63. [64]

    M. M. Muru, J. Silk, N. I. Libeskind, S. Gottloeber, and Y. Hoffman, Phys. Rev. Lett.135, 161005 (2025), arXiv:2508.06314 [astro-ph.HE]

  64. [65]

    The Fermi Galactic Center GeV Excess and Implications for Dark Matter

    M. Ackermannet al.(Fermi-LAT), Astrophys. J.840, 43 (2017), arXiv:1704.03910 [astro-ph.HE]

  65. [66]

    D. Song, O. Macias, S. Horiuchi, R. M. Crocker, and D. M. Nataf, MNRAS507, 5161 (2021), arXiv:2102.00061 [astro- ph.HE]

  66. [67]

    G. L. Case and D. Bhattacharya, ApJ504, 761 (1998), arXiv:astro-ph/9807162 [astro-ph]

  67. [68]

    T. A. Porter, G. Johannesson, and I. V. Moskalenko, Astrophys. J.846, 67 (2017), arXiv:1708.00816 [astro-ph.HE]

  68. [69]

    M. Su, T. R. Slatyer, and D. P. Finkbeiner, ApJ724, 1044 (2010), arXiv:1005.5480 [astro-ph.HE]

  69. [70]

    The Spectrum and Morphology of the Fermi Bubbles

    M. Ackermannet al.(Fermi-LAT), Astrophys. J.793, 64 (2014), arXiv:1407.7905 [astro-ph.HE]