The Fermi Large Area Telescope has revealed two spatially extended GeV gamma-ray excesses: the Galactic Center excess (GCE) in the Milky Way and an excess toward the outer halo of M31. Burns et al. (Phys. Rev. D 103, 063023, 2021) showed that the two spectra are mutually consistent with a dark matter (DM) annihilation origin once the ratio of their line-of-sight squared-density (J) factors is taken into account, with both two-body and four-body annihilation channels giving good joint fits. The conclusion, however, rests on uncontrolled systematics that the authors themselves flag as open: the origin of the GCE high-energy tail (intrinsic feature versus foreground-modeling artifact), a factor of roughly 15 uncertainty in the M31 J-factor, neglected target-specific secondary emission (inverse Compton and bremsstrahlung), complementary constraints (dwarf spheroidals, antiprotons, direct detection, colliders) not yet folded into the joint fit, and the unresolved point-source (millisecond pulsar) versus diffuse DM ambiguity. The problem posed here is to convert this compatibility into a definitive identification of, or exclusion of, DM annihilation as the common origin of the two excesses through a joint, systematics-controlled analysis. As of 2026 no joint re-analysis has been performed, and the interpretation of each excess individually remains actively contested, so the problem is open.

Background

Indirect detection searches for the annihilation or decay products of particle dark matter (DM) in astrophysical targets. For annihilating DM, the gamma-ray flux from a target scales with the velocity-averaged annihilation cross section ⟨σv⟩\langle\sigma v\rangle and with the J-factor, J=∫ΔΩdΩ∫LoSds ρ2J=\int_{\Delta\Omega}d\Omega\int_{\mathrm{LoS}}ds\,\rho^2, the integral of the squared DM density along the line of sight and over the target solid angle. The density ρ\rho is commonly modeled by an NFW profile, a cuspy halo shape whose density falls as r−1r^{-1} toward the center. Because the annihilation signal scales as ρ2\rho^2, clumpy substructure inside a halo raises the effective JJ above the smooth-profile value by a so-called boost factor, whose size is uncertain since the minimum subhalo mass, the subhalo mass function, the concentration-mass relation, and the spatial distribution of subhalos are all poorly constrained.

Since 2009, the Fermi Large Area Telescope (Fermi-LAT) has observed an excess of GeV gamma rays from the Galactic Center, the Galactic Center excess (GCE), whose spectrum peaks at 1-3 GeV and whose approximately spherical morphology resembles what DM annihilation in the inner halo would produce; Daylan et al. (2016) and others characterized it as consistent with a roughly 30-50 GeV particle annihilating to bbˉb\bar b with close to the thermal relic cross section ⟨σv⟩≈3×10−26 cm3 s−1\langle\sigma v\rangle\approx 3\times10^{-26}\,\mathrm{cm^3\,s^{-1}} (the value a standard cosmological relic requires). Competing explanations are an unresolved population of millisecond pulsars (MSPs; rapidly rotating old neutron stars that are copious GeV emitters) and mismodeling of the foreground. The dominant systematic is the interstellar emission model (IEM), i.e., the model of diffuse gamma rays produced when Galactic cosmic rays interact with gas and radiation. The Fermi-LAT Collaboration (Ajello et al. 2016) quantified this uncertainty with four alternative IEMs in which the Galactic diffuse components interior to the Solar circle are modified either by scaling their spectral index (index-scaled models) or by freely scaling their intensity (intensity-scaled models). The intensity-scaled IEMs leave a hard high-energy tail in the extracted GCE spectrum above about 10 GeV whose origin - intrinsic to the signal or an artifact of foreground mismodeling - has been debated since 2016 (Linden et al. 2016). Meanwhile, the Milky Way's dwarf spheroidal satellite galaxies (dSphs), which are DM-dominated and astrophysically quiet and therefore give the cleanest annihilation limits, have shown no corresponding gamma-ray signal, in tension with a DM interpretation of the GCE.

Looking beyond the Milky Way, Karwin et al. (2019) analyzed 7.6 years of Fermi-LAT data toward M31 (the Andromeda galaxy) and reported an extended excess toward M31's outer halo reaching roughly 120-200 kpc (about 8-12 degrees) from its center, distinct from the modeled Milky Way foreground. Because conventional astrophysical backgrounds are expected to be weaker there than at the Galactic Center, the signal offered a potential cross-check of a DM origin. Burns et al. (2021) then performed the first joint interpretation of the GCE and the M31 outer-halo excess under DM annihilation. For a single DM scenario the two spectra should be related by the J-factor ratio Jr=JGC/JM31J_r=J_{GC}/J_{M31}. They adopted JGC=2.2×1022 GeV2 cm−5J_{GC}=2.2\times10^{22}\,\mathrm{GeV^2\,cm^{-5}} (15∘×15∘15^\circ\times15^\circ region, NFW γ=1\gamma=1) and, following the dedicated J-factor study of Karwin et al. (2021), JM31=(2.0-31.1)×1020 GeV2 cm−5J_{M31}=(2.0\text{-}31.1)\times10^{20}\,\mathrm{GeV^2\,cm^{-5}} - a factor of roughly 15 range dominated by halo-geometry, substructure-boost, and Milky Way line-of-sight uncertainties - giving Jr∈[7.07,110]J_r\in[7.07,110]. Within these ranges the two spectra are mutually consistent for the index-scaled IEMs; for the intensity-scaled IEMs the GCE high-energy tail creates tension, since M31 shows no corresponding tail. Joint fits to two-body final states (e.g., χχ→bbˉ\chi\chi\to b\bar b or τ+τ−\tau^+\tau^-) and to four-body final states (e.g., χχ→bbˉ bbˉ\chi\chi\to b\bar b\,b\bar b through a light mediator) both succeed, with the fits preferring the upper part of the JM31J_{M31} range. The authors neglected secondary emission - gamma rays produced when annihilation electrons inverse-Compton scatter ambient light or radiate bremsstrahlung in gas - because these components depend on the target-specific gas and interstellar radiation fields of the GC and M31, which differ.

Burns et al. conclude that the M31 and GC excesses are mutually consistent with a DM origin. The paper flags five interlocking open issues - as limitations of its analysis and as future prospects - that stand between this compatibility and a definitive identification or exclusion, and that together frame the problem stated here: the high-energy-tail origin and its impact on joint-fit viability; the large JM31J_{M31} uncertainty; the neglected secondary emission and environmental differences; the consistent combination of complementary indirect, direct-detection, and collider constraints; and the structural ambiguity between unresolved point sources and diffuse DM annihilation.

Problem Statement

Determine whether annihilating dark matter is, or can be excluded as, the common origin of the two Fermi-LAT gamma-ray excesses: the Galactic Center excess and the excess toward the outer halo of M31. A complete answer should jointly address the five systematics that the source analysis flags as keeping its interpretation short of a definitive conclusion: (i) establish whether the high-energy tail of the GCE - the source of the tension between the GC and M31 spectra under the intensity-scaled interstellar emission models - is intrinsic to the excess or an artifact of foreground mismodeling, and determine its consequence for the viability of joint fits across dark matter channels; (ii) propagate the full M31 J-factor uncertainty, arising from halo geometry, the Milky Way dark matter contribution along the line of sight, and substructure boost uncertainties (minimum subhalo mass, subhalo mass function, concentration-mass relation, subhalo spatial distribution, and number of substructure levels), into the inferred annihilation cross section ⟨σv⟩\langle\sigma v\rangle; (iii) include the target-specific secondary emission (inverse Compton and bremsstrahlung) and the environmental differences in gas and radiation fields between the GC and M31; (iv) fold in the complementary constraints - dwarf spheroidal galaxy limits, antiproton fluxes, direct-detection and collider bounds - with their own systematics; and (v) resolve, or explicitly bound the impact of, the point-source (unresolved millisecond pulsars) versus diffuse dark matter structural ambiguity for each excess. Items (i)-(v) are jointly required inputs to a single verdict rather than five independent deliverables: a complete answer must carry each of them into one joint assessment, but need not settle each in isolation. The completion boundary is that joint assessment, evaluated over the envelope fixed here: the adopted M31 J-factor range JM31=(2.0-31.1)×1020 GeV2 cm−5J_{M31}=(2.0\text{-}31.1)\times10^{20}\,\mathrm{GeV^2\,cm^{-5}} (equivalently Jr∈[7.07,110]J_r\in[7.07,110]), the four interstellar emission model variants (the index-scaled and intensity-scaled IEMs), and the alternative treatments of secondary emission, point-source versus diffuse decomposition, and complementary constraints spanned by items (iii)-(v). The assessment returns one verdict on the common-origin hypothesis: it identifies a dark matter annihilation scenario (mass, annihilation channel, cross section) consistent with both excesses and with all complementary constraints across that envelope; or it excludes the entire viable parameter region across that envelope; or it establishes that the joint data do not distinguish the common-origin hypothesis from its alternatives, which is itself a resolution of the task only when supported by the same envelope-wide analysis.

References

  1. Burns, A.-K., Fieg, M., Rajaraman, A., Karwin, C. M. (2021). Dark matter explanations of the gamma-ray excesses from the Galactic Center and M31. Physical Review D 103, 063023. DOI 10.1103/PhysRevD.103.063023. https://arxiv.org/abs/2010.11650
  2. Karwin, C. M., Murgia, S., Campbell, S., Moskalenko, I. V. (2019). Fermi-LAT observations of gamma-ray emission toward the outer halo of M31. The Astrophysical Journal 880, 95. DOI 10.3847/1538-4357/ab2880. https://arxiv.org/abs/1812.02958
  3. Karwin, C., Murgia, S., Moskalenko, I., Fillingham, S., Burns, A.-K., Fieg, M. (2021). Dark matter interpretation of the Fermi-LAT observations toward the outer halo of M31. Physical Review D 103, 023027. DOI 10.1103/PhysRevD.103.023027. https://arxiv.org/abs/2010.08563
  4. Zimmer, F., Macias, O., Ando, S., Crocker, R. M., Horiuchi, S. (2022). The Andromeda gamma-ray excess: background systematics of the millisecond pulsars and dark matter interpretations. Monthly Notices of the Royal Astronomical Society 516 (2022). DOI 10.1093/mnras/stac2464. https://arxiv.org/abs/2204.00636
  5. Recchia, S., Gabici, S., Aharonian, F. A., Niro, V. (2021). Giant cosmic-ray halos around M31 and the Milky Way. The Astrophysical Journal 914, 135. DOI 10.3847/1538-4357/abfda4. https://arxiv.org/abs/2101.05016
  6. Do, A., Duong, M., McDaniel, A., O'Connor, C., Profumo, S., Rafael, J., Sweeney, C., Vera III, W. (2021). Cosmic-ray transport and gamma-ray emission in M31. Physical Review D 104, 123016. DOI 10.1103/PhysRevD.104.123016. https://arxiv.org/abs/2012.14507
  7. Roy, M., Nath, B. B. (2022). Gamma-rays from the circumgalactic medium of M31. Monthly Notices of the Royal Astronomical Society 514, 1412. DOI 10.1093/mnras/stac1465. https://arxiv.org/abs/2205.12291
  8. Egorov, A. E. (2023). Nature of M31 gamma-ray halo in relation to dark matter annihilation. Physical Review D 108, 043028. DOI 10.1103/PhysRevD.108.043028. https://arxiv.org/abs/2305.07590
  9. Egorov, A. E. (2022). Updated constraints on WIMP dark matter annihilation by radio observations of M31. Physical Review D 106, 023023. DOI 10.1103/PhysRevD.106.023023. https://arxiv.org/abs/2205.01033
  10. Egorov, A. E. (2023). Updated constraints on WIMP dark matter by radio observations of M31 - all annihilation channels. Proceedings of Science, ECRS 2022, 120. DOI 10.22323/1.423.0120. https://arxiv.org/abs/2208.14186
  11. Xia, Z.-Q., Shen, Z.-Q., Pan, X., Feng, L., Fan, Y.-Z. (2021). Investigating the dark matter minispikes with the gamma-ray signal from the halo of M31. arXiv:2108.09204. https://arxiv.org/abs/2108.09204
  12. List, F., Rodd, N. L., Lewis, G. F. (2021). Extracting the Galactic Center excess' source-count distribution with neural nets. Physical Review D 104, 123022. DOI 10.1103/PhysRevD.104.123022. https://arxiv.org/abs/2107.09070
  13. Manconi, S., Calore, F., Donato, F. (2024). The Galactic center excess at the highest energies: morphology and photon-count statistics. Physical Review D 109, 123042. DOI 10.1103/PhysRevD.109.123042. https://arxiv.org/abs/2402.04733
  14. Manconi, S., Eckner, C., Calore, F., Donato, F. (2026). Stellarlike Galactic Center excess challenges particle dark matter. Physical Review D 114, 043053. DOI 10.1103/2wkq-xrsc. https://arxiv.org/abs/2511.03350
  15. Di Mauro, M. (2026). A precise measurement of the Fermi-LAT Galactic Center excess morphology and spectrum. arXiv:2605.22913. https://arxiv.org/abs/2605.22913
  16. McDaniel, A., Ajello, M., Karwin, C. M., Di Mauro, M., Drlica-Wagner, A., Sanchez-Conde, M. A. (2024). Legacy analysis of dark matter annihilation from the Milky Way dwarf spheroidal galaxies with 14 years of Fermi-LAT data. Physical Review D 109, 063024. DOI 10.1103/PhysRevD.109.063024. https://arxiv.org/abs/2311.04982
  17. Circiello, A., Di Mauro, M., Ajello, M., Karwin, C., Drlica-Wagner, A., Sanchez-Conde, M. A. (2026). Legacy analysis of Milky Way dwarf spheroidal satellite galaxies: an update. The Astrophysical Journal Letters 1004, L33. DOI 10.3847/2041-8213/ae71c7. https://arxiv.org/abs/2605.25586
  18. Ajello, M., et al. (Fermi-LAT Collaboration) (2016). Fermi-LAT observations of high-energy gamma-ray emission toward the Galactic Center. The Astrophysical Journal 819, 44. DOI 10.3847/0004-637X/819/1/44. https://arxiv.org/abs/1511.02938
  19. Linden, T., Rodd, N. L., Safdi, B. R., Slatyer, T. R. (2016). High-energy tail of the Galactic Center gamma-ray excess. Physical Review D 94, 103013. DOI 10.1103/PhysRevD.94.103013. https://arxiv.org/abs/1604.01026
  20. Daylan, T., Finkbeiner, D. P., Hooper, D., Linden, T., Portillo, S. K. N., Rodd, N. L., Slatyer, T. R. (2016). The characterization of the gamma-ray signal from the central Milky Way: a case for annihilating dark matter. Physics of the Dark Universe 12, 1. DOI 10.1016/j.dark.2015.12.005. https://arxiv.org/abs/1402.6703