The rise of the cosmic-ray positron fraction discovered by PAMELA requires, if it comes from annihilating dark matter, present-day effective annihilation rates roughly a thousand times the thermal relic value. Pato, Pieri & Bertone (Phys. Rev. D 80, 103510, 2009) showed that under standard assumptions about the Galactic halo, subhalos, cosmic-ray propagation and saturated Sommerfeld enhancement, every then-proposed candidate that fits the positron data overproduces antiprotons, gamma rays or radio synchrotron emission, and posed the question of whether the large required cross sections can be made consistent with all other observations once astrophysical uncertainties are properly quantified. Later work closed most of the standard parameter space: CMB anisotropy constraints, Fermi-LAT dwarf-spheroidal and diffuse gamma-ray limits, AMS-02 antiproton data, the measured shape of the positron spectrum, and observations by HAWC (the High-Altitude Water Cherenkov Observatory) and Fermi-LAT of gamma-ray halos around nearby pulsars that make pulsars the favored origin. What remains open is the precise surviving core: whether any velocity-dependent, resonant, non-thermal or spatially non-standard annihilating dark matter model can simultaneously reproduce the measured positron spectrum and satisfy all multi-messenger and cosmological constraints under quantified astrophysical uncertainties (subhalo boost below simulation resolution, Galactic-centre magnetic field, cosmic-ray propagation), or whether a coverage-complete exclusion can be established.

Background

Dark matter makes up about 27% of the energy density of the Universe; if it is a weakly interacting massive particle (WIMP), pairs of dark matter particles can annihilate into standard-model particles. For a particle that was in thermal equilibrium in the early universe (a thermal relic), the annihilation rate needed to leave the observed abundance is conventionally (σannv)∼3×10−26 cm3 s−1(\sigma_{\rm ann} v)\sim3\times10^{-26}\ {\rm cm^3\,s^{-1}}. Indirect detection searches for the annihilation products: photons, positrons, antiprotons and neutrinos.

A key observable is the positron fraction, the ratio of the positron flux to the combined electron-plus-positron flux in cosmic rays. In the conventional picture, cosmic-ray positrons are secondaries, produced when primary protons and nuclei strike interstellar gas; that prediction falls above about 10 GeV. The PAMELA satellite experiment (Payload for Antimatter Matter Exploration and Light-nuclei Astrophysics, a dedicated cosmic-ray detector in Earth orbit) instead measured the fraction rising between 10 and 100 GeV (Adriani et al. 2009), confirmed and extended to several hundred GeV by the Fermi Large Area Telescope (Fermi-LAT, a gamma-ray telescope in orbit) and the Alpha Magnetic Spectrometer (AMS-02, a particle detector on the International Space Station). Some nearby or pervasive source of high-energy e±e^\pm is required. One candidate is annihilation of TeV-scale dark matter that is leptophilic, i.e. annihilates mainly to charged leptons, so as not to overproduce the observed antiprotons. For a thermal relic this needs an effective rate roughly 10310^3 times the thermal value, a boost that can be supplied by the Sommerfeld enhancement: a non-relativistic quantum effect in which exchange of a new light force carrier distorts the incoming particles' wavefunction and enhances low-velocity annihilation, scaling roughly as 1/v1/v and saturating at a maximum Smax⁡S_{\max} set by the mediator's mass and coupling. Clumpiness of the Galactic dark matter distribution can also boost the signal, since the annihilation rate scales with density squared. High-resolution N-body simulations of Milky-Way-like halos (Via Lactea II and Aquarius) resolve the smooth halo and the massive subhalos, but the subhalo population below the simulation resolution — down to an adopted minimum mass such as Mmin=10−6 M⊙M_{min}=10^{-6}\ M_{\odot} — must be extrapolated, and this extrapolation is a major uncertainty.

Any dark matter model claiming to explain the positron excess must simultaneously respect other messengers: the measured antiproton flux (sensitive to the model for how cosmic rays diffuse through the Galaxy, such as the MED — medium — diffusion model, and to solar modulation near Earth); prompt gamma-ray limits from the Galactic centre (from H.E.S.S., the High Energy Stereoscopic System, a ground-based gamma-ray telescope) and from the extragalactic gamma-ray background; the inverse-Compton (IC) photons produced when the injected high-energy e±e^\pm up-scatter the cosmic microwave background and starlight (the source paper omitted IC from its extragalactic comparison); radio synchrotron emission from e±e^\pm spiralling in the Galactic-centre magnetic field, whose profile is poorly known; and — a channel the 2009 analysis did not include — the anisotropies of the cosmic microwave background (CMB), which are distorted if annihilation injects energy around the epoch of recombination.

Pato, Pieri & Bertone (2009) combined exactly these channels for the benchmark leptophilic and hadrophilic candidates proposed to explain the PAMELA excess, using Via Lactea II/Aquarius halos, MED propagation, Mmin=10−6 M⊙M_{min}=10^{-6}\ M_{\odot} and Sommerfeld enhancement saturated in subhalos. Their conclusion: every candidate that fits the positron data overproduces antiprotons, gamma rays or radio emission; only one (AH700, under Via Lactea II) marginally survives, and only if rescaled to (σannv)0∼10−27 cm3 s−1(\sigma_{\rm ann}v)_0\sim10^{-27}\ {\rm cm^3\,s^{-1}}, implying either that the particle would overclose the universe (make dark matter so abundant that the universe would recollapse) or that it is not the dominant dark matter component. They state the open question explicitly: whether the large cross sections needed to explain the positron data can be made consistent with other astrophysical observations, given the identified uncertainties — the inner dark matter profile and Galactic-centre magnetic field (which control the radio limits), the subhalo extrapolation below simulation resolution, the model dependence and saturation assumptions of the Sommerfeld enhancement, the omitted IC constraints, cosmic-ray propagation and solar modulation, and consistency with the relic abundance for thermal versus non-thermal production histories.

Problem Statement

Determine whether the large present-day annihilation cross sections required for annihilating dark matter to explain the cosmic-ray positron excess can be made consistent with all other observations, once the astrophysical and particle-physics uncertainties identified by Pato, Pieri & Bertone (2009) — the inner Galactic dark matter profile and Galactic-centre magnetic field, the subhalo extrapolation below simulation resolution, the velocity dependence and saturation of the Sommerfeld enhancement, the inverse-Compton channel, and cosmic-ray propagation — are treated self-consistently and quantitatively rather than by fixed conservative assumptions. The single scientific objective is a definitive viability verdict for the annihilating dark matter interpretation of the positron excess; the uncertainty quantification of each messenger channel is not an independent deliverable but defines the uncertainty band within which that verdict must hold. An admissible answer takes one of two forms. (1) Exhibit a fully specified particle-physics model — mass spectrum, mediator masses and couplings, the velocity-dependent annihilation cross section (for example non-saturated or resonant Sommerfeld enhancement computed with realistic halo and subhalo velocity dispersions), and production history (thermal or non-thermal) — together with an observationally motivated Galactic dark matter distribution (inner profile, subhalo mass function and concentrations down to the adopted minimum subhalo mass) and cosmic-ray propagation model, such that the model simultaneously: (i) reproduces the measured positron fraction, positron spectrum and total electron-plus-positron flux within their uncertainties; (ii) does not exceed the measured antiproton flux after marginalization over propagation uncertainties; (iii) does not exceed Galactic-centre, dwarf-galaxy and extragalactic gamma-ray limits, including the inverse-Compton component of the injected high-energy e±e^\pm; (iv) does not exceed radio-synchrotron limits under observationally allowed Galactic-centre magnetic field profiles; (v) satisfies cosmic microwave background anisotropy constraints on annihilation energy injection at recombination; and (vi) is consistent with the observed dark matter relic abundance under its production history. (2) Or establish a coverage-complete exclusion: demonstrate that no model within an explicitly stated, observationally motivated class covering the surviving escape routes identified above — velocity-dependent, resonant, non-thermal and spatially non-standard annihilating dark matter — satisfies conditions (i)-(vi), with each channel's astrophysical uncertainties propagated as uncertainty bands rather than fixed choices; an exclusion confined to a subclass already resolved (such as standard thermal, velocity-independent s-wave leptophilic models) does not meet this branch.

References

  1. M. Pato, L. Pieri, G. Bertone, 'Multimessenger constraints on the annihilating dark matter interpretation of the positron excess', Physical Review D 80, 103510 (2009), DOI:10.1103/PhysRevD.80.103510, arXiv:0905.0372, https://arxiv.org/abs/0905.0372
  2. O. Adriani et al. (PAMELA Collaboration), 'An anomalous positron abundance in cosmic rays with energies 1.5-100 GeV', Nature 458, 607-609 (2009), DOI:10.1038/nature07942, arXiv:0810.4995, https://arxiv.org/abs/0810.4995
  3. M. Cirelli, P. Panci, 'Inverse Compton constraints on the Dark Matter e+/- excesses', Nuclear Physics B 821, 399-416 (2009), DOI:10.1016/j.nuclphysb.2009.06.034, arXiv:0904.3830, https://arxiv.org/abs/0904.3830
  4. M. Cirelli, P. Panci, P. D. Serpico, 'Diffuse gamma ray constraints on annihilating or decaying Dark Matter after Fermi', Nuclear Physics B 840, 284-303 (2010), DOI:10.1016/j.nuclphysb.2010.07.010, arXiv:0912.0663, https://arxiv.org/abs/0912.0663
  5. R. M. Crocker, N. F. Bell, C. Balazs, D. I. Jones, 'Radio and gamma-ray constraints on dark matter annihilation in the Galactic center', Physical Review D 81, 063516 (2010), DOI:10.1103/PhysRevD.81.063516, arXiv:1002.0229, https://arxiv.org/abs/1002.0229
  6. D. P. Finkbeiner, L. Goodenough, T. R. Slatyer, M. Vogelsberger, N. Weiner, 'Consistent Scenarios for Cosmic-Ray Excesses from Sommerfeld-Enhanced Dark Matter Annihilation', Journal of Cosmology and Astroparticle Physics 05 (2011) 002, DOI:10.1088/1475-7516/2011/05/002, arXiv:1011.3082, https://arxiv.org/abs/1011.3082
  7. S. Galli, F. Iocco, G. Bertone, A. Melchiorri, 'Updated CMB constraints on Dark Matter annihilation cross-sections', Physical Review D 84, 027302 (2011), DOI:10.1103/PhysRevD.84.027302, arXiv:1106.1528, https://arxiv.org/abs/1106.1528
  8. T. R. Slatyer, N. Toro, N. Weiner, 'Sommerfeld-enhanced annihilation in dark matter substructure: Consequences for constraints on cosmic-ray excesses', Physical Review D 86, 083534 (2012), DOI:10.1103/PhysRevD.86.083534, arXiv:1107.3546, https://arxiv.org/abs/1107.3546
  9. M. S. Madhavacheril, N. Sehgal, T. R. Slatyer, 'Current Dark Matter Annihilation Constraints from CMB and Low-Redshift Data', Physical Review D 89, 103508 (2014), DOI:10.1103/PhysRevD.89.103508, arXiv:1310.3815, https://arxiv.org/abs/1310.3815
  10. M. Aguilar et al. (AMS Collaboration), 'First Result from the Alpha Magnetic Spectrometer on the International Space Station: Precision Measurement of the Positron Fraction in Primary Cosmic Rays of 0.5-350 GeV', Physical Review Letters 110, 141102 (2013), DOI:10.1103/PhysRevLett.110.141102, https://doi.org/10.1103/PhysRevLett.110.141102
  11. M. Aguilar et al. (AMS Collaboration), 'Antiproton Flux, Antiproton-to-Proton Flux Ratio, and Properties of Elementary Particle Fluxes in Primary Cosmic Rays Measured with the Alpha Magnetic Spectrometer on the International Space Station', Physical Review Letters 117, 091103 (2016), DOI:10.1103/PhysRevLett.117.091103, https://doi.org/10.1103/PhysRevLett.117.091103
  12. M. Aguilar et al. (AMS Collaboration), 'Towards Understanding the Origin of Cosmic-Ray Positrons', Physical Review Letters 122, 041102 (2019), DOI:10.1103/PhysRevLett.122.041102, https://doi.org/10.1103/PhysRevLett.122.041102
  13. J. M. Gaskins, 'A review of indirect searches for particle dark matter', Contemporary Physics 57, 496-525 (2016), DOI:10.1080/00107514.2016.1175160, arXiv:1604.00014, https://arxiv.org/abs/1604.00014
  14. A. Cuoco, M. Krämer, M. Korsmeier, 'Novel Dark Matter Constraints from Antiprotons in Light of AMS-02', Physical Review Letters 118, 191102 (2017), DOI:10.1103/PhysRevLett.118.191102, arXiv:1610.03071, https://arxiv.org/abs/1610.03071
  15. M. Ackermann et al. (Fermi-LAT Collaboration), 'Searching for Dark Matter Annihilation from Milky Way Dwarf Spheroidal Galaxies with Six Years of Fermi Large Area Telescope Data', Physical Review Letters 115, 231301 (2015), DOI:10.1103/PhysRevLett.115.231301, arXiv:1503.02641, https://arxiv.org/abs/1503.02641
  16. A. U. Abeysekara et al. (HAWC Collaboration), 'Extended gamma-ray sources around pulsars constrain the origin of the positron flux at Earth', Science 358, 911-914 (2017), DOI:10.1126/science.aan4880, arXiv:1711.06223, https://arxiv.org/abs/1711.06223
  17. D. Hooper, I. Cholis, T. Linden, K. Fang, 'HAWC Observations Strongly Favor Pulsar Interpretations of the Cosmic-Ray Positron Excess', Physical Review D 96, 103013 (2017), DOI:10.1103/PhysRevD.96.103013, arXiv:1702.08436, https://arxiv.org/abs/1702.08436
  18. M. Di Mauro, S. Manconi, F. Donato, 'Detection of a gamma-ray halo around Geminga with the Fermi-LAT data and implications for the positron flux', Physical Review D 100, 123015 (2019), DOI:10.1103/PhysRevD.100.123015, arXiv:1903.05647, https://arxiv.org/abs/1903.05647
  19. Y. Bai, J. Berger, S. Lu, 'Supersymmetric Resonant Dark Matter: a Thermal Model for the AMS-02 Positron Excess', Physical Review D 97, 115012 (2018), DOI:10.1103/PhysRevD.97.115012, arXiv:1706.09974, https://arxiv.org/abs/1706.09974
  20. Y.-C. Ding, Y.-L. Ku, C.-C. Wei, Y.-F. Zhou, 'Consistent explanation for the cosmic-ray positron excess in p-wave Sommerfeld-enhanced dark matter annihilation', Journal of Cosmology and Astroparticle Physics 09 (2021) 005, DOI:10.1088/1475-7516/2021/09/005, arXiv:2104.14881, https://arxiv.org/abs/2104.14881
  21. X.-J. Lv, X.-J. Bi, K. Fang, P.-F. Yin, M.-J. Zhao, 'Reexamining the dark matter scenario accounting for the positron excess in a new cosmic ray propagation model', Physical Review D 109, 023023 (2024), DOI:10.1103/PhysRevD.109.023023, arXiv:2307.07114, https://arxiv.org/abs/2307.07114
  22. K. M. Belotsky, M. L. Solovev, 'Dark Matter with Special Spatial Distribution as Possible Explanation of Positron Excess in Cosmic Rays', Physics of Particles and Nuclei 56, 599-603 (2025), DOI:10.1134/S1063779624701983, https://doi.org/10.1134/S1063779624701983
  23. S. Abdollahi et al. (Fermi-LAT, HAWC, H.E.S.S., MAGIC, VERITAS Collaborations), 'Combined dark matter search towards dwarf spheroidal galaxies with Fermi-LAT, HAWC, H.E.S.S., MAGIC, and VERITAS', Journal of Cosmology and Astroparticle Physics 03 (2026) 035, DOI:10.1088/1475-7516/2026/03/035, arXiv:2508.20229, https://arxiv.org/abs/2508.20229
  24. M. Cirelli, A. Strumia, J. Zupan, 'Dark Matter', SciPost Physics Reviews 1 (2026), DOI:10.21468/SciPostPhysRev.1, arXiv:2406.01705, https://arxiv.org/abs/2406.01705