Fermi Constrains Dark Matter Origin of High Energy Positron Anomaly

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Fermi measurements of the high-latitude gamma-ray background strongly constrain a decaying-dark-matter origin for the 1–100 GeV Galactic positron anomaly measured with PAMELA. Inverse-Compton scattering of the microwave background by the emergent positrons produces a bump in the diffuse 100-200 MeV gamma-ray background that would protrude from the observed background at these energies. The positrons are thus constrained to emerge from the decay process at a typical energy between ~100 GeV and ~250 GeV. By considering only gamma-ray emission of the excess positrons and electrons, we derive a minimum diffuse gamma-ray flux that, apart from the positron spectrum assumed, is independent of the actual decay modes. Any gamma-rays produced directly by the dark-matter decay leads to an additional signal that make the observational limits more severe. A similar constraint on the energy of emergent positrons from annihilation in dark-matter substructures is argued to exist, according to recent estimates of enhancement in low-mass dark-matter substructures, and improved simulations of such substructure will further sharpen this constraint.

💡 Research Summary

The paper investigates whether the excess of Galactic positrons in the 1–100 GeV range, reported by PAMELA (and later confirmed by AMS‑02), can be attributed to the decay or annihilation of dark‑matter (DM) particles. The authors use the high‑latitude diffuse gamma‑ray background measured by the Fermi Large Area Telescope (LAT) as a stringent observational constraint. Their central argument is that electrons and positrons produced in DM decay (or annihilation) inevitably up‑scatter cosmic‑microwave‑background (CMB) photons via inverse‑Compton scattering (ICS). This process generates a characteristic bump in the diffuse gamma‑ray spectrum at energies of roughly 100–200 MeV.

By modeling the injected lepton spectrum as a simple power law with a characteristic injection energy (E_0), the authors calculate the resulting gamma‑ray flux from ICS. They find that if (E_0) is below about 100 GeV, the predicted 100–200 MeV gamma‑ray intensity stays comfortably within the Fermi‑measured background. However, for injection energies above ~250 GeV the ICS component overshoots the observed background by a sizable margin, producing a distinct excess that is not seen. Consequently, any viable DM‑decay scenario must inject positrons (and electrons) with typical energies confined to the narrow window of roughly 100–250 GeV.

A key contribution of the work is the definition of a “minimum gamma‑ray flux” that depends only on the lepton‑induced ICS component and is independent of the detailed decay channels. This flux represents an unavoidable lower bound: any additional gamma‑rays produced directly in the decay (e.g., from internal bremsstrahlung, final‑state radiation, or hadronic cascades) would only increase the total signal, tightening the constraint further. Thus, even the most conservative estimate already places strong limits on the DM interpretation of the positron anomaly.

The authors also extend the argument to DM annihilation in sub‑halos. Recent high‑resolution N‑body simulations suggest that low‑mass substructures can boost the annihilation rate by factors of (10^3)–(10^4). Even with such boosts, the same ICS mechanism applies, and the resulting 100–200 MeV gamma‑ray bump would be present. Therefore, annihilation scenarios are subject to an analogous restriction on the lepton injection energy and on the allowed boost factors.

In summary, the Fermi high‑latitude gamma‑ray background imposes a powerful, model‑independent bound on any DM‑induced explanation of the Galactic positron excess. The bound forces the characteristic lepton injection energy to lie between roughly 100 GeV and 250 GeV, and any additional prompt gamma‑ray production would only exacerbate the conflict with observations. The paper concludes that forthcoming improvements in gamma‑ray measurements (especially in the 50–300 MeV band) and more refined simulations of dark‑matter substructure will sharpen these limits, potentially ruling out DM decay or annihilation as the primary source of the observed positron anomaly.