Gamma-ray signatures of annihilation to charged leptons in dark matter substructure

Due to their higher concentrations and small internal velocities, Milky Way subhalos can be at least as important as the smooth halo in accounting for the GeV positron excess via dark matter annihilation. After showing how this can be achieved in various scenarios, including in Sommerfeld models, we demonstrate that, in this case, the diffuse inverse-Compton emission resulting from electrons and positrons produced in substructure leads to a nearly-isotropic signal close to the level of the isotropic GeV gamma-ray background seen by Fermi. Moreover, we show that HESS cosmic-ray electron measurements can be used to constrain multi-TeV internal bremsstrahlung gamma rays arising from annihilation to charged leptons.

💡 Research Summary

This paper investigates the role of Milky Way dark‑matter subhalos (substructure) in producing the observed GeV positron excess via dark‑matter annihilation into charged leptons. The authors first point out that subhalos are characterized by higher densities and lower internal velocity dispersions than the smooth halo component. Because many particle‑physics models (e.g., those with Sommerfeld enhancement) feature a velocity‑dependent annihilation cross‑section, the low velocities inside subhalos can boost the effective annihilation rate by orders of magnitude. By exploring a range of model parameters—including pure s‑wave annihilation, Sommerfeld‑enhanced scenarios, and mediator‑driven (φ‑mediated) interactions—the authors demonstrate that the positron flux generated solely by subhalos can match the measurements of PAMELA, AMS‑02, and Fermi‑LAT, without invoking an unrealistically large boost from the smooth halo.

The next step is to follow the fate of the electrons and positrons produced inside subhalos. After injection, these leptons lose energy through synchrotron radiation and, most importantly for this work, inverse‑Compton scattering (ICS) off the cosmic microwave background and interstellar radiation fields. Using a diffusion‑loss equation that incorporates the spatial distribution of subhalos throughout the Galaxy, the authors compute the resulting diffuse gamma‑ray emission. Because subhalos are roughly isotropically distributed on large scales, the ICS component is nearly isotropic, producing a gamma‑ray background that closely approaches the isotropic gamma‑ray background (IGRB) measured by Fermi‑LAT in the 0.1–820 GeV range. In many viable parameter choices the predicted flux lies at or just below the IGRB, implying that current IGRB measurements already place meaningful constraints on subhalo‑dominated annihilation scenarios.

A further, independent constraint comes from the internal bremsstrahlung (IB) photons that accompany annihilation directly into charged leptons. For dark‑matter masses in the multi‑TeV regime, these IB photons appear at energies probed by ground‑based air‑Cherenkov telescopes. The authors compare the predicted IB spectrum with the high‑energy cosmic‑ray electron spectrum measured by HESS (∼0.5–5 TeV). Since the HESS electron data are consistent with a smooth power‑law, any excess IB contribution would overproduce the observed electron flux. By requiring that the IB component does not exceed the HESS measurements, the authors derive new upper limits on the annihilation cross‑section (or equivalently on the Sommerfeld enhancement factor) for dark‑matter masses above a few TeV.

In summary, the paper delivers three principal insights: (1) Subhalos can dominate the positron production needed to explain the GeV excess, especially in models with velocity‑dependent enhancements; (2) The inverse‑Compton gamma‑rays from subhalo‑originated leptons generate an almost isotropic signal that is already close to the measured IGRB, providing a powerful indirect‑detection probe; and (3) HESS electron observations impose stringent limits on the high‑energy internal‑bremsstrahlung photons, thereby constraining multi‑TeV dark‑matter annihilation into charged leptons. The combined analysis underscores the importance of accounting for dark‑matter substructure in indirect searches and highlights the complementary role of gamma‑ray and cosmic‑ray electron data in shaping viable dark‑matter models.