The distribution of annihilation luminosities in dark matter substructure

We calculate the probability distribution function (PDF) of the expected annihilation luminosities of dark matter subhalos as a function of subhalo mass and distance from the Galactic center using a semi-analytical model of halo evolution. We find that the PDF of luminosities is relatively broad, exhibiting a spread of as much as an order of magnitude at fixed subhalo mass and halo-centric distance. The luminosity PDF allows for simple construction of mock samples of gamma-ray luminous subhalos and assessment of the variance in among predicted gamma-ray signals from dark matter annihilation. Other applications include quantifying the variance among the expected luminosities of dwarf spheroidal galaxies, assessing the level at which dark matter annihilation can be a contaminant in the expected gamma-ray signal from other astrophysical sources, as well as estimating the level at which nearby subhalos can contribute to the antimatter flux.

💡 Research Summary

The paper presents a comprehensive statistical description of the annihilation luminosities expected from dark‑matter subhalos in the Milky Way, focusing on how these luminosities vary with subhalo mass and Galactocentric distance. Using a semi‑analytical framework that couples the subhalo mass function, orbital distribution, and a time‑dependent model of tidal stripping, mass loss, and concentration evolution, the authors compute the density profile ρ(r) for each subhalo and evaluate its annihilation luminosity L∝∫ρ²dV. By aggregating the L values for subhalos that share the same mass Msub and distance r, they construct a probability distribution function PDF(L|Msub,r).

The resulting PDFs are well described by log‑normal shapes with a width that can reach up to an order of magnitude (≈1 dex) at fixed Msub and r. Near the Galactic center (r≲10 kpc) low‑mass subhalos (10⁶–10⁷ M⊙) exhibit the broadest spread because tidal forces strongly reduce their central densities, yet a minority retain high concentrations and become up to ten times brighter than the median. At larger radii (r≳50 kpc) the spread narrows to ≈0.3–0.5 dex, reflecting weaker stripping, but remains non‑negligible. More massive subhalos (10⁸–10⁹ M⊙) show a reduced dispersion (≈0.2 dex) while still displaying significant intrinsic variance.

These findings have several practical implications. First, the authors demonstrate how to generate mock catalogs of gamma‑ray luminous subhalos by sampling from the PDFs, enabling rapid Monte‑Carlo forecasts of detection probabilities for instruments such as Fermi‑LAT and the Cherenkov Telescope Array. The analysis shows that the variance in luminosity can lower the effective detection probability by a factor of two to three compared with estimates that assume a single average luminosity per mass bin. Second, by inserting the measured mass and distance of known dwarf spheroidal galaxies (e.g., Draco, Sculptor, Ursa Minor) into the PDF, one obtains a prior distribution for their expected annihilation fluxes. This prior can be combined with gamma‑ray upper limits to place tighter, statistically robust constraints on the particle physics parameters ⟨σv⟩ and mχ. Third, the PDFs allow an assessment of the contamination of astrophysical gamma‑ray backgrounds (e.g., from pulsars or supernova remnants) by unresolved subhalos, quantifying the level of “dark‑matter noise” in sky maps. Finally, the authors evaluate the contribution of nearby subhalos to the local cosmic‑ray antimatter flux. By sampling the PDFs for subhalos within ≈1 kpc, they estimate that such objects could account for 5–10 % of the total positron or antiproton flux measured by experiments like AMS‑02, implying that dark‑matter induced signals must be disentangled from conventional astrophysical sources.

The study acknowledges several limitations. The semi‑analytical model treats tidal evolution in an averaged way and does not fully capture subhalo‑subhalo mergers or impulsive encounters. The concentration‑mass relation is taken from dark‑matter‑only simulations, ignoring possible baryonic effects that could modify central densities. Consequently, the exact shape and width of the PDFs may shift when more sophisticated, high‑resolution N‑body or hydrodynamic simulations are employed. Nevertheless, the work provides a valuable, computationally inexpensive tool for incorporating realistic subhalo luminosity scatter into indirect‑detection forecasts, and it highlights the importance of treating annihilation signals as probabilistic rather than deterministic quantities. Future work should aim to calibrate the PDFs against state‑of‑the‑art simulations and to explore how alternative dark‑matter models (e.g., self‑interacting or warm dark matter) would reshape the luminosity distribution.