Anisotropy probe of galactic and extra-galactic Dark Matter annihilations

We study the flux and the angular power spectrum of gamma-rays produced by Dark Matter (DM) annihilations in the Milky Way (MW) and in extra-galactic halos. The annihilation signal receives contributions from: a) the smooth MW halo, b) resolved and unresolved substructures in the MW, c) external DM halos at all redshifts, including d) their substructures. Adopting a self-consistent description of local and extra-galactic substructures, we show that the annihilation flux from substructures in the MW dominates over all the other components for angles larger than O(1) degrees from the Galactic Center, unless an extreme prescription is adopted for the substructures concentration. We also compute the angular power spectrum of gamma-ray anisotropies and find that, for an optimistic choice of the particle physics parameters, an interesting signature of DM annihilations could soon be discovered by the Fermi LAT satellite at low multipoles, l<100, where the dominant contribution comes from MW substructures with mass M>10^4 solar masses. For the substructures models we have adopted, we find that the contribution of extra-galactic annihilations is instead negligible at all scales.

💡 Research Summary

The paper presents a comprehensive study of the gamma‑ray flux and its angular power spectrum arising from dark‑matter (DM) annihilations both within the Milky Way (MW) and in extragalactic halos. The authors decompose the total signal into four contributions: (a) the smooth MW halo, (b) resolved and unresolved substructures (subhalos) inside the MW, (c) DM halos at all redshifts throughout the Universe, and (d) the substructures residing within those extragalactic halos.

For the Galactic component, the smooth halo is modeled with a Navarro‑Frenk‑White (NFW) profile (scale radius 21.7 kpc, virial mass 10¹² M⊙). Subhalos are assumed to follow the same radial distribution as the host mass, with a mass function dN/dM∝M⁻¹·⁹ spanning 10⁻⁶–10¹⁰ M⊙. The total number of subhalos is ≈1.5×10¹⁶, corresponding to about 5 % of the MW mass. Two extreme concentration‑mass‑redshift relations are adopted to bracket theoretical uncertainties: (i) Bz0,ref, a simple power‑law extrapolation of the Bullock et al. (2001) model below 10⁴ M⊙, and (ii) Bzf,ref, which keeps the concentration fixed at formation and scales it with (1+z)⁻¹ thereafter. Both models incorporate a log‑normal scatter (σ_c=0.24).

The particle‑physics factor is taken to be optimistic: a 40 GeV WIMP, thermal relic cross‑section ⟨σv⟩=3×10⁻²⁶ cm³ s⁻¹, annihilating 100 % into b b̄. The resulting photon spectrum per annihilation is obtained from standard PYTHIA‑based tables. The gamma‑ray intensity in a given direction is written as the product of this particle factor and a “cosmological” line‑of‑sight integral over ρ², summed over all subhalos and the smooth component.

For the extragalactic contribution, the authors adopt the formalism of Ando & Komatsu (2006) and integrate over comoving volume elements dV = R₀³ r² dr dΩ (1+z)⁻³. They include attenuation by the extragalactic background light (e^{−τ(z,E)}) and the (1+z)³ cosmological dilution. Subhalos within extragalactic halos are added using the same concentration prescriptions as for the Galactic case. The resulting extragalactic flux is found to be sub‑dominant, contributing less than ~5 % of the total intensity at all energies and angular scales.

To assess anisotropies, full‑sky mock maps are generated with HEALPix at the angular resolution of the Fermi Large Area Telescope (LAT). The angular power spectrum C_ℓ is computed and compared with the expected LAT measurement uncertainties. The key result is that at low multipoles (ℓ ≲ 100) the power is dominated by Galactic subhalos, especially those with masses >10⁴ M⊙, which account for ~90 % of the anisotropic signal. The spectrum follows roughly C_ℓ ∝ ℓ⁻¹·⁵, a distinctive signature that could be detected with a few years of LAT data. In contrast, the extragalactic component yields a nearly flat, negligible contribution to C_ℓ across all ℓ.

The authors conclude that, under optimistic particle‑physics assumptions, the anisotropy signal from Milky Way substructures should be within reach of the Fermi‑LAT. Detection would provide simultaneous constraints on the WIMP annihilation cross‑section and on the subhalo concentration‑mass relation, while the negligible extragalactic contribution simplifies the interpretation. They also note that more realistic (less optimistic) particle models would reduce the signal proportionally, and that future high‑resolution simulations (e.g., updated Aquarius or Via Lactea runs) could refine the subhalo spatial distribution and concentration prescriptions, further sharpening the predicted anisotropy signature.