Cosmological dark matter annihilations into $\gamma$ rays: A closer look

We investigate the prospects of detecting weakly interacting massive particle (WIMP) dark matter by measuring the contribution to the extragalactic gamma-ray radiation induced, in any dark matter halo and at all redshifts, by WIMP pair annihilations into high-energy photons. We perform a detailed analysis of the very distinctive spectral features of this signal, recently proposed in a short letter by three of the authors: The gamma-ray flux which arises from the decay of ${\pi }^0$ mesons produced in the fragmentation of annihilation final states shows a severe cutoff close to the value of the WIMP mass. An even more spectacular signature appears for the monochromatic gamma-ray components, generated by WIMP annihilations into two-body final states containing a photon: the combined effect of cosmological redshift and absorption along the line of sight produces sharp bumps, peaked at the rest frame energy of the lines and asymmetrically smeared to lower energies. The level of the flux depends both on the particle physics scenario for WIMP dark matter (we consider, as our template case, the lightest supersymmetric particle in a few supersymmetry breaking schemes), and on the question of how dark matter clusters. Uncertainties introduced by the latter are thoroughly discussed implementing a realistic model inspired by results of the state-of-the-art N-body simulations and semianalytic modeling in the cold dark matter structure formation theory. We also address the question of the potential gamma-ray background originating from active galaxies, presenting a novel calculation and critically discussing the assumptions involved and the induced uncertainties. Furthermore, we apply a realistic model for the absorption of gamma-rays on the optical and near-IR intergalactic radiation field to derive predictions for both the signal and background. Comparing the two, we find that there are viable configurations, in the combined parameter space defined by the particle physics setup and the structure formation scenario, for which the WIMP induced extragalactic gamma-ray signal will be detectable in the new generation of gamma-ray telescopes such as GLAST.