Gamma Rays from Dark Matter Annihilations Strongly Constrain the Substructure in Halos

To fit recent data, $e^{\pm }$ from dark matter (DM) needs a boosted annihilation rate. This may imply an observable level of gamma rays from nearby galaxy clusters for the Fermi satellite. Using EGRET data, we limit the minimum mass of DM substructures to be about $5\times {10}^3$ times larger than for cold DM, meaning a cutoff similar to, e.g., warm DM. We numerically simulate clusters to reliably model the background. If we assume no anomalous boost factor, we find comparable levels of gamma-ray emission from DM and cosmic ray interactions, giving a chance with future data to characterize the DM.

Figure 1

Left: differential spectra for 3 different clusters observed within a solid angle of radius $\Delta \theta =3.5$ degree (neglecting the contribution of the MW’s halo). We show the IC emission from DM annihilations (solid) as well as FSR (dashed-dotted). We include SFE and the enhancement from cluster substructures down to a limiting substructure mass of $M_{\lim }=5\times {10}^{-3}{M}_{\odot }$. We show the pion decay emission of our conservative model without galaxies with dashed lines. Right: we contrast the integrated spectrum of Virgo for the EGRET angular resolution, $\Delta \theta =5.8$ (red), with that of imaging air Čerenkov telescopes, $\Delta \theta =0.1$ (blue), and compare those to the point source sensitivity curves on the $5\sigma$ level of Fermi (2 yr all-sky survey) as well as MAGIC2 and CTA (50 hours). We choose $M_{\lim }=5\times {10}^{-3}{M}_{\odot }$, so that the resulting flux is just consistent with the EGRET upper limit [37]. This reduces the substructure boost from $\sim 220$ to 50.

Figure 2

Studying separately the contribution from substructure and the SFE to the differential spectra of Fornax within a solid angle of $\Delta \theta =3.5$ degree. Left: the DM annihilation spectra with SFE and $M_{\lim }=5\times {10}^{-3}{M}_{\odot }$ (red) is compared to the pion decay spectrum from CR interactions (blue). We show the pure contribution from the smooth cluster halo (dotted, $B_{\mathrm{sfe}}=490$, $B_{\mathrm{sub}}=1$), to which we add substructures (dashed, $B_{\mathrm{sfe}}=490$, $B_{\mathrm{sub}}=50$), and to which we additionally add the line-of-sight contribution due to the Milky Way’s halo towards Fornax (solid). Right: we compare the hadronically induced pion decay spectrum to the DM annihilation signal without SFE. The pion decay spectrum shown with (dotted) and without (solid) the contribution due to galaxies and dense point sources. The substructure boosted DM annihilation signal including the MW contribution (dash-dotted), but assuming a standard value for the limiting substructure mass of $M_{\lim }={10}^{-6}{M}_{\odot }$.