shows the gamma-ray flux for the Coma and Virgo clusters for a range of $\alpha_p$ and $\beta_p$, with $X_p=0.1$. In the computation, we assumed for both clusters the gas density profiles as given in Table 1 of [@pfrommer2004]. The curves indicate contours of constant integrated gamma-ray flux above 0.1 GeV, in units of $10^{-9}\ {\rm cm}^{-2}\ {\rm s}^{-1}$. For simplicity, we assume here a Fermi sensitivity for a point-source emission of $4\times10^{-9}\ {\rm cm}^{-2}\ {\rm s}^{-1}$, while the EGRET gamma-ray limits for Coma and Virgo are given in [@reimer]. Points below the blue line, in the central part of the panels, are predicted to be within the sensitivity of Fermi. The red lines indicate instead the EGRET limits: parameter space points below those lines are thus ruled out by current data [@reimer].

The shape of the gamma-ray emission contours is not unexpected: larger values of $\beta_p$ imply smaller gamma-ray fluxes, simply because they feature a flatter cosmic ray spatial distribution (see Eq. \[eq:spatial\]), which in turn integrates to smaller values. In addition, we find that the source function in Eq. (\[eq:crspec\]) implies that the largest gamma-ray fluxes correspond to intermediate values (2.1$\lesssim \alpha_p \lesssim2.7$) of the injection spectrum.

Dark Matter 