$X_p=0.1$ here in our Fermi simulated observations, we will consider a more conservative value of $X_p=0.01$ in our survey of galaxy clusters and groups in sec. \[sec:cat\] and in the Appendix, motivated e.g. by the results of Ref. [@nagaiando], which showed that Fermi could be sensitive (depending on $\alpha_p$) to $X_p$ smaller than a fraction of a percent for nearby massive clusters.

We summarize our benchmark cosmic ray models, with their names and parameters, in Table \[tab:cr\_models\]. “CR” stands for cosmic rays, while “H” and “S” respectively indicate a “*Hard*” and a “*Soft*” primary proton injection spectrum, $\alpha_p=2.1$ and 2.7, and “C” and “F” stand for “*Cuspy*” and “*Flat*”, respectively corresponding to $\beta_p=-0.5$ and to 1.

![Contours levels for the gamma-ray emission from cosmic rays in the Coma (left) and Virgo (right) clusters of galaxies. We assume that the cosmic rays have 10% of the gas energy density ($X_p=0.1$), and scan the plane $(\beta_p,\alpha_p)$ where $\beta_p$ characterizes the spatial distribution of cosmic ray sources, and $\alpha_p$ the primary proton injection spectrum. \[fig:alphabeta\]](alphabeta.eps "fig:"){width="14.cm"}\

As pointed out in previous studies, for a wide range of parameters Fermi will be able to detect a gamma-ray signal produced by cosmic rays: Figure \[fig:alphabeta\] 