data) sets the spatial distribution of the signal. We outline below a few motivated parameter space choices which define the benchmark models we employ to run our Fermi simulations. We then apply these models to the specific case of the Coma cluster.

-   As far as the injection spectral index, estimates come from theoretical arguments as well as from numerical simulations. For instance, Ref. [@Berrington:2002bh] showed that the minimum spectral index ranges from 2.1 to 2.8. In that range, larger values are typically associated to forward shocks and smaller masses. The larger the mass, the stronger the gravitational potential and the harder the predicted injection spectral index. Structure formation shock theory predicts injection spectral indices of $2.0<\alpha_p<2.5$ for strong shocks [@Miniati:2003ep], such as those expected for [*accretion*]{} shocks and [*strong merger*]{} shocks. We choose here $\alpha_p=2.1,\ 2.7$ as physically motivated cases. Specifically, the cosmic ray spectrum in our Galaxy is observed to be a power law with $\alpha_p=2.7$, which motivates the large $\alpha_p$ choice. On the other hand, clusters confine cosmic rays on cosmological time scales [@Volk:1994zz; @Berezinsky:1996wx], and are thus expected to give rise to a harder spectrum than that of the Galaxy: $\alpha_p=2.1$ is thus also a reasonable 