(see e.g. [@pfrommer2007]) and of other recent studies [@nagaiando] motivate our choices of $\beta_p=-0.5,1$ for our benchmark models. The case of $\beta_p=-0.5$, which we label as the “cuspy” profile, is found in simulations that include radiative effects. The profile in (\[eq:spatial\]) with $\beta_p=-0.5$ approximates the profile resulting from the radiative, hydrodynamical simulations of Ref. [@pfrommer2007]. Non-radiative simulations indicate instead a flatter profile with $\beta_p=1$; this is an extreme scenario where the density of cosmic ray sources relative to the thermal gas density grows linearly with radius. Although this might be on the verge of being unrealistic, the effects of cooling and heating in clusters are also somewhat uncertain, and we adopt this case as an extreme possibility [@pfrommer2007; @nagaiando]. We remark that in recent studies [@brunetticassano] it has been argued that cosmic ray activity in clusters is dominated by turbulent reacceleration. In this case, in the absence of shocks, the natural expectation for $\beta_p$ would be 0. This choice falls in between the two benchmark cases we consider here.

-   Lastly, in our Fermi simulations we assume that the cosmic ray energy density is 10% of the thermal gas energy density, i.e. we set $X_p=X_p(R_{500})=0.1$. The choice of the normalization 