Setting Z² = 1 in Eq. (23) is correct for a plasma of primordial element composition which consists of hydrogen and helium only, because $\langle n_{\rm N} Z^2 \rangle = n_{\rm N}$ in this case. This is a reasonable approximation owing to the small contamination of heavier elements in the ICM.

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... $\alpha _{\rm p}= \alpha _{\rm inj} + \alpha _{\rm diff}$

This seems to be in contradiction to the identity of injection and equilibrium spectral index for a system without escape claimed in Sect. 3.1. Formally, we had to include particle escape from the galaxy cluster in order to be able to have a finite steady state solution of the diffusion problem, as given by Eq. (57). In the realistic case of a finite age of the system the stationary solution is only approximately valid in the center of the galaxy cluster. However, only there exists a sufficiently high target density to detect the CRp population. Therefore, although we use a poor description of the CRp profile on large-scales, the estimated $\gamma$ -ray fluxes should be sufficiently accurate.

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... $\nu_{\rm GHz} = \nu/\mbox{GHz}$ .

Here we corrected for a missing factor of 2 in Eq. (4) in Enßlin (2002) and changed the slope of the ${\beta }$ -profile to $\beta = 0.75$ (Briel et al. 1992).

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... (INTEGRAL)

http://astro.esa.int/Integral/

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... (GLAST)

http://glast.gsfc.nasa.gov/science/

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... (CANGAROO)

http://www.physics.adelaide.edu.au/astrophysics/

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... (HESS)

http://www.mpi-hd.mpg.de/hfm/HESS/HESS.html

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... (VERITAS)

http://veritas.sao.arizona.edu/

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... (MAGIC)

http://hegra1.mppmu.mpg.de/MAGICWeb/

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