Simulating the γ-ray emission from galaxy clusters: a universal cosmic ray spectrum and spatial distribution

Entering a new era of high-energy gamma-ray experiments, there is an exciting quest for the first detection of gamma-ray emission from clusters of galaxies. To complement these observational efforts, we use high-resolution simulations of a broad sample of galaxy clusters, and follow self-consistent cosmic ray (CR) physics using an improved spectral description. We study CR proton spectra as well as the different contributions of the pion decay and inverse-Compton emission to the total flux and present spectral index maps. We find a universal spectrum of the CR component in clusters with surprisingly little scatter across our cluster sample. When CR diffusion is neglected, the spatial CR distribution also shows approximate universality; it depends however on the cluster mass. This enables us to derive a semi-analytic model for both the distribution of CRs as well as the pion decay gamma-ray emission and the secondary radio emission that results from hadronic CR interactions with ambient gas protons. In addition, we provide an analytic framework for the inverse-Compton emission that is produced by shock-accelerated CR electrons and is valid in the full gamma-ray energy range. Combining the complete sample of the brightest X-ray clusters observed by ROSAT with our gamma-ray scaling relations, we identify the brightest clusters for the gamma-ray space telescope Fermi and current imaging air Cerenkov telescopes (IACTs) (MAGIC, HESS, VERITAS). We reproduce the previous result of Pfrommer, but provide somewhat more conservative predictions for the fluxes in the energy regimes of Fermi and IACTs when accounting for the bias of 'artificial galaxies' in cosmological simulations. We find that it will be challenging to detect cluster gamma-ray emission with Fermi after the second year but this mission has the potential of constraining interesting values of the shock acceleration efficiency after several years of surveying. Comparing the predicted emission from our semi-analytic model to that obtained by means of our scaling relations, we find that the gamma-ray scaling relations underpredict, by up to an order of magnitude, the flux from cool-core clusters.