Abstract
We study the diffusive escape of cosmic rays from a central source inside a galaxy cluster to obtain the suppression in the outgoing flux appearing when the confinement times get comparable or larger than the age of the sources. We also discuss the attenuation of the flux due to the interactions of the cosmic rays with the cluster medium, which can be sizeable for heavy nuclei. The overall suppression in the total cosmic ray flux expected on Earth is important to understand the shape of the extragalactic contribution to the cosmic ray spectrum for E/Z < 1 EeV . This suppression can also be relevant to interpret the results of fits to composition-sensitive observables measured at ultra-high energies.
Highlights
Galaxy clusters are the largest virialized structures, having typical radii Rcl = 2–3 Mpc and masses Mcl ∼ 1013–1015M⊙
Γ rays from far away clusters would cascade down to energies of GeV–TeV by their interactions with the cosmic microwave background (CMB) and the infrared and optical extragalactic background light (EBL), the neutrinos, which have typical energies Ep/20, with Ep being the energies of the nucleons which produced them, could have a spectrum extending beyond the PeV range
This could be interesting in view of the recent results of the IceCube experiment that found an astrophysical contribution to the neutrino fluxes in the 20 TeV–few PeV range [7], several constraints exist and the expected fluxes from interactions in the cluster medium are in general below the observed ones [5,6]
Summary
Note that D increases with energy but tesc may still exceed the age of the clusters even for energies as high as 1017–1018 eV for protons, and Z times larger for CRs with charge Z This fact has led to consider clusters as reservoirs of CRs and considerable attention has been devoted to the possibility that the CRs trapped in clusters could interact with the intracluster gas or radiation to produce secondary fluxes of γ rays and neutrinos We explore in detail the possibility that this suppression could alternatively (or ) be due to the confinement of the low energy CRs directly in the clusters containing the sources In all these scenarios the resulting relative suppression of the heavier components at the energies for which the light component dominates is crucial to reduce the spread in the values of Xmax observed and should help to reproduce the observed overall spectrum
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