Deep observation of the NGC 1275 region with MAGIC: search of diffuse [gamma]-ray emission from cosmic rays in the Perseus cluster

Clusters of galaxies are expected to be reservoirs of cosmic rays (CRs) that should produce diffuse [gamma]-ray emission due to their hadronic interactions with the intra-cluster medium. The nearby Perseus cool-core cluster, identified as the most promising target to search for such an emission, has been observed with the MAGIC telescopes at very-high energies (VHE, E [> ~] 100GeV) for a total of 253h from 2009 to 2014. The active nuclei of NGC1275, the central dominant galaxy of the cluster, and IC310, lying at about 0.6[degrees] from the centre, have been detected as point-like VHE [gamma]-ray emitters during the first phase of this campaign. We report an updated measurement of the NGC1275 spectrum, which is described well by a power law with a photon index [Gamma] = 3.6 + or - 0.2 sub(stat)+ or - 0.2 sub(syst) between 90GeV and 1200GeV. We do not detect any diffuse [gamma]-ray emission from the cluster and so set stringent constraints on its CR population. To bracket the uncertainties over the CR spatial and spectral distributions, we adopt different spatial templates and power-law spectral indexes [alpha]. For [alpha] = 2.2, the CR-to-thermal pressure within the cluster virial radius is constrained to be [