Forming Clusters of Galaxies as the Origin of Unidentified GeV Gamma-Ray Sources

Over half of GeV gamma-ray sources observed by the EGRET experiment have not yet been identified as known astronomical objects. There is an isotropic component of such unidentified sources, whose number is about 60 in the whole sky. Here we calculate the expected number of dynamically forming clusters of galaxies emitting gamma-rays by high energy electrons accelerated in the shock wave when they form, in the framework of the standard theory of structure formation. We find that a few tens of such forming clusters should be detectable by EGRET and hence a considerable fraction of the isotropic unidentified sources can be accounted for, if about 5% of the shock energy is going into electron acceleration. We argue that these clusters are very difficult to detect in x-ray or optical surveys compared with the conventional clusters, because of their extended angular size of about 1 degree. Hence they define a new population of ``gamma-ray clusters''. If this hypothesis is true, the next generation gamma-ray telescopes such as GLAST will detect more than a few thousands of gamma-ray clusters. It would provide a new tracer of dynamically evolving structures in the universe, in contrast to the x-ray clusters as a tracer of hydrodynamically stabilized systems. We also derive the strength of magnetic field required for the extragalactic gamma-ray background by structure formation to extend up to 100 GeV as observed, that is about 10^{-5} of the shock-heated baryon energy density.