Galaxy clusters might be sources of TeV gamma rays emitted by high-energy protons and electrons accelerated by large scale structure formation shocks , galactic winds , or active galactic nuclei .
Furthermore , gamma rays may be produced in dark matter particle annihilation processes at the cluster cores .
We report on observations of the galaxy clusters Perseus and Abell 2029 using the 10 m Whipple Cherenkov telescope during the 2003-2004 and 2004-2005 observing seasons .
We apply a two-dimensional analysis technique to scrutinize the clusters for TeV emission .
In this paper we first determine flux upper limits on TeV gamma-ray emission from point sources within the clusters .
Second , we derive upper limits on the extended cluster emission .
We subsequently compare the flux upper limits with EGRET upper limits at 100 MeV and theoretical models .
Assuming that the gamma-ray surface brightness profile mimics that of the thermal X-ray emission and that the spectrum of cluster cosmic rays extends all the way from thermal energies to multi-TeV energies with a differential spectral index of -2.1 , our results imply that the cosmic ray proton energy density is less than 7.9 % of the thermal energy density for the Perseus cluster .