Galaxy clusters are predicted to produce gamma-rays through cosmic ray interactions and/or dark matter annihilation, potentially detectable by the Fermi Large Area Telescope (Fermi-LAT). We present a new, independent stacking analysis of Fermi-LAT photon count maps using the 78 richest nearby clusters (z<0.12) from the Two Micron All-Sky Survey (2MASS) cluster catalog. We obtain the lowest limit on the photon flux to date, 2.3e-11 ph/s/cm^2 (95% confidence) per cluster in the 0.8-100 GeV band, which corresponds to a luminosity limit of 3.5e44 ph/s. We also constrain the emission limits in a range of narrower energy bands. Scaling to recent cosmic ray acceleration and gamma-ray emission models, we find that cosmic rays represent a negligible contribution to the intra-cluster energy density and gas pressure.
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