  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.
