  Current theories predict relativistic hadronic particle populations in
clusters of galaxies in addition to the already observed relativistic leptons.
In these scenarios hadronic interactions give rise to neutral pions which decay
into $\gamma$ rays, that are potentially observable with the Large Area
Telescope (LAT) on board the Fermi space telescope. We present a joint
likelihood analysis searching for spatially extended $\gamma$-ray emission at
the locations of 50 galaxy clusters in 4 years of Fermi-LAT data under the
assumption of the universal cosmic-ray model proposed by Pinzke & Pfrommer
(2010). We find an excess at a significance of $2.7\sigma$ which upon closer
inspection is however correlated to individual excess emission towards three
galaxy clusters: Abell 400, Abell 1367 and Abell 3112. We discuss these cases
in detail and conservatively attribute the emission to unmodeled background
(for example, radio galaxies within the clusters). Through the combined
analysis of 50 clusters we exclude hadronic injection efficiencies in simple
hadronic models above 21% and establish limits on the cosmic-ray to thermal
pressure ratio within the virial radius, $R_{200}$, to be below 1.2-1.4%
depending on the morphological classification. In addition we derive new limits
on the $\gamma$-ray flux from individual clusters in our sample.

High Energy Astrophysical Phenomena;Cosmology and Nongalactic Astrophysics