We present the results of a search for high-energy gamma-ray emission from a large sample of galaxy clusters sharing the properties of three existing Fermi-LAT detections (in Perseus, Virgo and Abell 3392), namely a powerful radio source within their brightest cluster galaxy (BCG). From a parent, X-ray flux-limited sample of clusters, we select 114 systems with a core-dominated BCG radio flux above 50 or 75 mJy, stacking data from the first 45 months of the Fermi mission, to determine statistical limits on the gamma-ray fluxes of the ensemble of candidate sources. For a >300 MeV selection, the distribution of detection significance across the sample is consistent with that across control samples for significances <3 sigma, but has a tail extending to higher values, including three >4 sigma signals which are not associated with previously identified gamma-ray emission. Modelling of the data in these fields results in the detection of four non-2FGL Fermi sources, though none appear to be unambiguously associated with the BCG candidate. A search at energies >3 GeV hints at emission from the BCG in A 2055, which hosts a BL Lac object. There is no evidence for a signal in the stacked data, and the upper limit derived on the gamma-ray flux of an average radio-bright BCG in the sample is an order-of-magnitude more constraining than that calculated for individual objects. F(1 GeV)/F(1.4 GHz) <15, compared with ~120 for NGC 1275 in Perseus, which might indicate a special case for those objects detected at high energies; that beamed emission from member galaxies comprise the dominant bright gamma-ray sources in clusters.
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