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[Abridged] We present an analysis of optical spectroscopically-identified AGNto M*+1 in a sample of 6 self-similar SDSS galaxy clusters at z=0.07. Theseclusters are specifically selected to lack significant substructure at brightlimits in their central regions so that we are largely able to eliminate thelocal action of merging clusters on the frequency of AGN. We demonstrate thatthe AGN fraction increases significantly from the cluster centre to 1.5Rvirial,but tails off at larger radii. If only comparing the cluster core region toregions at ~2Rvirial, no significant variation would be found. We compute theAGN fraction by mass and show that massive galaxies (log(stellar mass)>10.7)are host to a systematically higher fraction of AGN than lower mass galaxies atall radii from the cluster centre. We attribute this deficit of AGN in thecluster centre to the changing mix of galaxy types with radius. We use the WHANdiagnostic to separate weak AGN from `retired' galaxies in which the mainionization mechanism comes from old stellar populations. These retired AGN arefound at all radii, while the mass effect is much more pronounced: we find thatmassive galaxies are more likely to be in the retired class. Further, we showthat our AGN have no special position inside galaxy clusters - they are neitherpreferentially located in the infall regions, nor situated at local maxima ofgalaxy density. However, we find that the most powerful AGN (with [OIII]equivalent widths <-10Ang) reside at significant velocity offsets in thecluster, and this brings our analysis into agreement with previous work onX-ray selected AGN. Our results suggest that if interactions with othergalaxies are responsible for triggering AGN activity, the time-lag betweentrigger and AGN enhancement must be sufficiently long to obfuscate theencounter site and wipe out the local galaxy density signal.

The drivers of AGN activity in galaxy clusters: AGN fraction as a function of mass and environment