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Galaxy mass and environment are known to play a key role in galaxy evolution:looking at galaxy colors at different redshifts, fixed galaxy mass andenvironment, offers a powerful diagnosis to disentangle the role of each. Inthis work, we study the simulateneous dependence of the fraction of bluegalaxies fblue on secular evolution, environment and galaxy mass with awell-controlled cluster sample. We are thus able to study the evolution andrespective role of the cessation of star formation history (SFH) in clustersdue to galaxy mass ("mass quenching") or to environment ("environmentalquenching"). We define an homogenous X-ray selected cluster sample (25 clusterswith 0 < z < 1 and one cluster at z \sim 2.2), having similar masses andwell-defined sizes. Using multicolor photometry and a large spectroscopicsample to calibrate photometric redshifts, we carefully estimate fblue for eachcluster at different galaxy mass and cluster-centric distance bins. We then fitwith a simple model the dependence of fblue on redshift (z), environment(r/r200) and galaxy mass (M). fblue increases with cluster-centric distancewith a slope $1.2^{+0.4}_{-0.3}$, decreases with galaxy mass with a slope$-3.8^{+0.6}_{-0.5}$, and increases with redshift with a slope$3.2^{+0.7}_{-0.5}$. The data also require for the first time a differentialevolution with galaxy mass of fblue with redshift, with lower mass galaxiesevolving slower by a factor $-4.1^{+1.1}_{-0.9}$. Our study shows that theprocesses responsible for the cessation of star formation in clusters areeffective at all epochs (z<2.2), and more effective in denser environments andfor more massive galaxies. We found that the mass and environmental quenchingsare separable, that environmental quenching does not change with epoch, andthat mass quenching is a dynamical process, i.e. its evolutionary rate ismass-dependent. [Abridged]

Galaxy mass, cluster-centric distance and secular evolution: their role in the evolution of galaxies in clusters in the last 10 Gyr