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Ongoing or recent star formation in galaxies is known to increase with increasing projected distance from the centre of a cluster out to several times its virial radius ( R  v ). Using a complete sample ( M  r ≤−20.5, 0.02 ≤ z ≤ 0.15) of galaxies in and around 268 clusters from the Sloan Digital Sky Survey's Fourth Data Release, we investigate how, at a given projected radius from the cluster centre, the stellar mass and star formation properties of a galaxy depend on its absolute line‐of‐sight velocity in the cluster rest frame, | v  LOS |. We find that for projected radii  R  &lt; 0.5  R  v , the fraction of high‐mass non‐brightest cluster galaxies increases towards the centre for low | v  LOS |, which may be the consequence of the faster orbital decay of massive galaxies by dynamical friction. At a given projected radius, the fraction of Galaxies with Ongoing or Recent (&lt;1–3 Gyr) Efficient Star Formation [GORES; with EW(Hδ) &gt; 2 Å &amp;  D n  4000 &gt; 1.5] is slightly but significantly lower for low | v  LOS | galaxies than for their high‐velocity counterparts. We study these observational trends with the help of a dark matter (DM) cosmological simulation. We classify DM particles as virial, infall and backsplash according to their present positions in ( r ,  v  r ) radial phase space and measure the frequencies of each class in cells of ( R , | v  LOS |) projected phase space. As expected, the virial class dominates at projected radii  R  &lt;  R  v , while the infall particles dominate outside, especially at high | v  LOS |. However, the backsplash particles account for at least one‐third (half) of all particles at projected radii slightly greater than the virial radius and | v  LOS | &lt; σ v  (| v  LOS | ≪σ v ). The deprojection of the GORES fraction leads to a saturated linear increase with radius. We fit simple models of the fraction of GORES as a function of class only or class and distance to the cluster centre (as in our deprojected fraction). While GORES account for 18 ± 1 per cent of all galaxies within the virial cylinder, in our best‐fitting model, they account for 13 ± 1 per cent of galaxies within the virial sphere, 11 ± 1 per cent of the virial population, 34 ± 1 per cent of the distant (for projected radii  R  &lt; 2  R  v ) infall population and 19 ± 4 per cent of the backsplash galaxies. Also, 44 ± 2 per cent of the GORES within the virial cylinder are outside the virial sphere. These fractions are very robust to the precise good‐fitting model and to our scheme for assigning simulation particle classes according to their positions in radial phase space (except for two of our models, where the fraction of GORES reaches 27 ± 4 per cent). Given the 1–3 Gyr lookback time of our GORES indicators, these results suggest that star formation in a galaxy is almost completely quenched in a single passage through the cluster.

The velocity modulation of galaxy properties in and near clusters: quantifying the decrease in star formation in backsplash galaxies