  We investigate the effect of ram-pressure from the intracluster medium on the
stripping of HI gas in galaxies in a massive, relaxed, X-ray bright, galaxy
cluster at z=0.2 from the Blind Ultra Deep HI Environmental Survey (BUDHIES).
We use cosmological simulations, and velocity vs. position phase-space diagrams
to infer the orbital histories of the cluster galaxies. In particular, we embed
a simple analytical description of ram-pressure stripping in the simulations to
identify the regions in phase-space where galaxies are more likely to have been
sufficiently stripped of their HI gas to fall below the detection limit of our
survey. We find a striking agreement between the model predictions and the
observed location of HI-detected and non-detected blue (late-type) galaxies in
phase-space, strongly implying that ram-pressure plays a key role in the gas
removal from galaxies, and that this can happen during their first infall into
the cluster. However, we also find a significant number of gas-poor, red
(early-type) galaxies in the infall region of the cluster that cannot easily be
explained with our model of ram-pressure stripping alone. We discuss different
possible additional mechanisms that could be at play, including the
pre-processing of galaxies in their previous environment. Our results are
strengthened by the distribution of galaxy colours (optical and UV) in
phase-space, that suggests that after a (gas-rich) field galaxy falls into the
cluster, it will lose its gas via ram-pressure stripping, and as it settles
into the cluster, its star formation will decay until it is completely
quenched. Finally, this work demonstrates the utility of phase-space diagrams
to analyze the physical processes driving the evolution of cluster galaxies, in
particular HI gas stripping.
