We find, using cosmological simulations of galaxy clusters, that the hot X-ray emitting intra-cluster medium (ICM) enclosed within the outer accretion shock extends out to $R_{\rm shock}\sim(2 - 3) R_{\rm vir}$, where $R_{\rm vir}$ is the standard virial radius of the halo. Using a simple analytic model for satellite galaxies in the cluster, we evaluate the effect of ram pressure stripping on the gas in the inner discs and in the haloes at different distances from the cluster centre. We find that significant removal of star-forming disc gas occurs only at $r \lesssim 0.5 R_{\rm vir}$, while gas removal from the satellite halo is more effective and can occur when the satellite is found between $ R_{\rm vir}$ and $R_{\rm shock}$. Removal of halo gas sets the stage for quenching of the star formation by starvation over $2\textrm{--}3\,\mathrm{Gyr}$, prior to the satellite entry to the inner cluster halo. This scenario explains the presence of quenched galaxies, preferentially discs, at the outskirts of galaxy clusters, and the delayed quenching of satellites compared to central galaxies.

Accepted to MNRAS, 22 December 2017