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tokens: host halo mass, and the green valley transition time-scale, τ Green , for both disc and elliptical RS satellite galaxies. We select all = 0 RS satellite galaxies that, at the time the galaxy became green ( t Green ), were also satellites (corresponding to of the satellite sample), and calculate the ratio between the satellite galaxy’s stellar mass and the host halo mass, log 10 M * / M 200 , at t Green . Throughout this section host halo mass refers to the halo mass 1 of the central galaxy within which the satellite galaxies are embedded. Fig. 7 shows the green valley transition time-scale, τ Green , as a function of log 10 M * / M 200 at t Green for RS satellite galaxies that are discs (blue dots) and ellipticals (red dots) at = 0. It can be seen that for both disc and elliptical satellite galaxies, τ Green tends to increase with M * / M 200 . This is highlighted by the best-fitting linear regression of the τ Green −log 10 M * / M 200 relation for elliptical (red dashed line) and disc (blue solid line) satellite galaxies. We find that τ Green correlates more strongly with M 200 than with M * , so that satellite galaxies embedded in cluster-sized haloes transition the green valley faster than their same-stellar mass satellite counterparts residing in lower mass haloes. Figure 7. Green valley transition time-scale, τ Green , of satellite galaxies as a function of the ratio between stellar mass and host halo mass, log 10 M * / M 200 , at the time when the galaxy left the blue cloud, t Green . The data points with error bars show the median τ Green values in bins of log 10 M * / M 200 for galaxies that have been satellites since t Green and at = 0 have κ co ≥ 0.4 (shown as blue dots) or κ co 0.4 (shown as red dots). The error bars correspond to the 25th−75th percentiles of the τ Green distribution in each mass bin. The lines correspond to the best-fitting linear regressions. The red satellite galaxies tend to have quenched more rapidly if they are elliptical and if their stellar mass is smaller relative to the total mass of their host halo. This relation is mostly driven by a dependence on halo mass, rather than on stellar mass. Fig. 7 shows that satellite galaxies embedded in clusters (log 10 M * / M 200 − 4 with haloes more massive than ) tend to cross the green valley over shorter time-scales than satellite galaxies residing in lower mass haloes, regardless of the galaxy’s morphological type. However, the spread in the τ Green distribution is large. In the case of central galaxies, although most of them reside in cluster-sized haloes, we do not find any correlation between τ Green and halo mass or M * / M 200 . This is in agreement with previous studies that suggest that environmental quenching is mostly associated with satellite galaxies rather than centrals (e.g. Peng et al. 2010 ; Darvish et al. 2016 ). Central galaxies show properties that are more associated with the galaxies’ stellar mass (i.e. on average more massive galaxies are