Left: the dependence of the satellite quenching time-scale (τ_quench) and gas depletion time-scale (τ_depl) on satellite stellar mass at M_⋆ ≳ 10⁸ M_⊙. The magenta, gold, and cyan coloured bands show the constraints for satellites in different mass host haloes derived from analysis of galaxy groups and clusters in the SDSS by Wetzel et al. (2013). The black square gives the typical quenching time-scale for lower mass satellites (∼10^8.5–10^9.5 M_⊙) from Wheeler et al. (2014). The solid and dashed black lines show the mass dependence of the gas depletion time-scale (H₂ + H i) derived from combining the observed gas fractions of Boselli et al. (2014) with the SFR–stellar mass relation of Salim et al. (2007) and Speagle et al. (2014), respectively. The solid blue and solid green lines give the corresponding predictions from the hydrodynamical and semi-empirical models of Davé, Oppenheimer & Finlator (2011) and Popping, Behroozi & Peeples (2015), respectively. The inferred satellite quenching time-scales at ≳ 10⁸ M_⊙ show broad agreement with the observed gas depletion time-scales for field systems, suggesting that starvation is the main driver of satellite quenching at these masses. Right: the dependence of the satellite quenching time-scale on satellite stellar mass at 10⁶ < M_⋆/M_⊙ < 10¹¹, including the estimates of τ_quench from Fig. 5. The light grey shaded regions highlight the expected dominant quenching mechanism and projected mass dependence of τ_quench, while the vertical hashed grey region demarcates the critical mass scale below which a more efficient physical process (e.g. ram-pressure stripping) drives relatively rapid quenching in the Local Group. At high masses (≳ 10⁸ M_⊙), satellite quenching is consistent with being driven by starvation; below ∼10⁸ M_⊙, however, we posit that ram-pressure stripping becomes increasingly effective, such that depletion (and thus quenching) time-scales are significantly shorter.