The dependence of the satellite quenching time-scale (τ_quench) on satellite stellar mass at M_⋆ ∼ 10⁶–10¹¹ M_⊙. The inset legend lists the typical host halo mass for each data set. 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 denotes the typical quenching time-scale for slightly lower mass satellites (∼10⁹ M_⊙) from Wheeler et al. (2014), with the horizontal error bars denoting the 25–75 per cent range in stellar mass probed by that work and the vertical error bars giving the variation in τ_quench corresponding to satellite quenched fractions of 25–55 per cent (as derived from analysis of subhalo populations in ELVIS, see Section 5). Our estimate for the low-mass satellite quenching time-scale in the Local Group is given by the black circles (τ_quench ∼ 1.4 Gyr, see Section 4.1), where our sample of subhaloes is divided into two stellar mass bins of 10⁶–10⁷ and 10⁷–10⁸ M_⊙. Each point gives the quenching time-scale for subhaloes in that mass bin assuming a satellite quenched fraction of 90 per cent, while the vertical error bars illustrate the variation in τ_quench corresponding to satellite quenched fractions of 80–100 per cent. Our results are largely independent of mass, with increased scatter at higher masses due to the smaller number (and thus increased stochasticity in the infall times) of massive subhaloes. The horizontal error bars show the quartiles of the subhalo mass distribution within each bin. At high masses, the quenching time-scale increases with decreasing stellar mass. Below M_⋆ ∼ 10⁸ M_⊙, we find that satellite quenching becomes dramatically more efficient, suggesting a likely change in the physical mechanisms at play.