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\label{fig:quench_times}  Environmental quenching timescales of satellite galaxies across the observable range of stellar mass, $\mstar$ (top axis shows subhalo $\mpeak$ from abundance matching).  Blue circles showtimes for  satellites of the MW and M31, obtained by matching the observed quiescent fractions in Figure~\ref{fig:quiescent_fraction} to virial-infall times of satellites from the ELVIS simulations \citep{Wetzel2015} in 1-dex bins of $\mstar$. At $\mstar=10^{4-5}\msun$ (light blue), some satellite may have been quenched prior to infall via reionization, so interpret with care.  Error bars are derived from the 68\% uncertainty in the observed quiescent fractions in Figure~\ref{fig:quiescent_fraction}.  Left panel uses time since first infall into the current MW/M31-like halos, MW/M31 halo,  while right panel uses time since first infall into \emph{any} host halo, including possible effects of group preprocessing.At $\mstar=10^{4-5}\msun$ (light blue), some satellite may have been quenched prior to infall via reionization, so interpret their quenching timescale with care.  Gray triangle shows lower limit for the LMC/SMC system using its  infall time from its measured proper motion \citep{Kallivayalil2013}. Red squares showtimescale inferred for  satellites with $\mstar=10^{8.5}$, $10^{9.5}\msun$ in SDSS \citep{Wheeler2014}, and green curve showstimescales inferred for  more massive satellites in groups of $\mvir=10^{12-13}$ in SDSS \citep{Wetzel2013}. The satellite dwarfs of the MW/M31 halos  quenched much more rapidly after infall than more massive satellites in other hosts, with the timescale being longest near Magellanic-Cloud-mass satellites. Magellanic-Cloud-masses.