deletions | additions       diff --git a/quenching_time.tex b/quenching_time.tex  index 3cab6eb..bee605d 100644  --- a/quenching_time.tex  +++ b/quenching_time.tex 
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While this matters for the fainter satellites, we find that it is most important at $\mstar=10^{8-9}$, because all such satellites (M32, NGC 205, LMC/SMC) reside $<61\kpc$ from the MW or M31.  Figure~\ref{fig:quench_times} shows the inferred environmental quenching timescales, that is, the time duration from first infall to being fully quenched/gas-poor, as a function of $\mstar$.  Blue circles show the satellitedwarf  galaxies in the MW and M31, and we shade the lowest $\mstar$ bin lighter to highlight caution in interpretation because of reionization, as explained above. We derived error bars from the 68\% uncertainty in the observed quiescent fractions in Figure~\ref{fig:quiescent_fraction}; these uncertainties are typically larger than the host-to-host scatter in satellites' infall times in ELVIS.  As explored in \citet{Wetzel2015}, many satellites first fell into a another host halo (group), typically of $\mvir=10^{10-12}\msun$, before falling into the MW/M31 halo.