deletions | additions       diff --git a/quenching_time.tex b/quenching_time.tex  index 6614c38..b915484 100644  --- a/quenching_time.tex  +++ b/quenching_time.tex 
...
As explored in \citet{Wetzel2015}, many satellite dwarf galaxies first fell into a another host halo (group), typically of $\mvir=10^{10-12}\msun$, before falling into the MW/M31 halo.  Because the importance this environmental preprocessing in such lower-mass groups remains unclear, we present the inferred environmental quenching timescales both including and neglecting such group preprocessing.  Thus, the left panel of Figure~\ref{fig:quench_times} uses time since infall into the MW/M31 halo, ignoring group preprocessing, while the right panel uses time since infall into \emph{any} host halo, including group preprocessing.  The latter necessarily results in longer quenching timescales, though it primarily shifts the upper 68\% 16\%  of the distribution. Both panels suggests shorter quenching timescales for less massive satellite dwarfs: $\sim5\gyr$ at $\mstar=10^{8-9}\msun$, $2-3\gyr$ at $\mstar=10^{7-8}\msun$, and $<1.5\gyr$ at $\mstar<10^7\msun$, depending on the importance of group preprocessing.  Moreover, the median timescale for two of the lowest $\mstar$ bins is $0\gyr$ because of the 100\% quiescent fractions there, which implies that quenching must be extremely rapid to eliminate all star-forming satellites (modulo uncertainty from the limited number of observed satellites).