deletions | additions       diff --git a/quenching_time.tex b/quenching_time.tex  index 70a5a33..efb83bb 100644  --- a/quenching_time.tex  +++ b/quenching_time.tex 
...
We now translate the quiescent fractions in Figure~\ref{fig:quiescent_fraction} into the typical timescales over which environmental processes quench satellites after they fall into a host halo, following the methodology of \citet{Wetzel2013}.  First, motivated by the dearth of \emph{isolated} galaxies with $\mstar<10^9\msun$ that are quiescent at $z\approx0$ (see Introduction), our model assumes that all satellites with $\mstar(z=0)<10^9\msun$ were actively star-forming prior to first infall.  However, because most galaxies with $\mstar(z=0)<10^4\msun$ may have been quenched at high redshift by cosmic reionization \citep[e.g.,][]{Weisz2014a, \citep[e.g.,][]{Weisz2014b,  Brown2014}, we do not model those masses. At $\mstar(z=0)=10^{4-5}\msun$, satellites' star-formation histories show a mix of complete quenching by $z\gtrsim3$ (e.g., Bootes I, Leo IV) and signs of star formation at $z\lesssim1$ (e.g., And XI, And XII, And XVI) \citep{Weisz2014a, Weisz2014c, Brown2014}, so quenching at these masses may come from a mix of reionization and the host-halo environment.  %Leo T had recent star formation, suggesting that galaxies at least down to logM_star ~ 5 can form stars today if not for environment.  That said, the 100\% quiescent fraction for satellites at this $\mstar$ means that if both processes are responsible, both are highly efficient. 
...
%Thus, the left panel of Figure~\ref{fig:quench_times} uses time since infall into the MW/M31 halos, ignoring group preprocessing, while the right panel uses time since infall into \emph{any} host halo, including group preprocessing.  The latter results in longer quenching timescales, though it primarily shifts the upper 16\% of the distribution.  Both panels show shorter median quenching timescales for less massive satellites: $\sim5\gyr$ at $\mstar=10^{8-9}\msun$, $2-3\gyr$ at $\mstar=10^{7-8}\msun$, and $<1.5\gyr$ replace_contentlt;1.5\gyr$  at $\mstar<10^7\msun$, depending on the inclusion of group preprocessing. Moreover, the median timescale for two of the lowest $\mstar$ bins is $0\gyr$ because 100\% of those satellites are quiescent, which implies extremely rapid quenching after infall.  We next compare these statistically based quenching timescales to infall timescales directly measured for satellites of the MW. 
...
Altogether, Figure~\ref{fig:quench_times} indicates a complex dependence of the environmental quenching timescale on satellite $\mstar$.  The typical timescale for the low-mass satellites in the MW/M31 halos increases with $\mstar$, from $\lesssim1\gyr$ at $\mstar<10^7\msun$ to $\sim5\gyr$ at $\mstar\approx10^{8.5}\msun$.  \citet{Wheeler2014} indicate that this mass dependence continues, though with a rapid increase ($\sim2\times$) to $\approx9.5\gyr$, and no change from $\mstar\approx10^{8.5}$ to $10^{9.5}\msun$.  This rapid increase implies some tension with our results based on the two quiescent satellites of M31, NGC 205 and M32 ($\mstar\approx10^{8.5}\msun$), unless both experienced unusually early infall $> replace_contentgt;  9.5\gyr$ ago or M31 quenched its satellites much more rapidly than the (more massive) hosts in \citet{Wheeler2014}. %(\citeauthor{Wheeler2014}'s results are consistent with the star-forming LMC/SMC of the MW.)  At higher $\mstar$, \citet{Wetzel2013} indicate that the quenching timescale rapidly \emph{decreases} by $5\times10^9\msun$, and it continues to decline with increasing $\mstar$.