deletions | additions       diff --git a/quenching_time.tex b/quenching_time.tex  index 8a60f4b..d278113 100644  --- a/quenching_time.tex  +++ b/quenching_time.tex 
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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} $\mstar<10^9\msun$  galaxies at $z\approx0$with $\mstar<10^9\msun$  that are quiescent (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, 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. 
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Altogether, Figure~\ref{fig:quench_times} indicates a complex dependence of the environmental quenching timescale on satellite $\mstar$.  Specifically, the typical timescale for 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 $>9.5\gyr$ 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 continues to decline with increasing $\mstar$.