deletions | additions       diff --git a/quenching_time.tex b/quenching_time.tex  index efb83bb..e4ffe7d 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} 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.,][]{Weisz2014b, \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.  That said, the 100\% quiescent fraction for satellites at this $\mstar$ means that if both processes are responsible, both are highly efficient. 
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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 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.  This mass trend is broadly consistent the results of \citep{Weisz2015} that more massive dwarf galaxies in the LG quenched more recently.  We next compare these statistically based quenching timescales to infall timescales directly measured for satellites of the MW.  The 3-D orbital velocity measured for the LMC/SMC strongly suggests that they are on their first infall and passed inside $\rvir$ of the MW $\approx2\gyr$ ago \citep{Kallivayalil2013}. 
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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 $\mstar$.