deletions | additions       diff --git a/quenching_time.tex b/quenching_time.tex  index abf2c04..efae4a2 100644  --- a/quenching_time.tex  +++ b/quenching_time.tex 
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Though, the 100\% quiescent fraction for satellites at this $\mstar$ means that if both processes are responsible, both are highly efficient, and that if satellites that were quenched by reionization have a similar virial-infall time distribution as those that were quenched by the host-halo environment, it would not affect our results.  Thus, we include this $\mstar$ in our modeling but label it distinctly to emphasize caution in interpretation.    Within each 1-dex bin of $\mstar$, we use the ELVIS simulations to compute the distribution of virial-infall times that satellites at $z = 0$ $z=0$  experienced. Assuming that environmental quenching likelihood correlates with time since infall, we designate those that fell in earliest as having been quenched, and we adjust the time-since-infall threshold for quenching until we match the observed quiescent fraction in each bin.  Several works have shown that this model successfully describes the dependence of satellite quiescent fractions on host-centric distance \citep[e.g.,][]{Wetzel2013, Wetzel2014, Wheeler2014} because of the correlation of virial-infall time with host-centric distance \citep[e.g.,][]{Wetzel2015}. 
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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 16\% of the distribution (error bars).  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$ $\lt1.5\gyr$  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 satellites are quiescent there, which implies that quenching must be nearly instantaneous to eliminate all star-forming satellites.  %(modulo uncertainty from the limited number of observed satellites).