deletions | additions       diff --git a/quenching_time.tex b/quenching_time.tex  index bfffd3f..3ce2128 100644  --- a/quenching_time.tex  +++ b/quenching_time.tex 
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\subsection{Inferred Environmental Quenching Timescales for Satellites}  Our goal is to translate the quiescent fractions in Figure~\ref{fig:quiescent_fraction} into the typical timescales that over which  satellites are quenched after first  falling into a more massive host halo, and we follow the methodology of \citet{Wetzel2013}, used also in \citet{Wheeler2014}. First, motivated by the dearth of isolated dwarf galaxies that are quiescent (see above), our models assumes that all satellite dwarf galaxies were actively star-forming prior to first virial infall.  Because ultra-faint dwarfs at $\mstar<10^4\msun$ likely quenched at via cosmic reionization \citep[e.g.,][]{Weisz2014a,Brown2014}, we do not model that mass scale. 
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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}.  However, this correlation means that we should account for observed satellite's distances, including incompleteness for fainter satellites, in computing their infall times.  Thus, in selecting satellites in ELVIS, we only use those out to the maximum host-centric distance that they are observed from the MW or M31 at each $\mstar$ bin.  While this obviously matters for the faintest satellites, it in fact matters most at our highest masses, $\mstar=10^{8-9}$, at which all known  satellites (M32, NGC 205, LMC/SMC) are $<61\kpc$ from lie within $61\kpc$ of  the MW or M31.Including all satellites in ELVIS within $\rvir$, regardless of distance, would bias to more recent infall times \citep{Wetzel2015} and thus would lead us to infer more rapid environmental quenching timescales.  Figure~\ref{fig:quench_times} shows the inferred environmental quenching timescales, that is, the timescale from first virial infall to becoming fully quenched/gas-poor, as a function of $\mstar$.  Blue circles show these results for the satellite dwarf galaxies in the MW and M31, and we shade the lowest $\mstar$ bin lighter to highlight caution in interpretation, as explained above.  Error bars are derived from the 68\% uncertainty in the observed quiescent fractions in Figure~\ref{fig:quiescent_fraction}, which are typically larger than the host-to-host scatter in satellites' virial-infall times in ELVIS.  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\% 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).  We can compare these quenching timescales, based on statistical satellite infall times via cosmological simulations, to the infall times directly measured for satellites in the MW.  In particular, the 3-D orbital velocity measured for the LMC/SMC strongly suggest that they are experiencing their first infall and first passed within $\rvir$ of the MW $\approx2\gyr$ ago \citep{Kallivayalil2013}.  Given that both are still star-forming, this places a firm lower limit to their quenching timescale, as the gray triangle in Figure~\ref{fig:quench_times} shows.  This limit is fully consistent with the timescales at $\mstar=10^{8-9}\msun$ from our statistical approach.  Similarly, the 3-D orbital velocity measured for Leo I ($\mstar=5.5\times10^6\msun$) indicates that it fell into the MW halo $\approx2.3\gyr$ ago, and its measured SFH indicates that it quenched $\approx1\gyr$ ago (coincident with its pericentric passage at $\approx90\kpc$), implying an environmental quenching timescale of $\approx1.3\gyr$ \citep{Sohn2013}, again fully consistent with Figure~\ref{fig:quench_times}.  The timescale from \citet{Wheeler2014} is based on combining the the galaxy catalog from \citet{Geha2012} with satellite virial-infall times in the Millennium II simulation.  In particular, \citet{Wheeler2014} used a subset of satellites from \citet{Geha2012} at $8.25 < log(\mstar/\msun) < 8.75$ and $9.25 < log(\mstar/\msun) < 9.65$.