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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 (see Introduction), our model assumes that all
satellites satellite dwarfs were actively star-forming prior to first infall.
Because However, because many 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.
The At $\mstar(z=0)=10^{4-5}\msun$, satellites' star-formation histories
for satellites at $\mstar(z=0)=10^{4-5}\msun$ 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
be driven by arise 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.
Furthermore, if satellites that were quenched by reionization have a similar infall-time distribution as those that were quenched by the host-halo environment, our modeling approach remains valid.
...
Within each 1-dex bin of $\mstar$, we use the ELVIS simulations to compute the distribution of infall times that satellites at $z=0$ 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 infall time
correlates with host-centric distance \citep[e.g.,][]{Wetzel2015}. \textbf{XXX what about Rocha et al.? AW - they did not look at the correlation of infall time with distance, but rather as a function of orbital energy, unless there is something else that you had in mind.}
However, this correlation means that we
should must account for observed satellite's distances, including incompleteness
at large distance 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 in each $\mstar$ bin.
While this matters for the fainter satellites,
we find that it is most important
for the highest masses, $\mstar=10^{8-9}$, at
which $\mstar=10^{8-9}$, because all
known such satellites (M32, NGC 205, LMC/SMC)
lie within reside $<61\kpc$
of from the MW or M31.
Figure~\ref{fig:quench_times} shows the inferred environmental quenching timescales, that is, the time duration from first infall to being fully quenched/gas-poor, as a function of $\mstar$.
Blue circles show the satellite dwarf galaxies in the MW and M31, and we shade the lowest $\mstar$ bin lighter to highlight caution in
interpretation, interpretation because of reionization, as explained above.
Error bars are We derived
error bars from the 68\% uncertainty in the observed quiescent fractions in
Figure~\ref{fig:quiescent_fraction}, which Figure~\ref{fig:quiescent_fraction}; these uncertainties are typically larger than the host-to-host scatter in satellites' infall times in ELVIS.
As explored in \citet{Wetzel2015}, many
satellite dwarf galaxies satellites 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 16\% of the
distribution (error bars). 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 less than $1.5\gyr$ 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 there, quiescent, which implies that quenching must be
nearly instantaneous to eliminate all star-forming satellites.
%(modulo uncertainty from the limited number of observed satellites). extremely rapid after infall.
We can compare these statistically based quenching timescales to infall times directly measured for satellites of the MW.
The 3-D orbital velocity measured for the LMC/SMC strongly
suggest suggests that they are experiencing their first infall and passed
within inside $\rvir$ of the MW $\approx2\gyr$ ago \citep{Kallivayalil2013}.
Given that both remain 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 timescale (gray triangle), which is consistent with
the timescales at $\mstar=10^{8-9}\msun$ from our statistical
approach. timescales at $\mstar=10^{8-9}\msun$.
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 star-formation history indicates that it quenched $\approx1\gyr$
ago (coincident with its pericentric passage at $\approx90\kpc$), ago, implying
an environmental a quenching timescale of $\approx1.3\gyr$ \citep{Sohn2013}, again
fully consistent with our results.
Also interesting is to %(coincident with its pericentric passage at $\approx90\kpc$)
We also compare these timescales for
dwarf galaxies at satellites with $\mstar\lesssim10^9\msun$ within the MW/M31 halos with previous studies of more massive satellites within other host halos.
The red squares in Figure~\ref{fig:quench_times} show the timescales from \citet{Wheeler2014}, who used nearly identical
methodology based on methodology, combining the the galaxy catalog from \citet{Geha2012} with satellite infall times (including group preprocessing) from the Millennium II simulation
(REF). \citep{BoylanKolchin2009}
They examined satellites with $\mstar\approx10^{8.5}$ and $10^{9.5}\msun$ around hosts with $\mstar>2.5\times10^{10}\msun$, which they found likely spans
halos with $\mvir\approx10^{12.5-14}\msun$.
%$8.25<\log(\mstar/\msun)<8.75$ and $9.25<\log(\mstar/\msun)<9.65$
%\citet{Wheeler2014} defined the infall time of a satellite as the first time that it became a satellite, so their definition include group preprocessing, with the caveat that if a satellite orbits beyond its host, as defined by the FoF group, becoming a backsplash/ejected satellite, and then falls back into a host again, they include only the latter infall time.
This is significantly These are much higher
masses than the MW/M31, which could mean that
their the quenching timescales
in \citet{Wheeler2014} are \emph{shorter} than for similar mass satellites of MW/M31-like hosts.
Similarly, the green curves in Figure~\ref{fig:quench_times} show the
quenching timescales for more massive satellites from \citet{Wetzel2013}, who also used identical methodology, combining galaxy groups from SDSS \citep{Tinker2011, Wetzel2012} with satellite infall times (including group preprocessing)
from measured in mock group catalogs in their cosmological simulation.
We show their result for groups with $\mvir=10^{12-13}\msun$, which are most similar to MW/M31 masses.
Summarize overlapping mass ranges and overall trends...
