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\subsection{Inferred Environmental Quenching Timescales for Satellites}
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
isolated dwarf \emph{isolated} galaxies
with $\mstar<10^9\msun$ that are quiescent (see Introduction), our model assumes that all
satellite dwarf galaxies satellites were actively star-forming prior to first infall.
Because many galaxies
with $\mstar(z=0)<10^4\msun$ may
be have been quenched at high redshift
due to by cosmic reionization \citep[e.g.,][]{Weisz2014a,Brown2014}, we do not model those masses.
Star-formation The star-formation histories for satellites at $\mstar(z=0)=10^{4-5}\msun$ show a mix of
them having completely quenched complete quenching by $z\gtrsim3$ (e.g., Bootes I, Leo IV) and
showing 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 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.
Though, That said, the 100\% quiescent fraction for satellites at this $\mstar$ means that if both processes are responsible, both are highly
efficient, and that efficient.
Furthermore, if satellites that were quenched by reionization have a similar
infall time infall-time distribution as those that were quenched by the host-halo environment,
it would not affect our
results. modeling approach remains valid.
Thus, we include this $\mstar$ in our
modeling results 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 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.
