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\section{Introduction}
Galaxies in denser environments are more likely to have suppressed (quiescent) star formation and little-to-no cold gas than galaxies of similar stellar mass, $\mstar$, in less dense environments.
The observed environmental effects
in within the Local Group
(LG), specifically (LG) on the satellite galaxies within the halos of the Milky Way (MW) and Andromeda
(M31), (M31) are particularly strong
\citep[e.g.,][]{Einasto1974,Mateo1998,McConnachie2012,Phillips2014,SlaterBell2014,Spekkens2014}, \citep[e.g.,][]{Einasto1974, Mateo1998, McConnachie2012, Phillips2014, SlaterBell2014, Spekkens2014}, even compared to the
already strong effects on (more massive) satellites within massive groups/clusters.
Specifically, the dwarf galaxies around the MW/M31 show a strikingly sharp and nearly complete transition in their properties within $\approx 300 \kpc$ (approximately the virial radius, $\rvir$, of the MW or M31),
transitioning from
(1) having irregular to spheroidal morphologies,
(2) from having most of their baryonic mass in cold atomic gas to having little-to-no measured cold gas, and
(3) being from actively star-forming to quiescent.
This trend has just a few exceptions: 4 gas-rich, star-forming galaxies persist within the halos of the MW (the LMC and SMC) and M31 (LGS 3 and IC 10), and 3 - 4 quiescent, gas-poor galaxies reside beyond $\rvir$ of the MW (Cetus and Tucana) and M31 (KKR 25 and possibly Andromeda XVIII), though Cetus and Tucana likely orbited within the MW halo \citep{Lewis2007, Fraternali2009, Teyssier2012}.
This efficient satellite quenching is particularly striking because, other than KKR 25, at $\mstar<10^9\msun$ \emph{all} known galaxies that are sufficiently isolated ($>1500\kpc$ from a more massive galaxy) are star-forming \citep{Geha2012, Phillips2014}.
Thus, the MW and M31 halos exert the strongest environmental influence on their satellites of any known systems, so the LG is
the most a compelling laboratory for studying environmental processes on galaxies.
Several
environmental such processes within a host halo can regulate the gas content, star formation, morphology, and eventual disruption of satellite galaxies, including gravitational tidal forces \citep[e.g.,][]{Dekel2003}, galaxy-galaxy interactions \citep[e.g.,][]{FaroukiShapiro1981} and mergers \citep[e.g.,][]{Deason2014a}, ram-pressure stripping of extended gas \citep[e.g.,][]{Larson1980, McCarthy2008} or of cold inter-stellar medium \citep[e.g.,][]{GunnGott1972, Tonnesen2009}, some of which may be assisted by stellar feedback within the satellite \citep[e.g.,][]{BaheMcCarthy2015}.
%tidal shocking and resonant interactions with the host \citep[e.g.,][]{Mayer2001,DOnghia2010},
The key astrophysical challenge is understanding the relative importance of these processes, including which (if any) dominate, and how they
might vary across both satellite and host
mass scales. masses.
One strong constraint for understanding
their the relative effects
of environmental processes is
in determining the timescale over which environmental quenching occurs,
including its dependence on the mass of both the satellites and the host, as previous works have explored at higher masses \citep[e.g.,][]{Balogh2000, Wetzel2013, Hirschmann2014, Wheeler2014}.
However, while some previous worked examined Some works have shown that the
relative efficiency of satellite environmental quenching
\emph{efficiency} for the satellite dwarf galaxies in the LG
\citep{Phillips2014,SlaterBell2014}, none have constrained the timescales over which environment acts to remove gas and quench star formation in is higher than than for more massive satellites in
massive groups/clusters \citep{Phillips2014, SlaterBell2014}, but no works yet have constrained the
LG. quenching \emph{timescales} at these masses.
In this letter, we combine the observed quiescent fractions for satellites in the LG with the typical infall times of such satellites from cosmological
simulations, as explored in \citet{Wetzel2015}, simulations to infer the
environmental quenching timescales
of over which environmental processes remove gas and quench star formation in the current satellite galaxies in the MW/M31 halos.
Motivated by the results of \citet{Wetzel2015}, we also consider the possible impact of group preprocessing on satellites before they fell into the MW/M31 halo.
