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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), from irregular to spheroidal morphologies, from having most of their baryonic mass in cold atomic gas to having little-to-no measured cold gas, and 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 4 - 5 quiescent, gas-poor galaxies reside well beyond $\rvir$ of either the MW or M31: Cetus \citep{Lewis2007}, Tucana \citep{Fraternali2009}, KKR 25 \citep{Makarov2012}, KKs 3 \citep{Karachentsev2015}, and possibly Andromeda XVIII, though Cetus and Tucana may have orbited within the MW halo \citep{Teyssier2012}.
This efficient satellite quenching is particularly striking because, other than KKR 25 and KKs 3, at $\mstar<10^9\msun$ 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 show the
strongest stongest signal of environmental influence
on over their satellites of any known systems,
so and the LG is a compelling laboratory for studying environmental processes on galaxies.
Several 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},
...
One strong constraint for understanding the relative effects of environmental processes is determining the timescale over which environmental quenching occurs, as previous works have explored at higher masses \citep[e.g.,][]{Balogh2000, Wetzel2013, Hirschmann2014, Wheeler2014}.
Some works have shown that the environmental quenching \emph{efficiency} for the satellite dwarf galaxies in the LG is higher than than for more massive satellites in massive groups/clusters \citep{Phillips2014, SlaterBell2014}, but no works yet have constrained the 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 simulatilons to infer the timescales 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 halos.