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\section{Discussion}  The dependence of quenching time with satellite mass at $\mstar\gtrsim10^9\msun$ may arise because of We conclude by briefly discussing  the intrinsic complex  dependence of gas fraction satellite quenching timescales  on galaxy mass, such that more massive satellites have less gas when they fall $\mstar$ from Figure~\ref{fig:quench_times}  inand thus exhaust it more quickly.  Conversely, at $\mstar<10^9\msun$, almost all isolated galaxies have enough gas to fuel star formation for a Hubble time, so  the trend there arises below lower-mass dwarfs have increasingly shallower potential wells, making context of  the combination underlying physics  ofinternal feedback plus  environmental stripping more efficient at lower masses.  So, LMC mass scales represent the transition between these effects.  In other words, there appears to be no quenching mechanism (either internal or external) that operates efficiently for LMC/SMC-mass galaxies.  They are too small for stellar feedback or AGN, but too big (potential too deep) for reionization, gravitational stripping, or ram pressure to remove ISM, and they have too much ISM for strangulation to operate.  See also \citet{Weisz2015}. quenching.  This trend with $\mstar$ At $\mstar\gtrsim10^9\msun$, the long quenching timescales suggests quenching driven by gas depletion  inFigure~\ref{fig:quench_times} resembles  the trend with galaxy $\mstar/\mvir$ (Tollerud et al. 2011a Fig 11 (right panel, Behroozi et al.), which peaks at somewhat higher but similar mass because that's where all absence of cosmic accretion after infall (``strangulation''), caused by gravitational tidal stripping and/or ram-pressure stripping of  the star formation has just happened/is happening.  At extended gas around  the high-mass end, satellite.  Furthermore, this scenario explains  the same stellar feedback that sets decline of  the lowering $\mstar/\mvir$ relation quenching timescale  with increasing mass also sets the lowering $\mstar$, because higher-mass galaxies generally have lower $\mgas/\mstar$ \citep[in either cold atomic or molecular gas, e.g.,][Bradford et al., submitted]{Schiminovich2010, Saintonge2011a, Huang2012, Boselli2014} and thus shorter  gas fraction depletion timescales in the absence of accretion.  Indeed, at $\mstar\sim10^9\msun$, galaxies transition through $\mgas/\mstar\approx1$,  with mass that causes more massive satellites gas depletion timescales comparable  to quench more rapidly.  At a Hubble time.  In this scenario,  the low-mass end, probably quenching timescales at $\mstar\gtrsim10^9\msun$ do not necessarily require strong additional environmental processes other than  the same shallower potential wells that make internal feedback more effective and causes lower $\mstar/\mvir$ that also allows external stripping lack of gas accretion  to occur more easily, possibly with a boost from the feedback-driven outflows. account for quenching in satellites \citep[see related discussions in, e.g.,][]{Wetzel2013, Wheeler2014, McGee2014}.  This analysis represents an overall statistical approach, but However, this scenario cannot explain the rollover  in future work we will combine the measured SFHs with the orbtal phase-space coordinates the quenching time at $\mstar\lessim10^9\msun$, because the star-forming dwarf galaxies  of each satellites the LG also have $\mgas\gtrsim\mstar$ \citep{GrgvichPutman2009}, and thus contain enough gas  to pursue fuel star formation for  a similar but Hubble time, even absent accretion.  Thus, the rapid decline of the environmental quenching time \emph{requires} an additional process that can remove gas from these dwarf galaxies after infall.  This likely arises from ram-pressure stripping of cold gas in such satellites, whose lower-mass host (sub)halos have shallower potential wells.  Furthermore, the same internal stellar feedback that regulates the low star-formation efficiency in such dwarf galaxies and likely drives significant gas flows to large radii \citep[e.g.,][]{Muratov2015} would strongly assist such environmental stripping to make even  more rigorous analysis on a satellite-by-satellite basis. efficient in dwarf galaxies.  In this sense, the rapid environmental quenching timescales for dwarf galaxies likely arise not just from the role of the external environment, but from the non-linear interplay of internal feedback and external stripping \citep[e.g.,][]{NicholsBlandHawthorn2011, BaheMcCarthy2015}.  The above scenario may also help to explain the curious similarity of Figure~\ref{fig:quench_times} with the mass dependence of the underlying galaxy-halo $\mstar/\mvir$ relation \citep[e.g.,][]{Behroozi2013}, which peaks at $\mstar\sim10^{10}\msun$ (higher but similar mass).  In particular, at high $\mstar$, the same process that lowers $\mstar/\mvir$ with increases mass also lowers the underlying gas fraction, which in turn causes more massive satellites to quench more rapidly after infall.  At low $\mstar$, the same shallower potential wells that allow internal feedback to lower $\mstar/\mvir$ also allows external stripping to occur more easily.  Overall, satellites with $\mstar\sim10^9\msun$ (near the Magellanic Clouds) represent the transition between these effects, and in general, there appears to be no quenching mechanism (either internal or external) that operates efficiently at such masses \citep[see also][]{Weisz2015}.  %This analysis represents a statistical approach, but in future work we will combine the measured SFHs with the orbtal phase-space coordinates of each satellites to pursue a similar but more rigorous analysis on a satellite-by-satellite basis.  While preparing this letter, we became aware of Fillingham et al.~2015 (submitted), who also used ELVIS to constrain theenvironmental  quenching timescales of satellites of the MW/M31.