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\section{Discussion}  The We suggest that the  trend at high mass may arise because of the intrinsic dependence of gas fraction on galaxy mass, such that more massive satellites have less gas when they fall in and thus exhaust it more quickly. Conversely, at M_star < 1e9 M_sun, 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 the combination of internal feedback + environmental stripping more efficient at lower masses. So ~LMC mass hits the sweet spot between these effects. Again, speculation. Figure~\ref{fig:quench_times} resembles the M/L ratio (Tollerud et al. 2011a Fig 11(right panel), Behroozi et al.  Put another way, the quenching timescale looks well-correlated with global $\mstar/\mvir$, which of course has a peak near $\mstar=10^9\msun$ because that's where all the star formation has just happened/is happening.  At the high-mass end, the same stellar feedback that sets the lowering $\mstar / \mvir$ relation with increasing mass also sets the lowering gas fraction with mass that causes more massive satellites to quench more rapidly.  At the low-mass end, probably the same shallower potential wells that make internal feedback more effective and causes lower $\mstar / \mvir$ that also allows external stripping to occur more easily, possibly with a boost from the feedback-driven outflows.  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.  Our analysis here represents a first-pass statistical argument, and our subsequent project would be a much more rigorous satellite-by-satellite version.