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\section{Discussion}  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, $\mstar<10^9\msun$,  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 the combination of internal feedback + plus  environmental stripping more efficient at lower masses. So ~LMC So, near 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.