  The vast majority of dwarf satellites orbiting the Milky Way and M31 are
quenched, while comparable galaxies in the field are gas-rich and star-forming.
Assuming that this dichotomy is driven by environmental quenching, we use the
ELVIS suite of N-body simulations to constrain the characteristic timescale
upon which satellites must quench following infall into the virial volumes of
their hosts. The high satellite quenched fraction observed in the Local Group
demands an extremely short quenching timescale (~ 2 Gyr) for dwarf satellites
in the mass range Mstar ~ 10^6-10^8 Msun. This quenching timescale is
significantly shorter than that required to explain the quenched fraction of
more massive satellites (~ 8 Gyr), both in the Local Group and in more massive
host halos, suggesting a dramatic change in the dominant satellite quenching
mechanism at Mstar < 10^8 Msun. Combining our work with the results of
complementary analyses in the literature, we conclude that the suppression of
star formation in massive satellites (Mstar ~ 10^8 - 10^11 Msun) is broadly
consistent with being driven by starvation, such that the satellite quenching
timescale corresponds to the cold gas depletion time. Below a critical stellar
mass scale of ~ 10^8 Msun, however, the required quenching times are much
shorter than the expected cold gas depletion times. Instead, quenching must act
on a timescale comparable to the dynamical time of the host halo. We posit that
ram-pressure stripping can naturally explain this behavior, with the critical
mass (of Mstar ~ 10^8 Msun) corresponding to halos with gravitational restoring
forces that are too weak to overcome the drag force encountered when moving
through an extended, hot circumgalactic medium.
