Observations suggest that satellite quenching plays a major role in the build-up of passive, low-mass galaxies at late cosmic times. Studies of low-mass satellites, however, are limited by the ability to robustly characterize the local environment and star-formation activity of faint systems. In an effort to overcome the limitations of existing data sets, we utilize deep photometry in Stripe 82 of the Sloan Digital Sky Survey, in conjunction with a neural network classification scheme, to study the suppression of star formation in low-mass satellite galaxies in the local Universe. Using a statistically-driven approach, we are able to push beyond the limits of existing spectroscopic data sets, measuring the satellite quenched fraction down to satellite stellar masses of ${sim}10^7~{rm M}_{odot}$ in group environments (${M}_{rm{halo}} = 10^{13-14}~h^{-1}~{rm M}_{odot}$). At high satellite stellar masses ($gtrsim 10^{10}~{rm M}_{odot}$), our analysis successfully reproduces existing measurements of the quenched fraction based on spectroscopic samples. Pushing to lower masses, we find that the fraction of passive satellites increases, potentially signaling a change in the dominant quenching mechanism at ${M}_{star} sim 10^{9}~{rm M}_{odot}$. Similar to the results of previous studies of the Local Group, this increase in the quenched fraction at low satellite masses may correspond to an increase in the efficacy of ram-pressure stripping as a quenching mechanism in groups.
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