We demonstrate that dwarf galaxies (107 M stellar 109 M ☉, –12 Mr –18) with no active star formation are extremely rare (0.06%) in the field. Our sample is based on the NASA-Sloan Atlas which is a reanalysis of the Sloan Digital Sky Survey Data Release 8. We examine the relative number of quenched versus star-forming dwarf galaxies, defining quenched galaxies as having no Hα emission (EWHα 2 ?) and a strong 4000 ? break. The fraction of quenched dwarf galaxies decreases rapidly with increasing distance from a massive host, leveling off for distances beyond 1.5?Mpc. We define galaxies beyond 1.5?Mpc of a massive host galaxy to be in the field. We demonstrate that there is a stellar mass threshold of M stellar 1.0 × 109 M ☉ below which quenched galaxies do not exist in the field. Below this threshold, we find that none of the 2951 field dwarf galaxies are quenched; all field dwarf galaxies show evidence for recent star formation. Correcting for volume effects, this corresponds to a 1σ upper limit on the quenched fraction of 0.06%. In more dense environments, quenched galaxies account for 23% of the dwarf population over the same stellar mass range. The majority of quenched dwarf galaxies (often classified as dwarf elliptical galaxies) are within 2 virial radii of a massive galaxy, and only a few percent of quenched dwarf galaxies exist beyond 4 virial radii. Thus, for galaxies with stellar mass less than 1.0 × 109 M ☉, ending star formation requires the presence of a more massive neighbor, providing a stringent constraint on models of star formation feedback.
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