  We investigate the lowest-mass quiescent galaxies known to exist in isolated
environments ($\mathrm{M^* = 10^{9.0-9.5} \ M_\odot}$; 1.5 Mpc from a more
massive galaxy). This population may represent the lowest stellar mass galaxies
in which internal feedback quenches galaxy-wide star formation. We present
Keck/ESI long-slit spectroscopy for 27 isolated galaxies in this regime: 20
quiescent galaxies and 7 star-forming galaxies. We measure emission line
strengths as a function of radius and place galaxies on the Baldwin Phillips
Terlevich (BPT) diagram. Remarkably, 16 of 20 quiescent galaxies in our sample
host central AGN-like line ratios. Only 5 of these quiescent galaxies were
identified as AGN-like in SDSS due to lower spatial resolution and
signal-to-noise. We find that many of the quiescent galaxies in our sample have
spatially-extended emission across the non-SF regions of BPT-space. When
considering only the central 1$^{\prime\prime}$, we identify a tight
relationship between distance from the BPT star-forming sequence and host
galaxy stellar age as traced by $\mathrm{D_n4000}$, such that older stellar
ages are associated with larger distances from the star-forming locus. Our
results suggest that the presence of hard ionizing radiation (AGN-like line
ratios) is intrinsically tied to the quenching of what may be the lowest-mass
self-quenched galaxies.
