  Although Lyman continuum (LyC) radiation from star-forming galaxies likely
drove the reionization of the Universe, observations of star-forming galaxies
at low redshift generally indicate low LyC escape fractions. However, the
extreme [O III]/[O II] ratios of the z=0.1-0.3 Green Pea galaxies may be due to
high escape fractions of ionizing radiation. To analyze the LyC optical depths
and ionizing sources of these rare, compact starbursts, we compare nebular
photoionization and stellar population models with observed emission lines in
the Peas' SDSS spectra. We focus on the six most extreme Green Peas, the
galaxies with the highest [O III]/[O II] ratios and the best candidates for
escaping ionizing radiation. The Balmer line equivalent widths and He I
{\lambda}3819 emission in the extreme Peas support young ages of 3-5 Myr, and
He II {\lambda}4686 emission in five extreme Peas signals the presence of hard
ionizing sources. Ionization by active galactic nuclei or high-mass X-ray
binaries is inconsistent with the Peas' line ratios and ages. Although stacked
spectra reveal no Wolf-Rayet (WR) features, we tentatively detect WR features
in the SDSS spectra of three extreme Peas. Based on the Peas' ages and line
ratios, we find that WR stars, chemically homogeneous O stars, or shocks could
produce the observed He II emission. If hot stars are responsible, the Peas'
optical depths are ambiguous. However, accounting for emission from shocks
lowers the inferred optical depth and suggests that the Peas may be optically
thin. The Peas' ages likely optimize the escape of Lyman-continuum radiation;
they are old enough for supernovae and stellar winds to reshape the
interstellar medium, but young enough to possess large numbers of UV-luminous O
or WR stars.
