  UV observations in the local universe have uncovered a population of
early-type galaxies with UV flux consistent with low-level recent or ongoing
star formation. We present resolved UV-optical photometry of a sample of 19
SDSS early-type galaxies at z~0.1 drawn from the sample originally selected by
Salim & Rich (2010) to lie in the bluer part of the green valley in the
UV-optical color-magnitude diagram as measured by GALEX. Utilizing
high-resolution HST far-UV imaging provides unique insight into the
distribution of UV light in these galaxies, which we call "extended
star-forming early-type galaxies" (ESF-ETGs) because of extended UV emission
that is indicative of recent star formation. The UV-optical color profiles of
all ESF-ETGs show red centers and blue outer parts. Their outer colors require
the existence of a significant underlying population of older stars in the
UV-bright regions. Analysis of stacked SDSS spectra reveals weak LINER-like
emission in their centers. Using a cross-matched SDSS DR7/GALEX GR6 catalog, we
search for other green valley galaxies with similar properties to these
ESF-ETGs and estimate that ~13% of dust-corrected green valley galaxies of
similar stellar mass and UV-optical color are likely ESF-candidates, i.e.,
ESF-ETGs are not rare. Our results are consistent with star formation that is
gradually declining in existing disks, i.e., the ESF-ETGs are evolving onto the
red sequence for the first time, or with rejuvenated star formation due to
accreted gas in older disks provided that the gas does not disrupt the
structure of the galaxy and the resulting star formation is not too recent and
bursty. ESF-ETGs may typify an important subpopulation of galaxies that can
linger in the green valley for up to several Gyrs, based on their resemblance
to nearby gas-rich green valley galaxies with low-level ongoing star formation.
(abridged)
