  We present a study of the morphological nature of redshift z~0.7 star-forming
galaxies using a combination of HST/ACS, GALEX and ground-based images of the
COSMOS field. Our sample consists of 8,146 galaxies, 5,777 of which are
detected in the GALEX near-ultraviolet band down to a limiting magnitude of
25.5 (AB). We make use of the UV to estimate star formation rates, correcting
for the effect of dust using the UV-slope, and compute, from the ACS F814W
images, the C,A,S,G,M20 morphological parameters for all objects in our sample.
We observe a morphological bimodality in the galaxy population and show that it
has a strong correspondence with the FUV - g color bimodality. We conclude that
UV-optical color predominantly evolves concurrently with morphology. We observe
many of the most star-forming galaxies to have morphologies approaching that of
early-type galaxies, and interpret this as evidence that strong starburst
events are linked to bulge growth and constitute a process through which
galaxies can be brought from the blue to the red sequence while simultaneously
modifying their morphology accordingly. We conclude that the red sequence has
continued growing at z~<0.7. We also observe z~0.7 galaxies to have physical
properties similar to that of local galaxies, except for higher star formation
rates. Whence we infer that the dimming of star-forming galaxies is responsible
for most of the evolution in the star formation rate density of the Universe
since that redshift, although our data are also consistent with a mild number
evolution. [abridged]
