  One of the key unanswered questions in the study of galaxy evolution is what
physical processes inside galaxies drive the changes in the SFRs in individual
galaxies that, taken together, produce the large decline in the global
star-formation rate density (SFRD) to redshifts since z~2. Many studies of the
SFR at intermediate redshifts have been made as a function of the integrated
stellar mass of galaxies but these did not use information on the internal
structural properties of the galaxies. In this paper we present a comparative
study of the dependence of SFRs on the average surface mass densities (SigmaM)
of galaxies of different morphological types up to z~1 using the zCOSMOS and
SDSS surveys. The main findings about the evolution of these relatively massive
galaxies are: 1) There is evidence that, for both SDSS ans zCOSMOS galaxies,
the mean specific SFR within a given population (either disk-dominated or
bulge-dominated) is independent of SigmaM; 2) The observed SSFR - SigmaM
step-function relation is due, at all investigated redshifts, to the changing
mix of disk-dominated and bulge-dominated galaxies as surface density increases
and the strong difference in the average SSFR between disks and bulges. We also
find a modest differential evolution in the size-mass relations of disk and
spheroid galaxies; 3) The shape of the median SSFR - SigmaM relation is
similar, but with median SSFR values that are about 5-6 times higher in zCOSMOS
galaxies than for SDSS, across the whole range of SigmaM, and in both spheroid
and disk galaxies. This increase matches that of the global SFRD of the
Universe as a whole, emphasizing that galaxies of all types are contributing,
proportionally, to the global increase in SFRD in the Universe back to these
redshifts (abridged).
