Galaxy Structure and Mode of Star Formation in the SFR-Mass Plane from z
  ~ 2.5 to z ~ 0.1
  We analyze the dependence of galaxy structure (size and Sersic index) and
mode of star formation (\Sigma_SFR and SFR_IR/SFR_UV) on the position of
galaxies in the SFR versus Mass diagram. Our sample comprises roughly 640000
galaxies at z~0.1, 130000 galaxies at z~1, and 36000 galaxies at z~2.
Structural measurements for all but the z~0.1 galaxies were based on HST
imaging, and SFRs are derived using a Herschel-calibrated ladder of SFR
indicators. We find that a correlation between the structure and stellar
population of galaxies (i.e., a 'Hubble sequence') is already in place since at
least z~2.5. At all epochs, typical star-forming galaxies on the main sequence
are well approximated by exponential disks, while the profiles of quiescent
galaxies are better described by de Vaucouleurs profiles. In the upper envelope
of the main sequence, the relation between the SFR and Sersic index reverses,
suggesting a rapid build-up of the central mass concentration in these
starbursting outliers. We observe quiescent, moderately and highly star-forming
systems to co-exist over an order of magnitude or more in stellar mass. At each
mass and redshift, galaxies on the main sequence have the largest size. The
rate of size growth correlates with specific SFR, and so does \Sigma_SFR at
each redshift. A simple model using an empirically determined SF law and
metallicity scaling, in combination with an assumed geometry for dust and stars
is able to relate the observed \Sigma_SFR and SFR_IR/SFR_UV, provided a more
patchy dust geometry is assumed for high-redshift galaxies.
