Predicting Quiescence: The Dependence of Specific Star Formation Rate on
  Galaxy Size and Central Density at 0.5<z<2.5
  In this paper, we investigate the relationship between star formation and
structure, using a mass-complete sample of 27,893 galaxies at $0.5<z<2.5$
selected from 3D-HST. We confirm that star-forming galaxies are larger than
quiescent galaxies at fixed stellar mass (M$_{\star}$). However, in contrast
with some simulations, there is only a weak relation between star formation
rate (SFR) and size within the star-forming population: when dividing into
quartiles based on residual offsets in SFR, we find that the sizes of
star-forming galaxies in the lowest quartile are 0.27$\pm$0.06 dex smaller than
the highest quartile. We show that 50% of star formation in galaxies at fixed
M$_{\star}$ takes place within a narrow range of sizes (0.26 dex). Taken
together, these results suggest that there is an abrupt cessation of star
formation after galaxies attain particular structural properties. Confirming
earlier results, we find that central stellar density within a 1 kpc fixed
physical radius is the key parameter connecting galaxy morphology and star
formation histories: galaxies with high central densities are red and have
increasingly lower SFR/M$_{\star}$, whereas galaxies with low central densities
are blue and have a roughly constant (higher) SFR/M$_{\star}$ at a given
redshift. We find remarkably little scatter in the average trends and a strong
evolution of $>$0.5 dex in the central density threshold correlated with
quiescence from $z\sim0.7-2.0$. Neither a compact size nor high-$n$ are
sufficient to assess the likelihood of quiescence for the average galaxy;
rather, the combination of these two parameters together with M$_{\star}$
results in a unique quenching threshold in central density/velocity.
