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 \sim 0.7-2.0 .
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 .