2023ApJ...958..183S

The specific star formation rate (sSFR) is commonly used to describe the level of galaxy star formation (SF) and to select quenched galaxies. However, since it is a relative measure of the young-to-old population, an ambiguity in its interpretation may arise because a low sSFR can be due to either a substantial previous mass buildup or SF activity that is low. We show, using large samples spanning 0 < z < 2, that the normalization of the star formation rate (SFR) by the physical extent over which SF is taking place (i.e., the SFR surface density, Σ_SFR) overcomes this ambiguity. Σ_SFR has a strong physical basis, being tied to the molecular gas density and the effectiveness of stellar feedback, so we propose Σ_SFR-M_* as an important galaxy evolution diagram to complement (s)SFR-M_* diagrams. Using the Σ_SFR-M_* diagram we confirm the Schiminovich et al. result that the level of SF along the main sequence today is only weakly mass-dependent-high-mass galaxies, despite their redder colors, are as active as blue, low-mass ones. At higher redshift, the slope of the “Σ_SFR main sequence” steepens, signaling the epoch of bulge buildup in massive galaxies. We also find that Σ_SFR based on the optical isophotal radius more cleanly selects both starbursting and spheroid-dominated (early-type) galaxies than the sSFR. One implication of our analysis is that the assessment of the inside-out versus outside-in quenching scenarios should consider both sSFR and Σ_SFR radial profiles, because ample SF may be present in bulges with low sSFRs (red color).