Non-Monotonic Relations of Galaxy Star Formation, Radius, and Structure at Fixed Stellar Mass

We investigate the relation between galaxy structure and star formation rate (SFR) in a sample of ∼2.9×10^4 central galaxies with z<0.0674 and axial ratios b/a>0.5. The star-forming main sequence (SFMS) shows a bend around the stellar mass of M_∗≤M_c=2×10^10M_⊙. At M_∗≤M_c the SFMS follows a power-law SFR∝M_∗^0.85, while at higher masses it flattens. M_c corresponds to a dark matter halo mass of M_vir∼10^11.8M_⊙ where virial shocks occurs. Some galaxy structure (e.g., half-light radius, R_e) exhibits a non-monotonic dependence across the SFMS at a fixed M_∗. We find SFR∝R_e^-0.28 at fixed M_∗, consistent with the global Kennicutt-Schmidt (KS) law. This finding suggests that galaxy sizes contribute to the scatter of the SFMS. However, at M_∗>M_c the relationship between SFR and R_e diminishes. Low-mass galaxies above the mean of the SFMS have smaller radii, exhibit compact and centrally concentrated profiles resembling green valley (GV) and quiescent galaxies at the same mass, and have higher M_H_2/M_HI. Conversely, those below the SFMS exhibit larger radii, lower densities, have no GV or quiescent counterparts at their mass and have lower M_H_2/M_HI. The above data suggest two pathways for quenching low-mass galaxies, M_∗≤M_c: a fast one that changes the morphology on the SFMS and a slow one that does not. Above M_c, galaxies below the SFMS resemble GV and quiescent galaxies structurally, implying that they undergo a structural transformation already within the SFMS. For these massive galaxies, CG are strongly bimodal, with SFMS galaxies exhibiting negative color gradients, suggesting most star formation occurs in their outskirts, maintaining them within the SFMS.