A Link Between Star Formation Quenching and Inner Stellar Mass Density in SDSS Central Galaxies

We study the correlation between galaxy structure and the quenching of star formation using a sample of SDSS central galaxies with stellar masses 9.75< log M_*/M_sun<11.25 and redshifts z<0.075. GALEX UV data are used to cleanly divide the sample into star-forming and quenched galaxies, and to identify galaxies in transition (the green valley). Despite a stark difference in visual appearance between blue and red galaxies, their average radial stellar mass density profiles are remarkably similar (especially in the outer regions) at fixed mass. The inner stellar mass surface density within a radius of 1 kpc, \Sigma_1, is used to quantify the growth of the bulge as galaxies evolve. When galaxies are divided into narrow mass bins, their distribution in the color-\Sigma_1 plane at fixed mass forms plausible evolutionary tracks. \Sigma_1 seems to grow as galaxies evolve through the blue cloud, and once it crosses a threshold value, galaxies are seen to quench at fixed \Sigma_1. The \Sigma_1 threshold for quenching grows with stellar mass, \Sigma_1 ~ M_*^{0.64}. However, the existence of some star-forming galaxies above the threshold \Sigma_1 implies that a dense bulge is necessary but not sufficient to quench a galaxy fully. This would be consistent with a two-step quenching process in which gas within a galaxy is removed or stabilized against star formation by bulge-driven processes (such as a starburst, AGN feedback, or morphological quenching), whereas external gas accretion is suppressed by separate halo-driven processes (such as halo gas shock heating). Quenching thus depends on an interplay between the inner structure of a galaxy and its surrounding dark matter halo, and lack of perfect synchrony between the two could produce the observed scatter in color vs. \Sigma_1. (Abridged)