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Galaxy Mass, Metallicity, Radius and Star Formation Rates

Working with 108,786 Sloan Digital Sky Survey low redshift galaxies we have examined the relation between galaxy mass, metallicity, radius, and star formation rates primarily in the central portions of galaxies. We subdivided the redshift range covered in our sample, 0.07<z<0.3, into three narrower redshift bins, and three sets of radial size. We show that for 72% of the galaxies the observed gas metallicities, Zx, are consistent with (i) a quantitative physical relation for star formation through episodic infall of gas of metallicity Zi = 0.125x10^-3 +/- 1.25x10^-3; (ii) thorough mixing of infalling and native gas before onset of star formation; (iii) a star formation rate (SFR) proportional to the 3/2 power of the infalling mass rate, Mi; and (iv) intermittent quiescent phases devoid of star formation during which the native gas in a galaxy exhibits a characteristic elevated gas metallicity, Z0, dependent on galaxy mass, M*, and a characteristic ratio of stellar mass to native mass of gas, Mg. Most if not all our star-forming galaxies with M* < 2.0x10^10 Msun, and many with M* > 2.0x10^10 Msun and large radii appear fed by infall. Smaller massive galaxies with high Zx and high star formation rates show more complex behavior. A mean-field-theory toy model for the physics of infall accounts for the (SFR) \propto Mi^(3/2) relation and permits us to estimate the mean densities and velocities of clumps of baryonic matter traversing the dark matter halos in which the SDSS galaxies may be embedded.