  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.
