Early-type galaxies in the Sloan Digital Sky Survey. II. Correlations between observables

A magnitude-limited sample of nearly 9000 early-type galaxies, in the redshift range 0.01 less than or equal to z less than or equal to 0.3, was selected from the Sloan Digital Sky Survey using morphological and spectral criteria. The sample was used to study how early-type galaxy observables, including luminosity L, effective radius R(o), surface brightness I(o), color, and velocity dispersion sigma, are correlated with one another. Measurement biases are understood with mock catalogs that reproduce all of the observed scaling relations and their dependences on fitting technique. At any given redshift, the intrinsic distribution of luminosities, sizes, and velocity dispersions in our sample are all approximately Gaussian. A maximum likelihood analysis shows that sigma proportional to L(0.25+/-0.012), R(o) proportional to L(0.63+/-0.025), and R(o) proportional to I(-0.75+/-0.02) in the r* band. In addition, the mass-to-light ratio within the effective radius scales as M(o)/L proportional to L(0.14+/-0.02) or M(o)/L proportional to M(o)(0.22+/-0.05), and galaxies with larger effective masses have smaller effective densities: Delta(o) proportional to M(o)(-0.52+/-0.03). These relations are approximately the same in the g*, i*, and z* bands. Relative to the population at the median redshift in the sample, galaxies at lower and higher redshifts have evolved only little, with more evolution in the bluer bands. The luminosity function is consistent with weak passive luminosity evolution and a formation time of about 9 Gyr ago.