Early-type Galaxies in the Sloan Digital Sky Survey. II. Correlations between Observables

A magnitude limited sample of nearly 9000 early-type galaxies, in theredshift range 0.01 < z < 0.3, was selected from the Sloan Digital Sky Surveyusing morphological and spectral criteria. The sample was used to study howearly-type galaxy observables, including luminosity L, effective radius R_o,surface brightness I_o, color, and velocity dispersion sigma, are correlatedwith one another. Measurement biases are understood with mock catalogs whichreproduce all of the observed scaling relations and their dependences onfitting technique. At any given redshift, the intrinsic distribution ofluminosities, sizes and velocity dispersions in our sample are allapproximately Gaussian. A maximum likelihood analysis shows that sigma ~L^{0.25\pm 0.012}, R_o ~ L^{0.63\pm 0.025}, and R_o ~ I^{-0.75\pm 0.02} in ther* band. In addition, the mass-to-light ratio within the effective radiusscales as M_o/L ~ L^{0.14\pm 0.02} or M_o/L ~ M_o^{0.22\pm 0.05}, and galaxieswith larger effective masses have smaller effective densities: Delta_o ~M_o^{-0.52\pm 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 moreevolution in the bluer bands. The luminosity function is consistent with weakpassive luminosity evolution and a formation time of about 9 Gyrs ago.Comment: 29 pages, 11 figures. Accepted by AJ (scheduled for April 2003). This paper is part II of a revised version of astro-ph/011034