  Bivariate luminosity functions (LFs) are computed for galaxies in the New
York Value-Added Galaxy Catalogue, based on the Sloan Digital Sky Survey Data
Release 4. The galaxy properties investigated are the morphological type,
inverse concentration index, Sersic index, absolute effective surface
brightness, reference frame colours, absolute radius, eClass spectral type,
stellar mass and galaxy environment. The morphological sample is flux-limited
to galaxies with r < 15.9 and consists of 37,047 classifications to an RMS
accuracy of +/- half a class in the sequence E, S0, Sa, Sb, Sc, Sd, Im. These
were assigned by an artificial neural network, based on a training set of 645
eyeball classifications. The other samples use r < 17.77 with a median redshift
of z ~ 0.08, and a limiting redshift of z < 0.15 to minimize the effects of
evolution. Other cuts, for example in axis ratio, are made to minimize biases.
A wealth of detail is seen, with clear variations between the LFs according to
absolute magnitude and the second parameter. They are consistent with an early
type, bright, concentrated, red population and a late type, faint, less
concentrated, blue, star forming population. This bimodality suggests two major
underlying physical processes, which in agreement with previous authors we
hypothesize to be merger and accretion, associated with the properties of
bulges and discs respectively. The bivariate luminosity-surface brightness
distribution is fit with the Choloniewski function (a Schechter function in
absolute magnitude and Gaussian in surface brightness). The fit is found to be
poor, as might be expected if there are two underlying processes.
