Bivariate Galaxy Luminosity Functions in the Sloan Digital Sky Survey

Bivariate luminosity functions (LFs) are computed for galaxies in the Sloan Digital Sky Survey Data Release 3 for a range of galaxy properties, including morphological type assigned by an artificial neural network, inverse concentration index, surface brightness (bivariate brightness distribution), eClass spectral type, reference frame colours, S\'ersic index, absolute Petrosian 90\% radius, stellar mass and galaxy environment. Several of the parameters are used in this way for the first time. In particular, the sample of 25,915 galaxies classified by Hubble type at the resolution E, S0, Sa ... Sd represents the largest such set in an LF by an order of magnitude. The morphological sample is flux limited to galaxies with $r<15.9$ while the other bivariate LFs use $r<17.6$ samples with a median redshift of $z \sim 0.1$. A wealth of detail is seen, with clear variation between the LFs according to absolute magnitude and the second parameter. They are consistent with a early type, bright, concentrated, red population and a late type, faint, less concentrated, blue, star forming population. This idea of bimodality has been explored by others as it suggests two major underlying physical processes. It is considered further in Ball et al. (2005, in preparation) in the context of galaxy colour and morphology. The LF bivariate with surface brightness is fit with the Cho{\l}oniewski function (a Schechter function in absolute magnitude and Gaussian in surface brightness) and the fit is found to be poor, as might be expected if the LF is a sum of more fundamental processes whose detail is visible in the dataset.