ar X iv : a st ro - p h / 99 10 06 6 v 1 4 O ct 1 99 9 The space density of spiral galaxies as function of their scale size , surface brightness and luminosity

The local space density of galaxies as a function of their basic structural parameters –luminosity, surface brightness and scale size– is still poorly known. Our poor knowledge is the result of strong selection biases against low surface brightness and small scale size galaxies in any optically selected sample. We derive bivariate space density distributions by correcting a sample of ∼1000 local Sb-Sdm spiral galaxies for its selection effects. We present a parameterization of these bivariate distributions, based on a Schechter type luminosity function and a log-normal scale size distribution at a given luminosity. We next calculate the bivariate distributions as function of redshift using the Hubble Deep Field, and conclude that at higher redshift there is a decrease in space density of luminous, large scale size galaxies, but the density of smaller galaxies stays nearly the same.