The local space density of Sb-Sdm galaxies as function of their scale size, surface brightness, and luminosity

We investigate the dependence of the local space density of spiral galaxies on luminosity, scale size, and surface brightness. We derive bivariate space density distributions in these quantities from a sample of about 1000 Sb-Sdm spiral galaxies, corrected for selection effects in luminosity and surface brightness. The structural parameters of the galaxies were corrected for internal extinction using a description depending on galaxy surface brightness. We find that the bivariate space density distribution of spiral galaxies in the (luminosity, scale size)-plane is well described by a Schechter luminosity function in the luminosity dimension and a log-normal scale-size distribution at a given luminosity. This parameterization of the scale-size distribution was motivated by a simple model for the formation of disks within dark matter halos, with halos acquiring their angular momenta through tidal torques from neighboring objects and the disk specific angular momentum being proportional to that of the parent halo. However, the fractional width of the scale-size distribution at a given luminosity is narrower than what one would expect from using the distribution of angular momenta of halos measured in N-body simulations of hierarchical clustering. We present several possible explanations for the narrowness of the observed distribution. Using our bivariate distribution, we find that determinations of the local luminosity function of spiral galaxies should not be strongly affected by the bias against low surface brightness galaxies, even when the galaxies are selected from photographic plates. This may not be true for studies at high redshift, where (1 + z)(4) surface brightness dimming would cause a significant selection bias against lower surface brightness galaxies, if the galaxy population did not evolve with redshift.