  We investigate the dependence of the local space density of spiral galaxies
on luminosity, scalesize 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, scalesize)-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 scalesize 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 scalesize
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. 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 can
cause a significant selection bias against lower surface brightness galaxies.

Astrophysics