Luminosity Functions of Type Ia Supernovae and their Host Galaxies from
  the Sloan Digital Sky Survey
  The sample of 137 low-redshift type Ia supernovae with 0.05 < z < 0.3
obtained from the SDSS-II Supernova Survey for the southern equatorial stripe
of 300 square degrees is used to derive the luminosity functions of type Ia
supernovae and of their host galaxies in the gri passbands. We show that the
luminosity function of type Ia supernova host galaxies matches well with that
of galaxies in the general field, suggesting that the occurrence of type Ia
supernovae does not favour a particular type of galaxies but is predominantly
proportional to the luminosity of galaxies. The only evidence that points to
possible correlation between the supernova rate and star formation activity is
that the supernova rate in late-type galaxies is higher than that in early-type
galaxies by 31+/-35%. The sample contains 8 type Ia supernovae whose host
galaxies were not identified, but it is shown that their occurrence is
consistent with them occurred in low luminous galaxies beyond the survey. The
luminosity function of type Ia supernovae is approximately Gaussian with the
full-width half maximum being a factor of 1.4 in luminosity. The Gaussian
distribution becomes tighter if the ratio of extinction to reddening, R_V, is
lower than the characteristic value for the Milky Way and if luminosity is
corrected for the light curve shape. The colour excess is ~0.07 mag which is
significantly smaller than reddening expected for field galaxies. This colour
excess does not vary with the distance of the supernovae from the centre of the
host galaxy to 15 kpc. This suggests that the major part of the colour excess
appears to be either intrinsic or reddening that arises in the immediate
environment of supernova, rather than interstellar reddening in host galaxies.
