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 evidence is weak that the supernovae rate varies with colour of host 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%. In our low redshift sample the component of type Ia supernova rate that is proportional to star formation activity is not manifest in the integrated supernova rate, while our observation is compatible with the current two-component models. 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, RV , 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, and most of type Ia supernovae take place in relatively dust free environment. Subject headings: supernovae : general