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 (SNe Ia) with 0.05 <= z <= 0.3 obtained from the Sloan Digital Sky Survey (SDSS)-II supernova survey for the southern equatorial stripe of 300 deg(2) is used to derive the luminosity functions (LFs) of SNe Ia and of their host galaxies in the g, r, i passbands. We show that the LF of SNe Ia host galaxies matches well with that of galaxies in the general field, suggesting that the occurrence of SNe Ia does not favor a particular type of galaxy but is predominantly proportional to the luminosity of galaxies. The evidence is weak that the SNe rate varies with the color of host galaxies. The only evidence that points to possible correlation between the SN rate and star formation activity is that the SN 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 SN rate that is proportional to star formation activity is not evident in the integrated SN rate, while our observation is compatible with the current two-component models. The sample contains eight SNe Ia whose host galaxies were not identified, but it is shown that their occurrence is consistent with them occurring in low-luminous galaxies beyond the survey. The LF of SNe Ia is approximately Gaussian with the full width at half-maximum being a factor of sigma = 0.24 mag or 1.67 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 average color excess is approximate to 0.07 mag, which is significantly smaller than reddening expected for field galaxies. This color excess does not vary with the distance of the SNe from the center of the host galaxy to 15 kpc. This suggests that the major part of the color excess appears to be either intrinsic or reddening that arises in the immediate environment of SNe, rather than interstellar reddening in host galaxies, and most of SNe Ia take place in a relatively dust-free environment.