The SDSS-II Supernova Survey: Parameterizing the Type Ia Supernova Rate as a Function of Host Galaxy Properties

Using data from the Sloan Digital Sky Supernova Survey-II, we measure the rate of Type Ia Supernovae (SNe Ia) as a function of galaxy properties at intermediate redshift. A sample of 342 SNe Ia with 0.05<z<0.25 is constructed. Using broad-band photometry we use the PEGASE spectral energy distributions (SEDs) to estimate host galaxy stellar masses and recent star-formation rates. We find that the rate of SNe Ia per unit stellar mass is significantly higher (by a factor of ~30) in highly star-forming galaxies compared to passive galaxies. When parameterizing the SN Ia rate (SNR_Ia) based on host galaxy properties, we find that the rate of SNe Ia in passive galaxies is not linearly proportional to the stellar mass, instead a SNR_Ia proportional to M^0.68 is favored. However, such a parameterization does not describe the observed SN Ia rate in star-forming galaxies. The SN Ia rate in star-forming galaxies is well fit by SNR_Ia = 1.05\pm0.16x10^{-10} M ^{0.68\pm0.01} + 1.01\pm0.09x10^{-3} SFR^{1.00\pm0.05} (statistical errors only), where M is the host galaxy mass and SFR is the star-formation rate. These results are insensitive to the selection criteria used, redshift limit considered and the inclusion of non-spectroscopically confirmed SNe Ia. We also show there is a dependence between the distribution of the MLCS light-curve decline rate parameter, \Delta, and host galaxy type. Passive galaxies host less luminous SNe Ia than seen in moderately and highly star-forming galaxies, although a population of luminous SNe is observed in passive galaxies, contradicting previous assertions that these SNe Ia are only observed in younger stellar systems. The MLCS extinction parameter, A_V, is similar in passive and moderately star-forming galaxies, but we find indications that it is smaller, on average, in highly star-forming galaxies. We confirm these results using the SALT2 light-curve fitter.