Type Ia supernova rate studies from the SDSS-II Supernova Survey

I present new measurements of the type Ia SN rate from the SDSS-II Supernova Survey. The SDSS-II Supernova Survey was carried out during the Fall months (Sept.-Nov.) of 2005-2007 and discovered ≈500 spectroscopically confirmed SNe Ia with densely sampled (once every ≈ 4 days), multi-color light curves. Additionally, the SDSS-II Supernova Survey has discovered several hundred SNe Ia candidates with well-measured light curves, but without spectroscopic confirmation of type. This total, achieved in 9 months of observing, represents ≈ 15-20% of the total SNe Ia discovered worldwide since 1885. I describe some technical details of the SN Survey observations and SN search algorithms that contributed to the extremely high-yield of discovered SNe and that are important as context for the SDSS-II Supernova Survey SN Ia rate measurements.;I describe 3 separate SN Ia studies: (1) A precise measurement of the SN Ia rate at low-redshift (z < 0.12) based on a highly pure sample of SNe Ia with a well measured selection function. (2) A measurement of the type Ia SN rate to a redshift limit z ≲ 0.3, based on ≈ 350 SNe Ia. (3) A measurement of the type Ia SN rate in galaxy clusters in the redshift range 0.03 < z < 0.30.;The low-redshift SN Ia rate measurement includes 17 SNe Ia at redshift z ≤ 0.12. Assuming a flat cosmology with Om = 0.3 = 1 - OLambda, we find a volumetric SN Ia rate of 2.93 +0.17-0.04&parl0;systematic&parr0; +0.90-0.71statistical &sqbr0;x10-5 SNe Mpc-3 h370 year-1, at a volume-weighted mean redshift of 0.09. This result is consistent with previous measurements of the SN Ia rate in a similar redshift range. The systematic errors are well controlled, resulting in the most precise measurement of the SN Ia rate in this redshift range. We use a maximum likelihood method to fit SN rate models to the SDSS-II Supernova Survey data in combination with other rate measurements, thereby constraining models for the redshift-evolution of the SN Ia rate. Fitting the combined data to a simple power-law evolution of the volumetric SN Ia rate, rV ∝ (1 + z)beta, we obtain a value of beta = 1.5 +/- 0.6, i.e. the SN Ia rate is determined to be an increasing function of redshift at the ∼ 2.5sigma level. Fitting the results to a model in which the volumetric SN rate, rV = Arho(t) + B r&d2; (t), where rho(t) is the stellar mass density and r&d2; (t) is the star formation rate, we find A = (2.8 +/- 1.2) x 10-14 SNe M-1⊙ year-1, B = &parl0;9.3+3.4-3.1&parr0;x 10-4 SNe M-1⊙ .;The SN rate measurement to a redshift limit z ≲ 0.3 provides an order of magnitude improvement in the statistics for SN Ia rate measurement in this redshift range. Although systematic uncertainties on the SN rate for 0.2 < z < 0.3 are significant, the SN rate is determined precisely for z ≲ 0.2 based on a sample of ≈ 132 SNe Ia, with the majority being spectroscopically confirmed. The large sample of SNe Ia included in this study allow us to place constraints on the redshift dependence of the SN Ia rate in the redshift range covered by the SDSS-II Supernova Survey, based on the SDSS-II Supernova Survey data alone.;The SN rate in galaxy clusters has been measured with much less statistical significance than the cosmic SN rate due in part to the relative rarity of galaxy clusters. The measurement of the cluster SN Ia rate from the first two seasons of the SDSS-II Supernova Survey includes 5 events in clusters at z ≲ 0.17 (c4 clusters), and 12 events in clusters in the redshift range 0.1 < z < 0.3 (maxBCG clusters). There are additionally 3 SNe Ia in low-redshift c4 clusters from the third season of the SDSS-II Supernova Survey. These measurements represent significant contributions to the study of the SN rate in galaxy clusters, in terms of both statistical significance and redshift coverage. We find values of the SN Ia rate of 0.10+0.068-0.043 SNuM h2 and 0.12+0.046-0.034 SNuM h2 in c4 and maxBCG clusters, respectively. The SN rate in galaxy clusters as a function of redshift is consistent with a constant rate, which supports the idea that cluster SNe Ia are primarily produced by an old stellar population, with a rate that is weakly dependent on time delay with respect to star formation. (Abstract shortened by UMI.).