A Measurement of the Rate of type-Ia Supernovae at Redshift \(z\approx\) 0.1 from the First Season of the SDSS-II Supernova Survey

We present a measurement of the rate of type Ia supernovae (SNe Ia) from the first of three seasons of data from the SDSS-II Supernova Survey. For this measurement, we include 17 SNe Ia at redshift \(z\le0.12\). Assuming a flat cosmology with \(\Omega_m = 0.3=1-\Omega_\Lambda\), we find a volumetric SN Ia rate of \([2.93^{+0.17}_{-0.04}({\rm systematic})^{+0.90}_{-0.71}({\rm statistical})] \times 10^{-5} {\rm SNe} {\rm Mpc}^{-3} h_{70}^3 {\rm year}^{-1}\), 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, \(r_V \propto (1+z)^{\beta}\), we obtain a value of \(\beta = 1.5 \pm 0.6\), i.e. the SN Ia rate is determined to be an increasing function of redshift at the \(\sim 2.5 \sigma\) level. Fitting the results to a model in which the volumetric SN rate, \(r_V=A\rho(t)+B\dot \rho(t)\), where \(\rho(t)\) is the stellar mass density and \(\dot \rho(t)\) is the star formation rate, we find \(A = (2.8 \pm 1.2) \times 10^{-14} \mathrm{SNe} \mathrm{M}_{\sun}^{-1} \mathrm{year}^{-1}\), \(B = (9.3^{+3.4}_{-3.1})\times 10^{-4} \mathrm{SNe} \mathrm{M}_{\sun}^{-1}\).