A Measurement of the Rate of Type Ia Supernovae at Redshift z 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 <IMG SRC="eq-00001.gif" ALT="z\leq 0.12"/> z [?] 0.12. Assuming a flat cosmology with <IMG SRC="eq-00002.gif" ALT="\Omega _{m}=0.3=1-\Omega _{\Lambda }"/> Om = 0.3 = 1 [?] OL, we find a volumetric SN Ia rate of <IMG SRC="eq-00003.gif" ALT="[ 2.93^{+0.17}_{-0.04}(\mathrm{systematic}\,) ^{+0.90}_{-0.71}(\mathrm{statistical}\,) ] \times 10^{-5}\ \mathrm{SNe}\,\ \mathrm{Mpc}\,^{-3}\ h^{3}_{70}\ \mathrm{yr}\,^{-1}"/> [ 2.93+ 0.17[?]0.04(systematic)+ 0.90[?]0.71(statistical) ] x 10[?]5 SNe Mpc [?]3 h370 yr [?]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, <IMG SRC="eq-00004.gif" ALT="r_{V}\propto (1+z) ^{\beta }"/> rV [?] (1 + z)b, we obtain a value of <IMG SRC="eq-00005.gif" ALT="\beta =1.5\pm 0.6"/> b = 1.5 +- 0.6, i.e., the SN Ia rate is determined to be an increasing function of redshift at the ~2.5 s level. Fitting the results to a model in which the volumetric SN rate is rV = Ar(t) + Br(t) <IMG SRC="eq-00006.gif" ALT="r_{V}=A\rho (t) +B\dot{\rho }(t) "/><LATEX>$r_V = Aρ (t) + B˙{ρ }(t) $</LATEX> , where <IMG SRC="eq-00007.gif" ALT="\rho (t) "/> r (t) is the stellar mass density and r(t) <IMG SRC="eq-00008.gif" ALT="\dot{\rho }(t) "/><LATEX>$˙{ρ }(t) $</LATEX> is the star formation rate, we find <IMG SRC="eq-00009.gif" ALT="A=(2.8\pm 1.2) \times 10^{-14}\ \mathrm{SNe}\,\ M^{-1}_{\odot }\ \mathrm{yr}\,^{-1}"/> A = (2.8 +- 1.2) x 10[?]14 SNe M[?]1 yr [?]1, <IMG SRC="eq-00010.gif" ALT="B=(9.3^{+3.4}_{-3.1}) \times 10^{-4}\ \mathrm{SNe}\,\ M^{-1}_{\odot }"/> B = (9.3+ 3.4[?]3.1) x 10[?]4 SNe M[?]1.