The Type Ia Supernova Rate at z$\sim 0.4$

We present the first measurement of the rate of Type Ia supernovae at high redshift. The result is derived using a large subset of data from the Supernova Cosmology Project. Three supernovae were discovered in a surveyed area of 1.7 square degrees. The survey spanned a $\sim 3$ week baseline and used images with $3\sigma$ limiting magnitude of $R\sim 23$. We present our methods for estimating the numbers of galaxies and the number of solar luminosities to which the survey is sensitive, and the supernova detection efficiency which is used to determine the control time, the effective time for which the survey is sensitive to a Type Ia event. We derive a rest-frame Type Ia supernova rate at $z\sim 0.4$ of $0.82{}_{-0.37}^{+0.54}{}_{-0.25}^{+0.37}$ $h^2$ SNu (1 SNu = 1 SN per century per ${10}^{10}$\Lbsun), where the first uncertainty is statistical and the second includes systematic effects. For the purposes of observers, we also determine the rate of SNe, per sky area surveyed, to be $34.4{}_{-16.2}^{+23.9}$ SNe\ $\mathrm{y}\mathrm{e}\mathrm{a}{\mathrm{r}}^{-1}\mathrm{d}\mathrm{e}{\mathrm{g}}^{-2}$ for SN magnitudes in the range $21.3<R<22.3$.