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Supernovae in the Subaru Deep Field: the rate and delay-time distribution of type Ia supernovae out to redshift 2

The type Ia supernova (SN Ia) rate, when compared to the cosmic star formation history (SFH), can be used to derive the delay-time distribution (DTD) of SNe Ia, which can distinguish among progenitor models. We present the results of a SN survey in the Subaru Deep Field (SDF). Over a period of 3 years, we have observed the SDF on 4 independent epochs with Suprime-Cam on the Subaru 8.2-m telescope, with 2 nights of exposure per epoch, in the R, i', and z' bands. We have discovered 150 SNe out to redshift z~2. Using 11 photometric bands from the observer-frame far-ultraviolet to the near-infrared, we derive photometric redshifts for the SN host galaxies (for 24 we also have spectroscopic redshifts). This information is combined with the SN photometry to determine the type and redshift distribution of the SN sample. Our final sample includes 28 SNe Ia in the range 1.0<z<1.5 and 10 in the range 1.5<z<2.0. Our SN Ia rate measurements are consistent with those derived from the HST/GOODS sample, but the overall uncertainty of our 1.5<z<2.0 measurement is a factor of 2 smaller, of 35-50%. We find that the SN Ia rate evolution levels off at 1.0<z<2.0, but shows no sign of declining. Combining our SN Ia rate measurements and those from the literature, and comparing to a wide range of possible SFHs, the best-fit DTD is a power law of the form Psi(t) ~ t^beta, with beta = -1.1 +/- 0.1 (statistical) +/- 0.17 (systematic). This result is consistent with other recent DTD measurements at various redshifts and environments, and is in agreement with a generic prediction of the double-degenerate progenitor scenario for SNe Ia. By combining the contribution to iron production from core-collapse SNe, based on the wide range of SFHs, with that from SNe Ia, calculated with the best-fit DTD, we predict that the mean present-day cosmic iron abundance is in the range Z(Fe) = (0.09-0.37) Z(Fe,Sun) (abridged).