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).
