  The delay time distribution (DTD) of type Ia supernovae (SNe Ia) from star
formation is an important clue to reveal the still unknown progenitor system of
SNe Ia. Here we report on a measurement of the SN Ia DTD in a delay time range
of t_Ia = 0.1-8.0 Gyr by using the faint variable objects detected in the
Subaru/XMM-Newton Deep Survey (SXDS) down to i' ~ 25.5. We select 65 SN
candidates showing significant spatial offset from nuclei of the host galaxies
having old stellar population at z ~ 0.4-1.2, out of more than 1,000 SXDS
variable objects. Although spectroscopic type classification is not available
for these, we quantitatively demonstrate that more than ~80% of these should be
SNe Ia. The DTD is derived using the stellar age estimates of the old galaxies
based on 9 band photometries from optical to mid-infrared wavelength. Combined
with the observed SN Ia rate in elliptical galaxies at the local universe, the
DTD in t_Ia ~ 0.1-10 Gyr is well described by a featureless power-law as
f_D(t_Ia) \propto t_Ia^{-1}. The derived DTD is in excellent agreement with the
generic prediction of the double-degenerate scenario, giving a strong support
to this scenario. In the single-degenerate (SD) scenario, although predictions
by simple analytic formulations have broad DTD shapes that are similar to the
observation, DTD shapes calculated by more detailed binary population synthesis
tend to have strong peaks at characteristic time scales, which do not fit the
observation. This result thus indicates either that the SD channel is not the
major contributor to SNe Ia in old stellar population, or that improvement of
binary population synthesis theory is required. Various sources of systematic
uncertainties are examined and tested, but our main conclusions are not
affected significantly.
