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.
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