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 ^ { \prime } \sim 25.5 .
We select 65 SN candidates showing significant spatial offset from nuclei of the host galaxies having old stellar population at z \sim 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 \sim 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 } \sim 0.1–10 Gyr is well described by a featureless power-law as f _ { D } ( t _ { Ia } ) \propto t _ { Ia } ^ { \alpha } with \alpha \sim - 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 .