The Lifetime of Type Ia Supernova Progenitors Deduced from the Chemical Evolution in the Solar Neighborhood

Using the chemical evolution model which allows the material infall from outside the disk region, we have determined the lifetime tIa of Type Ia supernova progenitors and the timescale tin of the infall that simultaneously reproduce the major observational features in the solar neighborhood, such as the evolutionary change in [O/Fe] against [Fe/H] and the [Fe/H] abundance distribution function of long-lived stars. A full survey in the parameter space, including the linear and nonlinear relations between the star formation rate and the gas density, shows that a value of [Fe/H] at which the [0/Fe] break occurs is sensitive mostly to tIain. This decoupling enables a reliable determination of tIa from the [O/Fe] break almost independently of tinIa ∼1.5 Gyr from the observed [O/Fe] break at [Fe/H] ∼-1 and tin ∼5 Gyr from the observed paucity of long-lived stars below [Fe/H] ∼-1 in the solar neighborhood. We have furthermore examined what would happen if the lifetime of SN Ia progenitors has a range using some heuristic distribution functions of tIa. We conclude from extensive calculations that its range is strictly confined within tIa = 0.5-3 Gyr, otherwise it is ruled out by the data. In addition, comparing the 0 and Fe yields determined by the chemical evolution model with the supernova nucleosynthesis yields, we discuss the mass range of the IMF and the mass fraction of SN Ia progenitors which can be expressed in terms of the IMF slope index.