Abstract Type Ia supernovae (SNe Ia) play a key role in measuring cosmological parameters, in which the Phillips relation is adopted. However, the origin of the relation is still unclear. Several parameters are suggested, e.g. the relative content of carbon to oxygen (C/O) and the central density of the white dwarf (WD) at ignition. These parameters are mainly determined by the WD's initial mass and its cooling time, respectively. Using the progenitor model developed by Meng & Yang, we present the distributions of the initial WD mass and the cooling time. We do not find any correlation between these parameters. However, we notice that as the range of the WD's mass decreases, its average value increases with the cooling time. These results could provide a constraint when simulating the SN Ia explosion, i.e. the WDs with a high C/O ratio usually have a lower central density at ignition, while those having the highest central density at ignition generally have a lower C/O ratio. The cooling time is mainly determined by the evolutionary age of secondaries, and the scatter of the cooling time decreases with the evolutionary age. Our results may indicate that WDs with a long cooling time have more uniform properties than those with a short cooling time, which may be helpful to explain why SNe Ia in elliptical galaxies have a more uniform maximum luminosity than those in spiral galaxies.

Keywords stars: white dwarfs — stars: supernovae: general

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