Delay times and rates for Type Ia supernovae and thermonuclear explosions from double-detonation sub-Chandrasekhar mass models

We present theoretical delay times and rates of thermonuclear explosions that are thought to produce Type Ia supernovae (SNe Ia), including the double-detonation sub-Chandrasekhar mass model, using the population synthesis binary evolution code STARTRACK. If detonations of sub-Chandrasekhar mass carbon-oxygen white dwarfs following a detonation in an accumulated layer of helium on the white dwarf's surface ('double-detonation' models) are able to produce thermonuclear explosions which are characteristically similar to those of SNe Ia, then these sub-Chandrasekhar mass explosions may account for at least some substantial fraction of the observed SN Ia rate. Regardless of whether all double-detonations look like 'normal' SNe Ia, in any case the explosions are expected to be bright and thus potentially detectable. Additionally, we find that the delay time distribution of double-detonation sub-Chandrasekhar mass SNe Ia can be divided into two distinct formation channels: the 'prompt' helium-star channel with delay times <500 Myr (13 per cent of all sub-Chandras), and the 'delayed' double white dwarf channel, with delay times greater than or similar to 800 Myr spanning up to a Hubble time (87 per cent). These findings coincide with recent observationally derived delay time distributions which have revealed that a large number of SNe Ia are prompt with delay times <500 Myr, while a significant fraction also have delay times spanning similar to 1 Gyr to a Hubble time.