Using the population synthesis binary evolution code StarTrack, we present
theoretical rates and delay times of Type Ia supernovae arising from various
formation channels. These channels include binaries in which the exploding
white dwarf reaches the Chandrasekhar mass limit (DDS, SDS, and helium-rich
donor scenario) as well as the sub-Chandrasekhar mass scenario, in which a
white dwarf accretes from a helium-rich companion and explodes as a SN Ia
before reaching the Chandrasekhar mass limit. We find that using a common
envelope parameterization employing energy balance with alpha=1 and lambda=1,
the supernova rates per unit mass (born in stars) of sub-Chandrasekhar mass SNe
Ia exceed those of all other progenitor channels at epochs t=0.7 - 4 Gyr for a
burst of star formation at t=0. Additionally, the delay time distribution of
the sub-Chandrasekhar model can be divided in to two distinct evolutionary
channels: the `prompt' helium-star channel with delay times < 500 Myr, and the
`delayed' double white dwarf channel with delay times > 800 Myr spanning up to
a Hubble time. These findings are in agreement with recent
observationally-derived delay time distributions which predict that a large
number of SNe Ia have delay times < 1 Gyr, with a significant fraction having
delay times < 500 Myr. We find that the DDS channel is also able to account for
the observed rates of SNe Ia. However, detailed simulations of white dwarf
mergers have shown that most of these mergers will not lead to SNe Ia but
rather to the formation of a neutron star via accretion-induced collapse. If
this is true, our standard population synthesis model predicts that the only
progenitor channel which can account for the rates of SNe Ia is the
sub-Chandrasekhar mass scenario, and none of the other progenitors considered
can fully account for the observed rates.Comment: 6 pages, 1 figure, 1 table, to appear in proceedings for "Binary Star
Evolution: Mass Loss, Accretion and Mergers
