It has recently been proposed that one sub-class of type Ia supernovae (SNe
Ia) is sufficiently both distinct and common to be classified separately from
the bulk of SNe Ia, with a suggested class name of "type Iax supernovae" (SNe
Iax), after SN 2002cx. However, their progenitors are still uncertain. We study
whether the population properties of this class might be understood if the
events originate from a subset of sub-Chandrasekhar mass explosions. In this
potential progenitor population, a carbon--oxygen white dwarf (CO WD)
accumulates a helium layer from a non-degenerate helium star; ignition of that
helium layer then leads to ignition of the CO WD. We incorporated detailed
binary evolution calculations for the progenitor systems into a binary
population synthesis model to obtain rates and delay times for such events. The
predicted Galactic event rate of these explosions is ~1.5\times10^{-3}{yr}^{-1}
according to our standard model, in good agreement with the measured rates of
SNe Iax. In addition, predicted delay times are ~70Myr-800Myr, consistent with
the fact that most of SNe Iax have been discovered in late-type galaxies. If
the explosions are assumed to be double-detonations -- following current model
expectations -- then based on the CO WD masses at explosion we also estimate
the distribution of resulting SN brightness (-13 \gtrsim M_{bol} \gtrsim
-19mag), which can reproduce the empirical diversity of SNe Iax. We speculate
on why binaries with non-degenerate donor stars might lead to SNe Iax if
similar systems with degenerate donors do not. We suggest that the high mass of
the helium layer necessary for ignition at the lower accretion rates typically
delivered from non-degenerate donors might be necessary to produce SN
2002cx-like characteristics, perhaps even by changing the nature of the CO
ignition.Comment: 8 pages, 10 figures, 1 table, accepted for publication in Astronomy
and Astrophysic
