  We present a numerical parameter survey of sub-Chandrasekhar mass white dwarf
(WD) explosions. Carbon-oxygen WDs accreting a helium shell have the potential
to explode in the sub-Chandrasekhar mass regime. Previous studies have shown
how the ignition of a helium shell can either directly ignite the WD at the
core-shell interface or propagate a shock wave into the the core causing a
central ignition. We examine the explosions of WDs from 0.6 - 1.2 M$_\odot$
with helium shells of 0.01, 0.05 and 0.08 M$_\odot$. Distinct observational
signatures of sub-Chandrasekhar mass WD explosions are predicted for two
categories of shell size. Thicker-shell models show an early time flux excess,
which is caused by the presence of radioactive material in the ashes of the
helium shell, and red colors due to these ashes creating significant line
blanketing in the UV through the blue portion of the spectrum. Thin shell
models reproduce several typical Type Ia supernova signatures. We identify a
relationship between Si II velocity and luminosity which, for the first time,
identifies a sub-class of observed supernovae that are consistent with these
models. This sub-class is further delineated by the absence of carbon in their
atmospheres. We suggest that the proposed difference in the ratio of selective
to total extinction between the high velocity and normal velocity Type Ia
supernovae is not due to differences in the properties of the dust around these
events, but is rather an artifact of applying a single extinction correction to
two intrinsically different populations of supernovae.
