Can Helium-detonation Model Explain the Observed Diversity of Type Ia
  Supernovae?
  We study a sample of 16 Type Ia supernovae (SNe Ia) having both spectroscopic
and photometric observations within 2 $-$ 3 days after the first light. The
early $B-V$ colors of such a sample tends to show a continuous distribution.
For objects with normal ejecta velocity (NV), the C~II $\lambda$6580 feature is
always visible in the early spectra while it is absent or very weak in the
high-velocity (HV) counterpart. Moreover, the velocities of the detached
high-velocity features (HVFs) of Ca~II NIR triplet (CaIR3) above the
photosphere are found to be much higher in HV objects than in NV objects, with
typical values exceeding 30,000 km~s$^{-1}$ at 2 $-$ 3 days. We further analyze
the relation between %velocities of Si~II~$\lambda$6355 at maximum, $v_{\rm
Si,max}$, the velocity shift of late-time [Fe~II] lines ($v_{\rm [Fe~II]}$) and
host galaxy mass. We find that all HV objects have redshifted $v_{\rm [Fe~II]}$
while NV objects have both blue- and redshifted $v_{\rm [Fe~II]}$. It is
interesting to point out that the objects with redshifted $v_{\rm [Fe~II]}$ are
all located in massive galaxies, implying that HV and a portion of NV objects
may have similar progenitor metallicities and explosion mechanisms. We propose
that, with a geometric/projected effect, the He-detonation model may account
for the similarity in birthplace environment and the differences seen in some
SNe Ia, including $B-V$ colors, C~II feature, CaIR3 HVFs at early time and
$v_{\rm [Fe~II]}$ in the nebular phase. Nevertheless, some features predicted
by He-detonation simulation, such as the rapidly decreasing light curve,
deviate from the observations, and some NV objects with blueshifted nebular
$v_{\rm [Fe~II]}$ may involve other explosion mechanisms.
