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, $v_{\rm Si,max}$,thevelocityshiftoflate-time[FeII]lines($v_{\rm [Fe~II]}$) and host galaxy mass. We find that all HV objects have redshifted $v_{[\mathrm{F}\mathrm{e}\mathrm{I}\mathrm{I}]}$ while NV objects have both blue- and redshifted $v_{[\mathrm{F}\mathrm{e}\mathrm{I}\mathrm{I}]}$. It is interesting to point out that the objects with redshifted $v_{[\mathrm{F}\mathrm{e}\mathrm{I}\mathrm{I}]}$ 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 $v_{[\mathrm{F}\mathrm{e}\mathrm{I}\mathrm{I}]}$ 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 $v_{[\mathrm{F}\mathrm{e}\mathrm{I}\mathrm{I}]}$ may involve other explosion mechanisms.