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The ejecta velocity is a very important parameter in studying the structureand properties of Type Ia supernovae (SNe Ia). It is also a candidate keyparameter in improving the utility of SNe Ia for cosmological distancedeterminations. Here we study the velocity distribution of a sample of 311 SNeIa from the kaepora database. The velocities are derived from the Si II$\lambda$6355 absorption line in optical spectra measured at (or extrapolatedto) the time of peak brightness. We statistically show that the observedvelocity has a bimodal Gaussian distribution consisting of two groups of SNeIa: Group I with a lower but narrower scatter ($\mu_1 = 11000 \text{kms}^{-1}$, $\sigma_1 = 700 \text{km s}^{-1}$), and Group II with a higher butbroader scatter ($\mu_2 = 12300 \text{km s}^{-1}$, $\sigma_2 = 1800 \text{kms}^{-1}$). The population ratio of Group I to Group II is 201:110 (65%:35%).There is substantial degeneracy between the two groups, but for SNe Ia withvelocity $v > 12000 \text{km s}^{-1}$, the distribution is dominated by GroupII. The true origin of the two components is unknown, though there could bethat naturally there exist two intrinsic velocity distributions as observed.However, we try to use asymmetric geometric models through statisticalsimulations to reproduce the observed distribution assuming all SNe Ia sharethe same intrinsic distribution. In the two cases we consider, 35\% of SNe Iaare considered to be asymmetric in Case 1, and all SNe Ia are asymmetric inCase 2. Simulations for both cases can reproduce the observed velocitydistribution but require a significantly large portion ($>35\%$) of SNe Ia tobe asymmetric. In addition, the Case 1 result is consistent with recentpolarization observations that SNe Ia with higher Si II $\lambda$6355 velocitytend to be more polarized.

Distribution of Si II $\lambda$6355 Velocities of Type Ia Supernovae and Implications for Asymmetric Explosions