Carnegie supernova project:Classification of type Ia supernovae

We use the spectroscopy and homogeneous photometry of 97 Type Ia supernovae obtained by the \emph{Carnegie Supernova Project} as well as a subset of 36 Type Ia supernovae presented by Zheng et al. (2018) to examine maximum-light correlations in a four-dimensional (4-D) parameter space: $B$-band absolute magnitude, $M_B$, \ion{Si}{2}~$\lambda6355$ velocity, \vsi, and \ion{Si}{2} pseudo-equivalent widths pEW(\ion{Si}{2}~$\lambda6355$) and pEW(\ion{Si}{2}~$\lambda5972$). It is shown using Gaussian mixture models (GMMs) that the original four groups in the Branch diagram are well-defined and robust in this parameterization. We find three continuous groups that describe the behavior of our sample in [$M_B$, \vsi] space. Extending the GMM into the full 4-D space yields a grouping system that only slightly alters group definitions in the [$M_B$, \vsi] projection, showing that most of the clustering information in [$M_B$, \vsi] is already contained in the 2-D GMM groupings. However, the full 4-D space does divide group membership for faster objects between core-normal and broad-line objects in the Branch diagram. A significant correlation between $M_B$ and pEW(\ion{Si}{2}~$\lambda5972$) is found, which implies that Branch group membership can be well-constrained by spectroscopic quantities alone. In general, we find that higher-dimensional GMMs reduce the uncertainty of group membership for objects between the originally defined Branch groups. We also find that the broad-line Branch group becomes nearly distinct with the inclusion of \vsi, indicating that this subclass of SNe Ia may be somehow different from the other groups.
26 pages, 19 figures, ApJ, in press