Statistical Analysis of Early Spectra in Type II and IIb Supernovae

We present a comprehensive analysis of the early spectra of type II and type IIb supernovae (SNe) to explore their diversity and distinguishable characteristics. Using 866 publicly available spectra from 393 SNe, 407 from type IIb SNe (SNe IIb) and 459 from type II SNe (SNe II), we analysed H$α$ and He~I 5876 A at early phases ($<40$ days from the explosion) to identify possible differences between these two SN types. By comparing the pseudo-equivalent width (pEW) and full width at half maximum (FWHM), we find that the strength of the absorption component of these lines serves as a quantitative discriminator, with SNe IIb exhibiting stronger lines at all times. The most significant differences emerge within the first 10-20 days. To assess the statistical significance of these differences, we apply statistical methods and machine-learning techniques. Population density evolution reveals a clear distinction in both pEW and FWHM. Quadratic Discriminant Analysis confirms distinct evolutionary patterns, particularly in pEW, while FWHM variations are less pronounced. A combination of t-distributed Stochastic Neighbour Embedding and Linear Discriminant Analysis effectively separates the two SN types. Additionally, a Random Forest Classifier demonstrates the robustness of pEW and FWHM as classification criteria, allowing for accurate classification of newly observed SNe II and IIb based on computed classification probabilities. Applying our method to low-resolution spectra obtained from the Zwicky Transient Facility Bright Transient, a magnitude-limited survey, we identified 34 misclassified SNe. This revision increases the estimated fraction of SNe IIb from 4.0% to 7.26%. This finding suggests that misclassification significantly impacts the estimated core-collapse SN rate. Our approach enhances classification accuracy and provides a valuable tool for future supernova studies.