Magnetars as Powering Sources of Gamma-Ray Burst Associated Supernovae, and Unsupervised Clustering of Cosmic Explosions

We present the semi-analytical light curve modelling of 13 supernovae associated with gamma-ray bursts (GRB-SNe) along with two relativistic broad-lined (Ic-BL) SNe without GRBs association (SNe 2009bb and 2012ap), considering millisecond magnetars as central-engine-based power sources for these events. The bolometric light curves of all 15 SNe in our sample are well-regenerated utilising a \(\chi^2-\)minimisation code, \(\texttt{MINIM}\), and numerous parameters are constrained. The median values of ejecta mass (\(M_{\textrm{ej}}\)), magnetar's initial spin period (\(P_\textrm{i}\)) and magnetic field (\(B\)) for GRB-SNe are determined to be \(\approx\) 5.2 M\(_\odot\), 20.5 ms and 20.1 \(\times\) 10\(^{14}\) G, respectively. We leverage machine learning (ML) algorithms to comprehensively compare the 3-dimensional parameter space encompassing \(M_{\textrm{ej}}\), \(P_\textrm{i}\), and \(B\) for GRB-SNe determined herein to those of H-deficient superluminous SNe (SLSNe-I), fast blue optical transients (FBOTs), long GRBs (LGRBs), and short GRBs (SGRBs) obtained from the literature. The application of unsupervised ML clustering algorithms on the parameters \(M_{\textrm{ej}}\), \(P_\textrm{i}\), and \(B\) for GRB-SNe, SLSNe-I, and FBOTs yields a classification accuracy of \(\sim\)95%. Extending these methods to classify GRB-SNe, SLSNe-I, LGRBs, and SGRBs based on \(P_\textrm{i}\) and \(B\) values results in an accuracy of \(\sim\)84%. Our investigations show that GRB-SNe and relativistic Ic-BL SNe presented in this study occupy different parameter spaces for \(M_{\textrm{ej}}\), \(P_\textrm{i}\), and \(B\) than those of SLSNe-I, FBOTs, LGRBs and SGRBs. This indicates that magnetars with different \(P_\textrm{i}\) and \(B\) can give birth to distinct types of transients.