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 $χ^2-$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.