Magnetars as powering sources of gamma-ray burst associated supernovae, and unsupervized 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 GRB 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 utilizing a χ²-minimization code, MINIM, and numerous parameters are constrained. The median values of ejecta mass (M_ej), magnetar's initial spin period (P_i), and magnetic field (B) for GRB-SNe are determined to be ≈5.2 M, 20.5 ms, and 20.1 × 10¹⁴ G, respectively. We leverage machine learning (ML) algorithms to comprehensively compare the three-dimensional parameter space encompassing M_ej, P_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 unsupervized ML clustering algorithms on the parameters M_ej, P_i, and B for GRB-SNe, SLSNe-I, and FBOTs yields a classification accuracy of ∼95 per cent. Extending these methods to classify GRB-SNe, SLSNe-I, LGRBs, and SGRBs based on P_i and B values results in an accuracy of ∼84 per cent. Our investigations show that GRB-SNe and relativistic Ic-BL SNe presented in this study occupy different parameter spaces for M_ej, P_i, and B than those of SLSNe-I, FBOTs, LGRBs, and SGRBs. This indicates that magnetars with different P_i and B can give birth to distinct types of transients.