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 χ²-minimisation code, MINIM, and numerous parameters are constrained. The median values of ejecta mass (Mₑⱼ), magnetar's initial spin period (Pᵢ) 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 3-dimensional parameter space encompassing Mₑⱼ, Pᵢ, 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 Mₑⱼ, Pᵢ, and B for GRB-SNe, SLSNe-I, and FBOTs yields a classification accuracy of ~95%. Extending these methods to classify GRB-SNe, SLSNe-I, LGRBs, and SGRBs based on Pᵢ and B values results in an accuracy of ~84%. Our investigations show that GRB-SNe and relativistic Ic-BL SNe presented in this study occupy different parameter spaces for Mₑⱼ, Pᵢ, and B than those of SLSNe-I, FBOTs, LGRBs and SGRBs. This indicates that magnetars with different Pᵢ and B can give birth to distinct types of transients.