Unifying the Circumstellar Environment in Broad-lined Type Ic Radio Supernovae toward Off-axis Gamma-Ray Burst Exploration

Abstract Decades have passed since the first confirmed association between a broad-lined Type Ic supernova (Type IcBL SN) and a long gamma-ray burst (GRB), and the number of known GRB-SN associations has steadily increased. However, it is important to note that the radiation from GRB afterglows and the radio emission from SNe may both be produced by outflows evolving within the same ambient medium. In this study, we present the first comprehensive theoretical predictions of radio emission from a Type IcBL supernova associated with a GRB jet, explicitly accounting for the structure of the ambient medium. We model each component of the radio emission, with particular emphasis on exploring wide ranges of isotropic explosion energy and viewing angle in our GRB afterglow calculations. We show that, within specific regions of parameter space, the composite radio light curve exhibits a characteristic double-peaked structure. This clear double-peaked feature emerges when either (1) the isotropic explosion energy is small (low-luminosity GRB) or (2) the viewing angle is large (off-axis GRB). Our results demonstrate that follow-up radio observations carried out within a few years of the optical discovery of nearby Type IcBL SNe (100 Mpc) can provide a unique diagnostic of off-axis GRBs that would otherwise remain undetected in Type IcBL SNe. This represents a step toward revealing the nature of long GRB progenitors and clarifying their connection to Type IcBL SNe.