Modeling the Multi-band Light Curves of the Optical–NIR Afterglows of Four Gamma-Ray Bursts and Their Associated Supernovae

In this paper, we use (broken) power-law plus Ni models to fit the multi-band light curves of the optical and near-infrared (NIR) counterparts of four gamma-ray bursts (GRBs 011121, 100316D, 130702A, and GRB 161219B). We find that the models can account for the light curves of the optical– NIR counterparts which can be divided into the GRB afterglows and their associated supernovae (SNe 2001ke, 2010bh, 2013dx, and 2016jca, respectively). The most parameters we derive are consistent with previous studies. However, the Ni masses we derive are higher than that in the literatures (except for that of GRB 100316D/SN 2010bh). The difference of the Ni masses might be due to the fact that the Ni masses in the literatures are obtained by fitting the quasi-bolometric light curves which are usually (significantly) underestimated, and dimmer than the theoretical bolometric light curves reproduced by the best-fitting parameters we derive. Our results demonstrate that the spectral energy distributions (SEDs) of SNe associated with GRBs can be well described by the blackbody model, and the Ni model can account for their multi-band light curves. We suggest that the Ni masses of a fraction of GRB-SNe have been underestimated.