Very-High-Energy Gamma-Ray Afterglows of GRB 201015A and GRB 201216C

Gamma-ray bursts (GRBs) 201015A and 201216C are valuable cases with detection of very high energy (VHE) gamma-ray afterglows. By analysing their prompt emission data, we find that GRB 201216C is an extremely energetic long GRB with a hard gamma-ray spectrum, while GRB 201015A is a relative sub-energetic, soft spectrum GRB. Attributing their radio-optical-X-ray afterglows to the synchrotron radiation of the relativistic electrons accelerated in their jets, we fit their afterglow lightcurves with the standard external shock model and infer their VHE afterglows from the synchrotron self-Compton scattering process of the electrons. It is found that the jet of GRB 201015A is mid-relativistic ($\Gamma_0=44$) surrounded by a very dense medium ($n=1202$ cm$^{-3}$) and the jet of GRB 201216C is ultra-relativistic ($\Gamma_0=331$) surrounded by a moderate dense medium ($n=5$ cm$^{-3}$). The inferred peak luminosity of the VHE gamma-ray afterglows of GRB 201216C is approximately $10^{-9}$ erg cm$^{-2}$ s$^{-1}$ at $57-600$ seconds after the GRB trigger, making it can be detectable with the MAGIC telescopes at a high confidence level, even the GRB is at a redshift of 1.1. Comparing their intrinsic VHE gamma-ray lightcurves and spectral energy distributions with GRBs~180720B, 190114C, and 190829A, we show that their intrinsic peak luminosity of VHE gamma-ray afterglows at $10^{4}$ seconds post the GRB trigger is variable from $10^{45}$ to $5\times 10^{48}$ erg s$^{-1}$, and their kinetic energy, initial Lorentz factor, and medium density are diverse among bursts.