Relativistic supernova ejecta colliding with a circumstellar medium: an application to the low-luminosity GRB 171205A

We perform multi-wavelength light curve modeling of the recently discovered low-luminosity gamma-ray burst (GRB) 171205A. The emission model is based on the relativistic ejecta-circumstellar medium (CSM) interaction scenario. The collision of freely expanding spherical ejecta traveling at mildly relativistic velocities with the CSM produces the reverse and forward shocks, which dissipate a part of the kinetic energy of the mildly relativistic ejecta. We show that the early gamma-ray emission followed by an X-ray tail can be well explained by the radiation diffusing out from the shocked gas. Mildly relativistic ejecta with a kinetic energy of $5\times10^{50}$ erg and a wind-like CSM with a mass-loss rate of a few $10^{-4}\ M_\odot$ yr$^{-1}$ for a wind velocity of $10^3$ km s$^{-1}$, which extends up to $\sim 3\times 10^{13}$ cm, are required to account for the gamma-ray luminosity and duration of GRB 171205A. We also calculate the photospheric and non-thermal emission after the optically thick stage, which can fit the late-time X-ray, optical, and radio light curves. Our results suggest that the relativistic ejecta-CSM interaction can be a potential power source for low-luminosity GRBs and other X-ray bright transients.