Probing Thermal Electrons in GRB Afterglows

Particle-in-cell simulations have unveiled that shock-accelerated electrons do not follow a pure power-law distribution, but have an additional low-energy "thermal" part, which owns a considerable portion of the total energy of electrons. Investigating the effects of these thermal electrons on gamma-ray burst (GRB) afterglows may provide valuable insights into the particle acceleration mechanisms. We solve the continuity equation of electrons in the energy space, from which multi-wavelength afterglows are derived by incorporating processes including synchrotron radiation, synchrotron self-absorption, synchrotron self-Compton scattering, and gamma-gamma annihilation. First, there is an underlying positive correlation between temporal and spectral indices due to the cooling of electrons. Moreover, thermal electrons would result in the simultaneous non-monotonic variation in both spectral and temporal indices at multi-wavelength, which could be individually recorded by the 2.5-meter Wide Field Survey Telescope and Vera Rubin Observatory Legacy Survey of Space and Time (LSST). The thermal electrons could also be diagnosed from afterglow spectra by synergy observation in the optical (with LSST) and X-ray bands (with the Microchannel X-ray Telescope on board the Space Variable Objects Monitor). Finally, we use Monte Carlo simulations to obtain the distribution of peak flux ratio ($R_{\rm X}$) between soft and hard X-rays, and of the time delay ($\Delta t$) between peak times of soft X-ray and optical light curves. The thermal electrons significantly raise the upper limits of both $R_{\rm X}$ and $\Delta t$. Thus the distribution of GRB afterglows with thermal electrons is more dispersive in the $R_{\rm X} - \Delta t$ plane.