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

Probing Thermal Electrons in GRB Afterglows