Ejecta Width and Magnetization Reflected in Gamma-Ray Burst Early Afterglows: Implication for Reverse Shock Component and Shallow Decay Phase

Abstract: To study the ejecta property dependence of the gamma-ray burst (GRB) afterglow, we carry out spherically symmetrical one-dimensional special relativistic magneto-hydrodynamic simulations of magnetized outflows with an adaptive mesh refinement method. The Lorentz factor evolutions of forward and reverse shocks induced by the interaction between magnetized ejecta and an ambient medium are investigated for a wide range of magnetization and width of the ejecta. The forward shock evolution is described by the magnetic acceleration, coasting, transition, and self-similar deceleration phases. According to our simulation results, we numerically calculate the corresponding radiation. Based on our numerical results, to model afterglow light curves in general cases, we construct semi-analytical formulae for the Lorentz factor evolutions. The magnetization and ejecta width dependence are clearly seen in the reverse shock light curves. The transition phase with a reasonable ejecta width can reproduce the shallow decay phase in the observed GRB afterglow. The inverse Compton emission in the magnetic acceleration phase can be responsible for the very steep rise of the early TeV emission in GRB221009A.