A Generic Dynamical Model of Gamma-ray Burst Remnants

The conventional generic model is deemed to explain the dynamics of $\gamma$-ray burst remnants very well, no matter whether they are adiabatic or highly radiative. However, we find that for adiabatic expansion, the model could not reproduce the Sedov solution in the non-relativistic phase, thus the model needs to be revised. In the present paper, a new differential equation is derived. The generic model based on this equation has been shown to be correct for both radiative and adiabatic fireballs, and in both ultra-relativistic and non-relativistic phase.Comment: 10 pages, LaTeX, 4 postscript figures, accepted for publication in MNRA