A mechanical model for magnetized relativistic blastwaves

The evolution of a relativistic blastwave is usually delineated under the assumption pressure balance between forward- and reverse-shocked regions. However, such treatment violates energy conservation law, inconsistent with existing MHD numerical simulation results. A mechanical model non-magnetized blastwaves was proposed in previous work to solve problem. In this paper, we generalize case driven by an ejecta arbitrary magnetization parameter $\sigma_{\rm ej}$. We test our modified considering long-lasting magnetized found that it much better than pressure-balance terms conservation. For constant central engine wind luminosity $L_{\rm ej} = 10^{47}{\rm erg~s^{-1}}$ < 10$, deviation from negligibly small at radii, but only reaches less $25\%$ even $10^{19}{\rm cm}$ engine. finite life time engine, reverse shock crosses earlier for higher ej}$, which consistent analytical general, more precise traditional models results closer those simulations.