http://arxiv.org/abs/2104.06450
The evolution of a relativistic blastwave is usually delineated under the assumption of pressure balance between forward- and reverse-shocked regions. However, such a treatment usually violates the energy conservation law. A mechanical model of non-magnetized blastwaves was proposed in previous works to solve the problem. In this paper, we generalize the mechanical model to the case of a blastwave driven by an ejecta with an arbitrary magnetization parameter $\sigma_{\rm ej}$. We test our modified mechanical model by considering a long-lasting magnetized ejecta and found that it is much better in terms of energy conservation than the pressure-balance treatment. For a constant luminosity $L_{\rm ej} = 10^{47}{\rm erg~s^{-1}}$ and $\sigma_{\rm ej} < 10$, the deviation from energy conservation is negligibly small at small radii, but only reaches less than $25\%$ even at $10^{19}{\rm cm}$ from the central engine. Assuming a finite lifetime of the central engine, the reverse shock crosses the magnetized ejecta earlier for the ejecta wiith a higher $\sigma_{\rm ej}$. After shock crossing, all the ejecta energy is injected into the blastwave.
S. Ai and B. Zhang
Thu, 15 Apr 2021
41/59
Comments: 7 pages, 2 figures