A Mechanical Model for Magnetized Relativistic Blastwaves

TL;DR

This paper extends a mechanical model for relativistic blastwaves to include magnetization, improving energy conservation and aligning better with numerical simulations compared to traditional pressure-balance models.

Contribution

The authors generalize the mechanical model to magnetized ejecta, enhancing accuracy and energy conservation in modeling relativistic blastwaves with arbitrary magnetization.

Findings

The model conserves energy better than pressure-balance models.

Deviation from energy conservation is less than 25% at large radii.

Higher magnetization leads to earlier reverse shock crossing.

Abstract

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, and is inconsistent with existing MHD numerical simulation results. A mechanical model of non-magnetized blastwaves was proposed in previous work 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 than the pressure-balance treatment in terms of energy conservation. For a constant central engine wind 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. For a finite life time of the central engine, the reverse shock crosses the magnetized ejecta earlier for the ejecta with a higher $\sigma_{\rm ej}$, which is consistent with previous analytical and numerical results. In general, the mechanical model is more precise than the traditional analytical models with results closer to those of numerical simulations.