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arXiv 1102.2076astro-ph.HE
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自相似阶段磁环的相对论展开II:磁化外流与周围等离子体的相互作用

Relativistic Expansion of Magnetic Loops at the Self-similar Stage II: Magnetized outflows interacting with the ambient plasma

Hiroyuki R. Takahashi, Eiji Asano, Ryoji Matsumoto

摘要:

我们通过假设轴对称和纯径向流动,得到了相对论膨胀磁环的自相似解。忽略恒星自转和周围等离子体中的磁场。我们包括了中心恒星的牛顿引力。这些解决方案是从我们以前的工作(高桥,浅野,和松本2009),考虑到不连续性,如接触不连续性和冲击扩展。整体等离子体流包括三个区域,流出区域,后冲击区域,和周围的等离子体。它们被两个不连续性分开。解的特征在于径向速度,它在我们的解决方案中起着自相似参数的作用。激波洛伦兹因子随半径的增大而逐渐增大。它可以近似地用半径的幂来表示,幂律指数为0.25。我们还进行了磁流体动力学模拟的磁环的演变,研究我们的解析解的稳定性和通用性。我们使用解析解作为初始条件和内边界条件。我们证实,我们的解决方案是稳定的模拟时间,数值结果很好地恢复解析解。然后通过改变周围等离子体密度ρ_0 \propto r^{-δ}的幂律指数δ,进行了数值模拟,研究了我们解的一般性。我们改变了解析解中的幂律指数δ从3.5。在所有的模拟中,解析解被用作激波内部的初始条件。我们观察到,当δ大于3时,冲击洛伦兹因子随时间增加,而当δ小于3时,冲击洛伦兹因子随时间减小。激波洛伦兹因子与t^{(δ-3)/2}成正比。这些结果与Shapiro(1979)的分析研究一致。

英文摘要:

We obtained self-similar solutions of relativistically expanding magnetic loops by assuming axisymmetry and a purely radial flow. The stellar rotation and the magnetic fields in the ambient plasma are neglected. We include the Newtonian gravity of the central star. These solutions are extended from those in our previous work (Takahashi, Asano, & Matsumoto 2009) by taking into account discontinuities such as the contact discontinuity and the shock. The global plasma flow consists of three regions, the outflowing region, the post shocked region, and the ambient plasma. They are divided by two discontinuities. The solutions are characterized by the radial velocity, which plays a role of the self-similar parameter in our solutions. The shock Lorentz factor gradually increases with radius. It can be approximately represented by the power of radius with the power law index of 0.25. We also carried out magnetohydrodynamic simulations of the evolution of magnetic loops to study the stability and the generality of our analytical solutions. We used the analytical solutions as the initial condition and the inner boundary conditions. We confirmed that our solutions are stable over the simulation time and that numerical results nicely recover the analytical solutions. We then carried out numerical simulations to study the generality of our solutions by changing the power law index δof the ambient plasma density ρ_0 \propto r^{-δ}. We alter the power law index δfrom 3.5 in the analytical solutions. The analytical solutions are used as the initial conditions inside the shock in all simulations. We observed that the shock Lorentz factor increases with time when δis larger than 3, while it decreases with time when δis smaller than 3. The shock Lorentz factor is proportional to t^{(δ-3)/2}. These results are consistent with the analytical studies by Shapiro (1979).

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