自引力作用下的一般多变磁流体：空穴和激波
General Polytropic Magnetofluid under Self-Gravity: Voids and Shocks
摘要：
本文利用多方状态方程研究了自引力气体球中心准球形膨胀空洞（即空泡或气泡）的自相似磁流体动力学。我们显示了各种解析渐近解附近的空隙边界在不同的参数制度，并获得相应的空隙解决方案，通过广泛的数值探索。我们发现新的空的零密度的空边界的解决方案。这些新的空穴解只存在于一般的多变气体中，并具有壳型密度分布。这些空洞的解决方案，如果不遇到磁声临界曲线（MCC），一般接近渐近展开的解决方案，远离中心的空隙与径向距离成正比的速度。我们确定和检查自由膨胀的解决方案，爱因斯坦-德西特膨胀的解决方案，和热膨胀的解决方案，在三个不同的参数制度。在一定条件下，空洞解可以平滑地穿过MCC，也可以通过MHD激波穿过MCC，然后在远离中心的地方合并成具有有限速度和密度的渐近解。我们的一般多变MHD空洞的解决方案提供物理见解空洞的演变，并可能有天体物理学的应用，如大质量的恒星坍缩和爆炸，壳型超新星遗迹和热泡在星际和星系间介质，行星状星云。
英文摘要：
We study the self-similar magnetohydrodynamics (MHD) of a quasi-spherical expanding void (viz. cavity or bubble) in the centre of a self-gravitating gas sphere with a general polytropic equation of state. We show various analytic asymptotic solutions near the void boundary in different parameter regimes and obtain the corresponding void solutions by extensive numerical explorations. We find novel void solutions of zero density on the void boundary. These new void solutions exist only in a general polytropic gas and feature shell-type density profiles. These void solutions, if not encountering the magnetosonic critical curve (MCC), generally approach the asymptotic expansion solution far from the central void with a velocity proportional to radial distance. We identify and examine free-expansion solutions, Einstein-de Sitter expansion solutions, and thermal-expansion solutions in three different parameter regimes. Under certain conditions, void solutions may cross the MCC either smoothly or by MHD shocks, and then merge into asymptotic solutions with finite velocity and density far from the centre. Our general polytropic MHD void solutions provide physical insight for void evolution, and may have astrophysical applications such as massive star collapses and explosions, shell-type supernova remnants and hot bubbles in the interstellar and intergalactic media, and planetary nebulae.
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