辐射吸积盘的维里定理
Virial theorem for radiating accretion discs
摘要：
本文导出了一个围绕致密物体的辐射自引力吸积盘维里定理的连续形式。中心物体是点状的，但我们可以避免其引力势的正则化。这是通过将修改后的Pohozaev-Rellich恒等式仅应用于圆盘的引力势来实现的。该定理适用于一般的静止构形，包括不连续流（激波、接触不连续）。它是用来测试一个模型的自引力辐射吸积盘的数值解。本文提出的维里定理在分析天体物理学中那些中心质量与流体质量相当且都不可忽略的（可能是辐射的）流体动力系统时是有用的。
英文摘要：
A continuum version of the virial theorem is derived for a radiating self-gravitating accretion disc around a compact object. The central object is point-like, but we can avoid the regularization of its gravitational potential. This is achieved by applying a modified Pohozaev-Rellich identity to the gravitational potential of the disk only. The theorem holds for general stationary configurations, including discontinuous flows (shock waves, contact discontinuities). It is used to test numerical solutions of a model of self-gravitating radiative accretion discs. The presented virial theorem should be useful in the analysis of those (possibly radiating) hydrodynamical systems in astrophysics where the central mass and the mass of the fluid are comparable and none of them can be neglected.
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