Toomre准则的后牛顿修正
Post-Newtonian corrections to Toomre's criterion
摘要：
在后牛顿理论的背景下，研究了二维自引力差动旋转气体盘的引力稳定性。利用微扰方法，应用PN近似的第二迭代方程，得到了小扰动传播的相对论色散关系，并利用这个PN色散关系得到了Toomre局域稳定性判据的PN形式。换句话说，我们发现相对论修正Toomre的标准在第一PN近似。引入了与重力和压力有关的两个稳定性参数$η$和$μ$。我们说明如何确定这些参数的稳定性的牛顿和PN系统。此外，我们表明，在一般情况下，差分旋转流体磁盘是更稳定的PN理论的背景下，相对于牛顿的。此外，我们明确表明，虽然相对论PN校正不稳定的非旋转系统，他们有稳定的作用，在旋转薄盘。最后，我们将结果应用于超大质量中子星（HMNSs）周围的相对论盘，发现虽然牛顿描述预言了局部碎裂的发生，但PN理论仍然与相关模拟一致，并排除了局部碎裂的存在.
英文摘要：
The gravitational stability of a two-dimensional self-gravitating and differentially rotating gaseous disk in the context of post-Newtonian (hereafter PN) theory is studied. Using the perturbative method and applying the second iterated equations of PN approximation, the relativistic version of the dispersion relation for the propagation of small perturbations is found. We obtain the PN version of Toomre's local stability criterion by utilizing this PN dispersion relation. In other words, we find relativistic corrections to Toomre's criterion in the first PN approximation. Two stability parameters $η$ and $μ$ related to gravity and pressure are introduced. We illustrate how these parameters determine the stability of the Newtonian and PN systems. Moreover, we show that, in general, the differentially rotating fluid disk is more stable in the context of PN theory relative to the Newtonian one. Also, we explicitly show that although the relativistic PN corrections destabilize non-rotating systems, they have the stabilizing role in the rotating thin disks. Finally, we apply the results to the relativistic disks around hypermassive neutron stars (HMNSs), and find that although Newtonian description predicts the occurrence of local fragmentations, PN theory remains in agreement with the relevant simulations, and rules out the existence of local fragmentations.
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