A simple family of models for eccentric Keplerian fluid disks
A simple family of models for eccentric Keplerian fluid disks
复制标题
DOI：
10.1086/323713
复制
发表时间：
2001-11-01
影响因子：
5.3
通讯作者：
Statler, TS
中科院分区：
文献类型：
--
作者：
Statler, TS
为了实现长寿命配置，流体盘的密度应该沿着流线保持恒定，以防止在每个轨道上循环地进行压缩（PdV）功。在纯开普勒势中，沿匀速离心率排列的椭圆流线流动将满足这一条件。对于大多数密度剖面，由压力梯度驱动的差进动会破坏对中；然而，在极薄近似中，存在一组简单平衡，其中进动频率在所有半径上都是相同的。因此，这些圆盘可能在显著的离心率下寿命较长。在保持进动率的同时，通过放宽中心附近任意小的过渡区域沿流线的恒定要求，可以使密度达到轴对称r—>0。在小偏心极限下，模型可以看作是受声扰动的轴对称圆盘，进动速率符合线性理论。扰动是一种类似于海浪的行波，流体在中心质量的引力场中周期性地上升和下降。一般来说，偏心圆盘的预期发射线剖面显示出强烈的不对称，在极端情况下，容易被误解为具有显著速度偏移的单一窄线。
To be in a long-lived configuration, the density in a fluid disk should be constant along streamlines to prevent compressional (PdV) work from being done cyclically around every orbit. In a pure Kepler potential, flow along aligned elliptical streamlines of constant eccentricity will satisfy this condition. For most density profiles, differential precession driven by the pressure gradient will destroy the alignment; however, in the razor-thin approximation there is a family of simple equilibria in which the precession frequency is the same at all radii. These disks may therefore be long-lived at significant eccentricities. The density can be made axisymmetric as r-->0 while maintaining the precession rate by relaxing the requirement of constancy along streamlines in an arbitrarily small transition region near the center. In the limit of small eccentricity, the models can be seen as acoustically perturbed axisymmetric disks, and the precession rate is shown to agree with linear theory. The perturbation is a traveling wave similar to an ocean wave, with the fluid rising and falling epicyclically in the gravitational field of the central mass. The expected emission-line profiles from the eccentric disks are shown to be strongly asymmetric in general and, in extreme cases, prone to misinterpretation as single narrow lines with significant velocity offsets.