准开普勒系统中m=1模的起源、结构和流入
Origins, Structure, and Inflows of m=1 Modes in Quasi-Keplerian Disks
摘要：
模拟结果表明，在类开普勒势周围形成了偏心盘（m=1模），这是一个有趣的话题，可以为类星体提供燃料，形成超大质量黑洞，行星形成和迁移，解释像M31那样的核偏心恒星盘的起源和性质，并驱动模糊的活动星系核环面的形成。我们认为，全球性的，线性正常的m=1模式在无碰撞磁盘，没有限制，磁盘质量可以忽略不计的中心（开普勒）的质量。我们推导出它们的结构和关键的共振特征，并展示它们是如何产生的，向内传播，并驱动盘中的流入/流出和偏心率。我们比较流体动力学模拟这样的磁盘周围的超大质量BH，恒星形成，气体冷却和反馈。我们推导出正常模式结构对磁盘结构，质量分布，厚度，模式的速度和增长率的依赖关系。我们证明，如果在某些半径的盘有质量>~10%的中心质点，模式是线性不稳定的，是自生的。它们以“快模”的形式出现，其模式速度为这些半径处的局部角速度的量级。特征性的整体简正模具有与线性增长率相当的（G*M_0*R_0^{-3}）^{1/2}阶的模式速度，其中M_0是中心质量，R_{0}是封闭盘质量~ M_{0}的半径。它们通过激励偏心率向越来越小的半径向内传播，直到在小半径处这些是“慢模式”。在中等振幅下，在几个~R_0范围内的所有半径上，全球简正模都可以导致近爱丁顿速率的激波和显著的气体流入。
英文摘要：
Simulations show eccentric disks (m=1 modes) forming around quasi-Keplerian potentials, a topic of interest for fueling quasars, forming super-massive BHs, planet formation and migration, explaining the origin and properties of nuclear eccentric stellar disks like that in M31, and driving the formation of the obscuring AGN torus. We consider the global, linear normal m=1 modes in collisionless disks, without the restriction that the disk mass be negligible relative to the central (Keplerian) mass. We derive their structure and key resonance features, and show how they arise, propagate inwards, and drive both inflow/outflow and eccentricities in the disk. We compare with hydrodynamic simulations of such disks around a super-massive BH, with star formation, gas cooling, and feedback. We derive the dependence of the normal mode structure on disk structure, mass profiles, and thickness, and mode pattern speeds and growth rates. We show that, if the disk at some radii has mass of >~10% the central point mass, the modes are linearly unstable and are self-generating. They arise as 'fast modes' with pattern speed of order the local angular velocity at these radii. The characteristic global normal modes have pattern speeds comparable to the linear growth rate, of order (G*M_0*R_0^{-3})^{1/2}, where M_0 is the central mass and R_{0} is the radius where the enclosed disk mass ~M_{0}. They propagate inwards by exciting eccentricities towards smaller and smaller radii, until at small radii these are 'slow modes.' With moderate amplitude, the global normal modes can lead to shocks and significant gas inflows at near-Eddington rates at all radii inside several ~R_0.
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