黑洞吸积盘中惯性声学模的共转不稳定性：非正压流
Corotational Instability of Inertial-Acoustic Modes in Black-Hole Accretion Discs: Non-Barotropic Flows
摘要：
本文研究了共转共振对黑洞吸积盘惯性声波振荡（p模）的影响。以前的工作已经表明，正压流（其中的压力只取决于密度），波吸收在共转共振时，可以导致模式增长时，光盘涡度，$ζ=κ^2/(2ΩΣ)$（其中$Ω, κ, Σ$是旋转速率，径向周转频率和表面密度的光盘，分别），在共转半径有一个正梯度。本文将共转共振效应的分析推广到非正压流体。我们表明，模式不稳定性的标准是由有限的径向Brunt-Väsälä频率的光盘修改。我们推导了密度波入射到共转势垒时的反射率的解析表达式，并计算了具有不同$α$ -粘性参数化的圆盘模型的全局p模的频率和增长率.我们发现，对于具有恒定绝热指数$Γ$的圆盘流体，超反射和模式增长依赖于有效涡度的梯度，$ζ_{\rm eff} = ζ/S^{2/Γ}$（其中$S \equiv P/Σ^Γ$测量熵）：当$dζ_{\rm eff}/dr > 0$在共转半径时，波吸收导致p模式的放大。我们的计算表明，最低阶的p模式与方位波数$m=2, 3, 4,...$有最大的增长率，与频率近似（但不同）的$2:3:4...$相称的比例。我们讨论了我们的结果的影响，在吸积黑洞系统中观察到的高频准周期振荡。
英文摘要：
We study the effect of corotation resonance on the inertial-acoustic oscillations (p-modes) of black-hole accretion discs. Previous works have shown that for barotropic flows (where the pressure depends only on the density), wave absorption at the corotation resonance can lead to mode growth when the disc vortensity, $ζ=κ^2/(2ΩΣ)$ (where $Ω, κ, Σ$ are the rotation rate, radial epicyclic frequency and surface density of the disc, respectively), has a positive gradient at the corotation radius. Here we generalize the analysis of the corotation resonance effect to non-barotropic fluids. We show that the mode instability criterion is modified by the finite radial Brunt-Väsälä frequency of the disc. We derive an analytic expression for the reflectivity when a density wave impinges upon the corotation barrier, and calculate the frequencies and growth rates of global p-modes for disc models with various $α$-viscosity parameterizations. We find that for disc fluids with constant adiabatic index $Γ$, super-reflection and mode growth depend on the gradient of the effective vortensity, $ζ_{\rm eff} = ζ/S^{2/Γ}$ (where $S \equiv P/Σ^Γ$ measures the entropy): when $dζ_{\rm eff}/dr > 0$ at the corotation radius, wave absorption leads to amplification of the p-mode. Our calculations show that the lowest-order p-modes with azimuthal wave number $m=2, 3, 4,...$ have the largest growth rates, with the frequencies approximately in (but distinct from) the $2:3:4...$ commensurate ratios. We discuss the implications of our results for the high-frequency quasi-periodic oscillations observed in accreting black-hole systems.
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