Schwarzschild黑洞周围相对论性吸积盘中的有效声速
Effective sound speed in relativistic accretion discs around Schwarzschild black holes
摘要：
对于低角动量轴对称吸积流，在垂直方向上保持流体静力平衡时，临界点处的马赫数偏离1，导致临界点和音速点的非同构。这引入了一些不希望的复杂性，同时分析处理的固定积分吸积解决方案和相应的相图。我们建议，引入一个有效的动态声速可以解决这个问题，在一个优雅的方式。我们线性微扰完整的时空相关的广义相对论欧拉方程和连续性方程的结构和动力学的吸积盘周围的Schwarzschild黑洞的垂直平衡和识别的声音度规嵌入在固定的背景流。这种度规描述了线性声扰动在吸积流中的传播。我们构造对应于该声扰动的波动方程，并找到这种扰动的传播速度。最后指出，通常的热力学声速应该用通过动力学微扰得到的线性声波的传播速度来代替。这种替换将使临界点处的马赫数值等于1。使用上述有效声速将导致改进的固定盘结构，其中临界点和音速点将相同。
英文摘要：
For low angular momentum axially symmetric accretion flow maintained in hydrostatic equilibrium along the vertical direction, the value of the Mach number at the critical points deviates from unity, resulting in the non-isomorphism of the critical and the sonic points. This introduces several undesirable complexities while analytically dealing with the stationary integral accretion solutions and the corresponding phase portraits. We propose that introduction of an effective dynamical sound speed may resolve the issue in an elegant way. We linear perturb the full spacetime-dependent general relativistic Euler and the continuity equations governing the structure and the dynamics of accretion disc in vertical equilibrium around Schwarzschild black holes and identify the sonic metric embedded within the stationary background flow. Such metric describes the propagation of the linear acoustic perturbation inside the accretion flow. We construct the wave equation corresponding to that acoustic perturbation and find the speed of propagation of such perturbation. We finally show that the ordinary thermodynamic sound speed should be substituted by the speed of propagation of the linear acoustic wave which has been obtained through the dynamical perturbation. Such substitution will make the value of Mach number at the critical point to be equal to unity. Use of the aforementioned effective sound speed will lead to a modified stationary disc structure where the critical and the sonic points will be identical.
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