薄吸积盘中的慢压模
Slow pressure modes in thin accretion discs
摘要：
大质量致密天体周围的薄吸积盘可以支持具有方位波数$m=1$的线性区域中的缓慢压力振荡模式。我们认为有限的，平面的光盘组成的正压流体的各种表面密度分布和证明-通过WKB分析和数值解的特征值问题-这些模式是稳定的，并具有空间尺度相媲美的光盘的大小。我们表明，本征值方程可以映射到一个薛定谔方程。对该方程的分析表明，所有本征模都具有离散谱。我们发现，我们所考虑的所有模式支持负频率本征模式，然而，正本征频率模式只存在于幂律光盘，虽然物理上不感兴趣的值的幂律指数$β$和正压指数$γ$。
英文摘要：
Thin accretion discs around massive compact objects can support slow pressure modes of oscillations in the linear regime that have azimuthal wavenumber $m=1$. We consider finite, flat discs composed of barotropic fluid for various surface density profiles and demonstrate--through WKB analysis and numerical solution of the eigenvalue problem--that these modes are stable and have spatial scales comparable to the size of the disc. We show that the eigenvalue equation can be mapped to a Schrödinger-like equation. Analysis of this equation shows that all eigenmodes have discrete spectra. We find that all the models we have considered support negative frequency eigenmodes; however, the positive eigenfrequency modes are only present in power law discs, albeit for physically uninteresting values of the power law index $β$ and barotropic index $γ$.
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