We perform detailed variability analysis of two-dimensional viscous, radiation hydrodynamic numerical simulations of Shakura-Sunyaev thin disks around a stellar mass black hole. Disk models are initialized on both the gas-, as well as radiation-, pressure-dominated branches of the thermal equilibrium curve, with mass accretion rates spanning the range from $\dot{M} = 0.01 L_\mathrm{Edd}/c^2$ to $10 L_\mathrm{Edd}/c^2$. An analysis of temporal variations of the numerically simulated disk reveals multiple robust, coherent oscillations. Considering the local mass flux variability, we find an oscillation occurring at the maximum radial epicyclic frequency, $3.5\times 10^{-3}\,t_\mathrm{g}^{-1}$, a possible signature of a trapped fundamental ${\it g}$-mode. Although present in each of our simulated models, the trapped ${\it g}$-mode feature is most prominent in the gas-pressure-dominated case. The total pressure fluctuations in the disk suggest strong evidence for standing-wave ${\it p}$-modes, some trapped in the inner disk close to the ISCO, others present in the middle/outer parts of the disk. Knowing that the trapped ${\it g}$-mode frequency and maximum radial epicyclic frequency differ by only $0.01\%$ in the case of a non-rotating black hole, we simulated an additional initially gas-pressure-dominated disk with a dimensionless black hole spin parameter $a_* = 0.5$. The oscillation frequency in the spinning black hole case confirms that this oscillation is indeed a trapped ${\it g}$-mode. All the numerical models we report here also show a set of high frequency oscillations at the vertical epicyclic and breathing mode frequencies. The vertical oscillations show a 3:2 frequency ratio with oscillations occurring approximately at the radial epicyclic frequency, which could be of astrophysical importance in observed twin peak, high-frequency quasi-periodic oscillations.

中文翻译：

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几何薄圆盘的相对论、轴对称、粘性、辐射流体动力学模拟。二、椎间盘变异

我们对恒星质量黑洞周围的 Shakura-Sunyaev 薄盘的二维粘性、辐射流体动力学数值模拟进行了详细的可变性分析。盘模型在热平衡曲线的以气体和辐射为主的压力分支上初始化，质量吸积率的范围从 $\dot{M} = 0.01 L_\mathrm{Edd}/c ^2$ 到 $10 L_\mathrm{Edd}/c^2$。对数值模拟磁盘的时间变化的分析揭示了多个稳健、相干的振荡。考虑到局部质量通量的变化，我们发现在最大径向周转频率处发生振荡，$3.5\times 10^{-3}\,t_\mathrm{g}^{-1}$，这是被困基波的可能特征${\it g}$-模式。尽管存在于我们的每个模拟模型中，被困 ${\it g}$-mode 特征在气压主导的情况下最为突出。盘中的总压力波动表明存在驻波 ${\it p}$-模式的有力证据，一些被困在靠近 ISCO 的内盘中，其他存在于盘的中间/外部。知道在非旋转黑洞的情况下，被困 ${\it g}$-模式频率和最大径向周转频率仅相差 $0.01\%$，我们模拟了一个额外的初始气压主导盘无量纲黑洞自旋参数 $a_* = 0.5$。旋转黑洞情况下的振荡频率证实这种振荡确实是一个被困 ${\it g}$-模式。我们在此报告的所有数值模型还显示了一组在垂直周转和呼吸模式频率下的高频振荡。