吸积盘冷却中的重力不稳定性表征
Characterising the Gravitational Instability in Cooling Accretion Discs
摘要：
本文对冷却气体吸积盘中引力不稳定性引起的结构进行了数值分析。对于足够低的冷却速率达到准定常配置，与不稳定性饱和在一个有限的振幅在一个勉强稳定的磁盘。我们发现饱和振幅与冷却参数β = t_cool / t_dyn的平方根成反比，这表明不稳定性引起的加热速率与密度波的能量密度成正比.我们发现，在饱和状态下，弱冲击在每个动态时间内消耗的能量约为波能的20%。从傅立叶分析的光盘结构，我们发现，虽然方位波数是大致恒定的半径，平均径向波数随半径增加，与当地最不稳定的波长对应的主导模式。我们证明，在相对较低的质量盘激发的密度波总是接近共同旋转，偏离它约10%.This可以理解的流动多普勒频移相位马赫数-模式的速度自我调整，使进入螺旋臂的流动总是音速。这对通过自重进行的运输在多大程度上可以模拟为粘性过程产生了深远的影响。因此，我们的结果提供了（a）如何建立低冷却速率的自调节机制的详细描述，（b）描述通过有效粘度的自重力诱导的运输所需的条件的澄清，（c）在碎裂发生之前的密度扰动的最大幅度的估计，以及（d）估算不同热状态下密度扰动的简单方法。
英文摘要：
We perform numerical analyses of the structure induced by gravitational instabilities in cooling gaseous accretion discs. For low enough cooling rates a quasi-steady configuration is reached, with the instability saturating at a finite amplitude in a marginally stable disc. We find that the saturation amplitude scales with the inverse square root of the cooling parameter beta = t_cool / t_dyn, which indicates that the heating rate induced by the instability is proportional to the energy density of the induced density waves. We find that at saturation the energy dissipated per dynamical time by weak shocks due is of the order of 20 per cent of the wave energy. From Fourier analysis of the disc structure we find that while the azimuthal wavenumber is roughly constant with radius, the mean radial wavenumber increases with radius, with the dominant mode corresponding to the locally most unstable wavelength. We demonstrate that the density waves excited in relatively low mass discs are always close to co-rotation, deviating from it by approximately 10 per cent. This can be understood in terms of the flow Doppler-shifted phase Mach number -- the pattern speed self-adjusts so that the flow into spiral arms is always sonic. This has profound effects on the degree to which transport through self-gravity can be modelled as a viscous process. Our results thus provide (a) a detailed description of how the self-regulation mechanism is established for low cooling rates, (b) a clarification of the conditions required for describing the transport induced by self-gravity through an effective viscosity, (c) an estimate of the maximum amplitude of the density perturbation before fragmentation occurs, and (d) a simple recipe to estimate the density perturbation in different thermal regimes.
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