Warp diffusion in accretion discs: a numerical investigation
Warp diffusion in accretion discs: a numerical investigation
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吸积盘中的扭曲扩散：数值研究
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发表时间：
2007
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通讯作者：
Cambridge
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作者：
G. Lodato;J. C. D. O. Physics;Astronomy;U. I. D. O. Astronomy;Cambridge
本文用数值方法研究了翘曲吸积盘的演化。虽然以前的分析集中在光盘足够厚的情况下，翘曲作为波传播，我们在这里集中在相反的制度薄光盘，翘曲扩散发展。通过将数值结果与简单的扩散模型进行比较，我们能够确定翘曲的扩散系数α 2作为相关圆盘参数的函数，例如其厚度，特别是其粘度。我们发现，虽然在一般情况下，光盘的行为是很好地再现的扩散模型和相对较大的粘度的翘曲扩散是很好地描述的线性理论（特别是确认的翘曲扩散系数是成反比的粘度），显着的非线性效应是存在的粘度变小，但仍然占主导地位的波传播效应。特别地，我们发现扩散系数对粘度的反相关性在低粘度下破裂，因此α 2永远不会大于单位数量级的饱和值α max。这可能会对存在翘曲圆盘的系统的演化产生重大影响。特别是，它影响了Bardeen-Petterson效应中弯曲半径的位置，从而影响了星系核中超大质量黑洞的自旋。此外，我们还发现，虽然翘曲扩散的速率并不显着依赖于详细的粘度配方，产生的内部进动率的翘曲是强烈的影响，它。这样的效果时，应考虑与照顾翘曲盘的演变建模。这强调了需要使用不同的数值方案和更高的分辨率来测试上述结果，以研究数值模拟能够提供翘曲盘的复杂流体动力学的精确建模的程度。
In this paper we explore numerically the evolution of a warped accretion disc. While previous analyses have concentrated on the case where the disc is thick enough that the warp propagates as a wave, we focus here on the opposite regime of a thin disc, where the warp evolves diffusively. By comparing the numerical results to a simple diffusion model, we are able to determine the diffusion coefficient of the warp, α 2 , as a function of the relevant disc parameters, such as its thickness and especially its viscosity. We find that while in general the disc behaviour is well reproduced by the diffusion model and for relatively large viscosities the warp diffusion is well described by the linear theory (in particular confirming that the warp diffusion coefficient is inversely proportional to viscosity), significant non-linear effects are present as the viscosity becomes smaller, but still dominates over wave-propagation effects. In particular, we find that the inverse dependence of the diffusion coefficient on viscosity breaks down at low viscosities, so that α 2 never becomes larger than a saturation value α max of the order of unity. This can have major consequences in the evolution of systems where a warped disc is present. In particular, it affects the location of the warp radius in the Bardeen-Petterson effect and therefore the spin-up (or spin-down) of supermassive black holes in the nuclei of galaxies. Additionally, we also find that while the rate of warp diffusion does not depend significantly on the detailed viscosity formulation, the rate of internal precession generated by the warp is strongly affected by it. Such effects should be considered with care when modelling the evolution of warped discs. This emphasizes the need to test the above results using different numerical schemes, and with higher resolution, in order to investigate the degree to which numerical simulations are able to provide accurate modelling of the complex fluid dynamics of warped discs.