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arXiv 0708.1124astro-ph
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吸积盘中翘曲扩散的数值研究

Warp diffusion in accretion discs: a numerical investigation

Giuseppe Lodato, J. E. Pringle

摘要:

本文用数值方法研究了翘曲吸积盘的演化。在这里,我们集中在这里的制度,翘曲演变扩散。通过将数值结果与一个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。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。特别是,我们发现,在低粘度的扩散系数对粘度的反向依赖性打破,使$α_2$永远不会变得大于一个饱和值$α_{\rm max}$的顺序统一。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上升(或自旋下降)。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强烈影响它。这种影响应考虑与照顾时,翘曲盘的演变建模。这强调了需要测试上述结果使用不同的数值方案,并具有更高的分辨率,以调查的程度,数值模拟能够提供准确的建模复杂的流体动力学的翘曲盘。(节录)

英文摘要:

In this paper we explore numerically the evolution of a warped accretion disc. Here, we focus here on the regime 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. 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 $α_{\rm max}$ of order 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 modeling the evolution of warped discs. This emphasises 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 modeling of the complex fluid dynamics of warped discs. (Abridged)

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