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arXiv 0812.4793astro-ph
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准粘性吸积流-- I:平衡条件和渐近行为

Quasi-viscous accretion flow -- I: Equilibrium conditions and asymptotic behaviour

Jayanta K. Bhattacharjee, Atri Bhattacharya, Tapas K. Das, Arnab K. Ray

摘要:

在一种新的方法来研究粘性吸积流,粘度已被引入作为一个扰动效应,涉及一阶修正的$α$ -粘度参数。该方法将求解二阶非线性微分方程(纳维-斯托克斯方程)的问题归结为求解一阶有效方程的问题。粘性打破了稳定流入和流出的解决方案的平衡条件的不变性,并区分风吸积。在动力系统分类下,这种“准粘性”流的唯一可行临界点是鞍点和螺旋线。一个线性化和径向传播的时间相关的扰动引起长期的不稳定性大空间尺度的光盘。此外,在这些相同的长度尺度上,准粘性流的速度演化方程已被转化为与具有排斥势的薛定谔方程形式上的接近。兼容的角动量的光盘的外部区域的运输,粘度有限的长度尺度已被定义为整个空间范围内的吸积过程将是可行的。

英文摘要:

In a novel approach to studying viscous accretion flows, viscosity has been introduced as a perturbative effect, involving a first-order correction in the $α$-viscosity parameter. This method reduces the problem of solving a second-order nonlinear differential equation (Navier-Stokes equation) to that of an effective first-order equation. Viscosity breaks down the invariance of the equilibrium conditions for stationary inflow and outflow solutions, and distinguishes accretion from wind. Under a dynamical systems classification, the only feasible critical points of this "quasi-viscous" flow are saddle points and spirals. A linearised and radially propagating time-dependent perturbation gives rise to secular instability on large spatial scales of the disc. Further, on these same length scales, the velocity evolution equation of the quasi-viscous flow has been transformed to bear a formal closeness with Schrödinger's equation with a repulsive potential. Compatible with the transport of angular momentum to the outer regions of the disc, a viscosity-limited length scale has been defined for the full spatial extent over which the accretion process would be viable.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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