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arXiv 1806.08217astro-ph.HE
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对流占优吸积流的傅里叶分析

Fourier analysis of advection-dominated accretion flows

Asiyeh Habibi, Shahram Abbassi, Mohsen Shadmehri

摘要:

我们实现了一种新的半解析方法来研究稳态对流主导吸积流(ADAF)的径向自相似解。我们采用通常的$α$ -处方的粘度和所有组件的能量动量张量被认为是。在这种情况下,在球坐标中,问题简化为一组关于纬度角$θ$的八阶非线性微分方程。使用傅立叶展开的所有流量,我们转换为一个大的非线性代数方程组的傅立叶系数的控制微分方程。利用Newton-Raphson方法求解了代数方程组,并在较宽的模型参数范围内研究了ADAF的性质。我们还表明,实现的系列是真正收敛的。我们的数值方法的主要优点是,它不受通常的技术限制,可能会出现解决ADAF微分方程附近的极轴。为了检查的方法的可靠性,我们恢复一些广泛研究的解决方案。我们还介绍了一个新的变$α$粘度模型和新的流出和流入的ADAF的解决方案,提出了使用傅立叶展开级数。

英文摘要:

We implement a new semi-analytical approach to investigate radially self-similar solutions for the steady-state advection-dominated accretion flows (ADAFs). We employ the usual $α$-prescription for the viscosity and all the components of the energy-momentum tensor are considered. In this case, in the spherical coordinate, the problem reduces to a set of eighth-order, nonlinear differential equations with respect to the latitudinal angle $θ$. Using the Fourier expansions for all the flow quantities, we convert the governing differential equations to a large set of nonlinear algebraic equations for the Fourier coefficients. Using the Newton-Raphson method we solve the algebraic equations and ADAF properties are investigated over a wide range of the model parameters. We also show that the implemented series are truly convergent. The main advantage of our numerical method is that it does not suffer from the usual technical restrictions which may arise for solving ADAF differential equations near to the polar axis. In order to check the reliability of the approach, we recover some widely studied solutions. We also introduce a new varying $α$ viscosity model and new outflow and inflow solutions for ADAFs are presented using Fourier expansion series.

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