On the Structure of Advective Accretion Disks at High Luminosity
On the Structure of Advective Accretion Disks at High Luminosity
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高光度平流吸积盘的结构研究
DOI：
10.1086/319432
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发表时间：
2000
期刊：
影响因子：
--
通讯作者：
I. Novikov
中科院分区：
文献类型：
--
作者：
I. V. Artemova;G. Bisnovatyi;I. Igumenshchev;I. Novikov
构造了黑洞周围光学厚度平流吸积盘的整体解。通过数值求解对应于定常、轴对称、几何薄圆盘的一组常微分方程组，得到解。我们特别注意在方程的奇点上一致满足正则性条件。为此，我们在奇点处对解进行了解析展开，并在迭代数值过程中使用了展开系数。对于粘性参数α和质量吸积率的大范围取值，我们得到了一致的跨音速解。我们比较了粘性的两种不同公式的结果：第一种是假设剪应力与压力成正比，另一种是假设剪应力与角速度的梯度成正比。我们发现，在对应于剪应力与压力成正比的解中，存在两个奇点。内部奇点位于黑洞周围最后一个稳定轨道附近。该点根据α的值和吸积率将其类型从鞍点更改为节点。外奇点位于较大半径处，且始终为鞍型。我们认为，与前人的研究相反，节点型内奇点不会引入多重解。只有一条与唯一整体解对应的积分曲线同时通过内奇点和外奇点，而与内奇点的类型无关。当剪应力与角速度梯度成正比时，解有一个奇点，该奇点始终是鞍型的，并且对应于唯一的整体解。两种粘性应力处方所对应的吸积盘结构相似。
Global solutions of optically thick advective accretion disks around black holes are constructed. The solutions are obtained by solving numerically a set of ordinary differential equations corresponding to a steady, axisymmetric, geometrically thin disk. We pay special attention to consistently satisfying the regularity conditions at singular points of the equations. For this reason, we analytically expand the solution at the singular point and use coefficients of the expansion in our iterative numerical procedure. We obtain consistent transonic solutions for a wide range of values of the viscosity parameter α and mass accretion rate. We compare results for two different prescriptions for the viscosity: the first is to assume that the shear stress is proportional to the pressure, and the other is to assume that it is proportional to the gradient of the angular velocity. We find that there are two singular points in the solutions corresponding to a shear stress proportional to the pressure. The inner singular point is located close to the last stable orbit around the black hole. This point changes its type from a saddle to node depending on the value of α and the accretion rate. The outer singular point is located at a larger radius and is always of the saddle type. We argue that, contrary to the previous investigations, a nodal-type inner singular point does not introduce multiple solutions. Only one integral curve, which corresponds to the unique global solution, simultaneously passes the inner and outer singular points independently of the type of inner singular point. Solutions for the case when shear stress is proportional to the angular velocity gradient have one singular point which is always of the saddle type and corresponds to the unique global solution. The structure of accretion disks corresponding to the two prescriptions for the viscous stress are similar.