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arXiv 2006.03802astro-ph.HE
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有限光深吸积盘中辐射转移方程的解析解

Analytical Solutions of Radiative Transfer Equations in Accretion Discs with Finite Optical Depth

Maryam Samadi, Fahimeh Habibi, Shahram Abbassi

摘要:

本文的主要目的是获得与有限光深吸积盘垂直结构有关的辐射转移方程的解析解。在非灰色大气中,我们采用光学厚度相关的爱丁顿因子来定义平均强度和辐射应力张量之间的关系。解析解实现了两种情况下:(i)辐射平衡,和(ii)一个磁盘与均匀的内部加热,这两种情况下被假定为在局部热力学平衡(LTE),太。这些解使我们能够研究散射和光盘光学深度对出射强度和其他辐射量的可能作用。结果表明,对于第一种情况,爱丁顿因子为常数时的平均强度表面值比因子为可变时的平均强度表面值大3倍。此外,在第一种情况的假设下,散射在圆盘的垂直辐射结构中没有作用。另一方面,对于第二种情况,我们遇到的所有辐射量减少光子破坏概率降低(这相当于增加散射)。此外,对于总光学深度小于1的两种情况,朝向极方向的向外强度变得小于来自盘边缘的强度,这与边缘暗化相反。最后,我们将所得结果应用于基于两种动力学模型的吸积系统的谱计算。因此,我们可以看到总的光学深度是如何随频率变化的,并导致出射光谱的显着变化。

英文摘要:

The main purpose of this paper is to obtain analytical solutions for radiative transfer equations related to the vertical structure of accretion discs with finite optical depth. In the non-gray atmosphere, we employ the optical-depth dependent Eddington factor to define the relationship between the mean intensity and radiation stress tensor. Analytical solutions are achieved for two cases: (i) radiative equilibrium, and (ii) a disc with uniform internal heating and both cases are assumed to be in local thermodynamical equilibrium (LTE), too. These solutions enable us to study the probable role of scattering and disc optical depth on the emergent intensity and other radiative quantities. Our results show that for the first case, the surface value of mean intensity with constant Eddington factor is three times larger than that with a variable factor. Moreover, scattering has no role in the vertical radiative structure of discs with the assumptions of the first case. On the other hand, for the second case, we encounter reductions in all radiative quantities as the photon destruction probability decreases (which is equivalent to increasing scattering). Furthermore, for both cases with total optical depth less than unity, the outward intensity towards the polar direction becomes less than that from the edges of disc which is contrary to limb-darkening. In the end, we apply our results to find the spectrum from accretion systems, based on two dynamical models. Consequently, we can see how the total optical depth varies with frequency and causes remarkable changes in the emergent spectra.

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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