论文标题
自相似的进化溶液，用于具有有限电导率的紧凑物体周围磁流体
Self-similar Evolutionary Solutions for Accreting Magneto-fluid around a Compact Object with Finite Electrical Conductivity
论文作者
论文摘要
在本文中，我们研究了具有有限的电导率的积分磁流体的时间演化。对于薄磁盘的情况，流体方程与麦克斯韦方程是在简化的一维模型中得出的，该模型忽略了流动的纬度依赖性。通过欧姆定律考虑了有限的电导率；但是，剪切粘应力被忽略了，以及磁盘的自我重力。为了求解控制磁流体动力学行为的集成方程，我们使用了自相似的解决方案。我们介绍了两个无量纲变量，$ s_0 $和$ε_ρ$，它们分别显示了随时间的电导率和密度行为的幅度。研究了每种对磁盘结构的影响。虽然仅通过求解普通的微分方程来获得压力，但分析显示了密度，磁场，径向速度和旋转速度。解决方案表明，$ S_0 $和$ε_ρ$参数会影响磁盘的径向厚度。同样，径向速度和气压对磁盘内部区域的电导率更为敏感。此外，$ε_ρ$参数对小半径的物理量具有更大的影响。
In this paper, we investigate the time evolution an accreting magneto-fluid with finite conductivity. For the case of a thin disk, the fluid equations along with Maxwell equations are derived in a simplified, one-dimensional model that neglects the latitudinal dependence of the flow. The finite electrical conductivity is taken into account for the plasma through Ohm law; however, the shear viscous stress is neglected, as well as the self-gravity of the disk. In order to solve the integrated equations that govern the dynamical behaviour of the magneto-fluid, we have used a self-similar solution. We introduce two dimensionless variables, $S_0$ and $ε_ρ$, which show the magnitude of electrical conductivity and the density behaviour with time, respectively. The effect of each of these on the structure of the disk is studied. While the pressure is obtained simply by solving an ordinary differential equation, the density, the magnetic field, the radial velocity and the rotational velocity are presented analytically. The solutions show that the $S_0$ and $ε_ρ$ parameters affect the radial thickness of the disk. Also, the radial velocity and gas pressure are more sensitive to electrical conductivity in the inner regions of disk. Moreover, the $ε_ρ$ parameter has a more significant effect on physical quantities in small radii.
