有限电导率致密物体周围磁流体吸积的自相似演化解
Self-similar Evolutionary Solutions for Accreting Magneto-fluid around a Compact Object with Finite Electrical Conductivity
摘要：
本文研究了具有有限电导率的吸积磁流体的时间演化。对于薄盘的情况下，流体方程以及麦克斯韦方程组推导出一个简化的，一维的模型，忽略了纬度的依赖性的流量。通过欧姆定律考虑了等离子体的有限电导率，但忽略了剪切粘性应力以及圆盘的自重。为了求解控制磁流体动力学行为的积分方程，我们使用了自相似解。我们引入了两个无量纲变量，$S_0$和$ε_ρ$，分别表示电导率的大小和密度随时间的行为。每个这些对磁盘的结构的影响进行了研究。压力通过求解一个常微分方程得到，密度、磁场、径向速度和旋转速度通过解析的方法得到。结果表明，$S_0$和$ε_ρ$参数对圆盘径向厚度有影响。同时，径向速度和气体压力对圆盘内部区域的电导率更为敏感。此外，$ε_ρ$参数对小半径中的物理量具有更显著的影响。
英文摘要：
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.
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