发表机构
Astronomical Institute, Czech Academy of Sciences; Faculty of Mathematics and Physics, Charles University; Universidad de Valparaíso（捷克科学院天文研究所; 查理大学数学与物理学院; 瓦尔帕莱索大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
研究天体停泊层中磁分离面与流体分离面是否重合，证明在压力极值及非退化条件下，速度场与磁场零点共置，并推广至电阻及一般非理想MHD情形。
AI 中文摘要
天体停泊层可通过磁分离面或流体分离面来定义。对于恒星风与局部星际介质之间的边界层，可能出现两个分离面，即磁层顶和水层顶。问题在于它们是否相同。为解决此问题，我们研究了定义相应分离面的磁场和速度场的零点在何种条件下在空间上重合。我们分析了非单调压力分布驱动稳态反向流动的理想流体动力学（HD）流动的情况，并证明在三维情形下，压力极值的存在连同速度场上的非退化条件意味着该点也是驻点。转向理想磁流体动力学（MHD）并考虑所有场的正则性，我们构建了动量方程，揭示了其拟线性特性。这使我们能够通过检查矢量场的雅可比矩阵的秩来证明零点的出现。我们发现，对于在压力极值处速度场或磁场的一个给定零点，如果该场的雅可比矩阵非奇异，则对应的矢量场具有共置的零点。我们将分析扩展到电阻性MHD，并进一步扩展到具有一般非理想项的MHD，证明了如果至少一个一阶动量方程是理想的，则驻点和磁场零点共置。即使对于一般流体理论，只要广义非理想项的旋度在其中一个零点处为零或可由磁场和速度场中的线性算子表示，两个零点也共置。一般而言，不排除速度和磁场零点错位的情况。然而，这将需要非理想项旋度的特定性质，这会降低松弛准静态构型的概率。
英文摘要
Astropauses can be defined via magnetic or fluid separatrices. For the boundary layer between the stellar wind and the local interstellar medium, two separatrices can occur, the magnetopause and the hydropause. The question is whether they are identical. To address this, we investigate under which conditions the null points of the magnetic and velocity field, which define the corresponding separatrices, coincide spatially. We analysed the case of a non-monotonous pressure distribution driving stationary counterstreaming ideal HD flows and demonstrate that the existence of an extremum of the pressure in the 3D case together with a non-degeneracy condition on the velocity field implies that this point is also a stagnation point. Turning to ideal MHD and considering the regularity of all fields, we formulated the momentum equations, revealing their quasi-linearity. This allowed us to prove the occurrence of null points by examining the rank of the Jacobians of the vector fields. We found that for a given null point of either the velocity or the magnetic field at the pressure extremum, the pendant vector field has a co-located null if the Jacobian of this field is non-singular. We extended the analysis to resistive MHD and further to MHD with general non-ideal terms and proved that if at least one of the first-order momentum equations is ideal, the stagnation point and the magnetic null point are co-located. Even for general fluid theory, the two null points co-locate as long as the curl of the generalised non-ideal terms is zero at one of them or can be represented by a linear operator in the magnetic and velocity field. In general, it is not excluded that the velocity and magnetic nulls are dislocated. However, this would require specific properties of the curl of the non-ideal term, which would reduce the probability of a relaxed quasi-stationary configuration.
Comments8 pages, 2 figures, 1 table, accepted for publication in A&A
