Some Notes on Self-similar Axisymmetric Force-free Magnetic Fields and Rotating Magnetospheres

摘要: An axisymmetric force-free magnetic field in spherical coordinates has a relationship between its azimuthal component to poloidal flux-function. A power law dependence for the connection admits separable solutions but poses nonlinear eigenvalue boundary-value problem separation parameter (Low and Lou, Astrophys. J. 352, 343 (1990)).When atmosphere of star is rotating complexity increases. These Notes consider spectrum, providing an understanding eigen functions field's degree multi-polarity, rotation rate radial decay as illustrated through polytropic equation state. The are restricted uniform fields. Dominant effects presented changing spatial patterns from those without rotation. For differential nonaxisymmetric fields there may be even richer topological structure governing equations have remained intractable date. Perhaps methods discussion given here uniformly situation indicate possible procedure such problems that need solved urgently more complete stellar atmospheres.