Counter effects of meridional flows and magnetic fields in stationary axisymmetric self-gravitating barotropes under the ideal MHD approximation: clear examples - toroidal configurations

TL;DR

This paper derives the effects of meridional flows and magnetic fields on stationary axisymmetric self-gravitating barotropes, showing their opposing influences on structure, especially in toroidal configurations, under ideal MHD conditions.

Contribution

It provides a general formulation for current density and vorticity in such systems, highlighting the contrasting effects of flows and magnetic fields on their internal structures.

Findings

Meridional flows make toroids thinner and more compact.

Poloidal magnetic fields tend to elongate density contours.

The combined effects can cancel out, leading to structures similar to systems without these influences.

Abstract

We obtain the general forms for the current density and the vorticity from the integrability conditions of the basic equations which govern the stationary states of axisymmetric magnetized self-gravitating barotropic objects with meridional flows under the ideal magnetohydrodynamics (MHD) approximation. As seen from the stationary condition equations for such bodies, the presence of the meridional flows and that of the poloidal magnetic fields act oppositely on the internal structures. The different actions of these two physical quantities, the meridional flows and the poloidal magnetic fields, could be clearly seen through stationary structures of the toroidal gaseous configurations around central point masses in the framework of Newtonian gravity because the effects of the two physical quantities can be seen in an amplified way for toroidal systems compared to those for spheroidal stars. The meridional flows make the structures more compact, i.e. the widths of toroids thinner, while the poloidal magnetic fields are apt to elongate the density contours in a certain direction depending on the situation. Therefore, the simultaneous presence of the internal flows and the magnetic fields would work as if there were no such different actions within and around the stationary gaseous objects such as axisymmetric magnetized toroids with internal motions around central compact objects under the ideal MHD approximation, although these two quantities might exist in real systems.