General axisymmetric magnetohydrodynamic flows: Theory and solutions

We formulate the theory of general axisymmetric, steady state, nonrelativistic, ideal magnetohydrodynamic (MHD) flows in the presence of pressure and gravity. Magnetic flux is continuously advected by the flow and accumulates in a region around the axis of symmetry. This situation might have direct astrophysical applications in accretion outflow scenarios around compact objects in stellar systems and active galactic nuclei. The present work is fundamentally different from ail previous steady state analyses which have assumed that the poloidal flow velocity v(p) is parallel to the poloidal magnetic field B-p. We obtain the condition which determines the critical points of the flow. We also obtain self-consistent self-similar solutions which describe an accretion/outflow process around a compact object, under conditions allowing for magnetic flux advection.