A class of exact MHD models for astrophysical jets

This paper examines a new class of exact and self-consistent MHD solutions that describe steady and axisymmetric hydromagnetic outflows from the atmosphere of a magnetized and rotating central object with possibly an orbiting accretion disc. The plasma is driven against gravity by a thermal pressure gradient, as well as by magnetic rotator and radiative forces. At the Alfvénic and fast critical points the appropriate criticality conditions are applied. The outflow starts almost radially, but after the Alfvén transition and before the fast critical surface is encountered, the magnetic pinching force bends the poloidal streamlines into a cylindrical jet-type shape. The terminal speed, Alfvén number and cross-sectional area of the jet, as well as its final pressure and density, obtain uniform values at large distances from the source. The goal of the study is to give an analytical discussion of the two-dimensional interplay of the thermal pressure gradient, gravitational, Lorentz and inertial forces in accelerating and collimating an MHD flow. A parametric study of the model is also given, as well as a brief sketch of its applicability to a self-consistent modelling of collimated outflows from various astrophysical objects. The analysed model succeeds in giving for the first time an exact MHD solution for jet-type outflows extending from the stellar surface to infinity where the outflow can be superfast, in agreement with the MHD causality principle.