On the central core in MHD winds and jets

We analytically determine the structure of highly magnetized astrophysical jets at the origin in a region where the flow has been already collimated by an external medium, in both relativistic and non-relativistic regimes. We show that this can be achieved by solving a system of first-order ordinary differential equations that describe the transversal jet structure for a variety of external confining pressure profiles that collimate the jet to a near-cylindrical configuration. We obtain solutions for a central jet surrounded either by a self-similar wind or by an external pressure profile and derive the dependence of the velocity and the magnetic field strength along and across our jets. In particular, we find that the central core in a jet - the part of a flow with a nearly homogeneous magnetic field - must contain a poloidal field which is not much smaller than the critical value B(min). This allows us to determine the magnetic flux in a core which is much smaller than the total magnetic flux. We show that for such a small core flux the solutions with a magnetic field in a core much smaller than B(min) are non-physical. For astrophysical objects the value of the critical magnetic field is quite large: 1 G for active galactic nuclei, 10(10) G for gamma-ray bursts and 10(-1) G for young stellar objects. In a relativistic case for the core field greater than or of the order of B(min) we show analytically that the plasma Lorentz factor must grow linearly with the cylindrical radius. For non-relativistic highly magnetized jets we propose that an oblique shock exists near the base of the jet so that the finite gas pressure plays an important role in force balance.