MHD Self-Similar Solutions for Collimated Jets

Abstract

The MHD modelling of jets in axisymmetric geometry requires the treatment of the Bernoulli and the transfield equations, that can be treated following a self-similar approach. This technique is based on two main assumptions: i) the physical variables are factorized; ii) a suitable scaling law in one direction is prescribed. Solutions self-similar in the r direction (in a spherical frame of reference) have been studied to model collimated winds from disks (Blandford and Payne 1982). Here we present solutions self-similar in the θ direction, suitable to study the collimated wind around the polar axis of a rotating object (Tsinganos and Trussoni 1991, Sauty and Tsinganos 1994). Our basic assumptions are: –The magnetic flux function, that describes the poloidal components of velocity and magnetic field, is expressed as A(r, θ) ∝ f(r)sin2θ.–The density and the pressure of the plasma are assumed to scale linearly with A: ρ(r, θ) ∝ 1 + δA and P(r, θ) ∝ Po(r) (1 + KfA). Accordingly, the surfaces with equal poloidal Alfvén number M are spherical.