Self-similar force-free wind from an accretion disc

Abstract

We consider a self-similar force-free wind flowing out of an infinitely thin disc located in the equatorial plane. On the disc plane, we assume that the magnetic stream function P scales as P ∝ Rv, where R is the cylindrical radius. We also assume that the azimuthal velocity in the disc is constant: vφ = Mc, where M < 1 is a constant. For each choice of the parameters v and M, we find an infinite number of solutions that are physically well-behaved and have fluid velocity ≤ c throughout the domain of interest. Among these solutions, we show via physical arguments and time-dependent numerical simulations that the minimum-torque solution, i.e. the solution with the smallest amount of toroidal field, is the one picked by a real system. For v ≥ 1, the Lorentz factor of the outflow increases along a field line as γ ≈ M(z/Rfp)(2-v)/2 ≈ R/R A. where Rfp is the radius of the foot-point of the field line on the disc and RA = Rfp/M is the cylindrical radius at which the field line crosses the Alfvén surface or the light cylinder. For v < 1, the Lorentz factor follows the same scaling for z/Rfp