Stability and structure of analytical MHD jet formation models with a finite outer disk radius

¹ IASA and Section of Astrophysics, Astronomy and Mechanics, Department of Physics, University of Athens, Panepistimiopolis, 157 84 Zografos, Athens, Greece e-mail: mstute@phys.uoa.gr
² Dipartimento di Fisica Generale, Università degli Studi di Torino, via Pietro Giuria 1, 10125 Torino, Italy
³ School of Cosmic Physics, Dublin Institute of Advanced Studies, 31 Fitzwilliam Place, Dublin 2, Ireland

Received: 1 July 2008
Accepted: 6 September 2008

Abstract

Context. Finite radius accretion disks are a strong candidate for launching astrophysical jets from their inner parts and disk-winds are considered as the basic component of such magnetically collimated outflows. Numerical simulations are usually employed to answer several open questions regarding the origin, stability and propagation of jets. The inherent uncertainties, however, of the various numerical codes, applied boundary conditions, grid resolution, etc., call for a parallel use of analytical methods as well, whenever they are available, as a tool to interpret and understand the outcome of the simulations. The only available analytical MHD solutions to describe disk-driven jets are those characterized by the symmetry of radial self-similarity. Those exact MHD solutions are used to guide the present numerical study of disk-winds.

Aims. Radially self-similar MHD models, in general, have two geometrical shortcomings, a singularity at the jet axis and the non-existence of an intrinsic radial scale, i.e. the jets formally extend to radial infinity. Hence, numerical simulations are necessary to extend the analytical solutions towards the axis and impose a physical boundary at finite radial distance.

Methods. We focus here on studying the effects of imposing an outer radius of the underlying accreting disk (and thus also of the outflow) on the topology, structure and variability of a radially self-similar analytical MHD solution. The initial condition consists of a hybrid of an unchanged and a scaled-down analytical solution, one for the jet and the other for its environment.

Results. In all studied cases, we find at the end steady two-component solutions. The boundary between both solutions is always shifted towards the solution with reduced quantities. Especially, the reduced thermal and magnetic pressures change the perpendicular force balance at the “surface” of the flow. In the models where the scaled-down analytical solution is outside the unchanged one, the inside solution converges to a solution with different parameters. In the models where the scaled-down analytical solution is inside the unchanged one, the whole two-component solution changes dramatically to stop the flow from collapsing totally to the symmetry axis.

Conclusions. It is thus concluded that truncated exact MHD disk-wind solutions that may describe observed jets associated with finite radius accretion disks, are topologically stable.