A&A 491, 339-351 (2008)

DOI: 10.1051/0004-6361:200810499

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

**M. Stute**

^{1}, K. Tsinganos^{1}, N. Vlahakis^{1}, T. Matsakos^{2}, and J. Gracia^{3}^{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.

**Key words:**magnetohydrodynamics (MHD)

**--**methods: numerical

**--**ISM: jets and outflows

**--**stars: pre-main sequence

**©**

*ESO 2008*