Astron. Astrophys. 361, 207-225 (2000)

## Collimated outflows of rapidly rotating young stellar objects

### Wind equation, GSS equation and collimation

E. Breitmoser and M. Camenzind

Landessternwarte Königstuhl, 69117 Heidelberg, Germany

Received 14 September 1999 / Accepted 13 June 2000

Abstract

The magnetic field structure and the collimated outflow of rapidly rotating Young Stellar Objects (YSOs) are calculated from the stellar source to the asymptotic region. The calculations are based on ideal MHD and the further simplifying assumptions of stationarity and axisymmetry. The star-disk-jet system can be completely defined by the Grad-Shafranov (GSS) equation, describing the structure of the magnetospheres, and the wind equation, which are given by equilibrium perpendicular and parallel to the field lines. Both equations must be solved simultaneously to obtain a self-consistent solution. General solutions of the Grad-Shafranov equation are not yet available. Here we discuss an analytical model for the magnetic flux surfaces which is a solution for small and large radii. This model assumes a stellar dipole field and a gap between the star and a disk at a distance of a few stellar radii. Due to the features of the disk no field can penetrate the disk and the resulting opening of the field lines close to the polar cap is obtained as a computational result. In addition, our model guarantees the collimation of the outflow into a cylindrical shape at asymptotic jet radii of several thousand stellar radii. This model for collimated outflows reproduces all essential properties of magnetospheres for rapidly rotating stars. The result is used as input to the wind equation. This problem is completely integrable, determined by five constants of motion: the total energy E, the total angular momentum L, the total mass flux along a flux surface, and the total entropy S in a flux surface, together with the rotation of the field lines. For adiabatic plasma flows, this problem is algebraic and can easily be solved. Pressure is neglected in our computation.

The theory of axisymmetric magnetospheres around rapidly rotating stellar sources is outlined including electric fields due to the rapid rotation. Gravity of the central object is consistently built into this theory. Due to the injection of plasma either from the stellar surface or by interaction with a surrounding disk, these magnetospheres are neither vacuum solutions, nor force-free. A consistent wind theory is developed which contains the Newtonian theory as a classical limit.

Current-carrying plasma flows will lead to a collimation of the magnetospheric structure into a cylindrical shape. Particular solutions are discussed for the asymptotic collimation. We show that the asymptotic structure is essentially determined by electric forces in the pinch equation, and not by centrifugal and pressure forces.

Key words: Magnetohydrodynamics (MHD) stars: pre-main sequence stars: mass-loss ISM: jets and outflows

Send offprint requests to: Elena Breitmoser

Correspondence to: ebreitmo@lsw.uni-heidelberg.de