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Astron. Astrophys. 330, 1070-1076 (1998)

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2. The role of tearing instabilities

The accretion disk of a YSO is somehow connected with the the dipole magnetic field of the central object (see Fig. 1). The interaction of the dipole field with the disk can be quite complicated (e.g. Shu et al. 1994; Lovelace et al. 1995) but the rotation of the disk should result in a significant twist of closed magnetic flux tubes anchored at the surface of the YSO thereby injecting continuously magnetic helicity into the flux tubes (cf. Hayashi et al. 1996; Li 1996). Consequently, a sheared magnetic field configuration with electric currents flowing develops.

[FIGURE] Fig. 1. Illustration of the magnetic interaction of the YSO with the accretion disk.

This situation is favorable for magnetic reconnection and is very similar to the physics of rapid bursters (Aly and Kuijpers 1990; Kuijpers and Kuperus 1995), where neutron stars are interlinked magnetically with accretion disks, as well as to particle acceleration phenomena in the magnetospheres of active galactic nuclei (Lesch & Birk 1997). Moreover, it is well documented that solar flares are usually associated with sheared magnetic fields and thus, with current sheets (e.g. Sturrock 1972; Priest 1983, 1985; van Hoven 1979; Sturrock et al. 1984).

A generic spontaneous type of magnetic reconnection processes in current sheets is the resistive tearing instability which is caused by the Lorentz force between parallel electric currents. It has long been recognized as a potential candidate for initiating the release and conversion of magnetic energy stored in sheared astrophysical magnetic fields. This instability process can operate at locations where a magnetic field component reverses direction.

It results in a reconnection of magnetic field lines across the plane of field reversal with a subsequent conversion of free magnetic energy to plasma heating and particle acceleration. The acceleration of charged particles in magnetic field-aligned electric fields is a generic feature of reconnection processes (Schindler et al. 1991). The formation of tearing unstable current sheets in magnetospheres of YSO is illustrated in Fig. 2. The main idea is that a differentially rotating disk/magnetosphere in dynamical equilibrium (cf. Li 1996) gives rise to a toroidal magnetic field component (cf. Fig. 2a). Since the star-disk magnetosphere is not self-similar (cf. Paatz and Camenzind 1996) one particular flux tube among others is shown in Fig. 2a. Different flux tubes are characterized by different strengths of the toroidal components. The associated current sheets form along the twisted magnetic flux tubes. Since the rotation continuously injects magnetic helicity into the closed magnetic fields magnetic non-equilibrium has to be expected. The unstable dynamics are characterized by reconnection processes. As illustrated in Fig. 2b the resulting configuration that should be examined with respect to tearing instabilities can be approximated nicely by a one-dimensional electric current sheet. The main component of the magnetic field is directed along the current sheet (i.e. in the z -direction), the shear component changes the sign at the [FORMULA] -plane. Consequently, singular surfaces [FORMULA] where unstable tearing modes may operate with the wave vector ([FORMULA]) can be found in the plane perpendicular to the flux tube (Fig. 2b), i.e. the x -y -plane in the chosen geometry. The choice of a slab geometry for the analytical treatment can be justified by the fact that the tearing mode in plane current sheets is identical (besides the choice of coordinates) with the internal resistive kink mode (relevant for force-free equilibria in cylindrical geometry) in the long wave length limit, i.e. the [FORMULA] mode characterized by the fastest growing perturbations (cf. discussion in Priest 1987 and in Biskamp 1993). In course of the tearing dynamics charged particles can be accelerated and give rise to non-thermal radiation.

[FIGURE] Fig. 2. The magnetic interaction of the YSO with the accretion disk leads to the formation of twisted magnetic flux tubes (a) and thereby of rational surfaces (b) where unstable tearing modes may operate. In cylindrical geometry the differential rotation results in a finite [FORMULA] and thereby in a poloidal electric current.

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© European Southern Observatory (ESO) 1998

Online publication: January 27, 1998