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Astron. Astrophys. 364, 901-910 (2000)

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5. Discussion

We have obtained steady-state numerical solutions for the quasispherical accretion of matter onto the model magnetosphere of a star. In our models we use a specially designed inner boundary for the flow region which is intended to simulate the effects of the stellar magnetosphere. The shape of the magnetosphere in the accepted model is characterized by the presence of an impermeable surface represented by a contracted dipole magnetic field line and of holes in the polar regions. These holes can be interpreted as a result of the cusp disintegration caused by the Rayleigh-Taylor instability of the zero-approximation (totally impermeable) magnetospheric surface occurring in its equatorial regions. We also assumed that the magnetic axis and the rotation axis are aligned. This then allows us to use a simple gas dynamic approach in a two-dimensional geometry. We showed that steady solutions can exist for boundary conditions consistent with the accretion ability of the polar holes. This occurs for low values of the polytropic index, small rotation rates of the gas, and sufficiently large polar holes. These flows show a stationary shock front around the magnetosphere. Our results supplement unsteady solutions with expanding shock waves obtained by various authors.

The model of a stationary magnetosphere used in our calculations is overidealized in some aspects. The main simplification is in ignoring the details of the magnetic interaction of the star with the accretion flow. Our simplification, however, in contrast with that adopted by Toropin et al. (1999), represents another limit of the realistic phenomenon. The latter model implies that accretion can occur only due to the plasma diffusion through the magnetic field lines of the magnetosphere. To account for larger accretion rates, one must adopt in this case higher electric resistivity of accreting matter. In our approach, we choose another limit of a highly unsteady accretion process launched by the instability of the stellar magnetosphere. In doing so, we assume that some averaged stream of plasma originates beneath the zero-order impermeable magnetopause, thus reducing the problem to a purely hydrodynamic accretion through the holes opening in the vicinity of the polar cusps. One can argue which model is closer to reality. To improve both models, we must take into account physical details of the plasma penetration beneath the magnetopause. More detailed consideration of the radiative cooling effects will also be highly favorable, since it would affect the actual mass accretion rate due to the obvious dependence of cooling on the matter density. For this reason, we consider our present calculations as a starting point of more complex MHD simulations.

The assumption that the rotation axis of the star and/or of the accreting gas are aligned with the magnetic axis is not very realistic. All stellar X-ray sources which are observed as pulsars require a finite inclination angle between these axes. The problem in this case becomes fully three-dimensional. In our calculations we neglected the development of the penetration process beneath the magnetosphere occurring in its equatorial region according to Arons & Lea (1976). In this case the flow pattern would be much more complicated, consisting of several subsonic and supersonic regions with the formation of shocks around the magnetosphere as well as near the stellar surface. This is the subject of a future investigation. Nevertheless, even our two-dimensional symmetric calculations can describe some of the basic features of the wind accretion onto magnetized stars. On the other hand, one has to be aware that realistic treatment will require the study of the fully three-dimensional configurations.

Another important physical feature of the accretion phenomenon is connected with the radiative energy losses increasing as we approach the inner boundary. They lead to merging of the accreting matter with the matter of the star and to formation of standing shocks close to the stellar or magnetospheric surfaces. The steady-state position of these shocks will be determined by the radiative energy losses behind the shock.

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© European Southern Observatory (ESO) 2000

Online publication: January 29, 2001