Astron. Astrophys. 327, 392-403 (1997)

Astron. Astrophys. 327, 392-403 (1997)

1. Introduction

The solar wind flows out from the Sun with the approximate spherical symmetry and meets on its way the local interstellar matter (LISM). Since the wind is supersonic, the presence of the LISM cannot be communicated to the wind via hydromagnetic mechanisms, and deceleration of the flow is realized in the form of a shock wave. The position of this shock has been the subject of intensive studies during the last decade (Fahr et al. 1988, Fahr & Fichtner 1991, Grzedzielski & Ziemkiewicz; 1989, 1990, Donohue & Zank 1993, Ziemkiewicz & Banaszkiewicz 1996) and the expected radial distance was shown to lie somewhere between 50 and 150 AU. This discrepancy in the results shows that the knowledge of the LISM parameters and of the physical processes important in the outer heliosphere is still insufficient to give a clear answer to this question. The recent modelling studies (Zank et al. 1996a, 1996b, Pauls & Zank, 1996) as well as the results of space missions indicate that the range of shock radii is limited to 70-110 AU in the equatorial plane. As Voyager and Pioneer probes are now approaching the region where the shock may be found, the problem becomes very important.

The interstellar plasma interacts strongly with the plasma of the wind at the edges of the heliosphere. The neutral components of the LISM penetrate the heliosphere. Some of them (e.g. helium) have almost free access. Others, like hydrogen, react easily with the dense compressed plasma in the heliosheath. As the result their number density may be reduced by 50% and their bulk velocity may decrease from 26 to 20 km/s (Zank et al. 1996b). Since the LISM bulk velocity is much smaller than the solar wind velocity, such a freshly born ion may be considered to be at rest with respect to the Sun. These ions are immediately picked up by the solar wind electromagnetic fields to become the so called pickup ion population; the acceleration of these particles from v=0 to v=400 km/s results in the losses of the solar wind momentum and energy fluxes. The pickup ions and their effect on the solar wind flow have been studied theoretically in several papers (Fahr & Fichtner 1991, Isenberg 1995, Isenberg & Lee 1995, Zank et al. 1996a,b, Williams et al. 1995, Lee 1995). A small but important fraction of the pickup ions is injected at the shock into the process of the diffusive acceleration and becomes the anomalous cosmic rays (see below). In the present model the photoionisation of LISM neutrals and the charge-exchange between them and solar wind ions are taken into account in the form of source terms appearing in the hydrodynamic equations.

Thanks to their large diffusion coefficient, the galactic cosmic rays (GCR) can penetrate the heliosphere, where, because of the solar wind convection, their spectrum becomes modulated i.e. dependent on the distance to the Sun (McKibben et al., 1996). Several models of the cosmic ray modified solar wind have been constructed up to now (Webb & McKenzie 1984, Ko & Webb 1987,1988, Ko et al 1988, 1991, Ko 1991), among which the earliest study the cosmic rays in the test particle approximation, i.e. consider the undisturbed background flow, and the latest include all the nonlinear effects that arise in the system i.e. take into account not only the fact that the gradient force of the cosmic rays slows down the solar wind flow, which in turn changes the cosmic ray pressure etc., but also the interaction with the cosmic ray induced turbulence.

Acceleration of charged particles to superthermal energies should always be taken into account if the formation of a collisionless shock wave is considered. It is now commonly believed that the population less energetic (10-100 MeV/nucl.) than GCR, called the anomalous component cosmic rays (ACR), is produced at the solar wind termination shock (McKibben et al., 1996). This constituent, which diffuses in both directions outwards from the shock, can modify the background flow and take part in the nonlinear interaction. Diffusive acceleration of a small fraction of pickup ions with energy initially 1 keV/nucl. to energy 10 MeV/nucl. is an energetically expensive process; while the losses in the solar wind mass flux can be neglected, the sink in the energy flux is not negligible and should be taken into account. A number of papers (Donohue & Zank 1993, Fichtner et al. 1993, Zank et al. 1993, Barnes 1994, Chalov & Fahr 1994,1995, Ziemkiewicz 1994, 1995) dealt recently with this problem. The models describing the influence of cosmic rays and of interstellar gas on polytropic wind dynamics have been recently reviewed by Lee (1995).

The present paper is the first one in which the cosmic ray modified nonpolytropic solar wind interacting with the neutral interstellar gas is considered. The model relies on considering the three fluid medium : the background plasma and the massless, galactic as well as anomalous component cosmic rays. We are interested in the stationary, spherically symmetric, magnetized, non-polytropic background plasma. Because of numerous kinematical and dynamical effects present in the inner solar wind (such as changes of the wind parameters and interplanetary shock waves (Burton et al., 1996)), the shock is in a constant in and out motion (Barnes 1993, Story & Zank, 1995), therefore our stationary model can describe an average outer heliosphere configuration only (Donohue & Zank 1993, Ziemkiewicz 1994). The process of the solar wind interaction with interstellar neutrals, which leads to the formation of the pickup ion population, is taken into account in a self-consistent approach by introducing the appropriate source terms into the hydrodynamic equations. The model and the numerical algorithm are briefly outlined in the next section.

Since the recent results of the Ulysses mission (Goldstein et al., 1996, Feldman et al., 1996) show a qualitative and quantitative difference between the equatorial and high-latitude solar wind flows, we solve our problem for two sets of input parameters typical for either slow equatorial or fast polar winds. Also two sets of neutral gas parameters resulting in high and low reaction rates with the solar wind are considered. In Sect. 3 we present the results as they depend on three parameters that control the solutions: cosmic ray diffusion coefficients, position (distance) of the termination shock, and the efficiency of the cosmic ray production at the shock. In the last section we discuss the relevance of the obtained results and come to our conclusions.

Online publication: April 8, 1998
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