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Astron. Astrophys. 363, 295-305 (2000)

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1. Introduction to the exospheric view of the corona

Exospheric theories of the solar wind by Chamberlain (1960), Aamont & Case (1962), Jensen (1963), Brandt & Cassinelli (1966) revealed that above the coronal exobase a simple Maxwellian distribution can not be expected for either electrons or ions. Since in these theories the lower corona is considered to be the only source of particles, in a collisionless regime above the coronal exobase there are no particles which populate the sunward hyperbolic part of the velocity space. This part can be estimated by the so-called Pannekoek-Rosseland ambipolar polarisation potential impeding electrons from leaving the corona and given by:


Here [FORMULA] and [FORMULA] are the proton and electron masses, [FORMULA] and [FORMULA] are the mass and the radius of the sun, and G is the gravitational constant. No electrons placed in this impeded part of velocity space should exist (e.g. see Fahr & Shizgal 1983). Also their contribution to the total electron pressure, calculated on the basis of a full Maxwellian, is missing. Since these contributions amount to between 10 and 35 percent (Fahr et al. 1997), the question poses itself as to how much this pressure deficit could influence the effective solar wind acceleration and the solar wind thermodynamics. Studies of this influence were undertaken by Fahr et al. (1990), Pierrard & Lemaire (1996), and Meyer-Vernet & Issautier (1998).

The Pannekoek-Rosseland potential guarantees charge neutrality in a stationary solar corona, i.e it applies in the case of a vanishing solar wind outflow. In case of an expanding corona a selfconsistent polarisation field has to be found (see Sen 1969; Jokers 1970; Hollweg 1974, Lemaire & Scherer 1970, 1971, or for a review Fahr & Shizgal 1983). The effect of this pressure deficit on the solar wind dynamics can already be studied at least qualitatively in the work by Jokers (1970) showing that higher asymptotic solar wind velocities are associated with higher effective electron potential ramps. This forces the electron distribution function to better assimilate a full Maxwellian and thus reduces the electron pressure deficit. So far no selfconsistent polarisation field has been calculated in a satisfactorily consistent manner within exospheric corona theories with the inclusion of electrons in the hyperbolic as well as the elliptic branch, i.e. satellite particle branch. This is mainly because selfconsistency can only be achieved by inclusion of elliptic or trapped electron particle populations as was shown e.g. by Jokers (1970). These populations, however, are established by electrons suffering scattering processes above the exobase and are due to electrons which are trapped between some outer potential well and some inner magnetic mirror point. Within the frame of pure exospheric theory these elliptical electrons consequently should not exist at all, making the concept of an exospheric solar wind problematic, if not, at present, unviable.

The features of the observed electron distributions cannot be represented by collisionless exospheric concepts (Olbert 1983) since the validity of magnetic invariants induces much too anisotropic distribution functions. Introducing a collision-induced relaxation term of a BGK-type (Bhatnagar, Gross, Krook 1954) Olbert could show that the electron distribution with increasing solar distances develops into a so-called Strahl-configuration. As shown by Griffel & Davies (1969), Scudder & Olbert (1979a, 1979b) or Fahr & Shizgal (1983). Coulomb collisons cannot impede the electron distribution functions from degenerating into highly anisotropic functions. Only wave-particle interactions by electron Whistler waves (see Dum et al. 1980, Gary et al. 1994) or excited plasma instabilities of the firehose type may help as a remedy at larger distances (see e.g. Fahr & Shizgal 1983).

This is pointed out by ULYSSES measurements of electron distribution functions between 1 and 5 AU (Scime et al. 1994). As proven by these data, the inherent electron heat conduction flow drops off with increasing solar distance much faster than expected from a collisionfree expansion of solar wind electrons, although the magnitude of the heat conduction flow is much smaller than derived from the electron temperature gradient using the Spitzer-Härm value for the heat conduction coefficient (Spitzer & Härm 1953; Spitzer 1962). This also seems to prove that even at distances beyond 1 AU where Coulomb collisions are absolutely inefficient the solar wind electron plasma does not behave as "collisionfree" in a strict sense, but there seems to be an effective mechanism (like pitch-angle scattering and isotropization) operating which helps redistributing the energy in the heat conduction flow to randomized electron thermal energy. Not knowing, how to describe such a dissipation mechanism quantitatively, neither a selfconsistent polarisation potential nor an adequate electron pressure and temperature can be calculated. We therefore in the following develop an approximative method to study the effect of truncated electron distribution functions on associated electron pressure deficits and heat conduction flows

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© European Southern Observatory (ESO) 2000

Online publication: December 5, 2000