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Astron. Astrophys. 329, 735-746 (1998)

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1. Introduction

The formation of the solar corona and acceleration of the solar wind was discussed by Hammer (1982a, b) and, more recently, by Hansteen & Leer 1995 and Hansteen et al. 1997. In these model studies an energy flux from the sun, deposited as heat in the extended solar atmosphere, creates a hot corona and drives the solar wind. The portion of the energy flux being conducted into the chromosphere-corona transition region and the portion lost as solar wind energy flux are determined primarily by the location of the energy deposition. Heating of the inner corona leads to a large inward heat flux and a large transition region pressure. For extended coronal heating most of the energy flux is lost as solar wind gravitational and kinetic energy flux. Also the ratio between gravitational and kinetic energy flux in the solar wind depends upon where in the corona the energy is deposited.

In most studies of the solar wind the electrons play an important role in the force and energy balance of the flow. In thermally driven solar wind the asymptotic flow speed is generally small compared to the velocities observed in quasi-steady high speed solar wind streams in the ecliptic (e.g. Feldman et al. 1976) and at high solar latitudes, by the Ulysses spacecraft (e.g. McComas et al. 1995). In order to enhance the solar wind flow speed in these models one may allow for Alfvén waves. They propagate virtually undamped through the quasi-static corona and deposit most of their energy flux well beyond the critical point (Hollweg 1973; Leer et al. 1982), thereby increasing the asymptotic flow speed (Leer & Holzer 1980).

Low frequency Alfvén waves may propagate in the corona and in the solar wind, but they are not a likely candidate for transporting a significant energy flux into the corona from the lower solar atmosphere; the low-frequency Alfvén waves are reflected in the chromosphere-corona transition region. However, higher frequency Alfvén-mode waves, with a wavelength that is shorter than the Alfvén speed scale height, may play an important role in heating coronal holes (e.g. Parker 1991). Heating of the solar corona by relatively high frequency waves was also the physical basis for the coronal heating function used by McKenzie et al. 1995. They considered a model where all the energy flux from the sun is deposited in the proton fluid, in the inner corona. The proton heat conductive flux is taken to be zero, and all the energy flux deposited in the protons is lost as solar wind energy flux. As the solar wind mass flux is specified, the asymptotic flow speed is determined by the energy flux that is deposited in the corona. In the McKenzie et al. 1995study the energy flux is specified such that they obtain an asymptotic flow speed that is charactristic of quasi-steady, high speed solar wind streams. But in such a model, where the proton flux is specified and all the energy flux deposited in the protons is lost in the solar wind, "any" flow speed can be obtained. However, in the Hansteen & Leer 1995study, where proton heat conduction in the corona is taken into account, the asymptotic speed of the solar wind does not exceed [FORMULA].

The proton heat conductive flux in the outer corona and in the solar wind is certainly small, but in the very inner corona, where the collisional rate(s) are larger than the expansion rate, the heat flux in the proton gas and the collisional couplig to the electrons (and the electron heat conductive loss) will contribute to the transport of heat from the corona and into the transition region. This inward heat conductive flux determines the transition region pressure and the electron density in the inner corona (e.g. Withbroe 1988), and may therefore play a role in determining the solar wind mass flux.

The goal of the present study is to illustrate how heating of the coronal protons, relatively close to the sun, may produce high speed solar wind, without the deposition of an additional (e.g. Alfvén wave) energy flux in the outer solar wind. We consider two-fluid models of the corona-solar wind system. The corona is heated by a specified energy flux from the sun, and we study the structure of the corona and the solar wind proton flux and flow speed when we vary the amplitude of the energy flux from the sun, the dissipation length, and the distribution of the energy flux between electrons and protons. We make use of a "classical" expression for the proton heat conductive flux in the very inner corona, but the heat conduction coefficient is gradually reduced outwards, into the region where the protons are collisionless. We use a classical heat conductive flux for the electrons. It is shown how heating of the corona, in a region where the protons are collision-dominated, and in a region where the protons are collisionless, leads to different coronal structure and different solar wind outflow. We study both spherically symmetric flow and rapidly expanding flow geometries.

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© European Southern Observatory (ESO) 1998

Online publication: December 8, 1997
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