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

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3. Estimated effect of truncated distribution functions

Now we investigate a representation of solar wind electron pressures and heat conduction flows by means of truncated Maxwellians and compare these expressions with observational results.

We study first the effect of the truncated Maxwellians on solar wind electron pressure. Adopting an effective electron polarisation potential [FORMULA] we can easily calculate the resulting electron pressure associated with a truncated Maxwellian derived from Eq. (19) which leads to:

[EQUATION]

where [FORMULA] was given in Eq. (11) and [FORMULA] was introduced. In view of the highly subsonic character of the solar wind electrons in regions inside 20 AU (i.e. [FORMULA]) the second term in the outer bracket is of second order in magnitude and estimate purposes for may be neglected here. Using the relation between [FORMULA] and [FORMULA] given by Eq. (9) one then obtains the following expression:

[EQUATION]

where the [FORMULA] describes the pressure reduction with respect to the classical pressure [FORMULA] resulting from an untruncated Maxwellian. It must be concluded that [FORMULA] is obtained from Eq. (23) for a potential barrier increased to infinite height, i.e. for [FORMULA], or [FORMULA]. Realizing that [FORMULA], one thus arrives at the following expression for [FORMULA]:

[EQUATION]

In Figs. 3 and 4 of Fahr et al. (1997) it is demonstrated what effect a truncation of the Maxwellian has on the electron pressure. While in Fig. 3 of this paper the function [FORMULA] itself is shown, Fig. 4 displays the ratio [FORMULA] of the pressure gradients [FORMULA] and [FORMULA]. In both cases it is evident that a physically motivated truncation of the Maxwellians not only reduces the effective electron pressure but also its gradient which represents an important force term in the equation of motion of the magnetohydrodynamic solar wind as already analyzed in quantitative terms by Fahr et al. (1990). Here as evident from the work of Meyer-Vernet & Issautier (1998) we again confirm the importance of the escape branch of the electron distribution function for the global solar wind dynamics.

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© European Southern Observatory (ESO) 2000

Online publication: December 5, 2000
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