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

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8. Relevance of electron heating by waves

Now, we estimate the importance of the wave energy source given by Eq. (61) and evaluated for the region [FORMULA] and [FORMULA] by Eqs. (66) and (69). It is known that the level of magnetic field turbulences, essentially of Alfvénic type, at [FORMULA] AU is moderate (see Tu & Marsch 1995), implying that [FORMULA] where B is the background interplanetary magnetic field and [FORMULA] is the variance of the field fluctuations.

The level of fast magnetosonic waves (compressive MHD waves) responsible for the turbulent energy pumped into the dissipative whistler frequency domain can be estimated using relevant data of density fluctuations like those presented by Tu & Marsch (1995) yielding:

[EQUATION]

We may thus suppose that [FORMULA], also because in addition this estimate agrees with data given by Leamon et al. (1998). Using this result we finally obtain the following expression for the power [FORMULA] transfered from fast magnetosonic waves to electrons in form of thermal energy:

[EQUATION]

where [FORMULA] was obtained for region I: [FORMULA], and [FORMULA] was obtained for region II: [FORMULA]. Evaluation of [FORMULA] in the form:

[EQUATION]

with [FORMULA] AU; [FORMULA] km s-1; and [FORMULA] Gauss, yields:

[EQUATION]

A comparison of [FORMULA] given above with the mean value of the electron heat flow at 1 AU, i.e. [FORMULA], given by Scime et al. (1994) and also taken into account the radial dependence of this heat flow by [FORMULA], one can conclude that the direct heating of electrons by waves would not be sufficient to maintain the electron heatflow at regions [FORMULA] AU where [FORMULA] according to Eq. (62) is given by [FORMULA] and thus is falling off with distance faster than [FORMULA]. Wave heating may, however, become important at distances [FORMULA], since here [FORMULA] according to Eq. (66) is given by: [FORMULA], and thus drops off with r less rapidly than [FORMULA].

On the other hand, in our concept of truncated Maxwellians we need to assume that quasilinear electron- whistler-wave interaction via pitch-angle scattering by waves is operating which has to be energetically effective enough so that the wave energy input into the whistler frequency domain is about equivalent to the energy losses due to the growing truncation with increasing distance. Inspection of Eq. (47) then requires that:

[EQUATION]

which with [FORMULA] AU and Eqs. (39) and (40) simply requires that:

[EQUATION]

This shows that the concept of truncated Maxwellians presented above regulating the solar wind electron heat flow connected with energy absorption from fast magnetosonic waves cascading up in frequency to the whistler frequency domain, appears to be feasible and reasonable.

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© European Southern Observatory (ESO) 2000

Online publication: December 5, 2000
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