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

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7. Radial dependence of the dissipated wave energy

For purposes of an estimation we may base our considerations on the background field given by Parker's Archimedian spiral and hence given by:

[EQUATION]

where [FORMULA] is the ecliptic co-latitude and [FORMULA] is the solar rotation frequency. We now define for clarification a critical radius [FORMULA] where azimuthal and radial field components are just equal given by: [FORMULA]. One can then study the radial dependence of [FORMULA] for two distinct regions: i.e. for region I: [FORMULA], and for region II: [FORMULA].

Region I: [FORMULA]. In this region, with dominance of the radial field component, the following radial dependences can be assumed:

[EQUATION]

With these dependences one evaluates Eq. (58) into the following form:

[EQUATION]

Thus one finds that [FORMULA] has the following r-dependence:

[EQUATION]

For regions [FORMULA] AU HELIOS A/B data show that [FORMULA] (Tu & Marsch 1995). Comparing this result with Eq. (57) allows one to conclude that [FORMULA], i.e. a nearly flat power spectrum. Thus one derives the following radial dependence of [FORMULA]:

[EQUATION]

Therefore one can conclude that the heat source connected with the dissipated wave energy in this region falls off like: [FORMULA].

Region 2:[FORMULA]. In this region the azimuthal field is dominant and thus the following radial dependences have to be considered:

[EQUATION]

Evaluating again Eq. (61) we thus arrive at:

[EQUATION]

For a substantially flat spectrum with [FORMULA] one therefore derives in this region the following radial dependence:

[EQUATION]

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© European Southern Observatory (ESO) 2000

Online publication: December 5, 2000
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