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Astron. Astrophys. 360, 707-714 (2000)

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6. Conclusions

Our purpose was not to make extremely accurate matching of the theoretical and observational data. Instead, we designed a simple model of the solar atmosphere to show up trends and general properties caused by the turbulent velocity field. In accordance with this purpose we made several assumptions and simplifications. For example, we ignored sphericity, variation of g and [FORMULA], magnetic fields and nonadiabatic effects.

We constructed a solar model consisting of two regions. The lower region corresponds to the solar interior and photosphere. The upper region is the solar corona and chromosphere. The f -mode is a surface gravity wave which for [FORMULA] is peaked in amplitude below the solar surface (Rosenthal & Christensen-Dalsgaard 1995, Pinter & Goossens 1999).

Moreover, our model of the solar atmosphere is highly idealized. It is intended merely to be illustrative of the physics of the interfacial mode in a continuously stratified atmosphere. A plausible model would have to include the details of the structure of the chromosphere (e.g. Pinter & Goossens 1999). Therefore, it is clearly desirable to extend these models to more realistic stratifications of the solar atmosphere.

Although the obtained results are for a specific equilibrium (isothermal plasma) and turbulent flow, dispersion relation (21) is valid for arbitrary equilibrium profiles and turbulent flow. Moreover, the methodology we introduced to derive this equation can be applied to any model of the solar atmosphere. Although details of the effects of different models will vary, the general character of the effects that we stressed here are expected to be the same.

Despite of its shortcomings such as the assumption of isothermal convection zone, our simple model of the solar atmosphere and turbulent velocity field is able to give similar results to those observed by the SOHO/MDI instrument (Duvall et al. 1998) as well as agree with alternative explanations of the frequency shift due to magnetized atmosphere (Pinter & Goossens 1999) and variations in the temperature profile (Vanlommel & Cadez 1998, Vanlommel & Goossens 1999). Qualitatively all these effects influence the f -mode frequency in the same way. The overall agreement of the model frequency with the experimental data and former results offers encouragement for the further studies of the influence of the convection on the f -mode frequencies.

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© European Southern Observatory (ESO) 2000

Online publication: August 17, 2000