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Astron. Astrophys. 341, 902-911 (1999)

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6. Conclusions

We used a computer code that implements the Feautrier method to solve the radiative transfer equation for the polarized radiation in the continuum, which is produced by Rayleigh and Thomson scattering. We have given qualitative physical arguments that explain the dependence on wavelength and model atmosphere of the continuum polarization.

The wavelength dependence is due to the scattering coefficient, which varies according to the known [FORMULA] law for Rayleigh scattering, and to the CLV of the continuum intensity. It is interesting to note that even in a grey atmosphere the polarization is smaller at longer wavelengths because of the properties of the Planck function. For a given temperature difference the relative change of the Planck function decreases monotonically towards longer wavelengths, which results in less steep center-to-limb variations of the intensity.

The model dependence of the continuum polarization is mainly due to the limb darkening and the temperature gradient. The scattering coefficient is less important, because in the photosphere it is almost identical in all models. However, it does play a role in the flux-tube model (AYFLUXT1) and in one of the plage model atmospheres, where some contribution to the continuum polarization from the chromosphere is present due to a very high scattering coefficient there.

We introduced the analytical function (17) to describe the computed CLV of the continuum polarization for all nine model atmospheres and all visible wavelengths. For [FORMULA] this function follows from the simple assumption of an optically thin scattering layer lying above the layer of formation of the continuum intensity. Because our theoretical computations have revealed that this assumption is only partly satisfied, the parameter [FORMULA] has been introduced.

The expression (17) fits well the computed CLV curves of the continuum polarization, which proves the usefulness of this representation. The wavelength variations of both [FORMULA] and [FORMULA] have been given by simple analytical expressions, which allow us to retrieve the CLV of the polarization for all visible wavelengths and for [FORMULA]. Closer to the limb (within the last arcsec) the approximation (17) gets worse.

In future work we plan to measure the continuum polarization in selected windows in the visible part of the solar spectrum. The analytical function would then be fitted to the observed CLV curves. This will allow us to determine the problematic zero point of the polarization scale. The fitted values of [FORMULA] may also be used to constrain the model atmospheres. We further intend to explore the non-linear coupling between the continuum and the lines in order to gain a more complete understanding of the second solar spectrum.

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© European Southern Observatory (ESO) 1999

Online publication: December 16, 1998