5 Conclusions

The results presented in this work indicate that the CLV of the continuum contrast of magnetic features changes gradually with magnetogram signal (or magnetic filling factor), such that the contrasts of AR faculae and the network exhibit a very different CLV, in general agreement with the results of Topka et al. (1992, 1997) and Lawrence et al. (1993). A possible reason for the difference is that the populations of magnetic flux tubes found in the two kinds of features are, on average, different in size, in agreement with the conclusions of earlier investigations (Grossmann-Doerth et al. 1994; Keller 1992).

Stronger magnetogram signals, corresponding to wider flux tubes on average (Grossmann-Doerth et al. 1994), appear dark at disk centre, but bright near the limb, while the weakest signals (on average narrower flux tubes) are almost equally bright at disk centre and near the limb. This result is in good agreement with the predictions of theoretical flux tube models (Deinzer et al. 1984a, 1984b; Knölker et al. 1988; Knölker & Schüssler 1988) if there is a distribution of flux tube sizes present within an MDI pixel. Because network elements are bright over the whole solar disk their contribution to irradiance variations is significant and needs to be taken into account when reconstructing variations of the total solar irradiance.

One advantage of the present investigation relative to that of Topka et al. (1992, 1997) is that by using full disk MDI data we have a result for a very well defined spatial resolution, so that any models derived on the basis of these results can be directly used for reconstructing total and spectral solar irradiance, as for instance measured by VIRGO (Fröhlich et al. 1995), without further adjustment.

A new result of this work is that, with a simple expression, we can predict the contrast of a bright feature, from network and small tubes to faculae of different sizes, given its position and magnetic strength within a certain range, and reproduce simultaneously the $C_{{\rm fac}}(\mu)$ and $C_{{\rm fac}}(B/\mu)$ dependences.

In a next step the dependence of the contrast on wavelength (for given $\mu$and $B/\mu$) must be determined, as well as the dependence on spatial resolution. The later dependence is of particular interest also because the investigations of Lawrence et al. (1993) and Topka et al. (1997) give similar values of the contrast near $\mu =1$ as we find, although the spatial resolution of the La Palma data employed by these authors is almost an order of magnitude higher than that of the MDI full disk data ( $0.5\arcsec$ versus $4\arcsec$). Closer to the limb Topka et al. (1997) obtain contrasts a factor of two higher. Whether this is due to the different wavelengths observed or has another source needs to be investigated.

Acknowledgements

AO acknowledges financial support from the DURSI (Generalitat de Catalunya) grant 2001 TDOC 00021, as well as partial financial support from the Max-Planck-Institut für Aeronomie, from E. Ortiz and S. Carbonell, and from the European Space Agency (under contract ESA-ESTEC 14098/99/NL/MM). VD acknowledges partial financial support from the DURSI (Generalitat de Catalunya).