5 Comparison with others results

Several authors published mean values for the apparent solar radius, measured with different instruments and methods. Among those there, we kept solely here results of the most recent measure sets, and that are comparable to ours (Table 2).

Concerning the solar astrolabe of Calern, a recent analysis presents visual and CCD measures results done in parallel on the same instrument, between 1996 and 1998 ([Laclare et al. 1999]). For the visual measures, the observed solar limb would be in shrinking in relation to the real limb, in proportion to the zenith distance of the observation. This effect, due to the fact that the eye appreciates the solar side for a threshold of light intensity, that varies with the atmospheric absorption (therefore, largely, with zenithal distance of observation), duct to an obvious smaller solar radius that the real one. While extrapolating the raw visual measures to the zenith, the mean value of the apparent solar radius becomes identical to the one gotten by the CCD measures extrapolate to a null standard deviation of the points on the trajectories. The last two values presented on Table 2 take account of these corrections ([Laclare et al. 1999]).

In another work ([Bouzaria & Moussaoui 1996]; [Irbah 1998]) the CCD images have been cleaned by a wavelet analysis before the numeric derivation. This test shows that an adequate cleaning of images improves of meaningful manner the definition of the position of the solar limb (still by numeric derivation), but doesn't give any supplementary information to value other corrections. These information are now gotten thanks to the use of the model, that conducts directly to the solar radius freed of disruptive effects mentioned in the previous chapters. As all these effects have as result a decrease of the solar radius, the use of the model always gives a result closer to the real solar radius, contrary to other methods. We project to apply our model method to these cleaned images.

The measures made with the other solar astrolabe analyzed here are coherent, to the unique exception of measures of Santiago, which presents a relatively large shift comparatively to the others results. The results of the measures made with the astrolabe of Rio de Janeiro (observations without rotating shutter) are affected by an East - West effect, whose possible reasons would be the better quality of the atmosphere for observations to the East, or a bad functioning of the variable angle prism. Besides, at Calern, tests made by the authors with the variable angle prism put in evidence the same effect ([Sinceac 1998]). The solar astrolabe of San Fernando is a full pupil astrolabe, using one optical square instead prisms, and makes CCD measures without rotating shutter. Finally, the polyvalent astrolabe of Malatya will change the site and will function in CCD mode in 1999, with the same software than the Calern one.

Let's notice that the apparent solar radius variation is identical for all measures done with astrolabes (except Santiago), and in anticorrelation with the magnetic cycle of the Sun ([Laclare et al. 1996]; [Jilinski et al. 1999]). The differences obtained between the contemporary values could be owed to differences of quality of the atmosphere according to sites. Thus, the scale of mean result sizes obtained seems to indicate the order of the quality of astrolabe sites: the CCD images obtained to Calern show that the derivative width to half-height ($W_{\rm h}$) is smallest, therefore a better atmosphere quality and an obvious bigger solar radius. The utilization of the model for the reduction of measures done with every solar astrolabe could improve the consistency of results.

The results of measures of Drift-Scan ($\lambda=475.8$ nm), are row outputs, no corrected of atmospheric turbulence effects ([Wittmann 1997]). The big gap between the visual and CCD measures could be due to differences between the respective definitions of the solar limb. Besides, the big focal length of this instrument could generate errors which are difficult to evaluate.

Finally, measures done with Solar Disk Sextant, Solar Diameter Monitor and those of Limb-Darkening are freed of the atmospheric effects, by the reduction method used (Finite Fourrier Transform Definition), and one can notice that obtained results are nearly identical to those obtained by the model.