Analysis of solar radius determination obtained by the modern CCD astrolabe of the Calern Observatory - A new approach of the solar limb definition

A semi-empirical model of solar images is presented here and used to derive the solar radius from astrolabe observations made at the Cote d'Azur Observatory (OCA), at the Calern station. This model was elaborated in order to remove a systematic effect existing in the measurements. This effect is caused by the center to limb darkening existing in the apparent solar light intensity and is magnified by atmospheric and instrumental effects. The result is that the apparent or observed solar radius is always smaller than the true one. After a description of the observational methods used, a definition of the true solar radius is given and the model is described (Eqs. (1) or (3)). A new set of results is obtained using the model, which corresponds to observations made with a rotating shutter (used to separate the two solar images present in the focal plane). All the results are given for the unit distance. This paper presents two series of solar apparent radius (see Table 1). The first one (column derivative on Table I), obtained in a previous analysis uses only numerical methods, is affected by the perturbing effects of the center to limb darkening, atmospheric turbulence and attenuation and conducts to the mean value 959." 44 +/- 0." 02. Taking account of all the informations given by the CCD observations, correlations between the Fried parameter ro and the derivative width, and between ro and the solar radius R, are found, in the results obtained by purely numerical methods. These results give us the possibility to evaluate, for r(0) --> infinity, the corresponding values of the derivative width and the solar radius outside the terrestrial atmosphere. In these conditions, the mean solar radius is found to be equal to 959." 63 +/- 0." 08. The second series (column model on Table I) obtained by the use of the presented model, conducts directly to a corrected mean result R = 959." 64 +/- 0." 02. One can see that the corrected result of the first method agrees very well with the one obtained using the model, which has a better precision. By the same way, the parameters b, which represent the slope of the solar limb near the true inflection point, and pr which define the slope of the darkening effect near the Limb are given through and outside the atmosphere. As we hoped, the slope b of the derivative is much greater outside than inside the atmosphere (about two times). The contrary occurs for p, as the darkening is increased by the presence of the atmosphere and dust... The comparison with other results and method shows that the model has the strong advantage to give directly the correct result without any supplementary correction. Some observations done without the rotating shutter at Calern, Rio de Janeiro and San Fernando Observatories will be analyzed in a near future using our model, applied to these existing data. We hope so to analyze the future observations from Antalya where a CCD astrolabe will start a new campaign.