3 Results and discussion

The results presented here span over 7 months of observations, from January 10$^{\rm th}$ to July 31$^{\rm st}$, 1997. The data thus cover 3 seasons and sizeable ranges in observation length of transit, zenith distance and heliographic latitude, allowing for systematic trends to be searched for. The temperature during the observations varied from about +42 $^\circ$C in summertime (January) down to +25 $^\circ$C in winter (June); being some degrees higher in the afternoons than in the mornings. Figure 1 brings the residuals distribution about the overall semi-diameter average. The distribution shows a distinct normal pattern. We then retain here the measurements under $\pm$ 3$\sigma$,ascribing the others to observations under adverse meteorological conditions, bad seeing or defective observation. In all, 1149 observations were treated, corresponding to 125 east and west series of measurements of the solar diameter in 91 days. The distribution of the observations appears in Table 1.

  

Figure 1: Frequency distribution of the residuals of the measurements about the average, in units of the standard deviations. The east transits distribution is represented by the dashed line and the west one by the point line. The continuous line traces the histogram for the whole set of observations

  

Table 1: Number of observations and average solar semi-diameter, $\langle$SD$\rangle$.From January 10$^{\rm th}$ to July 31$^{\rm st}$, 1997. The "Series'' column brings the number of independent daily average semi-diameter values

  

Figure 2: Distribution of internal and external errors. Errors on the images treatment (1) - for details on the routines we refer the reader to Sinceac (1998); single measurements standard deviations (2) and dispersion of the daily results about the average (3), as given by the number of events (N). All the histograms are relative to east transits only. The west transits show an equivalent, but noisier distribution

The internal errors originate from the definition of the solar limb and the adjusting of the inflection points to a parabola and, then, from the adjusting of the parabolas' summits to crossing lines, from which the time of transit is deduced. Although sharing similar causes, we name external errors those giving a defective superposition of the measured diameters, for an east or west series. In Fig. 2 the distribution of the internal and external errors is presented. It is seen that the external errors are much larger. Thus the different options of adjustment of the parabolas and even variations on the definition of the solar limb are of minor importance. This supports the approach taken in the present work, in getting as many independent measurements as feasible in a series, to obtain a reliable average.

Figure 3 shows the east and west daily averages. No important trend is clearly apparent, either on the measured semi-diameters or on the errors. In order to verify whether the variation of observational parameters could interfere with the measured semi-diameter, we compared the outcome and the errors of each measurement with the zenith distance, and its trigonometric tangent, and heliographic latitude of transit, as well as with the time length and hour of observation, through a linear least square fit. Also a linear dependence with time was adjusted. The range of the parameters, for the period March-July and the results (angular coefficient) of linear fits of semi-diameters and errors against each of the observational parameters and time are displayed in Table 2. As seen from the table, no important dependence is found, but, perhaps, on tanZ. This result indicates that the relative nature of the measurements renders them unaffected by such variations. In case of the heliographic latitude it must be, however, considered that a longer period of observations would be required, in order to obtain data redundancy and to examine the effect of various degrees of the Sun activity. As for the higher values of the angular coefficient on the tanZ least squares fit, it indicates that at high zenith distances the agitation of the images can be of importance. The larger values for the west transits support this interpretation. However the errors associated to the so obtained coefficients indicated that such an effect would add up to the series noise, rather than develop a systematic trend. Certainly, with the progress of the project, this aspect can be re-addressed.

  

Table 2: Results from the linear fit of the measured solar semi-diameter and the corresponding error against observational parameters. The angular coefficients of the fittings are given for Julian Date (JD), Universal Time of observation, in hours, (UT), Length of the observation, in minutes, ($\Delta T$), Zenith Distance (Z), Trigonometric Tangent of Zenith Distance (tanZ) and Heliographic Latitude (b)

  

Figure 3: Daily results. Open circles are east transits and dark circles are west transits

Finally, in Table 3 the monthly averages are presented. Again there is no evidence for a trend or a cycle. Thus the only important effect that is apparent in the data set is the difference in the results and precision between the east and west transits, being larger for the later. The afore commented temperature gradient can explain the observed difference. The discrepancy between the averages for the eastern and western transits might be tied with the prototype variable prism observations, as long as this effect was not seen in the Calern series with zerodur fixed angle prisms (Laclare et al. 1996). Nevertheless the smaller number of western observations do not allow a final conclusion, nor to outcast them a priori. So, in spite of the better definition of the eastern transits, all the measurements are kept and the average of the 125 East and West transits is retained. The semi-diameter in this way is found to be 959$\hbox{$.\!\!^{\prime\prime}$}$21 $\pm$ 0$\hbox{$.\!\!^{\prime\prime}$}$03.