3 Solar radius measurements at Rio de Janeiro, 1997-2000

In a previous paper we discussed the solar radius measurements made at Rio de Janeiro and Santiago between 1997 and 1999 (Noël 2001). However, modifications introduced after our discussion in the results of the CCD astrolabe of Rio de Janeiro (Penna 2002) and the publication of the latest results of this astrolabe (Penna et al. 2002), provide new and quite interesting information for the problem of solar radius variations and give additional evidence that the apparent radius of the Sun varies in phase with solar magnetic activity.

In Fig. 2 we plot the daily mean values of the solar radius obtained with the CCD astrolabe of Rio de Janeiro during the period 1997-2000. These results can be obtained in electronic form at CDS and according to Penna et al. (2002) they

"... supersede all others based on preliminary data from this program.''

Therefore, the data of Rio de Janeiro that we shall discuss here are definitive.

The curve in Fig. 2 is a least squares second order fit with a standard deviation of $\pm0\hbox{$.\!\!^{\prime\prime}$ }31$. It shows a slowly decreasing trend of the solar radius during 1997-2000. Since the solar maximum of cycle 23 was probably around 2000.5, the solar radius observed at Rio de Janeiro would have a variation in time of opposing phase with solar activity over these four years. However, the set of points in Fig. 2 give the impression that there are two discontinuities or decreasing jumps in the values of the solar radius around 1998.0 and 1999.0. To verify this impression, we applied least squares linear fits to each set of annual points in Fig. 2. These fits are displayed in Fig. 3A and with its parameters given in Table 1, we obtained the following discontinuities of the radius values:

1998.0	1999.0	2000.0
$-0\hbox{$.\!\!^{\prime\prime}$ }660 \pm 0\hbox{$.\!\!^{\prime\prime}$ }136$	$-0\hbox{$.\!\!^{\prime\prime}$ }323 \pm 0\hbox{$.\!\!^{\prime\prime}$ }089$	$+0\hbox{$.\!\!^{\prime\prime}$ }063 \pm 0\hbox{$.\!\!^{\prime\prime}$ }089$.

These figures confirm the significant and quite large discontinuities at 1998.0 and 1999.0 in the solar radius observed with the CCD astrolabe of Rio de Janeiro.

  

Table 1: Parameters of annual linear fits applied to solar radius measurements with the CCD astrolabe of Rio de Janeiro during 1997-2000. A and B are the coefficients in the equation of the least square fitted lines and $\sigma$ is the standard deviation of the linear fits. n is the number of daily mean values of the solar radius involved in each fit.

$$\begin{tabular}{cccccccc} \hline \hline Year \hspace*{1.3cm} ... ...:\:\:\:\:\:\:\:\:\:0.248\:\:\:\:\:152$ \\ \hline \end{tabular}$$

It is quite difficult to imagine that these sudden jumps could be due to a systematic effect. We think that it is rather probable that they are due to changes in the instrumental system of the CCD astrolabe of Rio de Janeiro. Actually, at least one of these jumps coincides with a modification introduced in this instrument. Indeed, according to Jilinski et al. (1999), on January 1st, 1998, the filter after the image vehicle of the astrolabe of Rio de Janeiro was replaced by one with a narrower bandpass (see also Noël 2001). Since solar radius measurements with CCD cameras are very sensitive to instrumental modifications (Wittmann et al. 2000; Noël 2001), in our opinion it is obvious that the jump in the radius values in 1998.0 and the filter change must be closely related. Concerning the discontinuity around 1999.0, we did not find any information in the publications of Rio de Janeiro about instrumental modification at that epoch. Nevertheless, it being so similar to that of 1998.0 we consider that it was also due to changes in the instrumental system.

Figure 3: A). Least squares annual linear fits applied to the solar radius measurements with the CCD astrolabe of Rio de Janeiro. The parameters of these fits are given in Table 1. The origin of the discontinuities around 1998.0 and 1999.0 are discussed in the text. B). The same data displayed in A after a procedure of homogenisation (see text). The smoothing curves is a least squares second order fit with a standard deviation of $\pm0\hbox{$.\!\!^{\prime\prime}$ }28$. The maximum values of the curve coincide approximately with the maximum of solar cycle 23.

Given the large and sudden jumps in the solar radius observed with the astrolabe of Rio de Janeiro associated with at least one modification of its instrumental system, we think that it is not possible to consider these observational results as a homogeneous or internally consistent data set. However, with the computed values of the discontinuities at 1998.0 and 1999.0 given above, it could be possible, at least as a test, to homogenize the data set in order to study the behaviour of the homogeneous values. The results of this test can be seen in Fig. 3B which shows the solar radius observed after removing the jumps of 1998.0 and 1999.0 by applying as corrections the values of both jumps. A least square second order fit now gives a standard deviation of $\pm0\hbox{$.\!\!^{\prime\prime}$ }28$, which is an improvement of around $10\%$ in the internal consistency of the results. On the other hand, the smoothing curve shows its maximum values around year 2000, which is in agreement with a variation in time of the solar radius in phase with solar magnetic activity.

Figure 4: Monthly means of solar radius obtained with the CCD astrolabes of Antalya and Rio de Janeiro, and with the visual astrolabe of Santiago, and smoothed monthly means of sunspot numbers obtained from SIDC. The monthly values of the solar radius are represented by the center of circles with diameters equal to their mean errors. The smoothing curve for Antalya is a least squares second order fit ( $\sigma=\pm0\hbox{$.\!\!^{\prime\prime}$ }36$) applied to individual solar radius measurements made with a CCD astrolabe.