3 Instrumental facilities and data reduction

The Askania-Zeiss Abrahão de Moraes meridian circle, operated at the IAG/USP Valinhos Observatory ($\phi=46^\circ\ 58\hbox{$^\prime$}\ 03\hbox{$^{\prime\prime}$}$, $\lambda=-23^\circ\ 00\hbox{$^\prime$}06\hbox{$^{\prime\prime}$}$), is a 0.19 m refractor instrument with a focal distance of 2.6 m. A CCD detector Thomson 7895A with $512 \times 512$ pixel matrix and a pixel scale of $1.5\hbox{$^\prime$}$/pixel was used for the imaging (Paper I, Viateau et al. 1999). The observations are performed in a drift-scanning mode. So the integration time, for a declination $\delta$, is given by

$$t_{\rm int}= 51 \ \sec \delta \ s .$$ (1)

The observed field has a width of 13' in declination by an arbitrary interval in right ascension (some minutes to several hours). It is possible to obtain images of several thousands of stars per night, up to magnitudes as faint as $m_{\rm Val} =16.5$, depending on the transit time as reflected by Eq. (1) (we will use "$m_{\rm Val}$" to designate the magnitudes obtained with the Valinhos system ($V_{\rm V}$ filter) and "V" for magnitudes in the standard Jonhson system ($V_{\rm J}$ filter), see below).

The optimal magnitude interval for the observations is $9<m_{\rm Val}<14$, while the typical accuracy in the positions and magnitudes for a single measurement of a given night is shown in Fig. 1 of Paper I.

The filter we have used in this and other observational programmes is somewhat wider than the standard Johnson filter $V_{\rm J}$; allowing a larger coverage towards the infrared band in order to maximize the number of objects by taking advantage of the better quantum efficiency of the CCD in that region. Figure 2 of Paper I shows the response of the Valinhos filter $V_{\rm Val}$ together with the standard Johnson filter $V_{\rm J}$. The correlation between the filters, the method used for our programme and the limitations are described in Paper I. In the present work we have used the differences of magnitudes of the stars with respect to a standard reference set, as described in the next section.

The employed data reduction method requires a first step, where the sky background is subtracted by a linear polynomial fitted to each pixel column. Objects are identified when 3 consecutive pixels with a $2\sigma$ confidence level are detected, where $\sigma$ is the standard deviation of the mean count rate in each column. A two-dimensional Gaussian surface is fitted to the flux distribution of the objects, to obtain the x and y coordinates of the centroid, the flux and respective errors (Paper I, Viateau et al. 1999). In the following step, the celestial positions and magnitudes are calculated by solving a system (Eqs. (3-5) in Paper I) with respect to reference stars (Sect. 4). For our variability analysis we take these results, i.e., those obtained in the classical way, night-by-night.

After this process, the system is again solved in an iterative process, now for all stars detected in the field, by a global reduction, using the field overlap constraint among all observation nights (Eichhorn 1960; Benevides-Soares & Teixeira 1992 and Teixeira et al. 1992). At each step of iteration, the system is solved by least squares (Benevides-Soares & Teixeira; Teixeira et al. 1992). The process converges in a few iterations (typically less than 10 steps). This method is applied to obtain the best values to the positions, as can be seen in Appendix B.