3 Observations and data reduction

The Askania-Zeiss Abrahão de Moraes Meridian Circle, operated at the IAG/USP Valinhos Observatory ($\phi$ = $46^{\circ}$ 58' 03'', $\lambda$ = $-23^{\circ}$ 00' 06''), is a 0.19 m refractor instrument and 2.6 m focal distance. Recently, a CCD detector was installed as a part of the continuing Bordeaux Observatory-IAG/USP collaboration (Viateau et al. 1999). The capabilities of the Meridian Circle have thus been greatly increased and allowed reliable photometric (as well as the astrometric) measurements to be performed. The CCD detector Thomson 7895A installed at Valinhos has a $512 \; \times \, 512$ pixel matrix, with a pixel scale of 1.5''/pixel. It is cooled down to $- 40^{\circ}$C by a two stage thermocouple system. The observations are performed in a drift-scanning mode, that is, the speed of charge transfer by the CCD is the same as the speed of stellar transit for a fixed instrument position. Therefore the integration time for a given declination $\delta$ is

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

The observed field has a width of 13' in declination by an arbitrary time in right ascension (some minutes or hours). After the installation of the CCD detector, it became possible to obtain images of several thousands of stars per night, up to magnitudes as faint as $m_{V\rm al} \, = \, 16.5$, depending on the transit time as reflected by Eq. (1).

Although the accuracy of the position and magnitude measurements depend on several factors, like the magnitude of the observed star, they have been checked to be better than 0.05 of arcsec for the position and 0.05 for the magnitude (inside the optimal magnitude interval $9 \, < \, m_{V\rm al} \, < \, 14$, see Fig. 1).

  

Figure 1: Precision of the positions and magnitudes for one typical observation night

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 shows the response of the Valinhos filter $V_{\rm V}$ together with the standard Johnson filter $V_{\rm J}$, both curves already weighted with the CCD detector efficiency.

  

Figure 2: The response of the Valinhos and Jonhson filters, already weighted with detector quantum efficiency

In order to evaluate the difference between our magnitude system and Johnson's visual band, we selected a filter (kindly provided to us by the Laboratório Nacional de Astrofísica - LNA) capable to roughly reproducing the necessary spectral characteristics to mimic the $V_{\rm J}$band. We used this filter to perform a full observation night, aiming at several fields for wich we had good data with the broader filter. For the photometric reduction we made use of the Tycho catalogue V magnitude.

A correlation of the magnitude difference $V \, - \, m_{V\rm al}$ with the (poorly determined) color index (B - V) as reported in the Tycho catalog is shown in Fig. 3 and can be fitted by

$$V \, - \, m_{V\rm al} \, = 0.14 \, - \, 0.07 (B - V).$$ (2)

However, a large scattering of the data having various origins is present and precludes a straightforward utilization of Eq. (III.2). Moreover, given the intrinsic capabilities of the Meridian Circle we are not able to measure B band magnitudes properly because of focusing and detector limitations. This means that even though our claims about the photometric quality and long-term stability of the selected standards are quite secure, those stars should be recalibrated whenever other system is needed for purposes other than differential photometry. With this shortcome in mind, an approximate relationship between filters may be obtained as $m_{V\rm al} \, = \, 1.02 V \, - \, 0.28$for quick references purposes only.

  

Figure 3: Correlation of the magnitude difference ($V - m_{V\rm al}$) with the color index (B-V)

To select a set of standard stars we have performed 5 to 6 observations of $\rm \sim 1^{h}$ in right ascention each, centered in the selected windows. The main objective was to include as many Tycho stars as possible in each field to link the selected set to them. In addition, 10 short observations centered around the field coordinates given in Table 1, with a total duration of 3 to 6 minutes each (this is the standard duration of the observations), were employed to construct light curves for the candidates to reference stars and to check the stability of their magnitudes.

The employed data reduction method requires a preliminar reduction, with the sky background 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 curve is adjusted to the flux distribution of the objects, to obtain the x and y centroid coordinates, the flux and respective errors. In the following step, the celestial positions and magnitudes are calculated by a global reduction, using the field overlap among all observation nights (Eichhorn 1960; Benevides-Soares & Teixeira 1992, and Teixeira et al. 1992). In this procedure, first of all, each night is reduced independently of the remaning data by solving the following by least squares system, with respect to reference catalogue stars:

$$\alpha \, = \, a_{0} \, + \, a_{1} x \, + \, a_{2} y$$ (3)

$$\delta \, = \, b_{0} \, + \, b_{1} y \, + \, b_{2} x$$ (4)

$$m_{V\rm al} \, = \, m_{V\rm al0} \, - \, 2.5 \log F$$ (5)

where a₀ is the initial sidereal time of the observation of the field, b₀ is the central declination of the field and x and y are the relative coordinates. The x coordinate is measured in the diurnal motion direction while the y coordinate is in the perpendicular direction. The terms a₁ and b₁ are the scale in x and y, respectively, and a₂ and b₂ are corrections in the CCD orientation. A more robust model for the magnitude computation, using color index reported in Tycho catalog, are in development, but our tests demonstrated that actual results are confiable.

After this first reduction, the system of Eqs. (3-5) is again solved by using an iterative process, now for all stars detected in the field. At each step of iteration, the system is solved by least squares (Benevides-Soares & Teixeira 1992 and Teixeira et al. 1992). The process converges in a few iterations (typically less than 10 steps).

The Tycho Catalog is presented in the form of a multicolumn file in which a quality criterion is given for each object. This criterion guides the further utilization of the stars as standards for any purpose. We have concluded that the construction of secondary catalogues referred to Tycho stars of quality index worse than 5 can compromise the desired accuracy, and therefore we excluded such Tycho stars. Stars brighter than $m_{V\rm al} \, = \, 8.5$ have been also excluded because they have a saturated image in the CCD and their use would spoil the magnitude measurement of all the stars in the field. All the known variable stars were also taken out according to the GCVS (Khopolov et al. 1988) and NSV (Kukarkin et al. 1982) Catalogues, and the new variables found by the HIPPARCOS mission. With this criterion the final number of Tycho stars present in the "short" exposure lies between 1 and 8, and in the "long" exposures, between 31 and 89 stars.