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Astron. Astrophys. 349, 55-69 (1999)

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3. Data reduction

Bias subtraction and flat field corrections were performed using IRAF package (Tody 1993). It was necessary to correct the images for the slightly different pointing of the telescope and orientation of the CCD camera in the different runs. Therefore they were shifted and rotated with the ESO/MIDAS command REBIN/ROTATE with respect to the image No. 26, which is one of the best images and which was used as template. For this reason, the stars near the borderline have usually less measurements than those in the central part of the field, and the field actually surveyed is sligthly larger than the nominal one, that is about 3:084x3:084.

3.1. Photometry

The stellar photometry was performed by means of the IRAF/DAOPHOT package (Stetson 1987; Davis 1994). For each image a prelimary list of objects was detected with DAOFIND, and a prelimary aperture photometry was performed with DAOPHOT. In order to evaluate the point-spread-function, a group of stars were selected with PSTSELECT and then checked visually one by one. The point-spread-function model was then iteratively computed with the PSF-command using about 20 stars for each image. Due to the smallness of the field, a constant PSF model consisting of a gaussian plus a single empirical look-up table was adopted. Finally the photometry of all the selected stars was derived by means of ALLSTAR. New stars were then searched in the residual image, added to the previous list, and then ALLSTAR was executed again on this list. This procedure was finally repeated once again. The residual image that we got after the third analysis with ALLSTAR was generally clean, with no evident stellar images; only some residuals near the loci of the brightest stars, HII regions and galaxies were present. The tables containing the lists of the detected stars in each image were cross-correlated in order to look for the objects in common and reject the spurious ones. Two objects in two different images were considered to be the same star if the separation of their centers was less than 1 pixel.

The same reduction procedure was adopted for both Wh and [FORMULA] images.

3.2. Calibration

DAOPHOT produced a set of instrumental wh magnitudes for the stars in each frame, which could not be reduced to a standard system. The procedure for deriving a homogeneous magnitude scale was an iterative one, based on the 104 stars detected in all the frames. Let [FORMULA] be the magnitude value of the star i in the frame j, [FORMULA] the mean value for the frame j, n the number of stars, [FORMULA] the global mean value and k the number of frames. At the first step, the mean values are computed and then a new [FORMULA] value is calculated with the formula

[EQUATION]

At each subsequent step the mean values of the time series [FORMULA] are calculated using the new [FORMULA] values, excluding from each time series i the most deviating point if the deviation is larger than 2.5[FORMULA] from [FORMULA], and replacing this point with the corresponding [FORMULA]; then the new mean values [FORMULA] and [FORMULA] are recalculated. The final result of this iteration is the correcting term, [FORMULA], applied to each of the original data points. The number of steps is fourteen, however for most of the stars very few iterations are sufficient for obtaining stable mean values.

Since field A partially overlaps one of the fields observed by Freedman (1988b), we used the 158 common stars to tie our V and R observations to the standard VR system. We got the color index V-R for 512 stars from our data; for an additional 227 stars, which were not detected in both V and R frames but were detected in wh frames, we adopted the V-R value given by Freedman (1988b).

We selected a sample of stars for constructing a [FORMULA] system, useful for the discussion of the photometric results. The calibrating stars were selected according to the following criteria: a) more than 62 observed wh data points per star, b) stellar nonvariability or low scatter of data points, c) known V and R data; criteria a) and b) were needed in order to get a sample free of problems related to crowding. The resulting number of stars was 195, which gave the following statistical relations between wh, V and V-R

[EQUATION]

with rms residuals of 0.11 and 0.10 mag, respectively. Fig. 2 shows V (lower panel) and estimated wh from Eq. 1 (upper panel) against observed wh, and Fig. 3 shows V-wh against V-R. We derived the zero-point [FORMULA] of the final Wh magnitude scale, [FORMULA] from Eq. 2 assuming that V-[FORMULA] when V-[FORMULA], that is [FORMULA] or

[EQUATION]

[FIGURE] Fig. 2. Correlations among the photometric parameters of 195 selected stars. Lower panel: V against instrumental wh; upper panel: best fit given by Eq. 2

[FIGURE] Fig. 3. V-wh against V-R for 195 selected stars

The nonlinearity of Eq. 3 depends on the large Wh-bandwidth; V-wh appear to be more sensitive to [FORMULA] than V-R for cooler stars, and less sensitive for hotter stars. We will use occasionally the colour index V-Wh when the R measurement will not be available; we just note that, as a first approximation, from the linear correlation between V-Wh and V-R we have [FORMULA]. Analogously, [FORMULA].

In Fig. 4 we have reported the external error (or standard deviation) [FORMULA] for about 1700 stars with at least 24 data points (and [FORMULA]), against the mean value Wh of the star; in the upper panel, the standard deviation was calculated including all the data points, some of which are rather scattered; in the lower panel, the four most deviating points of each star have been excluded. The continuous line is a rough theoretical estimate of the expected external error.

[FIGURE] Fig. 4. Standard deviation [FORMULA] of the Wh observations (logarithmic scale) for stars with at least 24 data points and [FORMULA]. Upper panel: all the observed points have been included, some of which are largely deviating, owing e.g. to crowding problems; lower panel: the four most deviating points have been excluded from the time series of each star. The continuous line is a rough theoretical estimate of the expected external error.

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© European Southern Observatory (ESO) 1999

Online publication: August 25, 1999
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