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2 Observations and data reductions

The observations of NGC 7790 were carried out in B, V Johnson and I Cousins passbands using RCA SID 501 thinned back illuminated CCD detector at the f/3.29 Prime focus of the 2.3 meter Issac Newton Telescope (INT) at La Palma. At the Prime focus, a pixel of the $320 \times 512$ size CCD corresponds to 0 $\hbox{$.\!\!^{\prime\prime}$ }$74. Bias and dark frames were taken intermittantly. Flat-field exposures ranging from 1 to 10 seconds in each filter were made of the twilight sky. Nine Landolt (1983) standards, covering a range in brightness (10 < V < 13) as well as in colour (-0.19 < (V-I) < 1.41) were observed for calibration purpose. The region as shown in Fig. 1, was imaged on the nights of 1988 July 21 and 22. Altogether 9, 8 and 8 frames were taken in B, V and I passbands respectively. The exposure times were 50, 40 and 40 seconds in the respective passbands. Further details of the instrument and observing procedures have been given in Sagar & Griffiths (1991). Initial processing of the data frames as well as photometric reductions were carried out at Indian Institute of Astrophysics, Bangalore. The evenness of flat-field frames (summed for each colour band) is better than a few percent in all the filters. The magnitude estimation on each frame has been done using DAOPHOT profile fitting software (Stetson 1987, 1992). The stellar point spread function (PSF) was evaluated from several uncontaminated stars present in each frame. The image parameters and errors provided by DAOPHOT were used to reject poor measurements. About 10% stars were rejected in this process. DAOMASTER programme was used for cross identifying the stars measured on different frames of the cluster region. The values of atmospheric extinction coefficients in the V passband determined during the observations by the Carlsberg Automatic meridian circle were between 0.10 and 0.11 mag per unit air mass with almost negligible ($\sim -$0.003 mag) hourly rate of change of extinction. These along with mean (B-V) atmospheric extinction coefficients for the site were used in determining the colour equations for the CCD system using Landolt (1983) standards (see Sagar & Griffiths 1991). In order to convert accurately the CCD instrumental magnitudes into standard ones using this colour equations, precise knowledge of the zero-points is required. It can be achieved if standards in the imaged regions are present, as it avoids the errors introduced due to uncertainties in shutter timing and in correction between profile and aperture magnitudes etc. Fortunately, such standard stars are present in the imaged cluster region and their CCD photometric measurements have been carried out earlier by Christian et al. (1985) and recently by Odewahn et al. (1992). The two sets of measurements agree very well with each other. Zero-points for the calibration have therefore been determined from the Christian et al. (1985) standards. The zero-points thus derived are uncertain by $\sim $0.01 mag in B,V and I bands. The X and Y pixel coordinates as well as V, (B-V) and (V-I) magnitudes of the stars observed in NGC 7790 are listed in Table 1, which is available only in electronic form at the CDS in Strasbourgh and the open cluster database Web site at In order to avoid introductions of a new numbering and (X, Y) coordinate systems, we adopt them from the database given by Phelps & Janes (1994). Stars not observed earlier have number starting with 5000 and there are about 700 such stars. They are mostly fainter than V = 19 mag, as present photometric data are the deepest. Stars observed by others have been identified in the last column of Table 1. The internal errors as a function of brightness for each filter are estimated using artificial add-star experiment as described by Stetson (1987) and they are given in Table 2. The errors become large ($\ge$ 0.2 mag) for stars fainter than V = 20 mag, so the measurements should be considered unreliable below this magnitude.

\end{figure} Figure 2: The V, (B-V) and V, (V-I) diagrams for the stars observed by us in NGC 7790 region

2.1 Colour magnitude diagrams based on presentobservations

The apparent V, (B-V) and V, (V-I) diagrams of NGC 7790 generated from the present data are displayed in Fig. 2. These include all the stars with DAOPHOT $\sigma_{B-V}, \sigma_{V-I} < 0.07$. The deep CMDs extend down to V = 20 mag. A well defined cluster main-sequence (MS) contaminated by field-stars is clearly visible in both CMDs. The cluster sequences fainter than V = 20 have large scatter and perhaps not clearly defined. This may be due to large photometric errors present in our observations. In order to derive the most reliable cluster parameters, present data are not adequate as it covers only part of the cluster region (see Fig. 1) and also the cluster members brighter than V = 13.5 mag have not been observed. These stars are very important for estimating the cluster age and also for the study of stellar evolutionary status of the cluster. We have therefore combined all the broad band photometric data of the cluster available in the literature. For this, their inter-comparison is mandatory and the same has been done in the next section.

Table 2: Internal photometric errors as a function of brightness in NGC 7790 are tabulated. The standard deviation ($\sigma $) is per observation in magnitudes
Magnitude Range   $\sigma_{B}$   $\sigma_{V}$   $\sigma_{I}$  
15.0 - 16.0   0.01   0.01   0.03  
16.0 - 17.0   0.05   0.08   0.04  
17.0 - 18.0   0.09   0.11   0.08  
18.0 - 19.0   0.12   0.15   0.11  
19.0 - 20.0   0.14   0.17   0.18  
20.0 - 21.0   0.25   0.29   0.26  

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