4 Detection of variable stars

4.1 Selection criteria

We do not have all the observations in good photometric sky conditions. Therefore we have rejected all those data points showing photometric error of >0.2 mag. Further, for each star, the average DAOPHOT error and its standard deviation was calculated using its observations on different nights. Measurements with errors exceeding to average error by more than 3$\sigma$ were flagged as "bad'' and removed from further analysis. The whole procedure was iterated thrice. Normally 1 to 10 points were removed in this process. Because two different CCDs with different quantum efficiencies (see Table 1) and different exposure times (see Table 2) were used, limiting magnitudes were different in different years. Consequently some stars could not be identified in one or other years of observations. All the stars were not present in every frame due to different observing conditions and CCD orientations on various nights. In order to derive useful results, we consider only those stars in our further analysis which have more than 40 R data points. Stars which showed more than $5\sigma$variation in 3 consecutive data points are searched for variability. Only R band photometric data is used for this as the data sample in R filter (133) is larger than that in I filter (116). Also photometric errors at a given brightness are generally less in R filter (see Table 3). Finally we analysed the variability in these stars explicitly by visual monitoring and also using I filter data. In this way, we detected 359 variable stars in our field.

4.2 Period determination

To find periods from unequally spaced data, we used a modified version of the period-searching program by Press & Rybici (1989) based on the method of Horne & Baliunas (1986). The data were initially phased for all periods between 5 and 600 days searched in an increment step of 0.6 day. To further refine the period, an increment of 0.1 day was used around thus derived period. In this way, we could determine period of 141 variables. The remaining stars are either non-periodic or long-period variables.

4.3 Mean magnitude

We calculated phase weighted apparent mean magnitude for all the Cepheid variables as suggested by Saha et al. (1994)

$$\overline m = -2.5\log_{10} {\sum_{i=1} ^{n}}\ 0.5 (\phi_{i+1}-\phi_{i-1}) 10^{-0.4 m_{i}}$$

where n is the total number of observations, $\phi_{i}$ is the phase of ith observation in order of increasing phase after folding the period. The equation requires non-existent entities $\phi_{0}$ and $\phi_{n+1}$ which is set identical to $\phi_{n}$ and $\phi_{1}$ respectively. The estimation of mean magnitude by the phase-weighted method is superior to an ordinary mean, which minimizes the systematic biases from loss of faint measurements in the mean magnitude (Saha & Hoessel 1990). For other variables, mean magnitude is estimated simply by intensity averaging of all the data points.

4.4 Astrometry

Transformation equations were derived to convert pixel coordinates (X,Y) into celestial coordinates ( $\alpha_{2000}$, $\delta_{2000}$) using 324 reference star positions from the USNO catalogue. These coordinates agree within $\sim$0.1 arcsec with those given in Magnier catalogue (Magnier et al. 1992).