3 Selection of genuine variable stars

Figure 1: Effect of the selection procedure on the Max(LB,LR)distribution. Panel a) illustrates the effect of the steps (1) and (2) of the selection procedure indicated in Table 1. The hatched area corresponds to the pixels kept at step (1). The dashed and dotted histograms each show how this distribution is affected if this threshold is changed as indicated in Table 1. The thick line displays the effect of step (2). The dot-dashed lines correspond to the weakening/strengthening of this cut. Panel b) illustrates the effects of steps (4) and (5). The large amplitude histogram shows the distribution after step (3), the thick-line histogram shows the result of step (4), and the hatched area corresponds to pixels kept at the end of step (5). The dashed histograms show the sensitivity of this last threshold

We apply an automatic selection of genuine luminosity variations to the 91-92 dataset. Firstly, we introduce the definition of a variation. Secondly, we adjust the thresholds in order to keep genuine variations but reject most artifacts due to noise. Last, we carefully inspect selected light curves close to bad pixels.

3.1 Definition of a variation

A baseline flux ( $\phi_{\rm bl}$) is calculated for each super-pixel light curve by sorting all points in order of increasing flux, with $\phi_{\rm bl}$ being the 10$^{\rm th}$ sorted point. $\sigma_{\rm bl}$ is the error associated with the baseline flux determination. For a sample taken from a Gaussian distribution with a standard deviation $\sigma$this estimate lies 1.3 $\sigma$ below the mean value of the distribution.

Deviations from this baseline are recorded when measurements lie $3 \sigma_n$ above the baseline:

$$\sigma_n = \sqrt{{\sigma^{\prime}_{n}}^2 + {\sigma_{\rm bl}}^2}$$ (2)

where ${{\sigma}^{\prime}_{n}}$ is the error associated with each super-pixel flux computed in Paper I for night n. These deviations are quantified in each colour with a likelihood function (L):

$$L = -\ln \left(\prod_{n \in \mathrm{bump}} P(\phi \ge \phi_n)... ...rray}{c} \phi_{\rm bl} \\ \sigma_n \end{array} \right. \right)$$ (3)

where $\phi_n$ is the super-pixel flux for the measurement n. All the measurements above $\phi_{\rm bl}$ are accounted for.

3.2 Minimal threshold

With the definition introduced above, we apply the selection procedure summarised in Table 1.

First of all we excise the pixels, covering 3.4% of the CCD fields, which exhibit obvious spurious variations (such as bad columns). In addition, in order to remove automatically artifacts due to bad pixels, we remove from the light curves the epochs for which there is at least one pixel which datum is at zero within a 11$\times$11 window centred on the super-pixel. (1) We require a regularity condition to remove the noise: the ratio $\sigma_1/\sigma_2$ has to be smaller than 0.6 in at least one colour, with:

$${\sigma_1}^2={\frac{2}{3(N-2)} {\sum_{n=2}^{N-1}}\left[ \frac{\phi_{n+1} - \phi_{n-1}}{2} - \phi_n \right]^2}$$ (4)

$${\sigma_2}^2={\frac{1}{(N-1)} {\sum_{n=1}^{N}}\left[ \phi_{n} - \phi_{\rm mean} \right]^2}$$ (5)

where $\phi_{\rm mean}$ is the mean super-pixel flux and N is the total number of measurements on each light curve. (2) We then select the light curves which vary such that L>400 in at least one colour. As there are as many super-pixels as pixels, a genuine variable is expected to affect all the super-pixels within the seeing spot. (3) We search for clusters of super-pixels (using a Friend of Friends algorithm), and keep the central pixel of the clusters if (4) the previous requirements are also satisfied for these pixels and, if (5) the number $N_{\rm clus}$ of super-pixels that compose each cluster is larger than 6. These requirements eliminate most artifacts due to bright stars and CCD defects that do not exhibit a clear spatial PSF-like pattern. We finally keep 747 super-pixel light curves. The sensitivity of these thresholds is illustrated in Fig. 1. Among the 747 selected variations, two have been counted twice, leaving 745 independent light curves.

   
3.3 Artifact removals

Figure 2: Artifact removals. Panel a) displays the positions of the 116 rejected light curves on the CCD chips. Panel b) shows a similar distribution but for those among the 237 light curves close to CCD defects that have been kept. Each symbol corresponds to a different chip. Each panel corresponds to the size of the chips $x \in [0,400]$, $y \in [0,579]$

We select 237 light curves for which there is at least one bad pixel (saturated or set at zero) within a 21$\times$21 window centred on the selected pixel for at least one epoch and at least one colour. A careful visual inspection of these light curves shows 121 genuine variable stars against 116 artifacts, subsequently removed. Figure 2 shows that the removed light curves are mainly concentrated close to the edges, whereas the distribution of the kept light curves (among the 237) is more uniform. We finally end with a catalogue of 631 variable stars.