4 Going to one image per night

 The motivation of this pixel analysis is to increase the sensitivity to long duration events ($\ge 5$ days) in the mass range where all the known candidates have been observed. It is crucial to note that a sampling rate of 1 measurement per day is sufficient. The numerous images available each night (up to 20 per night) allow us to reduce the noise discussed in Sect. 3.5, by co-adding them, and are very useful for the error estimation as emphasised in Sect. 7.

4.1 Construction

 We average the images of each night. During the night n, we have, for each pixel p, N^p_n measurements of flux ($\phi^p_{n,j}$; j = 1,N^p_n). The number of measurements N^p_n available each night is shown in Fig. 5 and ranges between 1 and 20 with an average of 10. The mean flux $\phi^p_n$ of pixel p over the night is computed removing the fluxes which deviate by more than $3\sigma$ from the mean, in order to eliminate any large fluctuation due to cosmic rays, as well as CCD defects and border effects. Note that, due to this cut-off, the number of measurements N^p_n used for a given night can differ from pixel to pixel.

  

Figure 5: Number of images per night for one CCD field: in red a) and in blue b)

  

Figure 6: A stable pixel light curve before a) and after b) the mean is performed over each night

  

Figure 7: A variable pixel light curve before a) and after b) the mean is performed over each night

  

Figure 8: Relative flux stability achieved on pixel light curves after averaging the images of each night, on a $50\times 50$ patch of CCD 3

4.2 Results

Figure 6 shows the result of this operation on a typical pixel light curve. The dispersion in the data on the top panel (a) is reduced and included in the error bars (see in Sect. 7) as shown on the bottom panel (b). Figure 7 shows the same operation applied to a pixel light curve exhibiting a long time scale variation. One can notice that uncertainties in the data during full moon periods are not systematically larger than those corresponding to new moon periods. Figure 8 displays the histogram of relative stability for the resulting light curves, for the same area as for Fig. 4.

4.3 Additional remarks

Thanks to this procedure the PSF of the composite images will tend towards a Gaussian. This thus removes the inhomogeneity in the PSF shape that can be observed on raw images. In particular, the seeing on these composite images becomes more homogeneous with an average value of 3.0 arcsec in red and 2.9 arcsec in blue and a quite small dispersion of 0.25 arcsec. The seeing dispersion is divided by a factor 2 with respect to the initial individual images, whereas the average value is similar.

To summarise, this procedure improves the image quality, reduces the fluctuations that could come from the alignments and removes cosmic rays.