|Figure 4: Luminosity functions in blue (full line) and in red (dashed line) at the epoch JD = 2448678.3. The upper histograms a) correspond to the magnitudes estimated for all the stars with DAOPHOT. The lower histograms b) correspond to the magnitudes estimated as described in Sect. 4.1 for the selected variable stars|
Whereas this definition of the sky-background is rather robust to the crowding conditions, the magnitude estimation is not necessary so, as some additional flux (stellar background) could contribute to the super-pixel due to neighbours. We thus quantify the blending with the ratio computed as follows: the flux is the averaged value computed along the light curve of the central pixel of the super-pixel, and the flux is a similar average of the 8 surrounding pixels within the super-pixel. The behaviour of this parameter is described in the Appendix.
Optimised star detection with DAOPHOT allows to detect stars in blue and stars in red. The corresponding luminosity function computed with DAOPHOT for all the stars present on the studied field, exhibited in Fig. 3a, shows that the star detection is in first approximation complete down to magnitude 18 in red and 19 in blue. Figure 3b shows that the magnitude distributions at the same epoch for the selected variable stars peak at the bright end, whereas the stars are redder than average with . Whereas it is difficult to compute our detection efficiencies as no reliable theoretical distribution of variable stars is available, it is clear that we do not detect a population of variable stars unresolved at minimum, even though we do detect a tail of this distribution with very dim stars in at least one colour.
|Figure 5: CMD at JD = 2448678.3: small dots correspond to the stars detected with DAOPHOT, symbols to the 631 selected variations. The different symbols correspond to different ranges of the ratio: filled symbols correspond to stars with a high S/N ratio and not affected by crowding. The superimposed isochrones (full lines) are adapted from Bertelli et al. (1994) to the EROS system (Grison et al. 1995) with a foreground extinction and , deduced from reddening E(B-V)=0.15 measured by Schwering Israel (1991) with the extinction law from Cardelli et al. (1989). They correspond to LMC metalicity (Z=0.008), helium abundance (Y=0.25) with ages of (age) = 7.4, 8.4 and 9.4. The dashed lines show the uncertainties introduced on each isochrone by the photometric transformation|
As shown in Fig. 4, variable stars not significantly affected by crowding ( ) lie in areas of the colour-magnitude diagram corresponding to stars expected variable. Those affected by blending and crowding will have to be treated with caution. In the CMD areas where the larger number of LTLPV have been detected, in the magnitude ( ) and colour ( ) ranges, about 17% of the stars exhibit a variation detected with our analysis.
It is also clear that the vast majority of the detected variable stars are above the crowding limit. The few outliers that can be noticed correspond to stars unresolved in at least one colour, but their number does not exceed 5% of the total. In terms of microlensing, this means that events due to unresolved stars in the LMC will not be significantly contaminated by the bulk of variable stars. In further galaxies, like M31, variable stars will be a more troublesome affair, and will have to be carefully studied (e.g. Crotts & Tomaney 1996). However, high amplification microlensing events are far less likely to be mimicked by an intrinsic variation (Ansari et al. 1999), and will allow to probe possible biases introduced by variable stars.
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