1 Introduction

The amount and nature of Dark Matter present in the Universe is an important question for cosmology (see e.g. White et al. 1996, for current status). On galactic scales (Ashman 1992), dynamical studies (Zaritsky 1992) as well as macrolensing analyses (Carollo et al. 1995) show that up to 90% of the galactic masses might not be visible. One plausible explanation is that the stellar content of galaxies is embedded in a dark halo. Primordial nucleosynthesis (Walker et al. 1991; Copi et al. 1995) predicts a larger number of baryons than what is seen (Persic & Salucci 1992), and so dark baryons hidden in gaseous or compact objects (Carr 1994; Gerhard & Silk 1996) could explain, at least in part, the dark galactic haloes.

In 1986, Paczynski 1986 proposed microlensing techniques for measuring the abundance of compact objects in galactic haloes. The LMC stars are favourable targets for microlensing events searches. Since 1990 and 1992, the EROS (Aubourg et al. 1993) and MACHO (Alcock et al. 1993) groups have studied this line of sight. The detection of 10 microlensing events has been claimed in the large mass range $0.05~-~1~M_{\odot}$ (Aubourg et al. 1993; Alcock et al. 1996). This detection rate, smaller than expected with a full halo, indicates that the most likely fraction of compact objects in the dark halo is f = 0.5 (Alcock et al. 1996). Concurrently, the small mass range has been excluded for a wide range of galactic models by the EROS and MACHO groups. Objects in the mass range ($5~10^{-7} M_\odot < M < 5~10^{-4} M_\odot$) could not account for more than 20% of the standard halo mass (Alcock et al. 1998). In the meantime, the DUO (Alard et al. 1995), MACHO (Alcock et al. 1995) and OGLE (Udalski et al. 1995) groups look towards the galactic bulge where star-star events are expected. The detection rate is higher than expected from galactic models (see for instance Evans 1994; Alcock et al. 1995; Stanek et al. 1997). The events detected in these two directions demonstrate the efficacy of the microlensing techniques based on the monitoring of several millions of stars.

Microlensing searches with the pixel method

The detection of a larger number of events is one of the big challenges in microlensing searches. This basically requires the monitoring of a larger number of stars. The Pixel Method, initially presented by Baillon et al. (1993), gives a new answer to this problem: monitoring pixel fluxes. On images of galaxies, most of the pixel fluxes come from unresolved stars, which contribute to the background flux. If one of these stars is magnified by microlensing, the pixel flux will vary proportionally. Such a luminosity variation can be detected above a given threshold, provided the magnification is large enough. Unlike other approaches (namely star monitoring and Differential Image Photometry, see below), the Pixel Method does not perform a photometry of the stars but is designed to achieve a high efficiency for the detection of luminosity variations affecting unresolved stars. This means that we will work with pixel fluxes and not with star fluxes. A theoretical study of the pixel lensing method has been published by Gould (1996b).

This pixel monitoring approach has two types of application. Firstly, it allows us to investigate more distant galaxies and thus to study other lines of sight. This has led to observations of the M 31 galaxy. The AGAPE team (Ansari et al. 1997) has shown that this method works on M 31 data, and luminosity variations compatible with the expected microlensing events have been detected but the complete analysis is still in progress (Giraud-Héraud 1997). A similar approach, though technically different, called Differential Image Photometry is also investigated by the VATT/Columbia collaboration (Crotts 1992; Tomaney & Crotts 1996). Some prospective work has also been done towards M 87 (Gould 1995).

The second possibility is to apply pixel microlensing on existing data, thus extending the sensitivity of previous analyses to unresolved stars. This is precisely the subject of this paper and of the two which will follow: we present the implementation of the Pixel Method on CCD images of the LMC.

Pixel method on the LMC

We have applied for the first time a comprehensive pixel analysis on existing LMC images collected by the EROS collaboration. With respect to previous analyses (Queinnec 1994; Aubourg et al. 1995; Renault 1996), our analysis of the same data using pixel monitoring allows us to extend the mass range of interest up to $1\, M_\odot$ and to increase the sensitivity of microlensing searches. On these images, a large fraction of the stars remains unresolved: typically 5 to 10 stars contribute to 95% of the pixel flux in one square arc-second. Since this approach potentially uses all the image content (and not only the resolved stars), the volume of the data to handle is much larger. Hence we perform this first exploratory analysis on a relatively small data set: 0.25 deg² covering a period of observation of 120 days, which corresponds to 10% of the LMC CCD data (91-94).

This paper is the first of a series of three, describing the data treatment (this paper), the microlensing search (Melchior et al. 1998a, hereafter Paper II) and a catalogue of variable stars (Melchior et al. 1998b, hereafter Paper III). In the companion papers (Papers II and III), we show how the data treatment described here to produce pixel light curves allows us to perform analyses that increase the sensitivity to microlensing events and variable stars with respect to the star monitoring analysis applied on the same field: an order of magnitude in the number of detectable luminosity variations is gained.

To discover real variations, the images and light curves have to be corrected for various sources of fake variabilities, such as geometrical and photometric mismatch, or seeing changes between successive images. The construction of light curves cleaned from these effects is the subject of this first paper. If the flux of a given star contributes to the pixel flux, the latter can be expressed as follows:  

$$\phi_{\rm pixel}=f\times\phi_{\rm star}+\phi_{\rm bg} ,$$ (1)

where $\phi_{\rm star}$ is the flux of the given star, f the fraction of the star flux that enters the pixel, hereafter called seeing fraction and $\phi_{\rm bg}$ corresponds to the flux of all other contributing stars plus the sky background.

If this particular star exhibits a luminosity variation, then we will be able to detect it as a variation of the pixel flux:  

$$\Delta\phi_{\rm pixel}=f\times\Delta\phi_{\rm star},$$ (2)

provided it stands well above the noise. Actually, this pixel flux is affected by the variations of the observational conditions and our goal here is to correct for them. We discuss the level of noise achieved after these corrections and include this residual noise in error bars. The outline of this paper is as follows. In Sect. 2, we start with a short description of the data used. In Sect. 3, we successively describe the geometric and photometric alignments applied to the images. We are thus able to build pixel light curves and to discuss their stability after this preliminary operation. In Sect. 4, we average the images of each night, thus reducing the fluctuations due to noise considerably. In Sect. 5, we consider the benefits of using super-pixel light curves. In Sect. 6, we correct for seeing variations and obtain light curves cleaned from most of the changes in the observational conditions. At this stage, a level of fluctuations smaller than 2% is typically achieved on the super-pixel fluxes. In order to account for the noise present on the light curves, we estimate, in Sect. 7, an error for each super-pixel flux. We conclude in Sect. 8 that the light curves of super-pixels, resulting from the complete treatment, reach the level of stability close to the expected photon noise. They are therefore ready to be used to search for microlensing events and variable objects, as presented in the companion Papers II and III.