1. INTRODUCTION

The existence of a residual protoplanetary disk beyond the Neptune orbit was speculated by Kuiper [Kuiper 1951]. The recent discovery of hundreds of objects [Jewitt 1999], with radii from 50 to 200 km and located between 30 and 50 AU confirms the reality of the Kuiper hypothesis. A simple extrapolation of the observations allows us to predict the existence of 40000 to 70000 objects of more than 50 km radius in this region, and the existence of $10^{11}$ objects of more than 1 km radius. The observations also suggest that the differential size distribution is a power law $\rho^{-q}$ (where $\rho$ is the KBO radius) with an index $q\approx 4$ [Luu and Jewitt 1998]. This value is compatible with the guess that the Kuiper belt is the ``reservoir'' of short period comets. The total mass of these Kuiper Belt Objects (called KBOs hereinafter) is estimated from 0.1 to 0.3 Earth mass [Jewitt and Luu 1995]. Actually, the density of matter in the Outer Solar System seems surprisingly low beyond Neptune, and the Kuiper disk could be much larger than the present observations suggest. If the Kuiper Disk has a size distribution with such a constant index extending down to meter-sized objects, it would include a huge number of sub-kilometer-sized objects. However, a large collision rate could have destroyed the smaller objects. Anyway, the knowledge of the small KBO population is a key point because it could contain most of the Kuiper disk mass. The search for small KBOs is also a way to constrain the spatial distribution of the KBOs. The radial and the vertical extension of the Kuiper Belt are very poorly known. In particular, the outer limit of the Kuiper belt is unknown. It could continue extend to the Oort cloud with decreasing density. Furthermore, the Kuiper Belt could be similar to some circumstellar dust disks (as, for example, observed around HR4796 by [Schneider et al. 1999]) which have a typical size of 100 AU and could be the residue of planet formation.

More generally, the structure of the Kuiper belt, its size, thickness, mass and momentum distribution are key tools for the knowledge of planet formation, because the Kuiper belt is the most primitive part of the solar system since it was the outer part of the protoplanetary system: In the inner part of the disk, the planetesimals have collided to create larger bodies. Beyond Neptune, the reduced collision rate has prevented planet formation. From this time, the Kuiper disk suffers little evolution: Except the inner boundary, connected to a resonance with Neptune, the giant planets are too far to perturb the disk as they do for the asteroids belt. The mass and momentum distributions, important parameters for planet formation scenarii, are poorly known in the outer solar system where the time scales of the formation of Uranus and Neptune are not yet well understood.

Stellar occultations are a powerful tool for exploring the Outer Solar System: They have provided rich information on planetary atmospheres and ring systems [Elliot and Olkin 1996,Sicardy, Roques and Brahic 1991]. However, the observation of a stellar occultation by a given small object, such as a known comet or an asteroid, is quite difficult because the small angular size of the object prevents a precise prediction of the shadow path (cf. prediction of occultations by Pholus in [Stone, McDonald and Elliot 1999]). The possibility of detecting small objects of the Solar System by stellar occultations was introduced by [Bailey 1976] and [Dyson 1992]. More recently, [Brown and Webster 1997] have proposed to use the Macho experiment for detecting stellar extinction by KBOs, but, in these works, the diffraction effect during occultations has been neglected. We will show here that taking account of the star light diffraction is a sine qua non condition for addressing and implementing such a detection method.

We thus explore here the possibility of detecting KBOs by a method of ``serendipitous occultations'' by taking account of the diffraction effect: In section 2, we discuss and give an estimate of the statistical rate of occultation by KBOs using geometrical optics only, that is without taking into account diffraction effects. In section 3 we present a theoretical model of diffracted lightcurves produced during stellar occultation and we show that occultations could allow detection of rather distant and small objects. In section 4, we then use this model to estimate a more realistic occultation rate by KBOs than that estimated in section 2, and we give the probability of detecting occultations by KBOs within the present capabilities of the existing instruments. Section 5 explores the possibility of better exploiting the diffraction phenomenon for optimizing the detection of KBOs, especially when using high precision photometric instruments, and discuss other possible instrumental implementations of such a method. Finally, in Section 6 we discuss how to be confident that the observed dips on a lightcurve are due to occultation, and in particular, due to occultation by KBOs.