3.2.2 Smoothing the occultation lightcurve on the star disk.

We discuss here the fact that the occulted star is never a point source. Indeed, the apparent radius of a star projected at 40 AU ranges from a fraction of kilometer to several tens of kilometers (see section 5), i.e. of the same order of magnitude as the KBOs. Therefore, the lightcurve smoothing over the apparent stellar disk must be taken into account in our computation. In order to do so, the star is considered as a set of incoherent point sources, with polar coordinates $(s,\theta)$ in a frame centered on the stellar disk. If $r$ is now the distance, in the occulting object plane, from the star disk center to the object center, the normalized light intensity produced during an occultation of a stellar disk of apparent radius $R_\star$ (again expressed in Fsu) becomes:

$$I_\rho^\star(r) = \frac{2}{\pi R_\star^2} \int_{0}^{R_\star... ...!\!\!\!I_\rho\left(\sqrt{r^2+s^2+2rs\cos\theta}\right) d\theta$$ (12)

In Fig.2 we present occultation lightcurves computed with Eq.12 and produced by a 200m (top) or a 1 km (bottom) KBO radius (within the two cases a Fresnel scale of 1km), for several different apparent stellar radii. As expected, the diffraction fringes are strongly smoothed when the apparent stellar size is larger than the KBO itself. An apparent stellar size of 2km reduces the largest diffraction effect of a 200m (1km) occulting KBO to only about 2% (30%) of the star light instead of more than 10% (90%) with a small apparent stellar disk or a point source. The diffraction with a 10 km apparent star disk is no longer perceptible on this figure (though there is a 1% decrease in the light intensity for the 1km object, which is simply the ratio of the areas, i.e. as the object transits the star disk).

Figure 2: Occultation profiles of a 200m radius KBO (top) and a 1km radius KBO (bottom), smoothed on different sized stars, for a 1km Fresnel scale. The apparent stellar radii are 0. (thin black curve), 100m (dark blue), 500m (red), 1km (magenta), 2km (cyan), 10km (yellow).