6. THE VALIDITY OF THE DETECTION

The main limitation of this method is the uniqueness of the occultation. It is not possible to redo an observation to verify the reality of the detection. Moreover, the objects detectable with this method are mostly undetectable by other techniques. Then the question is: How can we be sure we have detected an occultation by a KBO and not an asteroid, a comet, or a bird or an electric discharge?

This question has already been encountered during studies of planetary rings. The Uranus and the Neptune ring system, undetectable from the ground until recently, have been discovered and explored by stellar occultations. The reality of an occultation by the Uranus rings have been confirmed by the symmetrical dips observed on the two sides of the planet. But the incomplete arcs of Neptune have been much more difficult to catch. To assess the reality of an arc detection, the observations were conducted on 2 nearby telescopes. Some occultations provided arc profiles with S/N ratio good enough to fit the dip with a semitransparent bar model and reject the hypothesis of a solid body [Sicardy, Roques and Brahic 1991].

During planetary occultations, isolated events were often observed with one telescope but with S/N not good enough to fit them [Nicholson et al. 1990]. One of them has been confirmed by simultaneous detection with nearby telescopes during an occultation by Uranus. It has been analyzed as the occultation by a 1.4 km object near Uranus [Sicardy et al. 1986]. Using the present work, we found that the probability of occultation by KBOs during such observations was some tens of percent per night. Then, several isolated events observed during the planetary occultations could be due to KBOs.

Different methods can be used to asses the reality of the occultation and to possibly discriminate an occultation from a false event or an occultation by another object in the Solar System:

• As for planetary occultations, the reality of an occultation can be confirmed by simultaneous observation from nearby telescopes, or with multi-object photometers. However, this does not allow us to determine the distance of the occulting object.

• The direction of the shadow motion can also be used, as done by the TAOS team who validate the event by successive detections by telescopes spaced a few kilometers apart on an east-west baseline.

• Table IV shows the parameters of the occultations in terms of the distance of the occulting object. The minimum size of detectable objects (last column) shows that asteroids of a few tens of meters could be detected. However, the asteroid population is probably $10^{5}$ times less numerous than the KBO population. Then, even if smaller objects are involved, the probability of occultation by KBOs is a thousand times larger than by asteroids.
  

  Table 4: Occultation parameters -Fresnel scale $Fs$, quadrature direction $\omega$, apparent velocity $v_{o}$ at the opposition and object size limit of detectability $\rho_{\rm{lim}}$- for various heliocentric distances $D_{\rm AU}$ of the occulting object.

  $D_{\rm AU}$	$Fs \dag$	$\omega$[quad.]	$v_{o}$[opp.]	$\rho_{\rm {lim}}\ddag$
  3.	245 m	55$^\circ$	13 km/s	25 m
  40.	1.1 km	81$^\circ$	25 km/s	130 m
  100.	1.7 km	84$^\circ$	27 km/s	200 m
  $10^{3}$	5.5 km	88$^\circ$	29 km/s	700 m
  $10^{4}$	17 km	89$^\circ$	30 km/s	4 km
  $10^{5}$	55 km	90$^\circ$	30 km/s	55 km

  at $0.4\mu$m detected at $4\sigma$ for $\sigma=1\%$ and $\Phi_\star \sim 0.003$ mas
  
  

  The velocity of a KBO in the sky plane for a given direction depends on the distance of the occulting object (Eq.5). The probability of occultation is minimal and the duration of the occultation is maximal toward the quadrature, that is 81 $\hbox{$^\circ$}$ from the opposition for objects at 40 AU from the Sun. But the direction of the quadrature changes with the distance of the occulting objects: When several events are detected, the number of events with respect to the direction of observation $\omega$ can be used to infer the distance of the population of occulting objects. The high occultation rates estimated above for large telescopes make these speculations plausible.

• If an occultation is observed at different wavelengths, the profiles are different (see Fig.5) and the comparison of the dip profiles could give information on the Fresnel scale and, then, on the distance of the occulting object.

  Figure 5: Synthesized lightcurve of the occultation of a star by a 0.2 km KBO observed at 0.4 $\mu$m (upper curve) and 1.2 $\mu$m (lower curve). The star radius projected at 40 AU is 0.3 km and the noise $\sigma$=1%.

  

• An occultation profile on a unique lightcurve with a high S/N and high speed acquisition should exhibits the diffraction fringes (see Fig.6 and [Roques 1999]). These features may be analyzed to retrieve the Fresnel scale and thus provide the distance of the occulting object (this analysis, as the previous point, are not in the scope of the present paper and will be done elsewhere).

  Figure 6: Synthesized lightcurve of a stellar occultation observed with high photometric precision $\sigma =0.001$ and exhibiting diffraction fringes. The object radius is 40m and the star radius is 100m, both projected at 40 AU. The acquisition frequency is 20Hz and the object apparent velocity is 3km/s.