5.1 Optimizing the apparent stellar size and the apparent velocity of KBOs

Let us firstly discuss what the best stars are for occultation by KBOs: as already said, the diameter of a typical star, projected at 40 AU, is between 0.1 and 100 km. As we saw in section 3, the smaller the occulted star, the smaller the smallest detectable KBO, and because small KBOs are more numerous, the larger the occultation rates. The small stars will thus be good candidates to detect KBOs especially if they are bright enough to provide a good signal to noise ratio. For a given magnitude, the blue stars are smaller than the red ones (see Table III): an O5 star of $M_V=12$ has a projected radius of 100 m. For the same magnitude, an M5 star has a projected radius of 10 km.

Table 3: Apparent stellar radii at 40 AU as a function of the spectral class and magnitude $M_{V}$.

$M_V=$	8.	10.	12.	14.
M5 star	50 km	20 km	8 km	3 km
F5 star	4 km	2 km	700 m	100 m
O5 star	800 m	300 m	100 m	50 m

In addition to the apparent size of the star, a critical observational parameter is the data acquisition frequency. As seen in section 2, the relative velocity $v_o$ of the KBOs with respect to the star varies from few to 25 km/s. Then the occultation length, which is roughly $\sim 2\rho_\epsilon/v_o$, is for most of them a fraction of second. The quadrature direction can be exploited as proposed by [Brown and Webster 1997] to search for occultations lasting several seconds. However, in this direction the occultation rate is lower than toward the opposition since $N_{\rm {occ}}\propto v_{o}$. So, if we use a photometer of sufficiently high speed, we will increase our chances of detecting KBOs by observing toward the opposition. Moreover, the frequency necessary to observe the diffraction fringes must be larger than $v_o/\sqrt{\lambda D/2}$. For visible wavelength, this minimum frequency varies from 1 to $20 \rm {Hz}$, which requires high speed photometry.