4 Asymmetry and planet occultation

We can now confirm that the majority of cometary occultations gives light curves with a very particular "rounded triangular'' shape (LVF 99 and Fig. 2). As described in LVF 99, this is simply explained by the occultation by the dense cometary head, then followed by the tail which gives only a smaller long lasting additional occultation.

However, in some configurations, the tail can be aligned with the line of sight. In these cases the light curve is more symmetric and can mimic a planetary occultation (Fig. 4, see also Figs. 2 and 3 of LVF 99). Because of the noise, it will be difficult from such observations to differentiate between a comet and a planet.

One of the major difference between a cometary and a planetary occultation is the time-symmetry of the planet occultation light curve. If the photometric variation $V(t)=(\Delta F/F)(t)$ is maximum at $t=t_{{\rm max}}$, then for a planet occultation we have $V(t_{{\rm max}}-\delta t)=V(t_{{\rm max}}+\delta t)$. We can define an "asymmetry factor'' by $AF\equiv {\rm Max}_{\delta t}\vert V(t_{{\rm max}}-\delta t)-V(t_{{\rm max}}+\delta t)\vert/V(t_{{\rm max}})$. Then, for an observation of a planetary occultation with a signal to noise ratio S/N, we have $AF \sim (S/N)^{-1}$, simply because $V(t_{{\rm max}}-\delta t)$ and $V(t_{{\rm max}}+\delta t)$ are two noisy measurements of the same value. Thus, cometary occultation light curves can be discriminated if they are asymetric enough with an asymmetry factor larger than a given value defined by the signal to noise ratio of the observation. With the full set of models available, we can evaluate the proportion of cometary occultation symmetric enough to mimic a planetary occultation at a given signal to noise ratio (Fig. 7). As an example, we find that with a signal to noise $S/N \sim 10$, about 5% of cometary occultation light curves can be considered to be symmetric. Following the results of LVF 99, with a survey of 30 000 stars at a photometric accuracy of 10^-4, we should be able to detect 100 to 1000 comet occultations per year. This gives about 5 to 50 detections of cometary occultations with symmetric light curves, which could be misinterpreted as planetary occultation. This number is of the same order as the expected number of real planetary occultations by Jupiter-like planets if each star has a planetary system resembling the solar system (LVF 99).