6 Statistics

From 1973 to 1999, we observed 60 different comets at Nançay (not counting multiple returns). 40 were clearly detected, and 12 marginally detected. Table 6 lists the distribution of these detections among different families of comets, as listed in Table 1. Among long-period comets (P > 200years), we have distinguished dynamically new comets (with semi major axis a > 20 000 years) from others (with smaller a, or for which a could not be precisely determined). Among short-period comets, we have separated Jupiter-family (P <20 years, small inclination) and Halley-type ( 20 < P < 200 years, random inclination) comets.

The upper limit that can be achieved on Q[OH] depends on r, $\Delta$ and the inversion i of the OH maser. For observations spread over one week ( $7 \times 1$ hour integration), the 3-$\sigma$ upper limit on the line area is $\approx$0.030 K km s^-1. This corresponds to an upper limit Q[OH] $< 1.3 \times 10^{28}$ s^-1 for a comet at $r = \Delta = 1$ AU with i = 0.3. Few comets, with better observing conditions, were detected with Q[OH] < 10²⁸ s^-1.

Figure 2 shows the distribution of comets with Q[OH] larger than a given value (Q being the strongest OH production rate obtained during the scheduled observations of the comet, as listed in Table 4). There is an average of one comet per year observed with Q[OH] >10²⁹ s^-1. We believe that we have not missed any comet at this production rate level, in the sky domain accessible to Nançay. Some comets, however, may have reached higher Q[OH] than those we observed, because radio observations of OH close to perihelion or at small heliocentric distances are more difficult (unfavourable OH maser inversion, higher quenching, smaller OH lifetime). Comets with small (< $3 \times 10^{28}$ s^-1) Q[OH] are grossly under represented, because of the detection limit discussed above, and because observations of such weak comets were less frequently scheduled.

Figures 3-7 show some other aspects of the distribution of the Nançay observations. No discrimination has been made between observations with or without detection. Figure 3 is the histogram of the number of daily observations per comet. Five comets with 100 or more observations were the object of a peculiarly long campaign of observation and represent 45% of all observations. They are 1P/Halley, C/1995 O1 (Hale-Bopp), 21P/Giacobini-Zinner (1985 return), C/1986 P1 (Wilson) and C/1989 X1 (Austin), in order of decreasing number of observations. In Figs. 3, 4, 5 and 7, these well-studied comets are shown as black histograms, superimposed over grey histograms for the full sample.

Figure 4 is the histogram of the observations as a function of UT time. At Nançay, civil time is UT $+ 8^{\rm m}$. The distribution shows that day-time observations are more numerous by a significant factor (1718 observations between 6.0 and 18.0 UT, to be compared to only 635 in the other UT hours). This is because observations were preferentially made when the comets are the most productive, which is when they are close to the Sun and therefore at small solar elongation. Why the distribution actually peaks in the afternoon is not understood. No significant trend is found in the distribution as a function of sideral time.

Figure 5 is the distribution of the heliocentric distances at which observations were made. More observations were made pre-perihelion rather than post-perihelion; the explanation is discussed with Fig. 7. Observations at more than $\approx$2 AU were only attempted in the brightest comets, among the five well-studied objects (except for comet Bowell (1982 I), which was observed - and undetected - at $\approx$4 AU post-perihelion).

Figure 6 shows together the distributions of heliocentric and geocentric distances of the observations (irrespective of the pre- or post-perihelion situation). We see that observations were generally made at smaller geocentric than heliocentric distances. This is still a consequence of our aim to make observations in the best observing conditions.

Figure 7 shows the distribution of the heliocentric radial velocities of the observations. This obviously uneven distribution can be easily understood: the excitation of the cometary OH maser strongly depends upon the heliocentric radial velocity and the signal is expected, in first approximation, to be proportional to the maser inversion. As a consequence, the observations were preferentially planned at the moments of strong inversions. The theoretical maser inversion is also plotted in the figure to show this correlation. Only for bright comets were observations made at the moment of weak inversion, to investigate other possible excitation mechanisms. On the average, the inversion is weaker post-perihelion (positive heliocentric velocities) compared to pre-perihelion. Accordingly, post-perihelion observations are less numerous.

Figure 6: Distribution of the observations as a function of heliocentric (in grey) and geocentric (plain thick line) distances.

Figure 7: Distribution of the observations as a function of heliocentric radial velocity. The OH maser inversion (from Despois et al. 1981) is also plotted.