6 Summary

CCD observations of comets in the region of 2.29 AU  $\leq R_{\rm h} \leq 5.72$ AU were carried out on the nights of the 8th - 15th June 1999 using the 1m JKT on the Island of La Palma. A total of 25 comets were targeted, from which photometric observations of 15 comets were obtained. Only four comets from this large sample displayed signs of distant activity. Those comets include 47P, 69P, 103P, and 137P. Based on a brightness profile analysis, eleven comets appeared stellar (2P, 14P, 19P, 43P, 45P, 49P, 61P, 97P, 104P, 118P, and 121P). The remaining 10 comets were undetected (30P, 44P, 46P, 64P, 67P, 75P, 83P, 111P, 113P, and P/1993 X1). VRI band photometry was performed on these comets to determine dimensions, colours, and dust production rates in terms of $Af\rho$.

The effective nuclear radius measurements for the unresolved comets range from 0.9 km  $\leq r_{\rm N} \leq 4.6$ km, and the upper limits for the active and undetected comets span the range 0.5 km  $\leq r_{\rm N} \leq 7.5$ km (for an assumed albedo of 0.04). These values are typical for Jupiter-family comets. A range of assumed albedos are also discussed for the unresolved comets (see Fig. 4). For the active and undetected comets, firm 3$\sigma$ upper limits for an assumed albedo of 0.02 are also presented. Even if one applies a maximum axis ratio of 2.6 and a minimum albedo of 0.02 to the undetected comets, their semi-major axes are all constrained to lie below 8.7 km.

The radius values derived here are compared with previous values. Those comets for which previous estimates exist are listed in Table 5. Each of the 3$\sigma$ upper limits obtained from this work are consistent with the previous measurements, with the exception of 137P/Shoemaker-Levy 2. If the nucleus of 137P/Shoemaker-Levy 2 is modelled as a biaxial ellipsoid, then this inconsistency implies a bare nucleus axial ratio lower limit of $\geq$ $1.8 \pm 0.2$. Comparison of previous photometry of comet 45P/Honda-Mrkos-Pajdusakova with that presented here implies an exceptionally large axial ratio of $\geq$3.0. This value sets a new limit to the amount of elongation that can be expected for cometary nuclei. The possibility of an unresolved dust coma confounding this result is unlikely, as activity levels for this comet are intrinsically low, even for small heliocentric distances (A'Hearn et al. 1995; Lamy et al. 1999). Therefore, considering that this comet was observed beyond 5 AU from the sun, dust contamination would be negligible and the above axial ratio lower limit may be regarded as firm. Comet 49P/Arend-Rigaux was observed at an outbound heliocentric distance of 3.34 AU, just over five months after the December 1998 observations. No jet structures were seen on this occasion, and it is apparent that, for the outbound leg of its orbit, the transition region from an outgassing state to one of complete inactivity may occur somewhere within 2.11-3.34 AU. Also, based on multiple observations, we present independent support of the nuclear rotation period of $\sim$25 hours for comet 19P/Borrelly (Lamy et al. 1998b).

The $Af\rho$ values obtained for the active comets range from 5.6 cm  $\leq Af\rho \leq 37.8$ cm, whereas the $Af\rho$ upper limits obtained for the undetected and unresolved comets range from 0.7 cm  $\leq Af\rho \leq 32.0$ cm. These values were compared with previous values. There are no obvious candidates for continuous sublimation throughout their orbits, but it is strongly suspected that several are inactive around aphelion, namely comets 19P, 44P, 45P, 49P, and 97P.

Multi-filter photometry was performed on a total of 6 comets (14P, 19P, 49P, 47P, 103P, and 137P). A rather small (V-R) colour index of $0.02 \pm 0.22$ for 14P/Wolf, could be explained by a lack of substantial mantle coverage. For 49P/Arend-Rigaux, the (V-R) and (R-I) colour indices are substantially redder than the solar values. This finding is consistent with previous investigations, which in turn implies that there has been no significant change in the nature of the mantle coverage since the previous investigations, despite recent periods of activity (Paper II).

By combining the results presented here with those from Papers I and II, ensemble properties of the Jupiter-family population were investigated. We find a value of $0.32 \pm 0.02$ for the slope of the Cumulative Luminosity Function. This value is similar to main-belt asteroids and Near-Earth Objects, but is shallower than that for Trans-Neptunian Objects. It is difficult to derive conclusions due to the different size ranges studied in these populations.

Correlations between the activity levels of the comets in our sample and their various orbital parameters were investigated. The only correlation to be found was that the extrapolated absolute R band magnitude for the active comets was seen to decrease with increasing perihelion distance. This may be explained by a discovery bias towards brighter comets or may offer support to the hypothesis of rubble-mantle formation.

With regards to the physical properties of cometary nuclei, this survey has greatly improved the database of physical parameters of the Jupiter-family comet population. This homogeneously-reduced CCD data has allowed us to place vital constraints on the dimensions of many individual comets and on the size distribution of the Jupiter-family population as a whole. A substantial difference between the size distributions of TNOs and that of the Jupiter-family comets has been uncovered, which may reflect upon the various processes occurring on or within the nuclei of comets as their orbits evolve from the Edgeworth-Kuiper belt to the inner Solar system. Or, these differences may provide clues to the collisional processes and/or accretion mechanisms occurring within the protoplanetary disc. Also, there would appear to be no correlation between nuclear absolute magnitude and perihelion distance, as previously suggested.

This survey also demonstrates that Jupiter-family comets show diverse and, in many cases, substantial levels of activity beyond heliocentric distances of 3 AU, where the sublimation of H₂O from the surface of the nucleus approaches negligible levels. Furthermore, comets such as 74P/Smirnova-Chernykh, 65P/Gunn, and P/Helin-Lawrence, are almost certainly continuously active throughout their entire orbits. Comets that display such high levels of distant activity render them excellent candidates for studies of the processes that induce distant sublimation.

Acknowledgements

We thank Dr. Paul Weissman of NASA's Jet Propulsion Laboratory and the anonymous referee for their detailed comments on earlier drafts of this paper. This work was carried out at The Queens University of Belfast with the support of the Department of Education for Northern Ireland. The Jacobus Kapteyn Telescope is operated on the island of La Palma by the Royal Greenwich Observatory at the Spanish Observatorio del Roque de los Muchachos of the Instituto de Astrofisica de Canarias. Image processing and photometry in this paper has been performed using the IRAF program. IRAF is distributed by the National Optical Astronomy Observatories, which is operated by the Association of Universities for Research in Astronomy, Inc. (AURA) under cooperative agreement with the National Science Foundation.