Nuclear Magnitudes and the Size Distribution of Jupiter Family Comets Gonzalo Tancredi(1), Julio A. Fern´andez(1), Hans Rickman(2) and Javier Licandro(3),(4) (1) Departamento de Astronom´ıa, Facultad de Ciencias, Igu´a4225, 11400 Montevideo, URUGUAY (gonzalo@fisica.edu.uy) (2) Astronomiska Observatoriet, Box 515, S-75120 Uppsala, SWEDEN (3)Isaac Newton Group of Telescopes, P.O.Box 321, Santa Cruz de La Palma, SPAIN (4) Instituto Astrof´ısico de Canarias, C/V´ıa L´actea s/n, 38200, La Laguna, SPAIN Number of pages: 47 Number of figures: 16 Number of tables: 5 1 Running head: Size Distribution of Jupiter Family Comets Mailing address: Gonzalo Tancredi Departamento de Astronom´ıa Facultad de Ciencias Igu´a4225 11400 Montevideo URUGUAY e-mail: gonzalo@fisica.edu.uy FAX: 598-2 525 0580 2 Abstract We present a new catalog of absolute nuclear magnitudes of Jupiter family (JF) comets, which is an updated version of our previous catalog (Tancredi et al. 2000). The full version of the catalog can be accessed on line at http://www.fisica.edu.uy/ gonzalo/catalog. ∼ From the new catalog we find a linear cumulative luminosity function (CLF) of slope 0.54 0.03 for JF comets with q < 2.5 AU. By considering this CLF combined with the few± measured geometric albedos∼ with their respective uncertainties, and assuming a canonical albedo of 0.035 0.012 for those comets with undetermined albedos, we derive a cumulative size distribution± that follows a power-law of index 2.7 0.3. The slope − ± is similar to that derived from some theoretical collisional models and from some pop- ulations of solar system bodies like the trans-Neptunian objects. We also discuss and compare our size distribution with those by other authors that have recently appeared in the literature. Some striking differences in the computed slopes are explained in terms of biases in the studied samples, the different weights given to the brightest members of the samples, and discrepancies in the values of a few absolute nuclear magnitudes. We also compute sizes and fractions of active surface area of JF comets from their estimated ab- solute nuclear magnitudes and their water production rates. With the outgassing model that we use, about 60% of the computed fractions f of active surface area are found to be smaller than 0.2, with one case (28P/Neujmin 1) of no more than 0.001, which suggests that JF comets may transit through stages of very low activity, or even dormancy. There is an indication that JF comets with radii RN > 3 km have active fractions f < 0.01, which might be due to the rapid formation of insulating∼ dust mantles on larger nuclei.∼ Keywords: Comets, nucleus; Comets, Jupiter Family; Comets, size distribution. 3 1 Introduction For some periodic comets we now have fairly good estimates of their nuclear size and albedo. In a few cases this has been possible through fly-by missions: 1P/Halley observed by the Giotto and Vega spacecrafts, 19P/Borrelly imaged by the Deep Space 1 mission from a distance as close as about 3400 km, and 81P/Wild 2 imaged by the Stardust spacecraft within a distance of only 236 km. A few other Jupiter family (JF) comets have been observed from the ground in the visible and thermal infrared on occasions when they had little or no activity at all. An important result is that practically all these comets show very low geometric albedos, mostly in the range p 0.02 0.06 with an average V ∼ − p 0.04 (Hartmann et al. 1987, Lamy et al. 2005). V ∼ Furthermore, the increased availability of telescopes with large apertures and the in- troduction of CCD cameras have revolutionized the photometric measurement of comets, which have become possible to observe at ever larger heliocentric distances. We are thus now able to obtain reliable nuclear magnitudes far from the Sun. In addition, high- resolution, space-borne photometric imaging, in particular using the HST (see, e.g., Lamy et al. 2005 for a complete list of their observations), have also provided an important set of nuclear magnitudes for comets closer to the Sun and hence more active, by offering a realistic possibility of coma subtraction. There are several important reasons to investigate the sample of nuclear magnitudes of JF comets. One of them has to do with explaining the dynamical origin of this pop- ulation. The most likely source region is the trans-Neptunian “scattered disk”, where several 102-km sized objects have been observed but smaller objects remain undiscovered. In order to fully establish this dynamical link, we need to confront the capture efficiency with both observable lifetimes and realistic estimates of numbers of objects. Since most of the observed JF cometary nuclei have diameters in the 1 10 km range, an extrapolation by means of a well-established size distribution is a necess− ary prerequisite. It may also be possible, by modeling the physical evolutionary effects on the JF size distribution, to relate the observed slope to the accretional and/or collisional evolution in the source region and, thus, to make some important inferences about cometary formation. We would also like to learn about the fraction of active surface area, since it has often been argued that comets may build insulating dust mantles that choke off ice sublima- tion after one or more perihelion passages. Different models for this phenomenon have been proposed by, e.g., Rickman et al. (1990) and K¨uhrt and Keller (1994), with different predictions as to the dependence on perihelion distance or nuclear radius. Statistics on the distribution of active fractions would provide a means to test these models. For this purpose, in addition to the absolute nuclear magnitudes, we may use gas production rates observed when comets are close to perihelion. The availability of a large enough sample of good nuclear magnitudes, a relevant sample of production rates, and reliable informa- tion on the distribution of albedos, is a prerequisite for this kind of analysis, and in this 4 paper we will make an attempt – using, for the moment, a very simple model of the H2O outgassing. The size distribution of any sample of observed comets is bound to be strongly biased by selection effects. If we look for statistical information representing the entire popula- tion, we have to apply algorithms to debias the observed sample. For that purpose, it is also natural to focus on the JF comets. These objects provide the most complete and reliable sample of cometary magnitude estimates. Because of their small orbital periods, most JF comets have been observed through most of their orbits, yielding a large number of magnitudes, some of them far from the Sun, where the comets show a “stellar” appear- ance without signs of gaseous activity. Observational materials of comparable quality are not available for any other category of comets. Five years ago we compiled a catalog of nuclear magnitudes of JF comets, based on the set of photometric data that then existed. Some of this was from our own observa- tions, but the majority came from a literature search of the published data on cometary nuclear magnitudes (see Tancredi et al. 2000 for a list of used sources). Using a debiassing technique, a size distribution was derived from these data. We now return to the problem again, since the number of good observations of cometary nuclear magnitudes has contin- ued to increase steadily, so our new catalog, presented here, is a real improvement over the previous one. We are also able this time to make comparisons with recent efforts by other authors, and to pay more attention to the role of the assumed albedos. We shall thus re-analyze the problem of nuclear sizes and the size distribution of JF comets. As a byproduct, we will use the new derived sizes to estimate fractions of active surface area. 2 Definition of populations A critical point when analyzing a given population of objects is to precisely define the common characteristics that distinguish its members. The definition of the Jupiter fam- ily of comets has recently experienced several adjustments, which we will now discuss. Let us start with the almost arbitrary classification into short-period comets as objects with periods less than 20 years, intermediate-period ones between 20 and 200 years and long-period comets with periods larger than 200 years. This is the classification still in use by the IAU Minor Planet Center (MPC). These groups show other dynamical differ- ences beside the period. While intermediate- and long-period comets present a mixture of prograde and retrograde orbits, short-period comets have only prograde ones. In the 1980’s, this led to the speculation that these populations may have different source re- gions: the intermediate-period comets came from the Oort cloud, while the short-period comets came from an, at that moment putative, trans-Neptunian (TN) belt (Fern´andez 1980; Duncan et al. 1988). This proposal was later confirmed by the discovery of trans- Neptunian objects (TNOs) and different numerical simulations that described the process of transfer from the TN belt to the visible region (Levison and Duncan 1997). 5 Another difference comes from the effect of Jupiter in the orbital evolution: while most of the short-period comets have low encounter velocities with the planet, the intermediate- period ones have much larger encounter velocities. This difference is expressed by the values of the Tisserand parameter, which is defined as a a T = J +2 (1 e2) cos i (1) a saJ − where a, e, and i are the semimajor axis, eccentricity and inclination of the comet, and aJ is the radius of Jupiter’s orbit, assumed to be circular.