The Size Distribution of Jupiter-family Cometary Nuclei

Introduction: We are continuing our program to determine the size distribution of cometary nuclei. We have compiled a catalog of 105 measurements of 57 cometary nuclei, drawn from the general literature, from our own program of CCD photometry of distant cometary nuclei (Lowry and Weissman [1]), and from unpublished observations by colleagues. We model the cumulative size distribution of the nuclei as a power law, N( > r) ∝ r where r is the radius, N is the number of comets with radius greater than r, and α is the slope of the cumulative power law. Previous determinations of the size distribution slope do not agree. Fernández et al. [2] found a slope of α = 2.65 ± 0.25 whereas Lowry et al. [3] and Weissman and Lowry [4] each found a slope of α = 1.60 ± 0.10. Determination of Nucleus Radii: The radii of cometary nuclei are determined through a variety of methods. The most reliable is resolved spacecraft imaging of nuclei but this has only been accomplished to date for comets 1P/Halley (1986) and 19P/Borrelly (2001). A more common technique is CCD photometry of the nuclei when they are far from the Sun and presumably inactive or the coma contribution is likely insignificant. By assuming a typical nucleus albedo of 0.04, the photometric measurements can be converted to an estimated radius. If lightcurve information is also obtained, one can obtain lower limits to the axial ratio, a/b, of a presumably tri-axial ellipsoid with axes (a, b, c), where a > b and b = c. Radii have also been measured using the high spatial resolution of the Hubble Space Telescope when comets are close to the Earth, in which case the coma contribution to the brightness must be modeled and subtracted, and then the nucleus size is obtained by assuming an albedo of 0.04. A fourth method is simultaneous, ground-based visual and infrared photometry, which solves for both the radius and the albedo of the nucleus. IR measurements have also been made for a few cometary nuclei with the ISO spacecraft. The Catalog: Our catalog consists only of reduced and calibrated measurements by professional astronomers. Of the 57 comets in the catalog, 54 are Jupiter-family comets (JFC: P < 20 years), which likely originated in the Kuiper belt, and three are Halley-type comets (HTC: 20 < P < 200 years), which likely originated in the Oort cloud (Levison [5]). Since these are two distinct dynamical reservoirs, likely with different collisional histories, we limit our size distribution fit to the Jupiter-family comets. We have normalized the measurements in our catalog to an assumed albedo of 0.04 except in cases where the albedo was directly measured. Multiple, independent measurements exist for 24 of the comets in our catalog and the agreement between observers is generally quite good. In cases of disagreement we favor spacecraft, HST, ISO, and simultaneous vis-IR measurements (in that order) over ground-based CCD measurements alone. We also favor CCD measurements of complete lightcurves over “snap-shot” observations that catch only a fragment of a nucleus rotation. In cases where there are no discriminating factors, we take the average of all observations. Results: Results are shown in Figure 1, which plots the cumulative number of JFC nuclei larger than radius r as a function of r. The plot shows a fairly constant slope between ~15 and 1.4 km (containing 41 nuclei), and then a sharp roll-off at radii < 1.4 km. We believe the latter is due to observational incompleteness; nuclei smaller than 1.4 km are exceedingly faint at large solar distances and thus difficult to measure. The least-squares fitted slope of the distribution for r ≥ 1.4 km is 1.59 ± 0.03, in excellent agreement with our earlier study [4]. We have also determined the slope for a subset of our sample with perihelion distances q < 2 AU and the values are identical within