An updated estimate of the number of Jupiter-family comets using a simple fading law

It has long been hypothesised that the Jupiter-family comets (JFCs) come from the scattered disc, an unstable planetesimal population beyond Neptune. This viewpoint has been widely accepted, but a few issues remain, the most prominent of which are the total number of visible JFCs with a perihelion distance q < 2.5 AU and the corresponding number of objects in the scattered disc. In this work we give a robust estimate of the number of visible JFCs with q < 2.5 AU and diameter D> 2.3 km based on recent observational data. This is combined with numerical simulations that use a simple fading law applied to JFCs that come close to the Sun. For this we numerically evolve thousands of comets from the scattered disc through the realm of the giant planets and keep track of their number of perihelion passages with perihelion distance q < 2.5 AU, below which the activity is supposed to increase considerably. We can simultaneously fit the JFC inclination and semi-major axis distribution accurately with a delayed power law fading function of the form Φm ∝ (M2 + m2)− k/ 2, where Φm is the visibility, m is the number of perihelion passages with q < 2.5 AU, M is an integer constant, and k is the fading index. We best match both the inclination and semi-major axis distributions when k ~ 1.4, M = 40, and the maximum perihelion distance below which the observational data is complete is qm ~ 2.3 AU. From observational data we calculate that a JFC with diameter D = 2.3 km has a typical total absolute magnitude HT = 10.8, and the steady-state number of active JFCs with diameter D > 2.3 km and q < 2.5 AU is of the order of 300 (but with large uncertainties), approximately a factor two higher than earlier estimates. The increased JFC population results in a scattered disc population of 6 billion objects and decreases the observed Oort cloud to scattered disc population ratio to 13, virtually the same as the value of 12 obtained with numerical simulations.