From the Kuiper Belt to Jupiter-Family Comets: The Spatial Distribution of Ecliptic Comets

Abstract

We present numerical orbital integrations of thousands of massless particles as they evolve from Neptune-encountering orbits in the Kuiper belt for up to 1 Gyr or until they either impact a massive body or are ejected from the Solar System. The median dynamical lifetime of these objects is 4.5 × 10 7years. We found that about 30% of these objects became visible comets. (We refer to a comet with perihelion distance <2.5 AU as a “visible” comet.) Of those, 99.7% were Jupiter-family comets (as defined by their Tisserand parameter, hereafter “JFCs”) when they first became visible, although some evolved out of the Jupiter family as time progressed. By comparing the observed orbital element distribution of JFCs to that produced by our simulations we deduce that JFCs are statistically most likely to have physical lifetimes of ∼12,000 years. Based on this estimate of physical lifetimes and the fact that there are ∼110 active, visible JFCs with H T< 9, we conclude that there are currently ∼1.2 × 10 7ecliptic comets (those with T> 2), of sizes consistent with this absolute magnitude, that originated in the Kuiper belt. This conclusion assumes that the rate of objects leaving the Kuiper belt has remained approximately constant over the history of the Solar System. We calculate the orbital distribution of this population and show that ∼90% are beyond the orbit of Neptune at any given time. In addition, we calculate the impact rates of these objects onto the planets. We find that a JFC impact onto Jupiter happens approximately once every 400 years and one on the Earth should occur once every 13 million years.