Capture of Halley-type comets from the near-parabolic flux

Abstract

The dynamical transfer of comets from nearly parabolic to short-period orbits is investigated, considering perturbations by the major planets Jupiter, Saturn, Uranus and Neptune, for 5 Gyr. The combined analytical and numerical scheme includes all the essential features of the dynamical evolution, namely mean-motion resonances, secular oscillations, secular resonances, and close encounters with planets. The orbital evolution of ∼105 randomly oriented near-parabolic orbits is considered, with initial inclinations i and perihelion distances q uniformly distributed respectively in cos i and each of the five ranges 0<q<4 au, 4<q<6 au, 6<q<10.5 au, 10.5<q<18 au and 18<q<31 au. The objects which eventually evolve into Halley-type orbits primarily originate from initial orbits of small perihelion distance, in contrast to those that evolve to Jupiter-family orbits. Most Halley-type comets originate from orbits with q in the range 0<q<4 au, with the majority coming from q<2 au. The inclination-averaged probability for evolution from a nearly parabolic orbit with 0<q<4 au into a Halley-type orbit, assuming an isotropic distribution of initial inclinations, is about 0.01. When we include non-gravitational forces (for example, taking typical values for Halley-type, short-period, and nearly parabolic comets), this figure increases to 0.02, 0.04 and >0.06 respectively. The probability for nearly parabolic orbits with initial perihelia in the range 10.5<q<18 au to evolve into Halley-type orbits is about 0.0002, again assuming an isotropic distribution of inclinations. However, the new-comet flux in the outer planetary region is expected to be much higher than that in the inner Solar system, so the outer Solar system flux may be a significant additional source of Halley-type comets. Our results show that the number of Halley-type objects arising from the observed nearly parabolic cometary flux with absolute magnitudes brighter than H10=7 and q<4 au is hundreds of times greater than the number of known Halley-type comets. The resolution of this discrepancy must lie in more observations and a deeper understanding of the physical evolution of comets, which together become the key issues for understanding the number of Halley-type objects and the terrestrial-planet impact rate due to both active and inactive objects in Halley-type orbits.