Chaotic motion in a primordial comet disk beyond Neptune and comet influx to the Solar System

Abstract

CHAOTIC dynamics, characterized by extremely sensitive dependence on initial conditions with exponential divergence of neighbouring trajectories and subsequent loss of predictability¹, have recently been demonstrated to be quite common in the Solar System. The long-standing problems of the delivery of meteorites to Earth-crossing orbits² and the existence of the Kirkwood gaps³ have essentially been solved by the discovery of the chaotic zones with divergence timescales of a few million years in the asteroid zone near orbital resonances of Jupiter^3–7. It has also been demonstrated⁸ that the orbit of Pluto is chaotic with divergence timescales of ∼20 Myr. Numerical mapping techniques, which underestimate chaotic behaviour, have determined that orbits lying between the outer planets can exhibit chaotic motions⁹, and recent numerical studies¹⁰ have indicated that even the inner planets exhibit chaotic motion with divergence timescales of ∼5 Myr. Previous calculations¹¹ using a heliocentric frame have shown that a scattered disk of cometesimals beyond Neptune develops chaotic motions with divergence timescales less than 1 Myr. Here we describe improved numerical simulations using a barycentric system and thus including the additional frequencies associated with motion of the Sun. Because the onset of chaotic motion is characterized by the appearance of broad-band noise, the inclusion of these additional perturbations should increase the likelihood of stochastic behaviour and thus the chaotic zone should be larger. Our results indeed indicate that comets in a low-eccentricity primordial disk beyond Neptune can exhibit chaotic motions which lead to interesting consequences for the dynamics of comets.