Orbital Evolution of Planetesimals due to the Galactic Tide: Formation of the Comet Cloud

Abstract

We have investigated the orbital evolution of planetesimals perturbed by the Galactic tide using analytical expressions. We consider the vertical component of the tidal force from the Galactic disk. The Galactic tide increases or decreases the perihelia and randomizes the inclination of planetesimals with large aphelion distances. We applied the analytical solutions to the orbital evolution of planetesimals that form the Oort Cloud from the planetesimal disk. Due to the Galactic tide, some planetesimals with small angular momentum show substantial inverse variations of the eccentricity and inclination. Also, some planetesimals show libration of the argument of perihelion ω around ω = 90° or 270° (the Lidov-Kozai mechanism). The planetesimals that gain perihelion distances great enough to leave the planetary region become members of the Oort Cloud. We find that due to the Galactic tide, planetesimals with semimajor axes 1000 AU increase their perihelion distances outside the planetary region (100 AU), and planetesimals with semimajor axes 20,000 AU spread their inclinations to the Galactic plane (the Galactic inclinations) over the range 0°-90° in 5 Gyr. We also consider the effect of a dense Galactic environment on the Oort Cloud formation and discuss the comet clouds for other planetary systems with different Galactic inclinations.