Effects of an eccentric inner Jupiter on the dynamical evolution of icy body reservoirs in a planetary scattering scenario

Abstract

Aims. We analyze the dynamics of small body reservoirs under the effects of an eccentric inner giant planet resulting from a planetary scattering event around a 0.5 M⊙ star. Methods. First, we used a semi-analytical model to define the properties of the protoplanetary disk that lead to the formation of three lupiter-mass planets. Then, we carried out N-body simulations assuming that the planets are close to their stability limit together with an outer planetesimal disk. In particular, the present work focused on the analysis of N-body simulations in which a single Jupiter-mass planet survives after the dynamical instability event. Results. Our simulations produce outer small body reservoirs with particles on prograde and retrograde orbits, and other ones whose orbital plane flips from prograde to retrograde and back again along their evolution ("Type-F particles"). We find strong correlations between the inclination i and the ascending node longitude Ω of Type-F particles. First Ω librates around 90° or/and 270°. This property represents a necessary and sufficient condition for the flipping of an orbit. Moreover, the libration periods of i and Ω are equal and they are out to phase by a quarter period. We also remark that the larger the libration amplitude of i, the larger the libration amplitude of Ω. We analyze the orbital parameters of Type-F particles immediately after the instability event (post IE orbital parameters), when a single Jupiter-mass planet survives in the system. Our results suggest that the orbit of a particle can flip for any value of its post IE eccentricity, although we find only two Type-F particles with post IE inclinations i ≾ 17°. Finally, our study indicates that the minimum value of the inclination of the Type-F particles in a given system decreases with an increase in the eccentricity of the giant planet.