Secular resonance sweeping and orbital excitation in decaying disks

TL;DR

This study investigates how secular resonance sweeping during protoplanetary disk dissipation can excite asteroid orbits, revealing that it can produce significant inclination increases but likely works in conjunction with other mechanisms.

Contribution

The paper develops a new integrator for modeling secular resonance sweeping with a decaying disk and thoroughly analyzes its effects on asteroid orbital excitation.

Findings

Inclination excitation over 10 degrees is possible in the asteroid belt.

Resonance crossing timing depends on planetary configurations and disk depletion.

Additional mechanisms are needed to explain the observed inclination spread.

Abstract

We revisit the problem of secular resonance sweeping during the dissipation of a protoplanetary disk and its possible role in exciting the orbits of primordial asteroids, in the light of recent models of solar system evolution. We develop an integrator that incorporates the gravitational effect of a uniformly (or not) depleting, axisymmetric disk with arbitrary surface density profile; its performance is verified by analytical calculations. The secular response of fictitious asteroids, under perturbations from Jupiter, Saturn and a decaying disk, is thoroughly studied. Note that the existence of a symmetry plane induced by the disk, lifts the inherent degeneracy of the two-planet system, such that the '$s_5$' nodal frequency can also play a major role. We examine different resonant configurations for the planets (2:1, 3:2, 5:3), disk models and depletion scenarios. For every case we compute the corresponding time paths of secular resonances, which show when and where resonance crossing occurs. The excitation of asteroids, particularly in inclination, is studied in the various models and compared to analytical estimates. We find that inclination excitation in excess of $\sim 10^{\circ}$ is possible in the asteroid belt, but the nearly uniform spread of $\Delta i\sim 20^{\circ}$ observed calls for the combined action of secular resonance sweeping with other mechanisms (e.g. scattering by Mars-sized embryos) that would be operating during terrestrial planet formation. Our results are also applicable to extrasolar planetary systems.