Inclination Excitation of Solar System Debris Disk due to Stellar Flybys

TL;DR

This paper studies how stellar flybys in star clusters can excite inclinations in debris disks, deriving analytical models and running N-body simulations to understand the resulting orbital distributions and their implications for the Solar System's history.

Contribution

It provides an analytical expression for inclination excitation during stellar flybys and uses N-body simulations to explore the resulting debris disk inclination distributions.

Findings

High inclination populations are produced by prograde stellar encounters.

The maximum inclination extent scales with the encounter's inclination angle.

Constraints on the Solar System's formation environment are derived from observed trans-Neptunian objects.

Abstract

Most stars form in clusters where relatively close encounters with other stars are common and can leave imprints on the orbital architecture of planetary systems. In this paper, we investigate the inclination excitation of debris disk particles due to such stellar encounters. We derive an analytical expression that describes inclination excitation in the hierarchical limit where the stellar flyby is distant. We then obtain numerical results for the corresponding particle inclination distribution in the non-hierarchical regime using a large ensemble of N-body simulations. For encounters with expected parameters, we find that the bulk inclination of the disk particles remains low. However, a distinct high inclination population is produced by prograde stellar encounters for particles with final pericenter distances above $50$AU. The maximum extent $i_t$ of the inclination distribution scales with the inclination of the encounter $\sin(i_s)$ for massive star flybys with low incoming velocity. The inclination distribution of observed trans-Neptunian objects places constraints on the dynamical history of our Solar System. For example, these results imply an upper limit on product of the number density $n$ of the solar birth cluster and the Sun's residence time $\tau$ of the form $n\tau\lesssim8\times10^4$ Myr pc$^{-3}$. Stronger constraints can be derived with future observational surveys of the outer Solar System.