Speed limit on Neptune migration imposed by Saturn tilting

TL;DR

This paper establishes a lower limit on Neptune's migration timescale based on Saturn's obliquity, showing that migration must be sufficiently slow to allow resonance capture and tilt.

Contribution

It introduces a new method to constrain Neptune's migration speed by linking Saturn's obliquity to resonance capture conditions.

Findings

Migration timescale tau must be >7 Myr for certain initial inclinations.

Faster migration prevents resonance capture, resulting in smaller Saturn obliquity.

The boundary depends strongly on Neptune's initial inclination.

Abstract

In this Letter, we give new constraints on planet migration. They were obtained under the assumption that Saturn's current obliquity is due to a capture in resonance with Neptune's ascending node. If planet migration is too fast, then Saturn crosses the resonance without being captured and it keeps a small obliquity. This scenario thus gives a lower limit on the migration time scale tau. We found that this boundary depends strongly on Neptune's initial inclination. For two different migration types, we found that tau should be at least greater than 7 Myr. This limit increases rapidly as Neptune's initial inclination decreases from 10 to 1 degree. We also give an algorithm to know if Saturn can be tilted for any migration law.