# Excitation of Planetary Obliquities Through Planet-Disk Interactions

## TL;DR

This paper explores a simple early-stage mechanism where planet-disk interactions can excite planetary obliquities through secular spin-orbit resonance, affecting planets within 0.3 to 2 AU, but likely not explaining Uranus and Neptune's high obliquities.

## Contribution

It identifies and analyzes a fundamental mechanism for obliquity excitation via planet-disk interactions and spin-orbit resonance crossing during planet formation.

## Key findings

- Obliquity can be excited when disk-induced orbital precession frequency crosses spin precession frequency.
- Planets between 0.3 and 2 AU are most affected by this mechanism.
- The mechanism is unlikely to explain Uranus and Neptune's high obliquities due to gravitational perturbations.

## Abstract

The tilt of a planet's spin axis off its orbital axis ("obliquity") is a basic physical characteristic that plays a central role in determining the planet's global circulation and energy redistribution. Moreover, recent studies have also highlighted the importance of obliquities in sculpting not only the physical features of exoplanets but also their orbital architectures. It is therefore of key importance to identify and characterize the dominant processes of excitation of non-zero axial tilts. Here we highlight a simple mechanism that operates early on and is likely fundamental for many extrasolar planets and perhaps even Solar System planets. While planets are still forming in the protoplanetary disk, the gravitational potential of the disk induces nodal recession of the orbits. The frequency of this recession decreases as the disk dissipates, and when it crosses the frequency of a planet's spin axis precession, large planetary obliquities may be excited through capture into a secular spin-orbit resonance. We study the conditions for encountering this resonance and calculate the resulting obliquity excitation over a wide range of parameter space. Planets with semi-major axes in the range $0.3 \ \mathrm{AU} \lesssim a \lesssim 2 \ \mathrm{AU}$ are the most readily affected, but large-$a$ planets can also be impacted. We present a case study of Uranus and Neptune and show that this mechanism likely cannot help explain their high obliquities. While it could have played a role if finely tuned and envisioned to operate in isolation, large-scale obliquity excitation was likely inhibited by gravitational planet-planet perturbations.