Ultraharmonics and Secondary Spiral Wakes Induced by a Planet

TL;DR

This paper explores how a planet in a protoplanetary disk excites complex spiral structures through nonlinear mode-coupling, especially emphasizing the role of ultraharmonics and multiple Fourier components in the planet's potential.

Contribution

It reveals the mechanism of ultraharmonics excitation via nonlinear mode-coupling and highlights the importance of multiple Fourier components in planetary potential for spiral structure formation.

Findings

Multi-armed spiral structures are excited by nonlinear mode-coupling.

Small azimuthal wavenumber responses are preferentially excited.

Multiple Fourier components are crucial for ultraharmonics wave generation.

Abstract

We investigate the ultraharmonics response of a protoplanetary disk to an orbiting planet. We find that the multi-armed spiral structure can be excited by the higher-order forcing due to nonlinear mode-coupling. In particular, the preferential excitation of gas response with small azimuthal wavenumber $(m\sim 2)$ is a direct consequence of mode-coupling among linear waves. The presence of multiple Fourier components in a planet's potential is a distinct feature compared to the previous studies in the context of spiral galaxies, which turns out to be crucial for the generation of ultraharmonics waves. This analysis may shed light on understanding some results regarding the spiral structures excited by a massive planet.