Planet-driven spiral arms in protoplanetary disks: I. Formation mechanism

TL;DR

This paper explains how a single planet can generate multiple spiral arms in a protoplanetary disk through linear resonant interactions and constructive interference of wave modes, with non-linear effects influencing arm strength and number.

Contribution

It provides a linear mechanism for the formation of multiple spiral arms by a single planet, clarifying the roles of planet mass and disk temperature in arm formation.

Findings

Multiple spiral arms can form via constructive interference of wave modes.

The number of arms depends on planet mass and disk temperature.

Large planet mass leads to only two primary arms, with others merging.

Abstract

Protoplanetary disk simulations show that a single planet can excite more than one spiral arm, possibly explaining recent observations of multiple spiral arms in some systems. In this paper, we explain the mechanism by which a planet excites multiple spiral arms in a protoplanetary disk. Contrary to previous speculations, the formation of both primary and additional arms can be understood as a linear process when the planet mass is sufficiently small. A planet resonantly interacts with epicyclic oscillations in the disk, launching spiral wave modes around the Lindblad resonances. When a set of wave modes is in phase, they can constructively interfere with each other and create a spiral arm. More than one spiral arm can form because such constructive interference can occur for different sets of wave modes, with the exact number and launching position of spiral arms dependent on the planet mass as well as the disk temperature profile. Non-linear effects become increasingly important as the planet mass increases, resulting in spiral arms with stronger shocks and thus larger pitch angles. This is found in common for both primary and additional arms. When a planet has a sufficiently large mass ($\gtrsim$ 3 thermal masses for $(h/r)_p=0.1$), only two spiral arms form interior to its orbit. The wave modes that would form a tertiary arm for smaller mass planets merge with the primary arm. Improvements in our understanding of the formation of spiral arms can provide crucial insights into the origin of observed spiral arms in protoplanetary disks.