Abstract
Abstract Protoplanetary disk simulations show that a single planet can excite more than one spiral arm, possibly explaining the 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 the spiral arms being dependent on the planet mass as well as the disk temperature profile. Nonlinear effects become increasingly important as the planet mass increases, resulting in spiral arms with stronger shocks and thus larger pitch angles. This is found to be common for both primary and additional arms. When a planet has a sufficiently large mass (≳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.
Highlights
A point mass perturber creates disturbances in differentially rotating (e.g., Keplerian) background disks, which appear in the form of wakes spiraling away from the perturber
We show that additional spiral arms form in a similar way to the primary arm: through constructive interference among appropriate sets of wave modes having different m
Numerical Simulations: Verifying the Linear Theory Prediction In Section 2, we showed that appropriate sets of wave modes having different azimuthal wavenumbers can be in phase from their launching points (n = 0 component) or as they propagate
Summary
A point mass perturber creates disturbances in differentially rotating (e.g., Keplerian) background disks, which appear in the form of wakes spiraling away from the perturber Such spiral structures are seen in observations and/or numerical simulations of a variety of astrophysical disks, including protoplanetary disks, circumplanetary disks, and disks around various binary systems (e.g., binary stars, binary black holes). The resulting structure in the gas disk can produce corresponding, enhanced features in dust emission and scattering, such that a single planet can be responsible for more than one main gap This mechanism possibly explains some of the multiple concentric gaps and rings seen in young protoplanetary disks (e.g., ALMA Partnership et al 2015; Andrews et al 2016; Ginski et al 2016; Isella et al 2016; Tsukagoshi et al 2016; Walsh et al 2016; Zhang et al 2016; van Boekel et al 2017). These structures can affect subsequent planet formation in such ringed/gapped disks by collecting solid particles preferentially in local gas pressure maxima (i.e., rings) through aerodynamic drag
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