Planet-driven density waves in protoplanetary discs: numerical verification of nonlinear evolution theory

TL;DR

This paper validates a semi-analytical model for the nonlinear evolution of planet-driven density waves in protoplanetary discs, focusing on low-mass planets, and provides tools for interpreting observational features and vortex formation.

Contribution

It offers a calibrated, semi-analytical framework for modeling nonlinear density wave evolution in discs, validated against numerical simulations, especially for low-mass planets.

Findings

The framework accurately captures wave evolution with proper calibration.

Fitting formulae for shock strength and shape are provided.

The model successfully predicts vortensity production in the disc.

Abstract

Gravitational coupling between protoplanetary discs and planets embedded in them leads to the emergence of spiral density waves, which evolve into shocks as they propagate through the disc. We explore the performance of a semi-analytical framework for describing the nonlinear evolution of the global planet-driven density waves, focusing on the low planet mass regime (below the so-called thermal mass). We show that this framework accurately captures the (quasi-)self-similar evolution of the wave properties expressed in terms of properly rescaled variables, provided that certain theoretical inputs are calibrated using numerical simulations (an approximate, first principles calculation of the wave evolution based on the inviscid Burgers equation is in qualitative agreement with simulations but overpredicts wave damping at the quantitative level). We provide fitting formulae for such inputs, in particular, the strength and global shape of the planet-driven shock accounting for nonlinear effects. We use this nonlinear framework to theoretically compute vortensity production in the disc by the global spiral shock and numerically verify the accuracy of this calculation. Our results can be used for interpreting observations of spiral features in discs, kinematic signatures of embedded planets in CO line emission ("kinks"), and for understanding the emergence of planet-driven vortices in protoplanetary discs.