Abstract
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 non-linear 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 non-linear effects. We use this non-linear 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.
Highlights
Gravitational coupling of young planets with the protoplanetary discs in which they form is known to give rise to global spiral density waves
We have studied the nonlinear evolution of density waves excited by planets embedded in inviscid, isothermal 2D cylindrical discs with the goal of verifying the weakly nonlinear theory of global density waves developed in Rafikov (2002a)
Weakly nonlinear theory and full hydrodynamical simulations with Athena++ we explored models for a variety of disc parameters, such as disc scale-heights and surface density slopes, and planet masses spanning two orders of magnitude Mp = (0.01−1) Mth
Summary
Gravitational coupling of young planets with the protoplanetary discs in which they form is known to give rise to global spiral density waves. The details of propagation and evolution (damping) of weakly nonlinear planet-driven waves have been studied in the local (homogeneous shearing sheet) approximation by Goodman & Rafikov (2001) (hereafter GR01). They showed that for low mass planets, Mp Mth, the problem of linear wave excitation by planetary gravity can be naturally separated from the subsequent wave propagation affected by nonlinear effects, and explored both stages. Mth is the characteristic mass scale, so called thermal mass
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