$\alpha\beta q_\mathrm{th}$-mapping of planet-induced density wave damping in protoplanetary discs

TL;DR

This study investigates how viscosity, cooling, and nonlinear effects influence the damping of planet-induced density waves in protoplanetary discs through hydrodynamic simulations.

Contribution

It provides a comprehensive analysis of the relative importance of different damping mechanisms across varying planetary masses, viscosities, and cooling timescales.

Findings

Nonlinear wave evolution and shock formation are primary damping mechanisms.

Cooling effects are significant for low-mass planets with short cooling times.

Viscosity requires high alpha values to significantly damp waves.

Abstract

Planets embedded in protoplanetary discs are capable of creating a wide variety of substructures through gravitational interactions. This process is mediated through the excitation and damping of density waves which carry angular momentum across the disc. Therefore, to interpret observations of substructures, it is critical to understand the physical processes which lead to deposition of wave angular momentum to the disc fluid. In this study, we explore the relative efficiency of viscosity ($\alpha$), cooling ($\beta$), and non-linear wave evolution ($q_\mathrm{th}$) in damping planet-generated density waves. We run a large suite of hydrodynamic simulations varying viscosity, cooling timescale, and planetary mass, from which we extract radial profiles of wave angular momentum deposition. We quantify the efficiency of different wave damping mechanisms as a joint function of planetary mass, viscosity and cooling time. We find that nonlinear wave evolution leading to shock formation is typically the most important cause of angular momentum deposition, but that cooling on timescales comparable to local orbital time reaches similar levels of importance for low mass planets (sub-thermal, $q_\mathrm{th}<1$). On the contrary, linear wave damping due to viscosity is rather inefficient, requiring $\alpha \gtrsim 10^{-1.5}$ to noticeably affect damping of waves launched by thermal mass planets. Even for lowest mass planets considered ($q_\mathrm{th}=0.025$), viscosity affects wave damping only if $\alpha \gtrsim 10^{-2.9}$. Our findings could be applied to interpret observations of protoplanetary discs; they are also important for understanding wave propagation in other types of astrophysical discs.