Density waves in protoplanetary discs excited by eccentric planets: linear theory

Abstract

Spiral density waves observed in protoplanetary discs have often been used to infer the presence of embedded planets. This inference relies both on simulations as well as the linear theory of planet-disc interaction developed for planets on circular orbits to predict the morphology of the density wake. In this work we develop and implement a linear framework for calculating the structure of the density wave in a gaseous disc driven by an eccentric planet. Our approach takes into account both the essential azimuthal and temporal periodicities of the problem, allowing us to treat any periodic perturbing potential (i.e. not only that of an eccentric planet). We test our framework by calculating the morphology of the density waves excited by an eccentric, low-mass planet embedded in a globally isothermal disc and compare our results to the recent direct numerical simulations (and heuristic wavelet analysis) of the same problem by Zhu and Zhang. We find excellent agreement with the numerical simulations, capturing all the complex eccentric features including spiral bifurcations, wave crossings and planet-wave detachments, with improved accuracy and detail compared with the wavelet method. This illustrates the power of our linear framework in reproducing the morphology of complicated time-dependent density wakes, presenting it as a valuable tool for future studies of eccentric planet-disc interactions.

arXiv comment11 pages, 6 figures, accepted in MNRAS

References in corpus (42)

• Dynamical Outcomes of Planet-Planet Scattering
• FARGO: a fast eulerian transport algorithm for differentially rotating disks
• Origins of Eccentric Extrasolar Planets: Testing the Planet-Planet Scattering Model
• Observations of Protoplanetary Disk Structures
• Discovery of Small-Scale Spiral Structures in the Disk of SAO 206462 (HD 135344B): Implications for the Physical State of the Disk from Spiral Density Wave Theory
• Eccentricity Evolution for Planets in Gaseous Disks
• Spiral Density Waves in a Young Protoplanetary Disk
• Planetary Torques as the Viscosity of Protoplanetary Disks
• Asymmetric features in the protoplanetary disk MWC758
• Spiral Arms in the Asymmetrically Illuminated Disk of MWC 758 and Constraints on Giant Planets
• The orbital eccentricity of small planet systems
• Exoplanet Orbital Eccentricities Derived From LAMOST-Kepler Analysis
• Structures in the protoplanetary disk of HD142527 seen in polarized scattered light
• Observational Signatures of Planets in Protoplanetary Disks II: Spiral Arms Observed in Scattered Light Imaging Can be Induced by Planets
• The Structure of Spiral Shocks Excited by Planetary-mass Companions
• Planet migration and gap formation by tidally-induced shocks
• The Disk Substructures at High Angular Resolution Project (DSHARP): III. Spiral Structures in the Millimeter Continuum of the Elias 27, IM Lup, and WaOph 6 Disks
• On the wake generated by a planet in a disc
• The Exoplanet Eccentricity Distribution from Kepler Planet Candidates
• Scattering outcomes of close-in planets: constraints on planet migration
• Planet Formation in AB Aurigae: Imaging of the inner gaseous Spirals observed inside the Dust Cavity
• Coorbital thermal torques on low-mass protoplanets
• Discovery of a point-like source and a third spiral arm in the transition disk around the Herbig Ae star MWC 758
• Density Waves Excited by Low-Mass Planets in Protoplanetary Disks II: High-Resolution Simulations of the Nonlinear Regime
• Planet-driven spiral arms in protoplanetary disks: I. Formation mechanism
• Discovery of a Two-Armed Spiral Structure in the Gapped Disk in HD 100453
• Eccentricity evolution during planet-disc interaction
• Growth of eccentric modes in disc-planet interactions
• How Bright are Planet-Induced Spiral Arms in Scattered Light?
• Planet-disk interaction in disks with cooling: basic theory
• Multiple spiral arms in the disk around intermediate-mass binary HD 34700A
• Evolution of eccentricity and inclination of hot protoplanets embedded in radiative discs
• On the planetary interpretation of multiple gaps and rings in protoplanetary disks seen by ALMA
• The Orbit of the Companion to HD 100453A: Binary-Driven Spiral Arms in a Protoplanetary Disk
• Secular evolution of eccentricity in protoplanetary discs with gap-opening planets
• Gaps and Rings in Protoplanetary Disks with Realistic Thermodynamics: The Critical Role of In-Plane Radiation Transport
• Super-Reflection in Fluid Discs: Corotation Amplifier, Corotation Resonance, Rossby Waves, and Overstable Modes
• Multiple Spiral Arms in Protoplanetary Disks: Linear Theory
• Subaru/HiCIAO $H{K}_{\mathrm{s}}$ imaging of LkH$\alpha$ 330 - multi-band detection of the gap and spiral-like structures
• Impact of thermal effects on the evolution of eccentricity and inclination of low-mass planets
• Spiral Arm Pattern Motion in the SAO 206462 Protoplanetary Disk
• A Simple Time-Dependent Method for Calculating Spirals: Applications to Eccentric Planets in Protoplanetary discs

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• Pushing the limits of eccentricity in planet-disc interactions
• Indirect forces in disc-planet interaction
• $\alpha \beta q_{\mathrm{th}}$-mapping of planet-induced density wave damping in protoplanetary discs