Hydrodynamic instability in eccentric astrophysical discs

Abstract

Eccentric Keplerian discs are believed to be unstable to three-dimensional hydrodynamical instabilities driven by the time-dependence of fluid properties around an orbit. These instabilities could lead to small-scale turbulence, and ultimately modify the global disc properties. We use a local model of an eccentric disc, derived in a companion paper, to compute the nonlinear vertical ("breathing mode") oscillations of the disc. We then analyse their linear stability to locally axisymmetric disturbances for any disc eccentricity and eccentricity gradient using a numerical Floquet method. In the limit of small departures from a circular reference orbit, the instability of an isothermal disc is explained analytically. We also study analytically the small-scale instability of an eccentric neutrally stratified polytropic disc with any polytropic index using a WKB approximation. We find that eccentric discs are generically unstable to the parametric excitation of small-scale inertial waves. The nonlinear evolution of these instabilities should be studied in numerical simulations, where we expect them to lead to a decay of the disc eccentricity and eccentricity gradient as well as to induce additional transport and mixing. Our results highlight that it is essential to consider the three-dimensional structure of eccentric discs, and their resulting vertical oscillatory flows, in order to correctly capture their evolution.

18 pages, 6 figures, to be published in MNRAS

References in corpus (18)

• Eccentricity Evolution for Planets in Gaseous Disks
• Disk eccentricity and embedded planets
• An Eccentric Disk Model for the Nucleus of M31
• Evolution of Giant Planets in Eccentric Disks
• Non-linear fluid dynamics of eccentric discs
• Highly inclined and eccentric massive planets I: Planet-disc interactions
• Simulations of eccentric disks in close binary systems
• Global m=1 modes and migration of protoplanetary cores in eccentric protoplanetary discs
• Nonlinear evolution of the tidal elliptical instability in gaseous planets and stars
• Eccentric-disk models for the nucleus of M31
• Slow modes in Keplerian disks
• Comprehensive simulations of superhumps
• Three-dimensional eccentric discs around Be stars
• Waves and instabilities in a differentially rotating disc containing a poloidal magnetic field
• Nonlinear evolution of the elliptical instability in the presence of weak magnetic fields
• Hydrodynamic instability in warped astrophysical discs
• Eccentricity of radiative discs in close binary-star systems
• The Local Instability of Steady Astrophysical Flows with non Circular Streamlines with Application to Differentially Rotating Disks with Free Eccentricity

Cited by in corpus (29)

• Cooling Requirements for the Vertical Shear Instability in Protoplanetary Disks
• Growth of eccentric modes in disc-planet interactions
• The Kozai-Lidov Mechanism in Hydrodynamical Disks. II. Effects of binary and disk parameters
• On the convective overstability in protoplanetary discs
• The Physics of Accretion Discs, Winds And Jets in Tidal Disruption Events
• Kozai-Lidov Disc Instability
• The Role of Disc Self-Gravity in Circumbinary Planet Systems: I. Disc Structure and Evolution
• Hydrodynamical turbulence in eccentric circumbinary discs and its impact on the in situ formation of circumbinary planets
• Gravito-turbulence and the excitation of small-scale parametric instability in astrophysical discs
• Eccentric Tidal Disruption Event Disks around Supermassive Black Holes: Dynamics and Thermal Emission
• Self-Destructing Spiral Waves: Global Simulations of a Spiral Wave Instability in Accretion Disks
• Magnetorotational instability in eccentric disks
• Non-linear hydrodynamic instability and turbulence in eccentric astrophysical discs with vertical structure
• Hamiltonian hydrodynamics of eccentric discs
• Tidal Disruption Event Disks around Supermassive Black Holes: Disk Warp and Inclination Evolution
• Local numerical simulations of warped discs
• Eccentric Modes in Disks With Pressure and Self-Gravity
• Vertical settling of pebbles in turbulent circumbinary discs and the in situ formation of circumbinary planets
• Dynamical structure of highly eccentric discs with applications to tidal disruption events
• The Role of Disc Self-Gravity in Circumbinary Planet Systems: II. Planet Evolution
• HFQPOs and discoseismic mode excitation in eccentric, relativistic discs. I. Hydrodynamic simulations
• Nonlinear hydrodynamical evolution of eccentric Keplerian discs in two dimensions: validation of secular theory
• Importance of magnetic fields in highly eccentric discs with applications to tidal disruption events
• Parametric instability in warped astrophysical discs: growth, saturation and feedback
• Three-dimensional evolution of radiative circumbinary discs: the size and shape of the inner cavity
• Developing a Non-Newtonian Fluid Model for Dust, for Application to Astrophysical Flows
• Probing dust and grain growth in the optically thick circumbinary ring of V892 Tau
• High resolution mapping of molecular tori with ALMA
• The stability of propagating plane inertial waves in rotating fluids