Polydisperse Streaming Instability II. Methods for solving the linear stability problem

Abstract

Occurring in protoplanetary discs composed of dust and gas, streaming instabilities are a favoured mechanism to drive the formation of planetesimals. The Polydispserse Streaming Instability is a generalisation of the Streaming Instability to a continuum of dust sizes. This second paper in the series provides a more in-depth derivation of the governing equations and presents novel numerical methods for solving the associated linear stability problem. In addition to the direct discretisation of the eigenproblem at second order introduced in the previous paper, a new technique based on numerically reducing the system of integral equations to a complex polynomial combined with root finding is found to yield accurate results at much lower computational cost. A related method for counting roots of the dispersion relation inside a contour without locating those roots is also demonstrated. Applications of these methods show they can reproduce and exceed the accuracy of previous results in the literature, and new benchmark results are provided. Implementations of the methods described are made available in an accompanying Python package psitools.

20 pages, 14 figures, accepted for publication in MNRAS. Code available at https://doi.org/10.5281/zenodo.4305344

References in corpus (24)

• SciPy 1.0--Fundamental Algorithms for Scientific Computing in Python
• The NumPy array: a structure for efficient numerical computation
• Streaming Instabilities in Protoplanetary Disks
• Rossby Wave Instability of Keplerian Accretion Disks
• The AAA algorithm for rational approximation
• Dynamics of Solids in the Midplane of Protoplanetary Disks: Implications for Planetesimal Formation
• Protoplanetary Disk Turbulence Driven by the Streaming Instability: Linear Evolution and Numerical Methods
• Dust Growth and Settling in Protoplanetary Disks and Disk Spectral Energy Distributions. I. Laminar Disks
• Particle-Gas Dynamics with Athena: Method and Convergence
• Resonant Drag Instabilities in protoplanetary disks: the streaming instability and new, faster-growing instabilities
• Asymptotically stable numerical method for multispecies momentum transfer: gas and multifluid-dust test suite and implementation in FARGO3D
• On linear dust-gas streaming instabilities in protoplanetary discs
• Streaming Instability for Particle-Size Distributions
• A thermodynamic view of dusty protoplanetary disks
• Streaming Instability in Turbulent Protoplanetary Disks
• How efficient is the streaming instability in viscous protoplanetary disks?
• Resonant drag instability of grains streaming in fluids
• Individual and collective behavior of dust particles in a protoplanetary nebula
• Gas and multi-species dust dynamics in viscous protoplanetary discs: the importance of the dust back-reaction
• Streaming Instability with Multiple Dust Species: I. Favourable Conditions for the Linear Growth
• Polydisperse Streaming Instability I. Tightly coupled particles and the terminal velocity approximation
• Streaming Instability of Multiple Particle Species in Protoplanetary Disks
• Channels for streaming instability in dusty discs
• A brief overview of planet formation

Cited by in corpus (17)

• Meridional Circulation of Dust and Gas in the Circumstellar Disk: Delivery of Solids onto the Circumplanetary Region
• Streaming Instability with Multiple Dust Species: II. Turbulence and Dust-Gas Dynamics at Nonlinear Saturation
• Polydisperse Streaming Instability III. Dust evolution encourages fast instability
• Formation of Comets
• Streaming instability of multiple particle species II -- Numerical convergence with increasing particle number
• Coagulation Instability in Protoplanetary Disks: A Novel Mechanism Connecting Collisional Growth and Hydrodynamical Clumping of Dust Particles
• Planetesimal formation via the streaming instability with multiple grain sizes
• Polydisperse Formation of Planetesimals: The dust size distribution in clumps
• Nonlinear Outcome of Coagulation Instability in Protoplanetary Disks II: Dust Ring Formation Mediated by Backreaction and Fragmentation
• Dynamics of Dusty Vortices II: Stability of 2D dust laden vortices
• The Acoustic Resonant Drag Instability with a Spectrum of Grain Sizes
• On Secular Gravitational Instability in Vertically Stratified Disks
• Resonant drag instabilities for polydisperse dust. II. The streaming and settling instabilities
• Resonant Drag Instabilities for Polydisperse Dust, I. The Acoustic Resonant Drag Instability
• Nonlinear Evolution of the Unstratified Polydisperse Dust Settling Instability
• Modelling dust coagulation, dynamical drag and turbulent mixing during star and disc formation
• Evading the dust fragmentation barrier with the streaming instability in protoplanetary disks