Convergence of the critical cooling rate for protoplanetary disk fragmentation achieved; the key role of numerical dissipation of angular momentum

Abstract

We carry out simulations of gravitationally unstable disks using smoothed particle hydrodynamics(SPH) and the novel Lagrangian meshless finite mass (MFM) scheme in the GIZMO code (Hopkins 2015). Our aim is to understand the cause of the non-convergence of the cooling boundary for fragmentation reported in the literature. We run SPH simulations with two different artificial viscosity implementations, and compare them with MFM, which does not employ any artificial viscosity. With MFM we demonstrate convergence of the critical cooling time scale for fragmentation at β_{crit} =3.. Non-convergence persists in SPH codes, although it is significantly mitigated with schemes having reduced artificial viscosity such as inviscid SPH (ISPH) (Cullen & Dehnen 2010). We show how the non-convergence problem is caused by artificial fragmentation triggered by excessive dissipation of angular momentum in domains with large velocity derivatives. With increased resolution such domains become more prominent. Vorticity lags behind density due to numerical viscous dissipation in these regions, promoting collapse with longer cooling times. Such effect is shown to be dominant over the competing tendency of artificial viscosity to diminish with increasing resolution. When the initial conditions are first relaxed for several orbits, the flow is more regular, with lower shear and vorticity in non-axisymmetric regions, aiding convergence. Yet MFM is the only method that converges exactly. Our findings are of general interest as numerical dissipation via artificial viscosity or advection errors can also occur in grid-based codes. Indeed for the FARGO code values of β_{crit} significantly higher than our converged estimate have been reported in the literature. Finally, we discuss implications for giant planet formation via disk instability.

arXiv commentplease check the ApJ version

References in corpus (43)

• The cosmological simulation code GADGET-2
• GIZMO: A New Class of Accurate, Mesh-Free Hydrodynamic Simulation Methods
• Nonlinear Outcome of Gravitational Instability in Cooling, Gaseous Disks
• Modelling Accretion in Protobinary Systems
• Improving convergence in smoothed particle hydrodynamics simulations without pairing instability
• Fundamental differences between SPH and grid methods
• A General Class of Lagrangian Smoothed Particle Hydrodynamics Methods and Implications for Fluid Mixing Problems
• Modelling discontinuities and Kelvin-Helmholtz instabilities in SPH
• Investigating fragmentation conditions in self-gravitating accretion discs
• An energy-conserving formalism for adaptive gravitational force softening in SPH and N-body codes
• Inviscid SPH
• The burst mode of accretion and disk fragmentation in the early embedded stages of star formation
• The Two Modes of Gas Giant Planet Formation
• Characterising the Gravitational Instability in Cooling Accretion Discs
• A Superbubble Feedback Model for Galaxy Simulations
• Hydrodynamics of Embedded Planets' First Atmospheres. II. A Rapid Recycling of Atmospheric Gas
• Resolving mixing in Smoothed Particle Hydrodynamics
• On the convergence of the critical cooling timescale for the fragmentation of self-gravitating discs
• Properties of gravitoturbulent accretion disks
• Non-convergence of the critical cooling timescale for fragmentation of self-gravitating discs
• SPHGal: Smoothed Particle Hydrodynamics with improved accuracy for Galaxy simulations
• Numerical requirements for simulations of self gravitating and non-self gravitating disks
• Angular momentum transport and disk morphology in SPH simulations of galaxy formation
• Gravitational instability in binary protoplanetary disks; new constraints on giant planet formation
• A lower fragmentation mass scale in high redshift galaxies and its implications on giant clumps: a systematic numerical study
• Numerical convergence in self-gravitating shearing sheet simulations and the stochastic nature of disc fragmentation
• On The Possibility of Enrichment and Differentiation in Gas Giants During Birth by Disk Instability
• Collapse of a molecular cloud core to stellar densities: the formation and evolution of pre-stellar discs
• On the gap-opening criterion of migrating planets in protoplanetary disks
• Hydrodynamics of Embedded Planets' First Atmospheres. I. A Centrifugal Growth Barrier for 2D Flows
• On the fragmentation criteria of self-gravitating protoplanetary discs
• Numerical convergence in self-gravitating disc simulations: initial conditions and edge effects
• Circumplanetary disks around young giant planets: a comparison between core-accretion and disk instability
• The collapse of protoplanetary clumps formed through disc instability: 3D simulations of the pre-dissociation phase
• Convergence of simulations of self-gravitating accretion discs II: Sensitivity to the implementation of radiative cooling and artificial viscosity
• The response of self-graviting protostellar discs to slow reduction in cooling timescale: the fragmentation boundary revisited
• Limits on the location of planetesimal formation in self-gravitating protostellar discs
• Triggered fragmentation in self-gravitating discs: forming fragments at small radii
• A Numerical Study of Brown Dwarf Formation via Encounters of Protostellar Disks
• The Properties of Prestellar Discs in Isolated and Multiple Prestellar Systems
• Fragmentation of protoplanetary disks around M-dwarfs
• Direct detection of precursors of gas giants formed by gravitational instability with the Atacama Large Millimetre/sub-millimetre Array
• The impact of numerical oversteepening on the fragmentation boundary in self-gravitating disks

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