ASSESSING QUANTITATIVE RESULTS IN ACCRETION SIMULATIONS: FROM LOCAL TO GLOBAL

By J. Hawley, X. Guan, Julian Krolik. 2011

152 citations recorded by the source corpus.

Discretized numerical simulations are a powerful tool for the investigation of nonlinear MHD turbulence in accretion disks. However, confidence in their quantitative predictions requires a demonstration that further refinement of the spatial grid scale would not result in any significant change. This has yet to be accomplished, particularly for global disk simulations. In this paper, we combine data from previously published stratified shearing box simulations and new global disk simulations to calibrate several quantitative diagnostics by which one can estimate progress toward numerical convergence of the magnetic field. Using these diagnostics, we find that the established criterion for an adequate numerical description of linear growth of the magneto-rotational instability (the number of cells across a wavelength of the fastest-growing vertical wavenumber mode) can be extended to a criterion for the adequate description of nonlinear MHD disk turbulence, but the standard required is more stringent. We also find that azimuthal resolution, which has received little attention in previous studies, can significantly affect the evolution of the poloidal magnetic field. We further analyze the comparative resolution requirements of a small sample of initial magnetic field geometries; not surprisingly, more complicated initial field geometries require higher spatial resolution. Otherwise, they tend to evolve to qualitatively similar states if evolved for sufficient time. Applying our quantitative resolution criteria to a sample of previously published global simulations, we find that, with perhaps a single exception, they are significantly underresolved, and therefore underestimate the magnetic turbulence and resulting stress levels throughout the accretion flow.

Subfields: Astronomy and Astrophysics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/3cf11f60df5ac730b4976a28cda984b0a2603553

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Citations in the corpus

Prograde and retrograde black holes: whose jet is more powerful? (2012, unknown): “9h2ϕ, has Qz ≈ Qϕ ≈ 100 and δr : rδθ : rδϕ ≈ 2 : 1 : 2 and is very well resolved according to MRI resolution criteria (e.g., Hawley et al. 2011; Sorathia et al. 2011).”
General relativistic magnetohydrodynamic simulations of magnetically choked accretion flows around black holes (2012, methodology): “Our new models without MRI suppression (i.e. all toroidal field models but not MB09D/Q) satisfy the convergence quality factors of Qθ,MRI & 10, Qφ,MRI & 20, and αmag ∼ 0.4 in Hawley et al. (2011) and r, θ, φ correlation lengths are well-resolved.”
A GLOBAL THREE-DIMENSIONAL RADIATION MAGNETO-HYDRODYNAMIC SIMULATION OF SUPER-EDDINGTON ACCRETION DISKS (2014, methodology): “The ratio between Maxwell stress and magnetic pressure, αm, is always found to be ∼ 0.4 − 0.5 in unstratified isothermal simulations (Guan et al. 2009; Sorathia et al. 2012), although a smaller number ∼ 0.3− 0.4 is also reported for stratified isothermal simulations (Hawley et al. 2011).”
Global simulations of axisymmetric radiative black hole accretion discs in general relativity with a mean-field magnetic dynamo (2014, unknown): “To verify that the adopted resolution is enough to resolve the fastest growing mode of the MRI we calculate the vertically averaged parameter Qθ (Hawley et al. 2011), Qθ = 2π Σ ∫ π 0 ρ 2π Ω∆xθ |Bθ | √ ρ √ gθθ dθ, (42) 2 Plots show the photosphere surface obtained by integrating the optical depth…”
Numerical simulations of super-critical black hole accretion flows in general relativity (2013, unknown): “To verify that the adopted resolution is enough to resolve the fastest growing mode of the MRI we calculate the parameter Qθ (Hawley et al. 2011), Qθ = 2π Ω∆xθ |Bθ | √ ρ , (53) where ∆xθ is the grid cell size in θ.”
LOCAL STUDY OF ACCRETION DISKS WITH A STRONG VERTICAL MAGNETIC FIELD: MAGNETOROTATIONAL INSTABILITY AND DISK OUTFLOW (2012, background): “Based on the quality factor criterion (Hawley et al. 2011), we expect all our simulations to well resolve the MRI turbulence.”
GRMHD simulations of magnetized advection‐dominated accretion on a non‐spinning black hole: role of outflows (2012, background): “Our numerical grid has dxφ̂/dxr̂ ≈ 3 at the mid-plane, which is safe according to Hawley et al. (2011) and borderline according to Sorathia et al. (2012).”
The Masses and Spins of Neutron Stars and Stellar-Mass Black Holes (2014, background): “Currently, the most convincing relativistic line profile and best data are from an observation of Serpens X-1 with NuSTAR, which give rNS ≤ 15 km (and thus a surface redshift zNS ≥ 0.16 for MNS = 1.4 M⊙) for a broad set of fits, and rNS ≤ 12.6 km if the disk extends to the ISCO ([283]).”
Hot Accretion Flows Around Black Holes (2014, background): “The effect of numerical resolution on global simulation results has been investigated recently by a number of authors (Sorathia et al. 2010; Hawley et al. 2011, 2013; Shiokawa et al. 2012).”