MHD simulations of the magnetorotational instability in a shearing box with zero net flux II. The effect of transport coefficients

By Sébastien Fromang, J. Papaloizou, Geo, roy Lesur, T. Heinemann. 2007

217 citations recorded by the source corpus.

Aims. We study the influence of the choice of transport coefficients (viscosity and resistivity) on MHD turbulence driven by the magnetorotational instability (MRI) in accretion disks. Methods. We follow the methodology described in Paper I: we adopt an unstratified shearing box model and focus on the case where the net vertical magnetic flux threading the box vanishes. For the most part we use the operator split code ZEUS, including explicit transport coefficients in the calculations. However, we also compare our results with those obtained using other algorithms (NIRVANA, the PENCIL code and a spectral code) to demonstrate both the convergence of our results and their independence of the numerical scheme. Results. We find that small scale dissipation affects the saturated state of MHD turbulence. In agreement with recent similar numerical simulations done in the presence of a net vertical magnetic flux, we find that turbulent activity (measured by the rate of angular momentum transport) is an increasing function of the magnetic Prandtl number Pm for all values of the Reynolds number Re that we investigated. We also found that turbulence disappears when the Prandtl number falls below a critical value Pmc that is apparently a decreasing function of Re. For the limited region of parameter space that can be probed with current computational resources, we always obtained Pmc > 1. Conclusions. We conclude that the magnitudes of the transport coefficients are important in determining the properties of MHD turbulence in numerical simulations in the shearing box with zero net flux, at least for Reynolds numbers and magnetic Prandtl numbers that are such that transport is not dominated by numerical effects and thus can be probed using current computational resources.

Subfields: Astronomy and Astrophysics

View Paper: https://www.semanticscholar.org/paper/20d37e2ae7db92ffa9637f0238b6d987a31c24ab

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Citations in the corpus

The subcritical baroclinic instability in local accretion disc models (2009, methodology): “The diffusivity corresponding to the viscosity we used is the same magnitude as the magnetic diffusivity used in Fromang et al. (2007) and as in their case we find that it is adequately resolved.”
Hot Accretion Flows Around Black Holes (2014, background): “However, when the net magnetic flux is zero, increasing the resolution actually causes α to decrease (Fromang & Papaloizou 2007, Fromang et al. 2007), with α going to zero in the limit of infinite resolution.”
SUSTAINED MAGNETOROTATIONAL TURBULENCE IN LOCAL SIMULATIONS OF STRATIFIED DISKS WITH ZERO NET MAGNETIC FLUX (2009, methodology): “Using the criteria of Fromang et al. (2007), we would probably have labeled the Re800Pm4 run as having sustained turbulence (over the first 100 orbits, which is the baseline used there), the Re1600Pm2 run as marginal, and the Re800Pm4 as either marginal or not having sustained turbulence, although…”
ZONAL FLOWS AND LONG-LIVED AXISYMMETRIC PRESSURE BUMPS IN MAGNETOROTATIONAL TURBULENCE (2008, methodology): “…we set the magnetic Prandtl number (defined as ratio of viscosity coefficient ν1 to resistivity coefficient η1) to approximately Pm ≡ ν1/η1 = 4 (following Fromang et al. 2007, who found that turbulence in zero net flux boxes without stratification is generally only sustained when Pm > 1).”
PROTOPLANETARY DISK STRUCTURES IN OPHIUCHUS (2009, background): “…with those found in numerical magnetohydrodynamics simulations, where the magnetorotational instability (Balbus & Hawley 1991) is the mechanism responsible for generating the anomalous turbulent viscosities (e.g., Hawley et al. 1995; Stone et al. 1996; Fleming & Stone 2003; Fromang et al. 2007).”
The excitation of spiral density waves through turbulent fluctuations in accretion discs – II. Numerical simulations with MRI-driven turbulence (2008, methodology): “In this case, we observe MRI turbulence that is, as in Fromang et al. (2007), sustained for several hundred orbits and expected to be numerically resolved for the values of the diffusion coefficients that we impose.”
ASSESSING QUANTITATIVE RESULTS IN ACCRETION SIMULATIONS: FROM LOCAL TO GLOBAL (2011, background): “…that the magnitude of a physical resistivity and viscosity as well as their ratios can have a significant impact on the turbulence levels (e.g. Fromang et al. 2007; Lesur & Longaretti 2007), at least for smaller magnetic Reynolds numbers (Oishi & MacLow 2011), nearly all global simulations…”
LOCAL STUDY OF ACCRETION DISKS WITH A STRONG VERTICAL MAGNETIC FIELD: MAGNETOROTATIONAL INSTABILITY AND DISK OUTFLOW (2012, background): “…Princeton University, Princeton, NJ 08544 2 Hubble Fellow 3 Current address: Institute for Theory and Computation, Harvard-Smithsonian Center for Astrophysics, 60 Garden St., MS51, Cambridge, MA 02138 Fromang et al. 2007; Lesur & Longaretti 2007), real disks involve vertical density stratification.”
THE RUNTS OF THE LITTER: WHY PLANETS FORMED THROUGH GRAVITATIONAL INSTABILITY CAN ONLY BE FAILED BINARY STARS (2009, background): “More restrictively this requires that other local transport mechanisms such as the MRI be weaker than currently predicted by simulations—they produce α ∼ 10−2 at least in disks with a net magnetic flux (Fleming et al. 2000; Fromang et al. 2007; Johansen et al. 2009).”
PROTOPLANETARY DISK STRUCTURES IN OPHIUCHUS. II. EXTENSION TO FAINTER SOURCES (2010, background): “…of inferred α values is in reasonable quantitative agreement with magnetohydrodynamics simulations where the viscosity is generated by turbulence from the magnetorotational instability in slightly ionized disks (Hawley et al. 1995; Stone et al. 1996; Fleming & Stone 2003; Fromang et al. 2007).”
IMPLEMENTATION OF THE SHEARING BOX APPROXIMATION IN ATHENA (2010, background): “This study was conducted to confirm the lack of convergence of the amplitude of the Maxwell stress in zero-net flux unstratified boxes discussed by Fromang et al. (2007), and indeed we confirm this result.”
Dynamics of Protoplanetary Disks (2010, background): “…level (and even the persistence) of turbulence has been observed to depend upon the magnetic Prandtl number Pm = ν/η, even at relatively high Reynolds numbers where Ohmic damping of linear modes should not be playing a role (Fromang et al. 2007, Longaretti & Lesur 2010, Simon & Hawley 2009).”
NONSTEADY ACCRETION IN PROTOSTARS (2008, background): “Mean azimuthal field models with effective PrM ∼ 1 Guan et al. (2008) are also not fully converged; they show that αM increases, albeit slightly, as the resolution is increased.”
The Sun’s Supergranulation (2010, background): “, 2009), and for the problem of angular momentum transport mediated by magneto-rotational turbulence in accretion discs (Lesur and Longaretti, 2007; Fromang et al., 2007).”
Magnetic Reconnection in Astrophysical and (2009, background): “It vies with other dissipation mechanisms to determine the saturation level and other properties of instabilities such as the magnetorotational instability (Fromang et al. 2007) and shear flow instabilities (Palotti et al. 2008).”
The Event Horizon General Relativistic Magnetohydrodynamic Code Comparison Project (2019, background): “Not only do the absolute dissipative length scales depend on resolution, but their ratio, given through the effective magnetic Prandtl number Prm, also varies with the Riemann solver, reconstruction method, magnetic field solver, grid, and resolution (e.g., Kritsuk et al. 2011).”
Gaps, Rings, and Non-Axisymmetric Structures in Protoplanetary Disks - From Simulations to ALMA Observations (2014, background): “Here, it was found that the convergence requires fixed diffusion terms (Fromang et al. 2007).”