MHD simulations of the magnetorotational instability in a shearing box with zero net flux

Abstract

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 Pm c 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 Pm c > 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.

The angular momentum transport by standard MRI in quasi-Kepler cylindrical Taylor-Couette flows

“…In particular, we did not find a decay of the angular momentum transport of the MRI for small magnetic Prandtl numbers, in contrast to the conclusions of Fromang et al (2007). As known from the bifurcation maps of the standard MRI, the actual value of the magnetic Prandtl number is not very important if only the basic rotation and the magnetic background field are normalized without use of the microscopic viscosity.…”

“…Hence, β must be quite small to excite nonaxisymmetric modes. The value of 400 used by Fromang et al (2007) is so high that the corresponding magnetic fields could be much too weak to excite nonaxisymmetric instability modes. Kitchatinov & Rüdiger (2010) …”

General Overview of Black Hole Accretion Theory

“…As illustrated in the top most panel of Figure 3, it is possible that a corona containing hot or energetic nonthermal electrons exists above and below the geometrically thin disk. This could be locally generated by, for example, flares associated with buoyant magnetic field lines in a manner analogous to the production of the solar corona (Galeev, Rosner & Vaiana 1979;Haardt & Maraschi 1991). Alpha disk models in which some fraction of the locally generated accretion power is dissipated in an external corona have been developed by Svensson & Zdziarski (1994).…”

Thermodynamics of the dead-zone inner edge in protoplanetary disks

“…We caution here that this number and radial profiles are to be taken with care. The α value is well known to be affected by numerical convergence (Beckwith et al 2011;Sorathia et al 2012) as well as physical convergence issues (Fromang et al 2007;Lesur & Longaretti 2007;Simon & Hawley 2009). This may also influence the temperature because it depends on the turbulent activity.…”