We examine the effects of density stratification on magnetohydrodynamic turbulence driven by the magnetorotational instability in local simulations that adopt the shearing box approximation. Our primary result is that, even in the absence of explicit dissipation, the addition of vertical gravity leads to convergence in the turbulent energy densities and stresses as the resolution increases, contrary to results for zero net flux, unstratified boxes. The ratio of total stress to midplane pressure has a mean of ∼ 0.01, although there can be significant fluctuations on long ( 50 orbit) timescales. We find that the time averaged stresses are largely insensitive to both the radial or vertical aspect ratio of our simulation domain. For simulations with explicit dissipation, we find that stratification extends the range of Reynolds and magnetic Prandtl numbers for which turbulence is sustained. Confirming the results of previous studies, we find oscillations in the large scale toroidal field with periods of ∼ 10 orbits and describe the dynamo process that underlies these cycles. Subject headings:
We present a scaling law that predicts the values of the stresses obtained in numerical simulations of saturated MRI-driven turbulence in non-stratified shearing boxes. It relates the turbulent stresses to the strength of the vertical magnetic field, the sound speed, the vertical size of the box, and the numerical resolution and predicts accurately the results of 35 numerical simulations performed for a wide variety of physical conditions. We use our result to show that the saturated stresses in simulations with zero net magnetic flux depend linearly on the numerical resolution and would become negligible if the resolution were set equal to the natural dissipation scale in astrophysical disks. We conclude that, in order for MRI-driven turbulent angular momentum transport to be able to account for the large value of the effective alpha viscosity inferred observationally, the disk must be threaded by a significant vertical magnetic field and the turbulent magnetic energy must be in near equipartition with the thermal energy. This result has important implications for the spectra of accretion disks and their stability.
We investigate the stability of incompressible, exact, non-ideal magnetorotational (MRI) modes against parasitic instabilities. Both Kelvin-Helmholtz and tearing-mode parasitic instabilities may occur in the dissipative regimes accessible to current numerical simulations. We suppose that a primary MRI mode saturates at an amplitude such that its fastest parasite has a growth rate comparable to its own. The predicted alpha parameter then depends critically on whether the fastest primary and parasitic modes fit within the computational domain and whether non-axisymmetric parasitic modes are allowed. Hence even simulations that resolve viscous and resistive scales may not saturate properly unless the numerical domain is large enough to allow the free evolution of both MRI and parasitic modes. To minimally satisfy these requirements in simulations with vertical background fields, the vertical extent of the domain should accommodate the fastest growing MRI mode while the radial and azimuthal extents must be twice as large. The fastest parasites have horizontal wavelengths roughly twice as long as the vertical wavelength of the primary.
During the last decade it has become evident that the magnetorotational instability is at the heart of the enhanced angular momentum transport in weakly magnetized accretion disks around neutron stars and black holes. In this paper, we investigate the local linear stability of differentially rotating, magnetized flows and the evolution of the magnetorotational instability beyond the weak-field limit. We show that, when superthermal toroidal fields are considered, the effects of both compressibility and magnetic tension forces, which are related to the curvature of toroidal field lines, should be taken fully into account. We demonstrate that the presence of a strong toroidal component in the magnetic field plays a non-trivial role. When strong fields are considered, the strength of the toroidal magnetic field not only modifies the growth rates of the unstable modes but also determines which modes are subject to instabilities. We find that, for rotating configurations with Keplerian laws, the magnetorotational instability is stabilized at low wavenumbers for toroidal Alfven speeds exceeding the geometric mean of the sound speed and the rotational speed. We discuss the significance of our findings for the stability of cold, magnetically dominated, rotating fluids and argue that, for these systems, the curvature of toroidal field lines cannot be neglected even when short wavelength perturbations are considered. We also comment on the implications of our results for the validity of shearing box simulations in which superthermal toroidal fields are generated.Comment: 24 pages, 12 figures. Accepted for publication in ApJ. Sections 2 and 5 substantially expanded, added Appendix A and 3 figures with respect to previous version. Animations are available at http://www.physics.arizona.edu/~mpessah/research
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