Sustained Magnetorotational Turbulence in Local Simulations of Stratified Disks With Zero Net Magnetic Flux

Abstract

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:

Electron thermodynamics in GRMHD simulations of low-luminosity black hole accretion

“…Turbulence, for example, takes kinetic and/or magnetic energy at the largest scales and cascades it down to a small dissipative scale where it is converted into internal energy. For a numerical scheme with no explicit viscosity, the scale at which dissipation occurs depends entirely on the resolution of the simulation, but we expect the heating rate itself will be fixed (in an averaged sense; see, e.g., Davis, Stone & Pessah 2010). We expect the same for forced reconnection at high β values, as in the disc midplane, where the largescale dynamics sets the rate at which the field lines of opposite sign are brought together.…”

Merger of a white dwarf–neutron star binary to 1029carat diamonds: origin of the pulsar planets

“…When the disk is ionized, turbulence due to the magnetorotational instability (MRI) provides a physical mechanism driving angular momentum transport (Balbus & Hawley 1991), with values of α 0.01 − 0.1 motivated by simulations of the MRI (e.g. Davis et al 2010) and observations (King et al 2007). Once the midplane temperature decreases to 1000 K and the disk material recombines to become neutral, the MRI may be suppressed or confined to a thin 'active' ionized layer on the disk surface (Gammie 1996, Hansen 2002.…”

Magnetic Helicity and Large Scale Magnetic Fields: A Primer

“…Essentially all MRI unstable simulations with large enough vertical domains, whether stratified, unstratified, local or global, show the generation of large scale toroidal fields of the same flux for cycle periods of ∼ 10 orbits (Brandenburg et al 1995, Lesur & Ogilvie 2008, Davis et al 2010Simon et al 2011;Guan & Gammie 2011;Sorathia et al 2012;Suzuki and Inusuka 2013;Ebrahimi & Bhattacharjee 2014). The patterns indicate a large scale dynamo operating contemporaneously with the small scale dynamo.…”

“…A plethora of numerical simulations now commonly reveal that the systems evolve to a nonlinear turbulent steady state whose Maxwell stress dominates the Reynolds stress and for which large scale ordered magnetic fields emerge with cycle periods ∼ 10 orbit periods (e.g. Brandenburg et al 1995;Davis et al 2010;Simon et al 2011;Guan & Gammie 2011;Sorathia et al 2012;Suzuki and Inutsuka 2013). With the caveat that angular momentum plays a comparatively subdominant role in structural support for stars, the coronae of stars and the emergence of large scale ordered fields that thread coronal holes of the sun (e.g.…”