Solar Nebula Magnetohydrodynamics

The dynamical state of the solar nebula depends critically upon whether or not the gas is magnetically coupled. The presence of a subthermal field will cause laminar flow to break down into turbulence. Magnetic coupling, in turn, depends upon the ionization fraction of the gas. The inner most region of the nebula ($\lesssim 0.1$ AU) is magnetically well-coupled, as is the outermost region ($\gtrsim 10$ AU). The magnetic status of intermediate scales ($\sim 1$ AU) is less certain. It is plausible that there is a zone adjacent to the inner disk in which turbulent heating self-consistently maintains the requisite ionization levels. But the region adjacent to the active outer disk is likely to be magnetically ``dead.'' Hall currents play a significant role in nebular magnetohydrodynamics. Though still occasionally argued in the literature, there is simply no evidence to support the once standard claim that differential rotation in a Keplerian disk is prone to break down into shear turbulence by nonlinear instabilities. There is abundant evidence---numerical, experimental, and analytic---in support of the stabilizing role of Coriolis forces. Hydrodynamical turbulence is almost certainly not a source of enhanced turbulence in the solar nebula, or in any other astrophysical accretion disk.Comment: 19 pages, LaTEX, ISSI Space Sciences Series No.

A Magnetohydrodynamic Nonradiative Accretion Flow in Three Dimensions

We present a global magnetohydrodynamic (MHD) three dimensional simulation of a nonradiative accretion flow originating in a pressure supported torus. The evolution is controlled by the magnetorotational instability which produces turbulence. The flow forms a nearly Keplerian disk. The total pressure scale height in this disk is comparable to the vertical size of the initial torus. Gas pressure dominates only near the equator; magnetic pressure is more important in the surrounding atmosphere. A magnetically dominated bound outflow is driven from the disk. The accretion rate through the disk exceeds the final rate into the hole, and a hot torus forms inside 10 r_g. Hot gas, pushed up against the centrifugal barrier and confined by magnetic pressure, is ejected in a narrow, unbound, conical outflow. The dynamics are controlled by magnetic turbulence, not thermal convection, and a hydrodynamic alpha model is inadequate to describe the flow. The limitations of two dimensional MHD simulations are also discussed.Comment: 5 pages, 2 figures, submitted to ApJ Letters. For web version and mpeg animations see http://www.astro.virginia.edu/~jh8h/nraf

An Exact, Three-Dimensional, Time-Dependent Wave Solution in Local Keplerian Flow

We present an exact three-dimensional wave solution to the shearing sheet equations of motion. The existence of this solution argues against transient amplification as a route to turbulence in unmagnetized disks. Moreover, because the solution covers an extensive dynamical range in wavenumber space, it is an excellent test of the dissipative properties of numerical codes.Comment: 22 pages, 4 figures. To appear Apj Dec 1 200

Chaos in Turbulence Driven by the Magnetorotational Instability

Chaotic flow is studied in a series of numerical magnetohydrodynamical simulations that use the shearing box formalism. This mimics important features of local accretion disk dynamics. The magnetorotational instability gives rise to flow turbulence, and quantitative chaos parameters, such as the largest Lyapunov exponent, can be measured. Linear growth rates appear in these exponents even when the flow is fully turbulent. The extreme sensitivity to initial conditions associated with chaotic flows has practical implications, the most important of which is that hundreds of orbital times are needed to extract a meaningful average for the stress. If the evolution time in a disk is less than this, the classical $\alpha$ formalism will break down.Comment: 6 pages, 8 figures. To be appear in MNRA

The interaction of a giant planet with a disc with MHD turbulence I: The initial turbulent disc models

This is the first of a series of papers aimed at developing and interpreting simulations of protoplanets interacting with turbulent accretion discs. Here we study the disc models prior to the introduction of a protoplanet.We study models in which a Keplerian domain is unstable to the magnetorotational instability (MRI). Various models with B-fields having zero net flux are considered.We relate the properties of the models to classical viscous disc theory.All models attain a turbulent state with volume averaged stress parameter alpha ~ 0.005. At any particular time the vertically and azimuthally averaged value exhibited large fluctuations in radius. Time averaging over periods exceeding 3 orbital periods at the outer boundary of the disc resulted in a smoother quantity with radial variations within a factor of two or so. The vertically and azimuthally averaged radial velocity showed much larger spatial and temporal fluctuations, requiring additional time averaging for 7-8 orbital periods at the outer boundary to limit them. Comparison with the value derived from the averaged stress using viscous disc theory yielded schematic agreement for feasible averaging times but with some indication that the effects of residual fluctuations remained. The behaviour described above must be borne in mind when considering laminar disc simulations with anomalous Navier--Stokes viscosity. This is because the operation of a viscosity as in classical viscous disc theory with anomalous viscosity coefficient cannot apply to a turbulent disc undergoing rapid changes due to external perturbation. The classical theory can only be used to describe the time averaged behaviour of the parts of the disc that are in a statistically steady condition for long enough for appropriate averaging to be carried out.Comment: 10 pages, 23 figures, accepted for publication in MNRAS. A gzipped postscript version including high resolution figures is available at http://www.maths.qmul.ac.uk/~rp

Viscous and Resistive Effects on the MRI with a Net Toroidal Field

Resistivity and viscosity have a significant role in establishing the energy levels in turbulence driven by the magnetorotational instability (MRI) in local astrophysical disk models. This study uses the Athena code to characterize the effects of a constant shear viscosity \nu and Ohmic resistivity \eta in unstratified shearing box simulations with a net toroidal magnetic flux. A previous study of shearing boxes with zero net magnetic field performed with the ZEUS code found that turbulence dies out for values of the magnetic Prandtl number, P_m = \nu/\eta, below P_m \sim 1; for P_m \gtrsim 1, time- and volume-averaged stress levels increase with P_m. We repeat these experiments with Athena and obtain consistent results. Next, the influence of viscosity and resistivity on the toroidal field MRI is investigated both for linear growth and for fully-developed turbulence. In the linear regime, a sufficiently large \nu or \eta can prevent MRI growth; P_m itself has little direct influence on growth from linear perturbations. By applying a range of values for \nu and \eta to an initial state consisting of fully developed turbulence in the presence of a background toroidal field, we investigate their effects in the fully nonlinear system. Here, increased viscosity enhances the turbulence, and the turbulence decays only if the resistivity is above a critical value; turbulence can be sustained even when P_m < 1, in contrast to the zero net field model. While we find preliminary evidence that the stress converges to a small range of values when \nu and \eta become small enough, the influence of dissipation terms on MRI-driven turbulence for relatively large \eta and \nu is significant, independent of field geometry.Comment: Accepted to ApJ; version 2 - minor changes following review; 35 pages (preprint format), 10 figure