James M. Stone

Dynamics of line-driven disk winds in active galactic nuclei

We present the results of axisymmetric time-dependent hydrodynamic calculations of line-driven winds from accretion disks in active galactic nuclei (AGNs). We assume the disk is flat, Keplerian, geometrically thin, and optically thick, radiating according to the ?-disk prescription. The central engine of the AGN is a source of both ionizing X-rays and wind-driving UV photons. To calculate the radiation force, we take into account radiation from the disk and the central engine. The gas temperature and ionization state in the wind are calculated self-consistently from the photoionization and heating rate of the central engine. We find that a disk accreting onto a 108 M? black hole at the rate of 1.8 M? yr-1 can launch a wind at ~1016 cm from the central engine. The X-rays from the central object are significantly attenuated by the disk atmosphere so they cannot prevent the local disk radiation from pushing matter away from the disk. However, in the supersonic portion of the flow high above the disk, the X-rays can overionize the gas and decrease the wind terminal velocity. For a reasonable X-ray opacity, e.g., ?X = 40 g-1 cm2, the disk wind can be accelerated by the central UV radiation to velocities of up to 15,000 km s-1 at a distance of ~1017 cm from the central engine. The covering factor of the disk wind is ~0.2. The wind is unsteady and consists of an opaque, slow vertical flow near the disk that is bounded on the polar side by a high-velocity stream. A typical column density through the fast stream is a few times 1023 cm-2 so the stream is optically thin to the UV radiation. This low column density is precisely why gas can be accelerated to high velocities. The fast stream contributes nearly 100% to the total wind mass-loss rate of 0.5 M? yr-1.

Density, Velocity, and Magnetic Field Structure in Turbulent Molecular Cloud Models

We use three-dimensional (3D) numerical magnetohydrodynamic simulations to follow the evolution of cold, turbulent, gaseous systems with parameters chosen to represent conditions in giant molecular clouds (GMCs). We present results of three model cloud simulations in which the mean magnetic field strength is varied (B0 = 1.4-14 ?G for GMC parameters), but an identical initial turbulent velocity field is introduced. We describe the energy evolution, showing that (1) turbulence decays rapidly, with the turbulent energy reduced by a factor 2 after 0.4-0.8 flow crossing times (~2-4 Myr for GMC parameters), and (2) the magnetically supercritical cloud models gravitationally collapse after time ?6 Myr, while the magnetically subcritical cloud does not collapse. We compare density, velocity, and magnetic field structure in three sets of model snapshots with matched values of the Mach number ? 9,7,5. We show that the distributions of volume density and column density are both approximately log-normal, with mean mass-weighted volume density a factor 3-6 times the unperturbed value, but mean mass-weighted column density only a factor 1.1-1.4 times the unperturbed value. We introduce a spatial binning algorithm to investigate the dependence of kinetic quantities on spatial scale for regions of column density contrast (ROCs) on the plane of the sky. We show that the average velocity dispersion for the distribution of ROCs is only weakly correlated with scale, similar to mean size-line width distributions for clumps within GMCs. We find that ROCs are often superpositions of spatially unconnected regions that cannot easily be separated using velocity information; we argue that the same difficulty may affect observed GMC clumps. We suggest that it may be possible to deduce the mean 3D size-line width relation using the lower envelope of the 2D size-line width distribution. We analyze magnetic field structure and show that in the high-density regime n 103 cm-3, total magnetic field strengths increase with density with logarithmic slope ~1/3-2/3. We find that mean line-of-sight magnetic field strengths may vary widely across a projected cloud and are not positively correlated with column density. We compute simulated interstellar polarization maps at varying observer orientations and determine that the Chandrasekhar-Fermi formula multiplied by a factor ~0.5 yields a good estimate of the plane-of sky magnetic field strength, provided the dispersion in polarization angles is 25?.

THE FORMATION AND STRUCTURE OF A STRONGLY MAGNETIZED CORONA ABOVE A WEAKLY MAGNETIZED ACCRETION DISK

We use three-dimensional magnetohydrodynmic (MHD) simulations to study the formation of a corona above an initially weakly magnetized, isothermal accretion disk. The simulations are local in the plane of the disk but extend up to 5 vertical scale heights above and below it. We describe a modi—- cation to time-explicit numerical algorithms for MHD that enables us to evolve such highly strati—ed disks for many orbital times. We —nd that for an initially toroidal —eld or a poloidal —elds with a van- ishing mean MHD turbulence driven by the magnetorotational instability (MRI) produces strong ampli- —cation of weak —elds within 2 scale heights of the disk midplane in a few orbital times. Although the primary saturation mechanism of the MRI is local dissipation, about 25% of the magnetic energy gener- ated by the MRI within 2 scale heights escapes because of buoyancy, producing a strongly magnetized corona above the disk. Most of the buoyantly rising magnetic energy is dissipated between 3 and 5 scale heights, suggesting that the corona will also be hot. Strong shocks with Mach numbers are contin- Z2 uously produced in the corona in response to mass motions deeper in the disk. Only a very weak mass out—ow is produced through the outer boundary at 5 scale heights, although this is probably a re—ection of our use of the local approximation in the plane of the disk. On long timescales the average vertical disk structure consists of a weakly magnetized (b D 50) turbulent core below 2 scale heights and a strongly magnetized corona that is stable to the MRI above. The large-scale —eld structure in (b ( 10~1) both the disk and the coronal regions is predominately toroidal. Equating the volume averaged heating rate to optically thin cooling curves, we estimate the temperature in the corona will be of order 104 K for protostellar disks and 108 K for disks around neutron stars. The functional form of the stress with vertical height is best described as —at within but proportional to the density above For ^2H z ^2H z . initially weak uniform vertical —elds, we —nd the exponential growth of magnetic —eld via axisymmetric vertical modes of the MRI produces strongly buoyant sheets of magnetic energy that break the disk apart into horizontal channels. These channels rise several scale heights vertically before the onset of the Parker instability distorts the sheets and allows matter to —ow back toward the midplane and reform a disk. Thereafter the entire disk is magnetically dominated and not well modeled by the local approx- imation. We suggest that this evolution may be relevant to the dynamical processes that disrupt the inner regions of a disk when it interacts with a strongly magnetized central object. Subject headings: accretion, accretion disksinstabilitiesMHDturbulence

Dissipation in Compressible Magnetohydrodynamic Turbulence

We report results of a three-dimensional, high resolution (up to 5123) numerical investigation of supersonic compressible magnetohydrodynamic turbulence. We consider both forced and decaying turbulence. The model parameters are appropriate to conditions found in Galactic molecular clouds. We find that the dissipation time of turbulence is of the order of the flow crossing time or smaller, even in the presence of strong magnetic fields. About half of the dissipation occurs in shocks. Weak magnetic fields are amplified and tangled by the turbulence, while strong fields remain well ordered.

Local Magnetohydrodynamic Models of Layered Accretion Disks

Using numerical MHD simulations, we have studied the evolution of the magnetorotational instability (MRI) in stratified accretion disks in which the ionization fraction (and therefore resistivity) varies substantially with height. This model is appropriate to dense, cold disks around protostars or dwarf nova systems, which are ionized by external irradiation of cosmic rays or high-energy photons. We find that the growth and saturation of the MRI occurs only in the upper layers of the disk where the magnetic Reynolds number exceeds a critical value; in the midplane the disk remains quiescent. The vertical Poynting flux into the dead central zone is small; however, velocity fluctuations in the dead zone driven by the turbulence in the active layers generate a significant Reynolds stress in the midplane. When normalized by the thermal pressure, the Reynolds stress in the midplane never drops below about 10% of the value of the Maxwell stress in the active layers, even though the Maxwell stress in the dead zone may be orders of magnitude smaller than this. Significant mass mixing occurs between the dead zone and active layers. Fluctuations in the magnetic energy in the active layers can drive vertical oscillations of the disk in models in which the ratio of the column density in the dead zone to that in the active layers is less than 10. These results have important implications for the global evolution of a layered disk; in particular, there may be residual mass inflow in the dead layer. We discuss the effects that dust in the disk may have on our results.

The Effect of Resistivity on the Nonlinear Stage of the Magnetorotational Instability in Accretion Disks

We present three-dimensional magnetohydrodynamic simulations of the nonlinear evolution of the magnetorotational instability (MRI) with a nonzero ohmic resistivity. The simulations begin from a homogeneous (unstratified) density distribution and use the local shearing-box approximation. The evolution of a variety of initial field configurations and strengths is considered for several values of the constant coefficient of resistivity ?. For uniform vertical and toroidal magnetic fields, we find unstable growth consistent with the linear analyses; finite resistivity reduces growth rates and, when large enough, stabilizes the MRI. Even when unstable modes remain, resistivity has significant effects on the nonlinear state. The properties of the saturated state depend on the initial magnetic field configuration. In simulations with an initial uniform vertical field, the MRI is able to support angular momentum transport even for large resistivities through the quasi-periodic generation of axisymmetric radial channel solutions rather than through the maintenance of anisotropic turbulence. Reconnective processes rather than parasitic instabilities mediate the resurgent channel solution in this case. Simulations with zero-net flux show that the angular momentum transport and the amplitude of magnetic energy after saturation are significantly reduced by finite resistivity, even at levels where the linear modes are only slightly affected. The MRI is unable to sustain angular momentum transport and turbulent flow against diffusion for ReM 104, where the Reynolds number is defined in terms of the disk scale height and sound speed, ReM = csH/?. As this is close to the Reynolds numbers expected in low, cool states of dwarf novae, these results suggest that finite resistivity may account for the low and high angular momentum transport rates inferred for these systems.

Magnetohydrodynamical non-radiative accretion flows in two dimensions

ABSTRA C T We present the results of axisymmetric, time-dependent magnetohydrodynamic simulations of accretion flows around black holes. The calculations begin from a rotationally supported thick torus which contains a weak poloidal field. Accretion is produced by growth and saturation of the magnetorotational instability (MRI) provided that the wavelength of the fastest growing mode is less than the thickness of the torus. Using a computational grid that spans more than two decades in radius, we compare the time-averaged properties of the flow with previous hydrodynamical simulations. The net mass accretion rate is small compared with the mass inflow and outflow rates at large radii associated with turbulent eddies. Turbulence is driven by the MRI rather than convection. The two-dimensional structure of the time-averaged flow is significantly different compared with the hydrodynamical case. We discuss the limitations imposed on our results by the assumption of axisymmetry and the relatively small radial domain.

A cluster merger and the origin of the extended radio emission in abell 3667

We present a numerical model for the extended steep-spectrum radio sources and the elongated X-ray structure in A3667 based on new three-dimensional MHD/N-body simulations. The X-ray and optical analyses of A3667 indicate that it has undergone a recent subcluster merger event. We believe that the Mpc-scale radio sources identified in A3667 are also a consequence of the merger. Our previous numerical simulations show that mergers often produce large-scale shocks and turbulence capable of both magnetic field amplification and in situ reacceleration of relativistic particles. Our model suggests that these radio structures, separated by ~2.6 h-1100 Mpc, are in fact causally linked via a slightly off-axis merger that occurred nearly in the plane of the sky approximately 1 Gyr ago with a subcluster having a total mass equal to ~20% of the primary cluster.

Kinetic and Structural Evolution of Self-gravitating, Magnetized Clouds: 2.5-Dimensional Simulations of Decaying Turbulence

The molecular component of the Galaxy is comprised of turbulent, magnetized clouds, many of which are self-gravitating and form stars. To develop an understanding of how these clouds kinetic and structural evolution may depend on their level of turbulence, mean magnetization, and degree of self-gravity, we perform a survey of direct numerical MHD simulations in which three parameters are independently varied. Our simulations consist of solutions to the time-dependent MHD equations on a two-dimensional grid with periodic boundary conditions; an additional half dimension is also incorporated as dependent variables in the third Cartesian direction. Two of our survey parameters, the mean magnetization parameter β≡c2sound/v2Alfven and the Jeans number nJ≡Lcloud/LJeans, allow us to model clouds that either meet or fail conditions for magneto-Jeans stability and magnetic criticality. Our third survey parameter, the sonic Mach number ≡σvelocity/csound, allows us to initiate turbulence of either sub- or super-Alfvenic amplitude; we employ an isothermal equation of state throughout. We evaluate the times for each cloud model to become gravitationally bound and measure each models kinetic energy loss over the fluid-flow crossing time. We compare the evolution of density and magnetic field structural morphology and quantify the differences in the density contrast generated by internal stresses for models of differing mean magnetization. We find that the values of β and nJ, but not the initial Mach number , determine the time for cloud gravitational binding and collapse: for mean cloud density nH2=100 cm-3, unmagnetized models collapse after ~5 Myr, and magnetically supercritical models generally collapse after 5-10 Myr (although the smallest magneto-Jeans stable clouds survive gravitational collapse until t~15 Myr), while magnetically subcritical clouds remain uncollapsed over the entire simulations; these cloud collapse times scale with the mean density as tg∝n−½H2. We find, contrary to some previous expectations, less than a factor of 2 difference between turbulent decay times for models with varying magnetic field strength; the maximum decay time, for B~14 μG and nH2=100 cm-3, is 1.4 flow crossing times tcross=L/σvelocity (or 8 Myr for typical giant molecular cloud parameters). In all models we find turbulent amplification in the magnetic field strength up to at least the level βpert≡c2sound/δv2Alfven=0.1, with the turbulent magnetic energy between 25% and 60% of the turbulent kinetic energy after one flow crossing time. We find that for non-self-gravitating stages of evolution, when clouds have =5-10, the mass-averaged density contrast magnitudes log(ρ/) are in the range 0.2-0.5, with the contrast increasing both toward low and high β. Although our conclusions about density statistics may be affected by our isothermal assumption, we note that only the more strongly magnetized models appear to be consistent with estimates of clump/interclump density contrasts inferred in Galactic giant molecular clouds.

The Effect of the Hall Term on the Nonlinear Evolution of the Magnetorotational Instability. II. Saturation Level and Critical Magnetic Reynolds Number

The nonlinear evolution of the magnetorotational instability (MRI) in weakly ionized accretion disks, including the effect of the Hall term and ohmic dissipation, is investigated using local three-dimensional MHD simulations and various initial magnetic field geometries. When the magnetic Reynolds number, ReM ≡ v/ηΩ (where vA is the Alfven speed, η is the magnetic diffusivity, and Ω is the angular frequency), is initially larger than a critical value ReM,crit, the MRI evolves into MHD turbulence in which angular momentum is transported efficiently by the Maxwell stress. If ReM < ReM,crit, however, ohmic dissipation suppresses the MRI, and the stress is reduced by several orders of magnitude. The critical value is in the range of 1-30 depending on the initial field configuration. The Hall effect does not modify the critical magnetic Reynolds number by much but enhances the saturation level of the Maxwell stress by a factor of a few. We show that the saturation level of the MRI is characterized by v/ηΩ, where vAz is the Alfven speed in the nonlinear regime along the vertical component of the field. The condition for turbulence and significant transport is given by v/ηΩ 1, and this critical value is independent of the strength and geometry of the magnetic field or the size of the Hall term. If the magnetic field strength in an accretion disk can be estimated observationally and the magnetic Reynolds number v/ηΩ is larger than about 30, this would imply that the MRI is operating in the disk.