Global General Relativistic Magnetohydrodynamic Simulations of Accretion Tori

This paper presents an initial survey of the properties of accretion flows in the Kerr metric from three-dimensional, general relativistic magnetohydrodynamic simulations of accretion tori. We consider three fiducial models of tori around rotating, both prograde and retrograde, and nonrotating black holes; these three fiducial models are also contrasted with axisymmetric simulations and a pseudo-Newtonian simulation with equivalent initial conditions to delineate the limitations of these approximations.Comment: Submitted to ApJ. 30 pages, 21 figures. Animations and high-resolution version of figures available at http://www.astro.virginia.edu/~jd5

Global MHD Simulations of Cylindrical Keplerian Disks

This paper presents a series of global three dimensional accretion disk simulations carried out in the cylindrical limit in which the vertical component of the gravitational field is neglected. The simulations use a cylindrical pseudo-Newtonian potential to model the main dynamical properties of the Schwarzschild metric. The disks are initially constant density with a Keplerian angular momentum distribution and contain a weak toroidal or vertical field. These simulations reaffirm many of the conclusions of previous local simulations. The magnetorotational instability grows rapidly and produces MHD turbulence with a significant Maxwell stress which drives accretion. Tightly-wrapped low-$m$ spiral waves are prominent. In some simulations radial variations in Maxwell stress concentrate gas into rings, creating substantial spatial inhomogeneities. There is a nonzero stress at the marginally stable orbit which produces a small decline in specific angular momentum inside the last stable orbit. Detailed comparisons between simulations are used to examine the effects of computational domain and equation of state. Simulations that begin with vertical fields have greater field amplification and higher ratios of stress to magnetic pressure compared with those beginning with toroidal fields. In contrast to MHD, hydrodynamics alone neither creates nor sustains turbulence.Comment: Submitted to the Astrophysical Journal Web version of paper and MPEG animations can be found at http://www.astro.virginia.edu/~jh8h/cylinder

Saturation of Magnetorotational Instability through Magnetic Field Generation

The saturation mechanism of Magneto-Rotational Instability (MRI) is examined through analytical quasilinear theory and through nonlinear computation of a single mode in a rotating disk. We find that large-scale magnetic field is generated through the alpha effect (the correlated product of velocity and magnetic field fluctuations) and causes the MRI mode to saturate. If the large-scale plasma flow is allowed to evolve, the mode can also saturate through its flow relaxation. In astrophysical plasmas, for which the flow cannot relax because of gravitational constraints, the mode saturates through field generation only.Comment: 9 pages, 10 figures to appear in ApJ, Jun 2009, 10 v69

Dependence of inner accretion disk stress on parameters: the Schwarzschild case

We explore the parameter dependence of inner disk stress in black hole accretion by contrasting the results of a number of simulations, all employing 3-d general relativistic MHD in a Schwarzschild spacetime. Five of these simulations were performed with the intrinsically conservative code HARM3D, which allows careful regulation of the disk aspect ratio, H/R; our simulations span a range in H/R from 0.06 to 0.17. We contrast these simulations with two previously reported simulations in a Schwarzschild spacetime in order to investigate possible dependence of the inner disk stress on magnetic topology. In all cases, much care was devoted to technical issues: ensuring adequate resolution and azimuthal extent, and averaging only over those time-periods when the accretion flow is in approximate inflow equilibrium. We find that the time-averaged radial-dependence of fluid-frame electromagnetic stress is almost completely independent of both disk thickness and poloidal magnetic topology. It rises smoothly inward at all radii (exhibiting no feature associated with the ISCO) until just outside the event horizon, where the stress plummets to zero. Reynolds stress can also be significant near the ISCO and in the plunging region; the magnitude of this stress, however, depends on both disk thickness and magnetic topology. The two stresses combine to make the net angular momentum accreted per unit rest-mass 7-15% less than the angular momentum of the ISCO.Comment: Accepted for publication in ApJ, 52 pages, 38 figures, AASTEX. High-resolution versions can be found at the following links: http://ccrg.rit.edu/~scn/papers/schwarzstress.ps, http://ccrg.rit.edu/~scn/papers/schwarzstress.pd

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 non-zero Ohmic resistivity. 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. 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. This occurs at magnetic 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.Comment: 8 figures, accepted for publication in Ap

High Resolution Simulations of the Plunging Region in a Pseudo-Newtonian Potential: Dependence on Numerical Resolution and Field Topology

New three dimensional magnetohydrodynamic simulations of accretion disk dynamics in a pseudo-Newtonian Paczynski-Wiita potential are presented. These have finer resolution in the inner disk than any previously reported. Finer resolution leads to increased magnetic field strength, greater accretion rate, and greater fluctuations in the accretion rate. One simulation begins with a purely poloidal magnetic field, the other with a purely toroidal field. Compared to the poloidal initial field simulation, a purely toroidal initial field takes longer to reach saturation of the magnetorotational instability and produces less turbulence and weaker magnetic field energies. For both initial field configurations, magnetic stresses continue across the marginally stable orbit; measured in units corresponding to the Shakura-Sunyaev alpha parameter, the stress grows from ~0.1 in the disk body to as much as ~10 deep in the plunging region. Matter passing the inner boundary of the simulation has ~10% greater binding energy and ~10% smaller angular momentum than it did at the marginally stable orbit. Both the mass accretion rate and the integrated stress fluctuate widely on a broad range of timescales.Comment: Accepted for publication in the Astrophysical Journal. For Web version with mpeg animations see http://www.astro.virginia.edu/VITA/papers/plunge

Accretion of low angular momentum material onto black holes: 2D magnetohydrodynamical case

We report on the second phase of our study of slightly rotating accretion flows onto black holes. We consider magnetohydrodynamical (MHD) accretion flows with a spherically symmetric density distribution at the outer boundary, but with spherical symmetry broken by the introduction of a small, latitude-dependent angular momentum and a weak radial magnetic field. We study accretion flows by means of numerical 2D, axisymmetric, MHD simulations with and without resistive heating. Our main result is that the properties of the accretion flow depend mostly on an equatorial accretion torus which is made of the material that has too much angular momentum to be accreted directly. The torus accretes, however, because of the transport of angular momentum due to the magnetorotational instability (MRI). Initially, accretion is dominated by the polar funnel, as in the hydrodynamic inviscid case, where material has zero or very low angular momentum. At the later phase of the evolution, the torus thickens towards the poles and develops a corona or an outflow or both. Consequently, the mass accretion through the funnel is stopped. The accretion of rotating gas through the torus is significantly reduced compared to the accretion of non-rotating gas (i.e., the Bondi rate). It is also much smaller than the accretion rate in the inviscid, weakly rotating case.Our results do not change if we switch on or off resistive heating. Overall our simulations are very similar to those presented by Stone, Pringle, Hawley and Balbus despite different initial and outer boundary conditions. Thus, we confirm that MRI is very robust and controls the nature of radiatively inefficient accretion flows.Comment: submitted in Ap

Vortices in Thin, Compressible, Unmagnetized Disks

We consider the formation and evolution of vortices in a hydrodynamic shearing-sheet model. The evolution is done numerically using a version of the ZEUS code. Consistent with earlier results, an injected vorticity field evolves into a set of long-lived vortices, each of which has a radial extent comparable to the local scale height. But we also find that the resulting velocity field has a positive shear stress, . This effect appears only at high resolution. The transport, which decays with time as t^-1/2, arises primarily because the vortices drive compressive motions. This result suggests a possible mechanism for angular momentum transport in low-ionization disks, with two important caveats: a mechanism must be found to inject vorticity into the disk, and the vortices must not decay rapidly due to three-dimensional instabilities.Comment: 8 pages, 10 figures (high resolution figures available in ApJ electronic edition

Physical Activity in Childhood May Be the Key to Optimizing Lifespan Skeletal Health

Physical activities undertaken in childhood, particularly activities which apply large forces quickly convey optimal benefits to bone mass, size, and structure. Evidence is accumulating that benefits persist well beyond activity cessation. This review examines the potential for early childhood activity to improve bone mineralization and structure and explores childhood activity as prevention for osteoporosis in later life