Global MHD Simulations of Cylindrical Keplerian Disks

John F. Hawley

Virginia Institute of Theoretical Astronomy,

Department of Astronomy, University of Virginia,

Charlottesville, VA 22903; jh8h@virginia.edu

Abstract:

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 radial grid domain runs out to 60 R_g to minimize the influence of the outer boundary on the inner disk evolution. The disks are initially constant density with a Keplerian angular momentum distribution and contain a weak toroidal or vertical field which serves as the seed for the magnetorotational instability. These simulations reaffirm many of the conclusions of previous local simulations. The MRI 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. As in previous global simulations, there is a nonzero stress at the marginally stable orbit. The stress is smaller than seen in stratified torus simulations, but nevertheless produces a small decline in specific angular momentum inside the last stable orbit. Detailed comparisons between simulations are used to examine the effects of various choices in computational setup. Because the driving instability is local, a reduction in the azimuthal computational domain to some fraction of does not create large qualitative differences. Similarly, the choice of either an isothermal or adiabatic equation of state has little impact on the initial evolution. 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.

Subject headings: accretion--accretion disks--instabilities--MHD--black holes

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Table of Contents

• 1. Introduction
• 2. Problem Setup
• 3. Simulation Results
  • 3.1 Disk with initial toroidal field
  • 3.2 Disk with initial vertical field
  • 3.3 Disk near the marginally-stable orbit
  • 3.4 Influence of phi domain
  • 3.5 Equation of State
• 4. A Hydrodynamic Disk
• 5. Discussion
  • 5.1 Evolution of Keplerian disks: local versus global
  • 5.2 Viscous Instability
  • 5.3 Stress at the Marginally Stable Orbit
  • 5.4 Hydrodynamic Stability
  • 5.5 Coherent structures
  • 5.6 Impact of numerical model assumptions
• 6. Conclusion
• References

 

Download a complete postscript version cylinder.ps

 

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TABLE
CYLINDRICAL KEPLERIAN DISK SIMULATIONS


Model	Domain	Grid	Equation of State	Initial Field	End time	Movie
CK5	1.5-61.5, , 2.0	256 x 58 x 24	isothermal	toroidal	3972	4.7 MBytes MPEG
HK5	1.5-61.5, , 2.0	256 x 58 x 24	isothermal	hydro	1400	3.4 MBytes MPEG
CK6	1.5-61.5, , 2.0	256 x 64 x 32	isothermal	vertical	4097	5.0 MBytes MPEG 3-D View
CK7	1.5-61.5, , 0.8	256 x 256 x 32	adiabatic	vertical	2575	2.4 MBytes MPEG
CK7a	1.5-61.5, , 0.8	256 x 64 x 32	adiabatic	vertical	1500
CK7b	1.5-61.5, , 0.8	256 x 64 x 32	isothermal	vertical	1500
NK1	0.25-3.75, , 0.2	128 x 128 x 32	isothermal	toroidal	71.1
NK1a	0.25-3.75, , 0.2	128 x 32 x 32	isothermal	toroidal	66.6