MHD of the inner regions of black hole accretion disks

Chris Reynolds (Astronomy Department, Univ. of Maryland, College Park)

In recent years there has been a revitalization of interest in magnetic fields near black holes. It is now widely believed that magneto-hydrodynamic turbulence driven by the magneto-rotational instability (MRI; aka Balbus-Hawley instability) drives the flow of matter and angular momentum through the accretion disk. With that development, the properties of the magnetic field near to the central black hole have been revisited by several authors. Treating the region within the radius of marginal stability as force-free, some authors have argued that the large-scale magnetic field near the black hole is always weak due to the relatively weak fields at which the MRI saturates (Ghosh & Abramowicz 1997; Livio, Ogilvie & Pringle 1999). If true, the extraction of the black hole spin energy via the Blandford-Znajek process may be insignificant. On the other hand, Krolik (1999; also see Agol & Krolik 2000) has made the opposite assumption (i.e. a dynamically insignificant magnetic field frozen into the plasma) and argued that the strongly sheared flow within the radius of marginal stability will amplify the field to very high values relative to the thermal pressure. Such fields may be effective at extracting the rotational energy of the black hole and/or creating a flow of energy and angular momentum from within the radius of marginal stability to outer parts of the accretion disk.

While such analytic studies are necessary to understand the physics, they require one to make symmetry and/or steady-state assumptions which are clearly invalid in a MHD-turbulent accretion disk. To address this important problem, I am involved in a program of 3-D MHD simulations of disk accretion across the radius of marginal stability of black hole accretion disks. This work is being performed in collaboration with Dr.Philip Armitage (St. Andrews, UK) and Dr.James Chiang (NASA-GSFC). Our preliminary investigation mimicked the effects of General Relativity with a Pseudo-Newtonian potential and studied accretion in a wedge of the disk with very simple equations of state (isothermal or adiabatic). Starting with a smooth equilibrium flow, we followed the development of the MRI instability into the highly non-linear regime until it saturates and a new quasi-steady state is achieved. Our preliminary investigation (Armitage, Reynolds & Chiang 2000) reveals that the field does indeed become strong within the radius of marginal stability, but there is very little transport of energy or angular momentum from this region to the outer accretion disk. In the language of accretion disk physics, the zero-torque boundary condition seems to be a good approximation. While several authors have presented similar calculations, these are some of the first such numerical experiments tailored at studying radiatively efficient black hole accretion disks. The figure to the right shows some representative results from one of our simulations. The left panel shows fractional density perturbations away from the (aximuthally and vertically) averaged density. The right panel shows the ratio of magnetic to thermal energy densities. The magnetic field is relatively stronger (denoted by red and yellow) within the innermost stable orbit.

We intend to build upon this early work and continue to investigate magnetic fields in the inner regions of black hole accretion disks. As the computer power available to us increases, we will improve these numerical experiments by simulating global accretion disks (rather than wedges), and using more realistic energy equations. Eventually, we intend to use fully relativistic codes in order to study the effects near the event horizon of the black hole (one may eventually hope to construct an astrophysically-motivated 3-D numerical model in which the Blandford-Znajek process is realized). These simulations will provide guidance for analytic models of magnetic field generation, diffusion and advection. The ultimate goal is to understand the magnetic field strengths and topologies in the central regions of the accretion disk and the near the event horizon. In the long term, we aim to have a complete model for the inner regions of the accretion disk in which we understand the generation/transport/dissipation of the magnetic field, the interaction of the magnetic field with the disk matter and the black hole, and the consequences of these phenomena for the production of jet, outflows and electromagnetic radiation.

References

• Agol E., Krolik J.H., 2000, ApJ, 528, 161
• Armitage P.J., Reynolds C.S., Chiang J., 2000, ApJ, in press
• Ghosh P., Abramowicz M.A., 1997, MNRAS, 292, 887
• Krolik J.H., 1999, ApJL, 515, 73
• Livio M., Ogilvie G., Pringle J.E., 1999, ApJ, 512, 100

More information

For more information about the topics covered on this web site, please contact Chris Reynolds .