For many years, the physical nature of angular momentum transport in accretion disks has been one of the great outstanding questions of high-energy astrophysics. As a result of nearly a decade of effort, it is now becoming increasingly clear that the mechanism is turbulent magnetic stress in which the energy for the magnetic field is largely drawn from the free energy of orbital shear (as reviewed by Balbus & Hawley 1998). Theoretical grounds for this conclusion were first found in the rediscovery of the magneto-rotational instability (MRI) by Balbus & Hawley (1991). Increasingly detailed simulations of local ``shearing boxes'' have bolstered our confidence that this is indeed the process found in nature (e.g., Hawley, Gammie & Balbus 1995, 1996; Brandenburg et al. 1995; Stone et al. 1996; Miller & Stone 2000).
What has been missing until recently is studies of the radial structure of disks accreting under the influence of magnetohydrodynamic (MHD) turbulent stresses. Hitherto, only a few such three-dimensional global simulations have been presented (Armitage 1998; Matsumoto 1999; Hawley 2000). In global simulations it is difficult to obtain adequate resolution over the wide range of length scales involved, namely the MHD turbulent length scales within the disk, the disk scale height H, and the radial distance from the central object R. These length scales are generally quite disparate, but near the inner boundary of an accretion disk they should become comparable. In this paper we present a global simulation of an accretion disk in which we focus on this inner region where adequate numerical resolution can be obtained.
With the results of this new simulation, we can begin to answer a number of questions of central interest to the mechanics of accretion. For example, the most common view of the inner portions of black hole accretion disks is based on the work of Novikov & Thorne (1973) (e.g. Abramowicz & Zurek 1981; Muchotrzeb & Paczynski 1982; Matsumoto et al. 1984). In this picture, the disk is (nearly) time-steady and axisymmetric. Page & Thorne (1974) argued on heuristic grounds that the R- component of the stress (the one responsible for angular momentum transport) should go to zero at the marginally stable orbit; later work by Abramowicz and Kato (1989) showed that if the stress is a (constant) small fraction of the local pressure, it automatically approaches zero near that location.
However, because the MHD turbulence is the result of a general, local, rapidly-growing instability, assumptions such as stationarity and axisymmetry are likely inappropriate. One might also question whether there is any reason for the stress to diminish at the disk's inner edge, given that the growth rate of the MRI does not appreciably diminish near the marginally stable orbit (cf. Krolik 1999; Gammie 1999; see also the footnote in Page & Thorne 1974 in which they speculate that their heuristic arguments might fail if strong magnetic fields were present). Further, because magnetic stresses do not automatically maintain a fixed ratio to the pressure, conclusions based upon parameterizations (e.g., Abramowicz & Kato 1989) may not directly apply. This issue is important because continued stress at the marginally stable orbit could alter both the energy and angular momentum with which matter arrives at the black hole; that is, this boundary condition determines the efficiency of accretion and the rate at which the black hole is spun up.
Because the greatest luminosity should be released near the inner edge of the accretion disk, the detailed behavior and structure of the region near the marginally stable orbit is crucial to understanding the observations of black hole systems. For example, the luminosity of essentially all accreting black holes exhibits sizable fluctuations with a very broad-band distribution of fluctuation power with timescale (e.g., as discussed by Sunyaev & Revnitsev 2000); can we identify the specific dynamics that drive these variations? Occasionally, the lightcurve exhibits quasi-periodic oscillations (QPOs); can we either identify the mechanism responsible for these, or test some of those mechanisms that have been proposed?
In the following section we will present a technical description of the three-dimensional global simulation we report. We will then set out our results in §3, with their qualitative implications outlined in § 4. In §5 we will discuss the degree to which limitations of our simulation hamper direct application of our results, and suggest in which directions the greatest improvement might soon be made. We summarize our conclusions in §6.