)
concentrated in small (parsec-sized) volumes. Indirect indications of accretion
include copious nonthermal radiation from active galactic nuclei, relativistic
expansion, and jets. Iron line observations (e.g., Tanaka et al. 1995)
show how, in principle, observations can probe directly the physics of
the strong-field region, distinguishing black hole accretion from accretion
onto white dwarfs or neutron stars.
With the emergence of a unified model to account for the wide variety of observational characteristics of both X-ray binaries and active galactic nuclei (AGN), it becomes increasingly important to support theory and observation with detailed numerical simulations of the physics of black hole accretion. Distinctive and astrophysically interesting effects are expected from accretion flows in the Kerr metric, and modeling will require development of new fully general relativistic (GR) simulation codes. This becomes especially relevant in light of results that suggest that most galactic core black holes are rotating (Elvis, Risaliti, & Zamorani 2002).
Most of the simulations to date of relativistic black hole accretion have been for hydrodynamics alone. Extensive work was done in the 1980s on the numerical simulation of hydrodynamics around black holes (Hawley, Smarr & Wilson 1984a, 1984b; hereafter HSWa and HSWb). This work was based on numerical techniques developed through the pioneering efforts of Wilson (1972). The HSWb GR hydrodynamics code was written in spherical polar Boyer-Lindquist coordinates, and used operator-split finite-differencing on a staggered grid, with piecewise linear representations for the fundamental variables. The GR hydrodynamic studies using this code (HSWb; Hawley & Smarr 1986; Hawley 1986) were two-dimensional (assuming axisymmetry) and dealt with the prompt infall of rotating gas toward a central black hole, the role of the centrifugal barrier, centrifugally-driven outflows, and the formation of pressure supported thick disks or tori. Since then, there have been other axisymmetric GR hydrodynamic simulations using a similar numerical approach (Yokosawa 1995; Igumenshchev & Beloborodov 1997).
It is now recognized that magnetic fields play an essential role in the outward transport of angular momentum in accretion disks through the action of the magnetorotational instability of Balbus and Hawley (1991). This implies the need for a general relativistic magnetohydrodynamics (MHD) simulation code. Here again, Wilson did pioneering work, carrying out two-dimensional simulations of magnetized accretion over two and a half decades ago (Wilson 1975; 1977; 1978). The task was arguably beyond the computers then available, however. Only recently have research groups returned to full GR MHD simulations (e.g., Koide, Shibata, & Kudoh 1999; Komissarov 1999).
Rather than employing full relativity, the most recent three-dimensional global black hole MHD accretion simulations (e.g., Hawley & Balbus 2002) use a pseudo-Newtonian potential that can emulate certain important characteristics of the Schwarzschild metric. Computing a three dimensional MHD accretion flow in a full Kerr metric is a more ambitious undertaking. It is our aim to develop a new three-dimensional GR MHD code to enable such global accretion disk studies. This paper represents a first step, specifically the initial development and application of the hydrodynamic portion of a Kerr metric GR code.
The culmination of the earlier GR hydrodynamics effort was a fully three-dimensional numerical investigation (Hawley 1991; hereafter H91) of the Papaloizou-Pringle instability (Papaploizou & Pringle 1984) for accretion tori in a Schwarzschild metric. In this paper we extend those simulations to Kerr (rotating) black holes, and consider the effect of black hole angular momentum on prograde and retrograde torus orbits. The Papaloizou-Pringle instability (PPI) remains an interesting topic of research, and it provides a nontrivial application of full three-dimensional general-relativistic hydrodynamics.
The plan of this paper is as follows. In §2 we outline the equations and the general numerical procedures. In §3 we discuss the properties of equilibrium gas tori in the Kerr metric, and the properties of the Papaloizou-Pringle instability to which these tori are vulnerable. The results of a series of numerical simulations of tori in the Kerr metric are presented in §4, and these results are discussed in §5.