Jean-Pierre De Villiers

Magnetically Driven Accretion Flows in the Kerr Metric. I. Models and Overall Structure

This is the first in a series of papers that investigate the properties of accretion flows in the Kerr metric through three-dimensional general relativistic magnetohydrodynamic simulations of tori with a nearly Keplerian initial angular velocity profile. We study four models with increasing black hole spin, from a/M = 0 to 0.998, for which the structural parameters of the initial tori are maintained nearly constant. The subsequent accretion flows arise self-consistently from stresses and turbulence created by the magnetorotational instability. We investigate the overall evolution and the late-time global structure in the resulting nonradiative accretion flows, including the magnetic fields within the disks, the properties of the flow in the plunging region, and the flux of conserved quantities into the black hole. Independent of black hole spin, the global structure is described in terms of five regions: the main disk body, the coronal envelope, the inner disk (consisting of an inner torus and plunging region), an evacuated axial funnel, and a biconical outflow confined to the corona-funnel boundary. We find evidence for lower accretion rates, stronger funnel-wall outflows, and increased stress in the near-hole region with increasing black hole spin.

Magnetically driven accretion in the kerr metric. III. Unbound outflows

We have carried out fully relativistic numerical simulations of accretion disks in the Kerr metric. In this paper we focus on the unbound outflows that emerge self-consistently from the accretion flow. These outflows are found in the axial funnel region and consist of two components: a hot, fast, tenuous outflow in the axial funnel proper and a colder, slower, denser jet along the funnel wall. The funnel-wall jet is excluded from the axial funnel by elevated angular momentum and is also pressure-confined by a magnetized corona. Inside the funnel, a large-scale poloidal magnetic field spontaneously arises from the coupled dynamics of accretion and outflow, although there was no large-scale field in the initial state. Black hole rotation is not required to produce these unbound outflows, but their strength is enhanced by black hole spin. When the black hole spins rapidly, the energy ejected can be tens of percent of the accreted rest mass. At low spin, kinetic energy and enthalpy of the matter dominate the outflow energetics; at high spin, the balance shifts to Poynting flux. We compare the outflows observed in our simulations with those seen in other simulations.

MAGNETICALLY DRIVEN ACCRETION FLOWS IN THE KERR METRIC. II. STRUCTURE OF THE MAGNETIC FIELD

We present a detailed analysis of the magnetic field structure found in a set of four general relativistic three-dimensional MHD simulations of accreting tori in the Kerr metric with different black hole spins. Among the properties analyzed are the field strength as a function of position and black hole spin, the shapes of field lines, the degree to which they connect different regions, and their degree of tangling. Strong magnetic field is found toward small radii, and field strength increases with black hole spin. In the main disk body, inner torus, and corona the field is primarily toroidal. Most field lines passing through a given radius in these regions wander through a narrow radial range, suggesting an overall tightly wound spiral structure. In the main disk body and inner torus sharp field-line bends on small spatial scales are superposed on the spirals, but the field lines are much smoother in the corona. The magnetic field in the plunging region is also comparatively smooth, being stretched out radially by the infalling gas. The magnetic field in the axial funnel resembles a split monopole, but with evidence of frame dragging of the field lines near the poles of the black hole. We investigate prior speculations about the structure of the magnetic fields and discuss how frequently certain configurations are seen in the simulations. For example, coronal loops are very rare, and field lines connecting high latitudes on the event horizon to the disk are not found at all. Almost the entire system is matter-dominated; the only force-free regions are in the axial funnel. We also analyze the distribution of current density, with a view toward identifying possible locations of magnetic energy dissipation. Regions of high current density are concentrated toward the inner torus and plunging region. Dissipation inside the marginally stable orbit may provide a new source of energy for radiation, supplementing the dissipation associated with torques in the stably orbiting disk body.

A NUMERICAL METHOD FOR GENERAL RELATIVISTIC MAGNETOHYDRODYNAMICS

This paper describes the development and testing of a general relativistic magnetohydrodynamic (GRMHD) code to study ideal MHD in the fixed background of a Kerr black hole. The code is a direct extension of the hydrodynamic code of Hawley, Smarr, & Wilson and uses Evans & Hawley constrained transport (CT) to evolve the magnetic fields. Two categories of test cases were undertaken. A one-dimensional version of the code (Minkowski metric) was used to verify code performance in the special relativistic limit. The tests include Alfven wave propagation, fast and slow magnetosonic shocks, rarefaction waves, and both relativistic and nonrelativistic shock tubes. A series of one- and two-dimensional tests were also carried out in the Kerr metric: magnetized Bondi inflow, a magnetized inflow test due to Gammie, and two-dimensional magnetized constant-l tori that are subject to the magnetorotational instability.

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. There are both qualitative and quantitative differences in the fiducial models, with many of these effects attributable to the location of the marginally stable orbit, rms(a), both with respect to the initial torus and in absolute terms. In the retrograde model, the initial inner edge of the torus is close to rms, and little angular momentum need be lost to drive accretion, whereas in the prograde case the gas must slowly accrete over a significant distance and shed considerable angular momentum. Evolution is driven by the magnetorotational instability and the nonzero Maxwell stresses produced by the turbulence and results in a redistribution of the specific angular momentum to near-Keplerian values. The magnetic energy remains subthermal within the turbulent disk, but dominates in the final plunging flow into the hole. The Maxwell stress remains nonzero in this plunging flow inside of rms, and the fluids specific angular momentum continues to drop. The accretion rate into the hole is highly time-variable and is determined by the rate at which gas from the turbulent disk is fed into the plunging flow past rms. The retrograde model, with the largest rms, shows the least variability in accretion rate. While accretion variability is a function of a, the turbulence itself is also intrinsically variable. A magnetized, backflowing corona and an evacuated, magnetized funnel are features of all models.

Evolution of Self-Gravitating Magnetized Disks. II. Interaction between Magnetohydrodynamic Turbulence and Gravitational Instabilities

We present three-dimensional magnetohydrodynamic (MHD) numerical simulations of the evolution of self-gravitating and weakly magnetized disks with an adiabatic equation of state. Such disks are subject to the development of both the magnetorotational and gravitational instabilities, which transport angular momentum outward. As in previous studies, our hydrodynamic simulations show the growth of a strong m = 2 spiral structure. This spiral disturbance drives matter toward the central object and disappears when the Toomre parameter, Q, has increased well above unity. When a weak magnetic field is present as well, the magnetorotational instability grows and leads to turbulence. In that case, the strength of the gravitational stress tensor is lowered by a factor of ~2 compared with the hydrodynamic run and oscillates periodically, reaching very small values at its minimum. We attribute this behavior to the presence of a second spiral mode with higher pattern speed than the one that dominates in the hydrodynamic simulations. It is apparently excited by the high-frequency motions associated with MHD turbulence. The nonlinear coupling between these two spiral modes gives rise to a stress tensor that oscillates with a frequency that is a combination of the frequencies of each of the modes. This interaction between MHD turbulence and gravitational instabilities therefore results in a smaller mass accretion rate onto the central object.

Three-dimensional Hydrodynamic Simulations of Accretion Tori in Kerr Spacetimes

This paper presents the results of three-dimensional simulations of global hydrodynamic instabilities in black hole tori, extending earlier work by Hawley to Kerr spacetimes. This study probes a three-dimensional parameter space of torus angular momentum, torus size, and black hole angular momentum. We have observed the growth of the Papaloizou-Pringle instability for a range of torus configurations and the resultant formation of m = 1 planets. We have also observed the quenching of this instability in the presence of early accretion flows; however, in one simulation, both early accretion and planet formation occurred. Although most of the conclusions reached in Hawleys earlier work on Schwarzschild black holes carry over to Kerr spacetime, the presence of frame dragging in the Kerr geometry adds an element of complexity to the simulations; we have seen especially clear examples of this phenomenon in the accretion flows that arise from retrograde tori.

Evolution of Self-Gravitating Magnetized Disks. I. Axisymmetric Simulations

In this paper and a companion work, we report on the first global numerical simulations of self-gravitating magnetized tori, subject in particular to the influence of the magnetorotational instability (MRI). In this work, Paper I, we restrict our calculations to the study of the axisymmetric evolution of such tori. Our goals are twofold: (1) to investigate how self-gravity influences the global structure and evolution of the disks and (2) to determine whether turbulent density inhomogeneities can be enhanced by self-gravity in this regime. As in non-self-gravitating models, the linear growth of the MRI is followed by a turbulent phase, during which angular momentum is transported outward. As a result, self-gravitating tori quickly develop a dual structure composed of an inner thin Keplerian disk fed by a thicker self-gravitating disk, whose rotation profile is close to a Mestel disk. Our results show that the effects of self-gravity enhance density fluctuations much less than they smooth the disk, giving it more coherence. We discuss the expected changes that will occur in three-dimensional simulations, the results of which are presented in a companion paper.

General Relativistic Magnetohydrodynamic Simulations of Black Hole Accretion Disks

Observations are providing increasingly detailed quantitative information about the accretion flows that power such high energy systems as X-ray binaries and active galactic nuclei. Analytic models of such systems must rely on assumptions such as regular flow geometry and a simple, parameterized stress. Global numerical simulations offer a way to investigate the basic physical dynamics of accretion flows without these assumptions. For black hole accretion studies one solves the equations of general relativistic magnetohydrodynamics. Magnetic fields are of fundamental importance to the structure and evolution of accretion disks because magnetic turbulence is the source of the anomalous stress that drives accretion. We have developed a three-dimensional general relatiyistic magnetohydrodynamic simulation code to evolve time-dependent accretion systems self-consistently. Recent global simulations of black hole accretion disks suggest that the generic structure of the accretion flow is usefully divided into five regimes: the main disk, the inner disk, the corona, the evacuated funnel, and the funnel wall jet. The properties of each of these regions are summarized.