arXiv subjects
Publications and source records attributed to John F. Hawley.
We present an exact three-dimensional wave solution to the shearing sheet equations of motion. The existence of this solution argues against transient amplification as a route to turbulence in unmagnetized disks. Moreover, because the solution covers an extensive dynamical range in wavenumber space, it is an excellent test of the dissipative properties of numerical codes.
We use a relativistic ray-tracing code to calculate the light curves observed from a global general relativistic magneto-hydrodynamic simulation of an accretion flow onto a Schwarzschild black hole. We apply three basic emission models to sample different properties of the time-dependent accretion disk. With one of these models, which assumes thermal blackbody emission and free-free absorption, we can predict qualitative features of the high-frequency power spectrum from stellar-mass black holes in the "Thermal Dominant" state. The simulated power spectrum is characterized by a power law of index Gamma ~ 3 and total rms fractional variance of <~ 2% above 10 Hz. For each emission model, we find that the variability amplitude should increase with increasing inclination angle. On the basis of a newly-developed formalism for quantifying the significance of quasi-periodic oscillations (QPOs) in simulation data, we find that these simulations are able to identify any such features with (rms/mean) amplitudes >~ 1 % near the orbital frequency at the inner-most stable orbit. Initial results indicate the existence of transient QPO peaks with frequency ratios of nearly 2:3 at a 99.9% confidence limit, but they are not generic features because at any given time they are seen only from certain observer directions. Additionally, we present detailed analysis of the azimuthal structure of the accretion disk and the evolution of density perturbations in the inner disk. These "hot spot" structures appear to be roughly self-similar over a range of disk radii, with a single characteristic size δϕ=25 deg and δr/r=0.3, and typical lifetimes T_l ~ 0.3 T_orb.
Simulations of black hole accretion have shown that magnetic stresses are present near and inside the innermost stable circular orbit (ISCO). This finding suggests that such flows may be more luminous than predicted by the standard accretion disk model. Here we apply a prescription for heat dissipation within the simulated accretion flows to estimate their implied radiative efficiency. We assume that dissipation is proportional to the current density squared, and find that the resulting azimuthally-averaged and shell-integrated radial profile is well-matched to the radial heat dissipation profile of the standard disk model for the region outside the ISCO, particularly when it is adjusted to account for additional stress at the ISCO. In contrast to the standard model, however, the dissipation profile derived from the current density continues past the ISCO and through the plunging region. The total predicted dissipation rate is between $\simeq 30%$ and $\simeq 100%$ greater than that predicted by the standard model, depending on the black hole spin. Most of the additional dissipation takes place just outside the ISCO. To predict luminosities, we assume instantaneous radiation and zero optical depth, but allow for photon capture. The net radiative efficiency seen by a distant observer is increased relative to the standard model by $\simeq 25%$--80%, with the largest fractional increase for intermediate black hole spins because the increase in dissipation from enhanced stress that occurs for rapid spin is partially offset by the increased likelihood that the additional photons will be captured by the hole.
We compute a series of three-dimensional general relativistic magnetohydrodynamic simulations of accretion flows in the Kerr metric to investigate the properties of the unbound outflows that result. The overall strength of these outflows increases sharply with increasing black hole rotation rate, but a number of generic features are found in all cases. The mass in the outflow is concentrated in a hollow cone whose opening angle is largely determined by the effective potential for matter orbiting with angular momentum comparable to that of the innermost stable circular orbit. The dominant force accelerating the matter outward comes from the pressure of the accretion disk's corona. The principal element that shapes the outflow is therefore the centrifugal barrier preventing accreting matter from coming close to the rotation axis. Inside the centrifugal barrier, the cone contains very little matter and is dominated by electromagnetic fields that rotate at a rate tied closely to the rotation of the black hole. These fields carry an outward-going Poynting flux whose immediate energy source is the rotating spacetime of the Kerr black hole. When the spin parameter a/M of the black hole exceeds ~0.9, the energy carried to infinity by these outflows can be comparable to the nominal radiative efficiency predicted in the Novikov-Thorne model. Similarly, the expelled angular momentum can be comparable to that accreted by the black hole. Both the inner electromagnetic part and the outer matter part can contribute in significant fashion to the energy and angular momentum of the outflow.
This paper continues the analysis of a set of general relativistic 3D MHD simulations of accreting tori in the Kerr metric with different black hole spins. We focus on bound matter inside the initial pressure maximum, where the time-averaged motion of gas is inward and an accretion disk forms. We use the flows of mass, angular momentum, and energy in order to understand dynamics in this region. The sharp reduction in accretion rate with increasing black hole spin reported in Paper I of this series is explained by a strongly spin-dependent outward flux of angular momentum conveyed electromagnetically; when a/M > 0.9, this flux can be comparable to the inward angular momentum flux carried by the matter. In all cases, there is outward electromagnetic angular momentum flux throughout the flow; in other words, contrary to the assertions of traditional accretion disk theory, there is in general no "stress edge", no surface within which the stress is zero. The retardation of accretion in the inner disk by electromagnetic torques also alters the radial distribution of surface density, an effect that may have consequences for observable properties such as Compton reflection. The net accreted angular momentum is sufficiently depressed by electromagnetic effects that in the most rapidly-spinning black holes mass growth can lead to spindown. Spinning black holes also lose energy by Poynting flux; this rate is also a strongly increasing function of black hole spin, rising to 10% or more of the rest-mass accretion rate at very high spin. As the black hole spins faster, the path of the Poynting flux changes from being predominantly within the accretion disk to predominantly within the funnel outflow.
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. Although a rotating black hole is not required to produce these unbound outflows, their strength is enhanced by black hole spin. The funnel-wall jet is excluded from the axial funnel due to elevated angular momentum, and is also pressure-confined by a magnetized corona. The tenuous funnel outflow accounts for a significant fraction of the energy transported to large distances in the higher-spin simulations. We compare the outflows observed in our simulations with those seen in other simulations.
We present a detailed analysis of the magnetic field structure found in general relativistic 3D 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. We investigate prior speculations about the structure of the magnetic fields and discuss how frequently certain configurations are seen in the simulations. We also analyze the distribution of current density, with a view toward identifying possible locations for magnetic energy dissipation.
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 near-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 non-radiative 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 bi-conical 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.
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.
The processes of planet formation and migration depend intimately on the interaction between planetesimals and the gaseous disks in which they form. The formation of gaps in the disk can severely limit the mass of the planet and its migration toward the protostar. We investigate the process of gap formation through magnetohydrodynamic simulations in which internal stress arises self-consistently from turbulence generated by the magnetorotational instability. The simulations investigate three different planetary masses and two disk temperatures to bracket the tidal (thermal) and viscous gap opening conditions. The results are in general qualitative agreement with previous simulations of gap formation, but show significant differences. In the presence of MHD turbulence, the gaps produced are shallower and asymmetrically wider than those produced with pure hydrodynamics. The rate of gap formation is also slowed, with accretion occurring across the developing gap. Viscous hydrodynamics does not adequately describe the evolution, however, because planets capable of producing gaps also may be capable of affecting the level MHD turbulence in different regions of the disk.
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, and Wilson, and uses Evans and 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 Alfvén wave propagation, fast and slow magnetosonic shocks, rarefaction waves, and both relativistic and non-relativistic 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.
This paper presents 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. Though most of the conclusions reached in Hawley's 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.
We review numerical simulations of MHD turbulence. The last decade has witnessed fundamental advances both in the technical capabilities of direct numerical simulation, and in our understanding of key physical processes. Magnetic fields tap directly into the free energy sources in a sufficiently ionized gas. The result is that adverse angular velocity and adverse temperature gradients, not the classical angular momentum and entropy gradients, destabilize laminar and stratified flow. This has profound consequences for astrophysical accretion flows, and has opened the door to a new era of numerical simulation experiments.}
We analyze three-dimensional magnetohydrodynamic (MHD) simulations of a nonradiative accretion flow around a black hole using a pseudo-Newtonian potential. The flow originates from a torus initially centered at 100 gravitational (Schwarzschild) radii. Accretion is driven by turbulent stresses generated self-consistently by the magnetorotational instability. The resulting flow has three well-defined dynamical components: a hot, thick, rotationally-dominated Keplerian disk; a surrounding magnetized corona with vigorous circulation and outflow; and a magnetically-confined jet along the centrifugal funnel wall. Inside of 10 gravitational radii, the disk becomes very hot, more toroidal, and highly intermittent. These results contrast sharply with quasi-spherical, self-similar viscous models. There are no significant dynamical differences between simulations that include resistive heating and those that do not. We conclude by deducing some simple radiative properties of our solutions, and apply the results to the accretion-powered Galactic center source Sgr A*.
The principles underlying a proposed class of black hole accretion models are examined. The flows are generally referred to as ``convection-dominated,'' and are characterized by inward transport of angular momentum by thermal convection and outward viscous transport, vanishing mass accretion, and vanishing local energy dissipation. We examine the viability of these ideas by explicitly calculating the leading order angular momentum transport of axisymmetric modes in magnetized, differentially rotating, stratified flows. The modes are destabilized by the generalized magnetorotational instability. There are no inward transporting modes at all unless the magnitude of the (imaginary) Brunt frequency is comparable to the epicyclic frequency, a condition requiring substantial levels of dissipation. When inward transporting modes do exist, they appear at long wavelengths, unencumbered by magnetic tension. Moreover, very general thermodynamic principles prohibit the complete recovery of irreversible dissipative energy losses, a central feature of convection-dominated models. Dissipation of the free energy of differential rotation inevitably requires outward angular momentum transport. Our results are in good agreement with global MHD simulations, which find significant levels of outward transport and energy dissipation, whether or not destabilizing entropy gradients are present.
What is meant by the "inner edge" of an accretion disk around a black hole depends on the property that defines the edge. We discuss four such definitions using data from recent high-resolution numerical simulations. These are: the "turbulence edge", where flux-freezing becomes more important than turbulence in determining the magnetic field structure; the "stress edge", where plunging matter loses dynamical contact with the outer accretion flow; the "reflection edge", the smallest radius capable of producing significant X-ray reflection features; and the "radiation edge", the innermost place from which significant luminosity emerges. All these edges are dependent on the accretion rate and are non-axisymmetric and time-variable. Although all are generally located in the vicinity of the marginally stable orbit, significant displacements can occur, and data interpretations placing the disk edge precisely at this point can be misleading. If observations are to be used successfully as diagnostics of accretion in strong gravity, the models used to interpret them must take careful account of these distinctions.
New three dimensional magnetohydrodynamic simulations of accretion disk dynamics in a pseudo-Newtonian Paczynski-Wiita potential are presented. These have finer resolution in the inner disk than any previously reported. Finer resolution leads to increased magnetic field strength, greater accretion rate, and greater fluctuations in the accretion rate. One simulation begins with a purely poloidal magnetic field, the other with a purely toroidal field. Compared to the poloidal initial field simulation, a purely toroidal initial field takes longer to reach saturation of the magnetorotational instability and produces less turbulence and weaker magnetic field energies. For both initial field configurations, magnetic stresses continue across the marginally stable orbit; measured in units corresponding to the Shakura-Sunyaev alpha parameter, the stress grows from ~0.1 in the disk body to as much as ~10 deep in the plunging region. Matter passing the inner boundary of the simulation has ~10% greater binding energy and ~10% smaller angular momentum than it did at the marginally stable orbit. Both the mass accretion rate and the integrated stress fluctuate widely on a broad range of timescales.
We present a global magnetohydrodynamic (MHD) three dimensional simulation of a nonradiative accretion flow originating in a pressure supported torus. The evolution is controlled by the magnetorotational instability which produces turbulence. The flow forms a nearly Keplerian disk. The total pressure scale height in this disk is comparable to the vertical size of the initial torus. Gas pressure dominates only near the equator; magnetic pressure is more important in the surrounding atmosphere. A magnetically dominated bound outflow is driven from the disk. The accretion rate through the disk exceeds the final rate into the hole, and a hot torus forms inside 10 r_g. Hot gas, pushed up against the centrifugal barrier and confined by magnetic pressure, is ejected in a narrow, unbound, conical outflow. The dynamics are controlled by magnetic turbulence, not thermal convection, and a hydrodynamic alpha model is inadequate to describe the flow. The limitations of two dimensional MHD simulations are also discussed.