arXiv subjects

John F. Hawley

Publications and source records attributed to John F. Hawley.

At least 19 recordsLinked to original sources

arXiv2019

Tilt Dependence of Alignment in Accretion Disks Subjected to Lense--Thirring Torques

We consider the effects of black hole tilt on accretion disk alignment, studying three initial black hole tilts,6 degrees, 12 degrees and 24 degrees, with both magnetohydrodynamic and (inviscid) hydrodynamic evolution. In a number of ways, but not all, the dynamics are homologous in the sense that the alignment fronts resulting from different initial tilts are very similar when analyzed in terms of the fraction of the initial tilt angle. Even when the initial misalignment is 24 degrees, which, for the sound speed studied, is 4 vertical scale heights at the disk fiducial radius, the surface density remains a smooth function of radius; i.e., we find no examples in which the disk inner aligned and outer misaligned regions separate, or "break".

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arXiv2018

Sound Speed Dependence of Alignment in Accretion Disks Subjected to Lense-Thirring Torques

We present a series of simulations in both pure hydrodynamics (HD) and magnetohydrodynamics (MHD) exploring the degree to which alignment of disks subjected to external precessional torques (e.g., as in the `Bardeen-Petterson' effect) is dependent upon the disk sound speed c_s. Across the range of sound speeds examined, we find that the influence of the sound speed can be encapsulated in a simple "lumped-parameter" model proposed by Sorathia et al. (2013a). In this model, alignment fronts propagate outward at a speed ~0.2 rOmega_precess(r), where Omega_precess is the local test-particle precession frequency. Meanwhile, transonic radial motions transport angular momentum both inward and outward at a rate that may be described roughly in terms of an orientation diffusion model with diffusion coefficient ~2c_s^2/Omega, for local orbital frequency Omega. The competition between the two leads, in isothermal disks, to a stationary position for the alignment front at a radius proportional to c_s^(-4/5). For alignment to happen at all, the disk must either be turbulent due to the magnetorotational instability in MHD, or, in HD, it must be cool enough for the bending waves driven by disk warp to be nonlinear at their launch point. Contrary to long-standing predictions, warp propagation in MHD disks is diffusive independent of the parameter c_s/(alpha v_orb$, for orbital speed v_orb and ratio of stress to pressure of alpha. In purely HD disks, i.e., those with no internal stresses other than bulk viscosity, warmer disks align weakly or not at all; cooler disks align qualitatively similarly to MHD disks.

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arXiv2015

Disks and Jets - Gravity, Rotation and Magnetic Fields

Magnetic fields are fundamental to the dynamics of both accretion disks and the jets that they often drive. We review the basic physics of these phenomena, the past and current efforts to model them numerically with an emphasis on the jet-disk connection, and the observational constraints on the role of magnetic fields in the jets of active galaxies on all scales.

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arXiv2015

A Steady-State Alignment Front in an Accretion Disk Subjected to Lense-Thirring Torques

Using only physical mechanisms, i.e., 3D MHD with no phenomenological viscosity, we have simulated the dynamics of a moderately thin accretion disk subject to torques whose radial scaling mimics those produced by lowest-order post-Newtonian gravitomagnetism. In this simulation, we have shown how, in the presence of MHD turbulence, a time-steady transition can be achieved between an inner disk region aligned with the equatorial plane of the central mass's spin and an outer region orbiting in a different plane. The position of the equilibrium orientation transition is determined by a balance between gravitomagnetic torque and warp-induced inward mixing of misaligned angular momentum from the outer disk. If the mixing is interpreted in terms of diffusive transport, the implied diffusion coefficient is ~(0.6--0.8)c_s^2/Omega for sound speed c_s and orbital frequency Omega. This calibration permits estimation of the orientation transition's equilibrium location given the central mass, its spin parameter, and the disk's surface density and scaleheight profiles. However, the alignment front overshoots before settling into an equilibrium, signaling that a diffusive model does not fully represent the time-dependent properties of alignment fronts under these conditions. Because the precessional torque on the disk at the alignment front is always comparable to the rate at which misaligned angular momentum is brought inward to the front by warp-driven radial motions, no break forms between the inner and outer portions of the disk in our simulation. Our results also raise questions about the applicability to MHD warped disks of the traditional distinction between "bending wave" and "diffusive" regimes.

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arXiv2013

MHD Simulation of a Disk Subjected to Lense-Thirring Precession

When matter orbits around a central mass obliquely with respect to the mass's spin axis, the Lense-Thirring effect causes it to precess at a rate declining sharply with radius. Ever since the work of Bardeen & Petterson (1975), it has been expected that when a fluid fills an orbiting disk, the orbital angular momentum at small radii should then align with the mass's spin. Nearly all previous work has studied this alignment under the assumption that a phenomenological "viscosity" isotropically degrades fluid shears in accretion disks, even though it is now understood that internal stress in flat disks is due to anisotropic MHD turbulence. In this paper we report a pair of matched simulations, one in MHD and one in pure (non-viscous) HD in order to clarify the specific mechanisms of alignment. As in the previous work, we find that disk warps induce radial flows that mix angular momentum of different orientation; however, we also show that the speeds of these flows are generically transonic and are only very weakly influenced by internal stresses other than pressure. In particular, MHD turbulence does not act in a manner consistent with an isotropic viscosity. When MHD effects are present, the disk aligns, first at small radii and then at large; alignment is only partial in the HD case. We identify the specific angular momentum transport mechanisms causing alignment and show how MHD effects permit them to operate more efficiently. Lastly, we relate the speed at which an alignment front propagates outward (in the MHD case) to the rate at which Lense-Thirring torques deliver angular momentum at smaller radii.

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arXiv2013

Testing Convergence for Global Accretion Disks

Global disk simulations provide a powerful tool for investigating accretion and the underlying magnetohydrodynamic turbulence driven by the magneto-rotational instability (MRI). Using them to predict accurately quantities such as stress, accretion rate, and surface brightness profile requires that purely numerical effects, arising from both resolution and algorithm, be understood and controlled. We use the flux-conservative Athena code to conduct a series of experiments on disks having a variety of magnetic topologies to determine what constitutes adequate resolution. We develop and apply several resolution metrics: Qz and Qphi, the ratio of the grid zone size to the characteristic MRI wavelength, alpha_mag, the ratio of the Maxwell stress to the magnetic pressure, and the ratio of radial to toroidal magnetic field energy. For the initial conditions considered here, adequate resolution is characterized by Qz > 15, Qphi > 20, alpha_mag = 0.45, and a field energy ratio of 0.2. These values are associated with > 35 zones per scaleheight, a result consistent with shearing box simulations. Numerical algorithm is also important. Use of the HLLE flux solver or second-order interpolation can significantly degrade the effective resolution compared to the HLLD flux solver and third-order interpolation. Resolution at this standard can be achieved only with large numbers of grid zones, arranged in a fashion that matches the symmetries of the problem and the scientific goals of the simulation.

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arXiv2013

Relaxation of Warped Disks: the Case of Pure Hydrodynamics

Orbiting disks may exhibit bends due to a misalignment between the angular momentum of the inner and outer regions of the disk. We begin a systematic simulational inquiry into the physics of warped disks with the simplest case: the relaxation of an unforced warp under pure fluid dynamics, i.e. with no internal stresses other than Reynolds stress. We focus on the nonlinear regime in which the bend rate is large compared to the disk aspect ratio. When warps are nonlinear, strong radial pressure gradients drive transonic radial motions along the disk's top and bottom surfaces that efficiently mix angular momentum. The resulting nonlinear decay rate of the warp increases with the warp rate and the warp width, but, at least in the parameter regime studied here, is independent of the sound speed. The characteristic magnitude of the associated angular momentum fluxes likewise increases with both the local warp rate and the radial range over which the warp extends; it also increases with increasing sound speed, but more slowly than linearly. The angular momentum fluxes respond to the warp rate after a delay that scales with the square-root of the time for sound waves to cross the radial extent of the warp. These behaviors are at variance with a number of the assumptions commonly used in analytic models to describe linear warp dynamics.

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arXiv2012

Three Dimensional MHD Simulation of Circumbinary Accretion Disks: Disk Structures and Angular Momentum Transport

We present the first three-dimensional magnetohydrodynamic (MHD) simulations of a circumbinary disk surrounding an equal mass binary. The binary maintains a fixed circular orbit of separation $a$. As in previous hydrodynamical simulations, strong torques by the binary can maintain a gap of radius $\simeq 2a$. Streams curve inward from $r \simeq 2a$ toward the binary; some of their mass passes through the inner boundary, while the remainder swings back out to the disk. However, we also find that near its inner edge the disk develops both a strong $m=1$ asymmetry and growing orbital eccentricity. Because the MHD stresses introduce more matter into the gap, the total torque per unit disk mass is $\simeq 14$ times larger than found previously. The inner boundary accretion rate per unit disk mass is $\simeq 40$ times greater than found from previous hydrodynamical calculations. The implied binary shrinkage rate is determined by a balance between the rate at which the binary gains angular momentum by accretion and loses it by gravitational torque. The large accretion rate brings these two rates nearly into balance, but in net, we find that $\dot a/a < 0$, and its magnitude is about 2.7 times larger than predicted by the earlier hydrodynamic simulations. If the binary comprises two massive black holes, the accretion rate may be great enough for one or both to be AGN, with consequences for the physical state of the gas both in the disk body and in its inner gap.

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arXiv2011

Radiative efficiency and thermal spectrum of accretion onto Schwarzschild black holes

Recent general relativistic magneto-hydrodynamic (MHD) simulations of accretion onto black holes have shown that, contrary to the basic assumptions of the Novikov-Thorne model, there can be substantial magnetic stress throughout the plunging region. Additional dissipation and radiation can therefore be expected. We use data from a particularly well-resolved simulation of accretion onto a non-spinning black hole to compute both the radiative efficiency of such a flow and its spectrum if all emitted light is radiated with a thermal spectrum whose temperature matches the local effective temperature. This disk is geometrically thin enough (H/r ~= 0.06) that little heat is retained in the flow. In terms of light reaching infinity (i.e., after allowance for all relativistic effects and for photon capture by the black hole), we find that the radiative efficiency is at least ~=6-10% greater than predicted by the Novikov-Thorne model (complete radiation of all heat might yield another ~6%). We also find that the spectrum more closely resembles the Novikov-Thorne prediction for a/M ~= 0.2--0.3 than for the correct value, a/M=0. As a result, if the spin of a non-spinning black hole is inferred by model-fitting to a Novikov-Thorne model with known black hole mass, distance, and inclination, the inferred a/M is too large by ~= 0.2--0.3.

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arXiv2011

Assessing Quantitative Results in Accretion Simulations: From Local to Global

Discretized numerical simulations are a powerful tool for investigation of nonlinear MHD turbulence in accretion disks. However, confidence in their quantitative predictions requires a demonstration that further refinement of the spatial gridscale would not result in any significant change. This has yet to be accomplished, particularly for global disk simulations. In this paper, we combine data from previously published stratified shearing box simulations and new global disk simulations to calibrate several quantitative diagnostics by which one can estimate progress toward numerical convergence. Using these diagnostics, we find that the established criterion for an adequate numerical description of linear growth of the magneto-rotational instability (the number of cells across a wavelength of the fastest-growing vertical wavenumber mode) can be extended to a criterion for adequate description of nonlinear MHD disk turbulence, but the standard required is more stringent. We also find that azimuthal resolution, which has not often been extensively examined in previous studies, can significantly affect the evolution of the poloidal magnetic field. We further analyze the comparative resolution requirements of a small sample of initial magnetic field geometries; not surprisingly, more complicated initial field geometries require higher spatial resolution. Otherwise, they tend to evolve to qualitatively similar states if evolved for sufficient time. Applying our quantitative resolution criteria to a sample of previously published global simulations, we find that, with perhaps a single exception, they are significantly under-resolved, and therefore underestimate the magnetic turbulence and resulting stress levels throughout the accretion flow.

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arXiv2011

Resistivity-driven State Changes in Vertically Stratified Accretion Disks

We investigate the effect of shear viscosity and Ohmic resistivity on the magnetorotational instability (MRI) in vertically stratified accretion disks through a series of local simulations with the Athena code. First, we use a series of unstratified simulations to calibrate physical dissipation as a function of resolution and background field strength; the effect of the magnetic Prandtl number, Pm = viscosity/resistivity, on the turbulence is captured by ~32 grid zones per disk scale height, H. In agreement with previous results, our stratified disk calculations are characterized by a subthermal, predominately toroidal magnetic field that produces MRI-driven turbulence for |z| < 2 H. Above |z| = 2 H, magnetic pressure dominates and the field is buoyantly unstable. Large scale radial and toroidal fields are also generated near the mid-plane and subsequently rise through the disk. The polarity of this mean field switches on a roughly 10 orbit period in a process that is well-modeled by an alpha-omega dynamo. Turbulent stress increases with Pm but with a shallower dependence compared to unstratified simulations. For sufficiently large resistivity, on the order of cs H/1000, where cs is the sound speed, MRI turbulence within 2 H of the mid-plane undergoes periods of resistive decay followed by regrowth. This regrowth is caused by amplification of toroidal field via the dynamo. This process results in large amplitude variability in the stress on 10 to 100 orbital timescales, which may have relevance for partially ionized disks that are observed to have high and low accretion states.

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arXiv2010

Dependence of inner accretion disk stress on parameters: the Schwarzschild case

We explore the parameter dependence of inner disk stress in black hole accretion by contrasting the results of a number of simulations, all employing 3-d general relativistic MHD in a Schwarzschild spacetime. Five of these simulations were performed with the intrinsically conservative code HARM3D, which allows careful regulation of the disk aspect ratio, H/R; our simulations span a range in H/R from 0.06 to 0.17. We contrast these simulations with two previously reported simulations in a Schwarzschild spacetime in order to investigate possible dependence of the inner disk stress on magnetic topology. In all cases, much care was devoted to technical issues: ensuring adequate resolution and azimuthal extent, and averaging only over those time-periods when the accretion flow is in approximate inflow equilibrium. We find that the time-averaged radial-dependence of fluid-frame electromagnetic stress is almost completely independent of both disk thickness and poloidal magnetic topology. It rises smoothly inward at all radii (exhibiting no feature associated with the ISCO) until just outside the event horizon, where the stress plummets to zero. Reynolds stress can also be significant near the ISCO and in the plunging region; the magnitude of this stress, however, depends on both disk thickness and magnetic topology. The two stresses combine to make the net angular momentum accreted per unit rest-mass 7-15% less than the angular momentum of the ISCO.

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arXiv2009

Viscous and Resistive Effects on the MRI with a Net Toroidal Field

Resistivity and viscosity have a significant role in establishing the energy levels in turbulence driven by the magnetorotational instability (MRI) in local astrophysical disk models. This study uses the Athena code to characterize the effects of a constant shear viscosity νand Ohmic resistivity ηin unstratified shearing box simulations with a net toroidal magnetic flux. A previous study of shearing boxes with zero net magnetic field performed with the ZEUS code found that turbulence dies out for values of the magnetic Prandtl number, P_m = ν/η, below P_m \sim 1; for P_m \gtrsim 1, time- and volume-averaged stress levels increase with P_m. We repeat these experiments with Athena and obtain consistent results. Next, the influence of viscosity and resistivity on the toroidal field MRI is investigated both for linear growth and for fully-developed turbulence. In the linear regime, a sufficiently large νor ηcan prevent MRI growth; P_m itself has little direct influence on growth from linear perturbations. By applying a range of values for νand ηto an initial state consisting of fully developed turbulence in the presence of a background toroidal field, we investigate their effects in the fully nonlinear system. Here, increased viscosity enhances the turbulence, and the turbulence decays only if the resistivity is above a critical value; turbulence can be sustained even when P_m < 1, in contrast to the zero net field model. While we find preliminary evidence that the stress converges to a small range of values when νand ηbecome small enough, the influence of dissipation terms on MRI-driven turbulence for relatively large ηand νis significant, independent of field geometry.

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arXiv2009

Transport of Large Scale Poloidal Flux in Black Hole Accretion

We report on a global, three-dimensional GRMHD simulation of an accretion torus embedded in a large scale vertical magnetic field orbiting a Schwarzschild black hole. This simulation investigates how a large scale vertical field evolves within a turbulent accretion disk and whether global magnetic field configurations suitable for launching jets and winds can develop. We find that a "coronal mechanism" of magnetic flux motion, which operates largely outside the disk body, dominates global flux evolution. In this mechanism, magnetic stresses driven by orbital shear create large-scale half-loops of magnetic field that stretch radially inward and then reconnect, leading to discontinuous jumps in the location of magnetic flux. In contrast, little or no flux is brought in directly by accretion within the disk itself. The coronal mechanism establishes a dipole magnetic field in the evacuated funnel around the orbital axis with a field intensity regulated by a combination of the magnetic and gas pressures in the inner disk. These results prompt a reevaluation of previous descriptions of magnetic flux motion associated with accretion. Local pictures are undercut by the intrinsically global character of magnetic flux. Formulations in terms of an "effective viscosity" competing with an "effective resistivity" are undermined by the nonlinearity of of the magnetic dynamics and the fact that the same turbulence driving mass motion (traditionally identified as "viscosity") can alter magnetic topology.

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arXiv2008

Simulations of Magnetorotational Turbulence with a Higher-Order Godunov Scheme

(abridged) We apply a second-order Godunov code, Athena, to studies of the magnetorotational instability using unstratified shearing box simulations with a uniform net vertical field and a sinusoidally varying zero net vertical field. The Athena results agree well with similar studies that used different numerical algorithms. We conduct analyses to study the flow of energy from differential rotation to turbulent fluctuations to thermalization. A study of the temporal correlation between the time derivatives of volume-averaged energy components shows that energy injected into turbulent fluctuations dissipates on a timescale of $Ω^{-1}$, where $Ω$ is the orbital frequency of the local domain. Magnetic dissipation dominates over kinetic dissipation, although not by as great a factor as the ratio of magnetic to kinetic energy. We Fourier-transform the magnetic and kinetic energy evolution equations and, using the assumption that the time-averaged energies are constant, determine the level of numerical dissipation as a function of length scale and resolution. By modeling numerical dissipation as if it were physical in origin, we characterize numerical resistivity and viscosity in terms of effective Reynolds and Prandtl numbers. The resulting effective magnetic Prandtl number is $\sim 2$, independent of resolution or initial field geometry. MRI simulations with effective Reynolds and Prandtl numbers determined by numerical dissipation are not equivalent to those where these numbers are set by physical resistivity and viscosity. These results serve, then, as a baseline for future shearing box studies where dissipation is controlled by the inclusion of explicit viscosity and resistivity.

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arXiv2008

Direct calculation of the radiative efficiency of an accretion disk around a black hole

Numerical simulation of magnetohydrodynamic (MHD) turbulence makes it possible to study accretion dynamics in detail. However, special effort is required to connect inflow dynamics (dependent largely on angular momentum transport) to radiation (dependent largely on thermodynamics and photon diffusion). To this end we extend the flux-conservative, general relativistic MHD code HARM from axisymmetry to full 3D. The use of an energy conserving algorithm allows the energy dissipated in the course of relativistic accretion to be captured as heat. The inclusion of a simple optically thin cooling function permits explicit control of the simulated disk's geometric thickness as well as a direct calculation of both the amplitude and location of the radiative cooling associated with the accretion stresses. Fully relativistic ray-tracing is used to compute the luminosity received by distant observers. For a disk with aspect ratio H/r ~ 0.1 accreting onto a black hole with spin parameter a/M = 0.9, we find that there is significant dissipation beyond that predicted by the classical Novikov-Thorne model. However, much of it occurs deep in the potential, where photon capture and gravitational redshifting can strongly limit the net photon energy escaping to infinity. In addition, with these parameters and this radiation model, significant thermal and magnetic energy remains with the gas and is accreted by the black hole. In our model, the net luminosi ty reaching infinity is 6% greater than the Novikov-Thorne prediction. If the accreted thermal energy were wholly radiated, the total luminosity of the accretion flow would be ~20% greater than the Novikov-Thorne value.

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arXiv2008

Athena: A New Code for Astrophysical MHD

A new code for astrophysical magnetohydrodynamics (MHD) is described. The code has been designed to be easily extensible for use with static and adaptive mesh refinement. It combines higher-order Godunov methods with the constrained transport (CT) technique to enforce the divergence-free constraint on the magnetic field. Discretization is based on cell-centered volume-averages for mass, momentum, and energy, and face-centered area-averages for the magnetic field. Novel features of the algorithm include (1) a consistent framework for computing the time- and edge-averaged electric fields used by CT to evolve the magnetic field from the time- and area-averaged Godunov fluxes, (2) the extension to MHD of spatial reconstruction schemes that involve a dimensionally-split time advance, and (3) the extension to MHD of two different dimensionally-unsplit integration methods. Implementation of the algorithm in both C and Fortran95 is detailed, including strategies for parallelization using domain decomposition. Results from a test suite which includes problems in one-, two-, and three-dimensions for both hydrodynamics and MHD are given, not only to demonstrate the fidelity of the algorithms, but also to enable comparisons to other methods. The source code is freely available for download on the web.

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arXiv2008

The Influence of Magnetic Field Geometry on the Evolution of Black Hole Accretion Flows: Similar Disks, Drastically Different Jets

Because the magneto-rotational instability is capable of exponentially amplifying weak preexisting magnetic fields, it might be hoped that the character of the magnetic field in accretion disks is independent of the nature of the seed field. However, the divergence-free nature of magnetic fields in highly conducting fluids ensures that their large-scale topology is preserved, no matter how greatly the field intensity is changed. By performing global two-dimensional and three-dimensional general relativistic magnetohydrodynamic disk simulations with several different topologies for the initial magnetic field, we explore the degree to which the character of the flows around black holes depends on the initial topology. We find that while the qualitative properties of the accretion flow are nearly independent of field topology, jet-launching is very sensitive to it: a sense of vertical field consistent for at least an inner disk inflow time is essential to the support of strong jets.

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