How important is non-ideal physics in simulations of sub-Eddington accretion on to spinning black holes?

How important is non-ideal physics in simulations of sub-Eddington accretion on to spinning black holes?

Foucart, Francois; Chandra, Mani; Gammie, Charles F.; Quataert, Eliot; Tchekhovskoy, Alexander

Black holes with accretion rates well below the Eddington rate are expected to be surrounded by low-density, hot, geometrically thick accretion disks. This includes the two black holes being imaged at sub-horizon resolution by the Event Horizon Telescope. In these disks, the mean free path for Coulomb interactions between charged particles is large, and the accreting matter is a nearly collisionless plasma. Despite this, numerical simulations have so far modeled these accretion flows using ideal magnetohydrodynamics. Here, we present the first global, general relativistic, 3D simulations of accretion flows onto a Kerr black hole including the non-ideal effects most likely to affect the dynamics of the disk: the anisotropy between the pressure parallel and perpendicular to the magnetic field, and the heat flux along magnetic field lines. We show that for both standard and magnetically arrested disks, the pressure anisotropy is comparable to the magnetic pressure, while the heat flux remains dynamically unimportant. Despite this large pressure anisotropy, however, the time-averaged structure of the accretion flow is strikingly similar to that found in simulations treating the plasma as an ideal fluid. We argue that these similarities are largely due to the interchangeability of the viscous and magnetic shear stresses as long as the magnetic pressure is small compared to the gas pressure, and to the sub-dominant role of pressure/viscous effects in magnetically arrested disks. We conclude by highlighting outstanding questions in modeling the dynamics of low collisionality accretion flows.

The Radiative Efficiency and Spectra of Slowly Accreting Black Holes from Two-temperature GRRMHD Simulations

The Radiative Efficiency and Spectra of Slowly Accreting Black Holes from Two-temperature GRRMHD Simulations

Ryan, Benjamin R.; Ressler, Sean M.; Dolence, Joshua C.; Tchekhovskoy, Alexander; Gammie, Charles; Quataert, Eliot

We present axisymmetric numerical simulations of radiatively inefficient accretion flows onto black holes combining general relativity, magnetohydrodynamics, self-consistent electron thermodynamics, and frequency-dependent radiation transport. We investigate a range of accretion rates up to {10}-5 {\dot{M}}{Edd} onto a {10}8 {M}⊙ black hole with spin {a}\star =0.5. We report on averaged flow thermodynamics as a function of accretion rate. We present the spectra of outgoing radiation and find that it varies strongly with accretion rate, from synchrotron-dominated in the radio at low \dot{M} to inverse-Compton-dominated at our highest \dot{M}. In contrast to canonical analytic models, we find that by \dot{M}≈ {10}-5 {\dot{M}}{Edd}, the flow approaches ˜ 1 % radiative efficiency, with much of the radiation due to inverse-Compton scattering off Coulomb-heated electrons far from the black hole. These results have broad implications for modeling of accreting black holes across a large fraction of the accretion rates realized in observed systems.

The disc-jet symbiosis emerges: modelling the emission of Sagittarius A* with electron thermodynamics

The disc-jet symbiosis emerges: modelling the emission of Sagittarius A* with electron thermodynamics

Ressler, S. M.; Tchekhovskoy, A.; Quataert, E.; Gammie, C. F.

We calculate the radiative properties of Sagittarius A* – spectral energy distribution, variability and radio-infrared images – using the first 3D, physically motivated black hole accretion models that directly evolve the electron thermodynamics in general relativistic MHD simulations. These models reproduce the coupled disc-jet structure for the emission favoured by previous phenomenological analytic and numerical works. More specifically, we find that the low frequency radio emission is dominated by emission from a polar outflow while the emission above 100 GHz is dominated by the inner region of the accretion disc. The latter produces time variable near-infrared (NIR) and X-ray emission, with frequent flaring events (including IR flares without corresponding X-ray flares and IR flares with weak X-ray flares). The photon ring is clearly visible at 230 GHz and 2 μm, which is encouraging for future horizon-scale observations. We also show that anisotropic electron thermal conduction along magnetic field lines has a negligible effect on the radiative properties of our model. We conclude by noting limitations of our current generation of first-principles models, particularly that the outflow is closer to adiabatic than isothermal and thus underpredicts the low frequency radio emission.

Resolution Dependence of Magnetorotational Turbulence in the Isothermal Stratified Shearing Box

Resolution Dependence of Magnetorotational Turbulence in the Isothermal Stratified Shearing Box

Ryan, Benjamin R.; Gammie, Charles F.; Fromang, Sebastien; Kestener, Pierre

Magnetohydrodynamic turbulence driven by the magnetorotational instability can provide diffusive transport of angular momentum in astrophysical disks, and a widely studied computational model for this process is the ideal, stratified, isothermal shearing box. Here we report results of a convergence study of such boxes up to a resolution of N = 256 zones per scale height, performed on blue waters at NCSA with ramses-gpu. We find that the time and vertically integrated dimensionless shear stress \overline{α }˜ {N}-1/3, i.e., the shear stress is resolution dependent. We also find that the magnetic field correlation length decreases with resolution, λ ˜ {N}-1/2. This variation is strongest at the disk midplane. We show that our measurements of \overline{α } are consistent with earlier studies, and we discuss possible reasons for the lack of convergence.

grim: A Flexible, Conservative Scheme for Relativistic Fluid Theories

grim: A Flexible, Conservative Scheme for Relativistic Fluid Theories

Chandra, M.; Foucart, F.; Gammie, C. F.

Hot, diffuse, relativistic plasmas such as sub-Eddington black hole accretion flows are expected to be collisionless, yet are commonly modeled as a fluid using ideal general relativistic magnetohydrodynamics (GRMHD). Dissipative effects such as heat conduction and viscosity can be important in a collisionless plasma and will potentially alter the dynamics and radiative properties of the flow from that in ideal fluid models; we refer to models that include these processes as Extended GRMHD. Here we describe a new conservative code, \grim, that enables all the above and additional physics to be efficiently incorporated. \grim~combines time evolution and primitive variable inversion needed for conservative schemes into a single step using an algorithm that only requires the residuals of the governing equations as inputs. This algorithm enables the code to be physics agnostic as well as flexibility regarding time-stepping schemes. \grim~runs on CPUs, as well as on GPUs, using the \emph{same} code. We formulate a performance model, and use it to show that our implementation runs optimally on both architectures. \grim~correctly captures classical GRMHD test problems as well as a new suite of linear and nonlinear test problems with anisotropic conduction and viscosity in special and general relativity.  As tests and example applications, we resolve the shock substructure due to the presence of dissipation, and report on relativistic versions of the magneto-thermal instability and heat flux driven buoyancy instability, which arise due to anisotropic heat conduction, and of the firehose instability, which occurs due to anisotropic pressure (i.e. viscosity). Finally, we show an example integration of an accretion flow around a Kerr black hole, using Extended GRMHD.

Large-Eddy Simulations of Magnetohydrodynamic Turbulence in Heliophysics and Astrophysics

Large-Eddy Simulations of Magnetohydrodynamic Turbulence in Heliophysics and Astrophysics

Miesch, Mark; Matthaeus, William; Brandenburg, Axel; Petrosyan, Arakel; Pouquet, Annick; Cambon, Claude; Jenko, Frank; Uzdensky, Dmitri; Stone, James; Tobias, Steve; Toomre, Juri; Velli, Marco

We live in an age in which high-performance computing is transforming the way we do science. Previously intractable problems are now becoming accessible by means of increasingly realistic numerical simulations. One of the most enduring and most challenging of these problems is turbulence. Yet, despite these advances, the extreme parameter regimes encountered in space physics and astrophysics (as in atmospheric and oceanic physics) still preclude direct numerical simulation. Numerical models must take a Large Eddy Simulation (LES) approach, explicitly computing only a fraction of the active dynamical scales. The success of such an approach hinges on how well the model can represent the subgrid-scales (SGS) that are not explicitly resolved. In addition to the parameter regime, heliophysical and astrophysical applications must also face an equally daunting challenge: magnetism. The presence of magnetic fields in a turbulent, electrically conducting fluid flow can dramatically alter the coupling between large and small scales, with potentially profound implications for LES/SGS modeling. In this review article, we summarize the state of the art in LES modeling of turbulent magnetohydrodynamic (MHD) flows. After discussing the nature of MHD turbulence and the small-scale processes that give rise to energy dissipation, plasma heating, and magnetic reconnection, we consider how these processes may best be captured within an LES/SGS framework. We then consider several specific applications in heliophysics and astrophysics, assessing triumphs, challenges, and future directions.

Iron Opacity Bump Changes the Stability and Structure of Accretion Disks in Active Galactic Nuclei

Iron Opacity Bump Changes the Stability and Structure of Accretion Disks in Active Galactic Nuclei

Jiang, Yan-Fei; Davis, Shane W.; Stone, James M.

Accretion disks around supermassive black holes have regions where the Rosseland mean opacity can be larger than the electron scattering opacity due to the large number of bound–bound transitions in iron. We study the effects of this iron opacity “bump” on the thermal stability and vertical structure of radiation-pressure-dominated accretion disks, utilizing three-dimensional radiation magnetohydrodynamic (MHD) simulations in the local shearing box approximation. The simulations self-consistently calculate the heating due to MHD turbulence caused by magneto-rotational instability and radiative cooling by using the radiative transfer module based on a variable Eddington tensor in Athena. For a 5 × 108 solar mass black hole with ˜3% of the Eddington luminosity, a model including the iron opacity bump maintains its structure for more than 10 thermal times without showing significant signs of thermal runaway. In contrast, if only electron scattering and free–free opacity are included as in the standard thin disk model, the disk collapses on the thermal timescale. The difference is caused by a combination of (1) an anti-correlation between the total optical depth and the midplane pressure, and (2) enhanced vertical advective energy transport. These results suggest that the iron opacity bump may have a strong impact on the stability and structure of active galactic nucleus (AGN) accretion disks, and may contribute to a dependence of AGN properties on metallicity. Since this opacity is relevant primarily in UV emitting regions of the flow, it may help to explain discrepancies between observation and theory that are unique to AGNs.

Magnetorotational Turbulence and Dynamo in a Collisionless Plasma

Magnetorotational Turbulence and Dynamo in a Collisionless Plasma

Kunz, Matthew W.; Stone, James M.; Quataert, Eliot

We present results from the first 3D kinetic numerical simulation of magnetorotational turbulence and dynamo, using the local shearing-box model of a collisionless accretion disc. The kinetic magnetorotational instability grows from a subthermal magnetic field having zero net flux over the computational domain to generate self-sustained turbulence and outward angular-momentum transport. Significant Maxwell and Reynolds stresses are accompanied by comparable viscous stresses produced by field-aligned ion pressure anisotropy, which is regulated primarily by the mirror and ion-cyclotron instabilities through particle trapping and pitch-angle scattering. The latter endow the plasma with an effective viscosity that is biased with respect to the magnetic-field direction and spatio-temporally variable. Energy spectra suggest an Alfv\’en-wave cascade at large scales and a kinetic-Alfv\’en-wave cascade at small scales, with strong small-scale density fluctuations and weak non-axisymmetric density waves. Ions undergo non-thermal particle acceleration, their distribution accurately described by a kappa distribution. These results have implications for the properties of low-collisionality accretion flows, such as that near the black hole at the Galactic center.

GRMHD in Athena++ Using Advanced Riemann Solvers and Staggered-Mesh Constrained Transport

GRMHD in Athena++ Using Advanced Riemann Solvers and Staggered-Mesh Constrained Transport

C. J. White, J. M. Stone, C. F. Gammie

We present a new general relativistic magnetohydrodynamics (GRMHD) code integrated into the Athena++ framework. Improving upon the techniques used in most GRMHD codes, ours allows the use of advanced, less diffusive Riemann solvers, in particular HLLC and HLLD. We also employ a staggered-mesh constrained transport algorithm suited for curvilinear coordinate systems in order to maintain the divergence-free constraint of the magnetic field. Our code is designed to work with arbitrary stationary spacetimes in one, two, or three dimensions, and we demonstrate its reliability through a number of tests. We also report on its promising performance and scalability.

Evolution of Accretion Discs around a Kerr Black Hole using Extended Magnetohydrodynamics

Evolution of Accretion Discs around a Kerr Black Hole using Extended Magnetohydrodynamics

F. Foucart, M. Chandra, C. F. Gammie, and E. Quataert

Black holes accreting well below the Eddington rate are believed to have geometrically thick, optically thin, rotationally supported accretion discs in which the Coulomb mean free path is large compared to $GM/c^2$. In such an environment, the disc evolution may differ significantly from ideal magnetohydrodynamic predictions. We present non-ideal global axisymmetric simulations of geometrically thick discs around a rotating black hole.  The simulations are carried out using a new code {\tt grim}, which evolves a covariant extended magnetohydrodynamics model derived by treating non-ideal effects as a perturbation of ideal magnetohydrodynamics. Non-ideal effects are modeled through heat conduction along magnetic field lines, and a difference between the pressure parallel and perpendicular to the field lines. The model relies on an effective collisionality in the disc from wave-particle scattering and velocity-space (mirror and firehose) instabilities. We find that the pressure anisotropy grows to match the magnetic pressure, at which point it saturates due to the mirror instability.  The pressure anisotropy produces outward angular momentum transport with a magnitude comparable to that of MHD turbulence in the disc, and a significant increase in the temperature in the wall of the jet.  We also find that, at least in our axisymmetric simulations, conduction has a small effect on the disc evolution because (1) the heat flux is constrained to be parallel to the field and the field is close to perpendicular to temperature gradients, and (2) the heat flux is choked by an increase in effective collisionality associated with the mirror instability.