An Extended Magnetohydrodynamics Model for Relativistic Weakly Collisional Plasmas
Mani Chandra, Charles F. Gammie, Francois Foucart, Eliot Quataert
Black holes that accrete far below the Eddington limit are believed to accrete through a geometrically thick, optically thin, rotationally supported plasma that we will refer to as a radiatively inefficient accretion flow (RIAF). RIAFs are typically collisionless in the sense that the Coulomb mean free path is large compared to $GM/c^2$, and relativistically hot near the event horizon. In this paper we develop a phenomenological model for the plasma in RIAFs, motivated by the application to sources such as Sgr A* and M87. The model is derived using Israel-Stewart theory, which considers deviations up to second order from thermal equilibrium, but modified for a magnetized plasma. This leads to thermal conduction along magnetic field lines and a difference in pressure, parallel and perpendicular to the field lines (which is equivalent to anisotrotropic viscosity). In the non-relativistic limit, our model reduces to the widely used Braginskii theory of magnetized, weakly collisional plasmas. We compare our model to the existing literature on dissipative relativistic fluids, describe the linear theory of the plasma, and elucidate the physical meaning of the free parameters in the model. We also describe limits of the model when the conduction is saturated and when the viscosity implies a large pressure anisotropy. In future work, the formalism developed in this paper will be used in numerical models of RIAFs to assess the importance of non-ideal processes for the dynamics and radiative properties of slowly accreting black holes.
The Effect of Anisotropic Viscosity on Cold Fronts in Galaxy Clusters
ZuHone, J. A.; Kunz, M. W.; Markevitch, M.; Stone, J. M.; Biffi, V.
Cold fronts—contact discontinuities in the intracluster medium (ICM) of galaxy clusters—should be disrupted by Kelvin-Helmholtz (K-H) instabilities due to the associated shear velocity. However, many observed cold fronts appear stable. This opens the possibility of placing constraints on microphysical mechanisms that stabilize them, such as the ICM viscosity and/or magnetic fields. We performed exploratory high-resolution simulations of cold fronts arising from subsonic gas sloshing in cluster cores using the grid-based Athena MHD code, comparing the effects of isotropic Spitzer and anisotropic Braginskii viscosity (expected in a magnetized plasma). Magnetized simulations with full Braginskii viscosity or isotropic Spitzer viscosity reduced by a factor f ~ 0.1 are both in qualitative agreement with observations in terms of suppressing K-H instabilities. The rms velocity of turbulence within the sloshing region is only modestly reduced by Braginskii viscosity. We also performed unmagnetized simulations with and without viscosity and find that magnetic fields have a substantial effect on the appearance of the cold fronts, even if the initial field is weak and the viscosity is the same. This suggests that determining the dominant suppression mechanism of a given cold front from X-ray observations (e.g., viscosity or magnetic fields) by comparison with simulations is not straightforward. Finally, we performed simulations including anisotropic thermal conduction, and find that including Braginskii viscosity in these simulations does not significantly affect the evolution of cold fronts; they are rapidly smeared out by thermal conduction, as in the inviscid case.
Radiation Feedback in ULIRGs: Are Photons Movers and Shakers?
Davis, Shane W.; Jiang, Yan-Fei; Stone, James M.; Murray, Norman
We perform multidimensional radiation hydrodynamics simulations to study the impact of radiation forces on atmospheres composed of dust and gas. Our setup closely follows that of Krumholz & Thompson, assuming that dust and gas are well-coupled and that the radiation field is characterized by blackbodies with temperatures >~ 80 K, as might be found in ultraluminous infrared galaxies (ULIRGs). In agreement with previous work, we find that Rayleigh-Taylor instabilities develop in radiation supported atmospheres, leading to inhomogeneities that limit momentum exchange between radiation and dusty gas, and eventually providing a near balance of the radiation and gravitational forces. However, the evolution of the velocity and spatial distributions of the gas differs significantly from previous work, which utilized a less accurate flux-limited diffusion (FLD) method. Our variable Eddington tensor simulations show continuous net acceleration of the gas and never reach a steady state. In contrast, our FLD results show little net acceleration of the gas and settle into a quasi-steady, turbulent state with low velocity dispersion. The discrepancies result primarily from the inability of FLD to properly model the variation of the radiation field around structures that are less than a few optical depths across. We consider the effect of varying the optical depth and study the differences between two-dimensional and three-dimensional runs. We conclude that radiation feedback remains a plausible mechanism for driving high-Mach number turbulence in ULIRGs with sufficiently high optical depths. We discuss implications for observed systems and galactic-scale numerical simulations of feedback.
A Global Three-dimensional Radiation Magneto-hydrodynamic Simulation of Super-Eddington Accretion Disks
Jiang, Yan-Fei; Stone, James M.; Davis, Shane W.
We study super-Eddington accretion flows onto black holes using a global three-dimensional radiation magneto-hydrodynamical simulation. We solve the time-dependent radiative transfer equation for the specific intensities to accurately calculate the angular distribution of the emitted radiation. Turbulence generated by the magneto-rotational instability provides self-consistent angular momentum transfer. The simulation reaches inflow equilibrium with an accretion rate ~220 L Edd/c 2 and forms a radiation-driven outflow along the rotation axis. The mechanical energy flux carried by the outflow is ~20% of the radiative energy flux. The total mass flux lost in the outflow is about 29% of the net accretion rate. The radiative luminosity of this flow is ~10 L Edd. This yields a radiative efficiency ~4.5%, which is comparable to the value in a standard thin disk model. In our simulation, vertical advection of radiation caused by magnetic buoyancy transports energy faster than photon diffusion, allowing a significant fraction of the photons to escape from the surface of the disk before being advected into the black hole. We contrast our results with the lower radiative efficiencies inferred in most models, such as the slim disk model, which neglect vertical advection. Our inferred radiative efficiencies also exceed published results from previous global numerical simulations, which did not attribute a significant role to vertical advection. We briefly discuss the implications for the growth of supermassive black holes in the early universe and describe how these results provided a basis for explaining the spectrum and population statistics of ultraluminous X-ray sources.
Observational appearance of inefficient accretion flows and jets in 3D GRMHD simulations: Application to Sagittarius A*
Mościbrodzka, Monika; Falcke, Heino; Shiokawa, Hotaka; Gammie, Charles F.
Context. Radiatively inefficient accretion flows (RIAFs) are believed to power supermassive black holes in the underluminous cores of galaxies. Such black holes are typically accompanied by flat-spectrum radio cores indicating the presence of moderately relativistic jets. One of the best constrained RIAFs is associated with the supermassive black hole in the Galactic center, Sgr A*.
Aims: Since the plasma in RIAFs is only weakly collisional, the dynamics and the radiative properties of these systems are very uncertain. Here we want to study the impact of varying electron temperature on the appearance of accretion flows and jets.
Methods: Using three-dimensional general relativistic magnetohydrodynamics accretion flow simulations, we use ray tracing methods to predict spectra and radio images of RIAFs allowing for different electron heating mechanisms in the in- and outflowing parts of the simulations.
Results: We find that small changes in the electron temperature can result in dramatic differences in the relative dominance of jets and accretion flows. Application to Sgr A* shows that radio spectrum and size of this source can be well reproduced with a model where electrons are more efficiently heated in the jet. The X-ray emission is sensitive to the electron heating mechanism in the jets and disk and therefore X-ray observations put strong constraints on electron temperatures and geometry of the accretion flow and jet. For Sgr A*, the jet model also predicts a significant frequency-dependent core shift which could place independent constraints on the model once measured accurately.
Conclusions: We conclude that more sophisticated models for electron distribution functions are crucial for constraining GRMHD simulations with actual observations. For Sgr A*, the radio appearance may well be dominated by the outflowing plasma. Nonetheless, at the highest radio frequencies, the shadow of the event horizon should still be detectable with future Very Long Baseline Interferometric observations.
bhlight: General Relativistic Radiation Magnetohydrodynamics with Monte Carlo Transport
Ryan, Benjamin R.; Dolence, Joshua C.; Gammie, Charles F.
We present bhlight, a numerical scheme for solving the equations of general relativistic radiation magnetohydrodynamics (GRRMHD) using a direct Monte Carlo solution of the frequency-dependent radiative transport equation. bhlight is designed to evolve black hole accretion flows at intermediate accretion rate, in the regime between the classical radiatively efficient disk and the radiatively inefficient accretion flow (RIAF), in which global radiative effects play a sub-dominant but non-negligible role in disk dynamics. We describe the governing equations, numerical method, idiosyncrasies of our implementation, and a suite of test and convergence results. We also describe example applications to radiative Bondi accretion and to a slowly accreting Kerr black hole in axisymmetry.
The Effects of Irradiation on Cloud Evolution in Active Galactic Nuclei
Proga, Daniel; Jiang, Yan-Fei; Davis, Shane W.; Stone, James M.; Smith, Daniel
We report on the first phase of a study of cloud irradiation. We study irradiation by means of numerical, two-dimensional, time-dependent radiation hydrodynamic simulations of a strongly irradiated cloud. We adopt a very simple treatment of the opacity, neglect photoionization and gravity, and focus instead on assessing the role of the type and magnitude of the opacity on the cloud evolution. Our main result is that even relatively dense clouds that are radiatively heated (i.e., with significant absorption opacity) do not move as a whole; instead, they undergo very rapid and major evolution in shape, size, and physical properties. In particular, the cloud and its remnants become optically thin in less than 1 sound-crossing time and before they can travel a significant distance (a few initial-cloud radii). We also find that a cloud can be accelerated as a whole under quite extreme conditions, i.e., the opacity must be dominated by scattering. However, the acceleration due to the radiation force is relatively small, and unless the cloud is optically thin, it quickly undergoes changes in size and shape. We discuss implications for the modeling and interpretation of the broad-line regions of active galactic nuclei.
Firehose and Mirror Instabilities in a Collisionless Shearing Plasma
Kunz, Matthew W.; Schekochihin, Alexander A.; Stone, James M.
Hybrid-kinetic numerical simulations of firehose and mirror instabilities in a collisionless plasma are performed in which pressure anisotropy is driven as the magnetic field is changed by a persistent linear shear S. For a decreasing field, it is found that mostly oblique firehose fluctuations grow at ion Larmor scales and saturate with energies ∝S1/2; the pressure anisotropy is pinned at the stability threshold by particle scattering off microscale fluctuations. In contrast, nonlinear mirror fluctuations are large compared to the ion Larmor scale and grow secularly in time; marginality is maintained by an increasing population of resonant particles trapped in magnetic mirrors. After one shear time, saturated order-unity magnetic mirrors are formed and particles scatter off their sharp edges. Both instabilities drive sub-ion-Larmor-scale fluctuations, which appear to be kinetic-Alfvén-wave turbulence. Our results impact theories of momentum and heat transport in astrophysical and space plasmas, in which the stretching of a magnetic field by shear is a generic process.
Radiation Magnetohydrodynamic Simulations of the Formation of Hot Accretion Disk Coronae
Jiang, Yan-Fei; Stone, James M.; Davis, Shane W.
A new mechanism to form a magnetic pressure supported, high temperature corona above the photosphere of an accretion disk is explored using three dimensional radiation magnetohydrodynamic (MHD) simulations. The thermal properties of the disk are calculated self-consistently by balancing radiative cooling through the surfaces of the disk with heating due to dissipation of turbulence driven by magneto-rotational instability (MRI). As has been noted in previous work, we find the dissipation rate per unit mass increases dramatically with height above the mid-plane, in stark contrast to the α-disk model which assumes this quantity is a constant. Thus, we find that in simulations with a low surface density (and therefore a shallow photosphere), the fraction of energy dissipated above the photosphere is significant (about 3.4% in our lowest surface density model), and this fraction increases as surface density decreases. When a significant fraction of the accretion energy is dissipated in the optically thin photosphere, the gas temperature increases substantially and a high temperature, magnetic pressure supported corona is formed. The volume-averaged temperature in the disk corona is more than 10 times larger than at the disk mid-plane. Moreover, gas temperature in the corona is strongly anti-correlated with gas density, which implies the corona formed by MRI turbulence is patchy. This mechanism to form an accretion disk corona may help explain the observed relation between the spectral index and luminosity from active galactic nucleus (AGNs), and the soft X-ray excess from some AGNs. It may also be relevant to spectral state changes in X-ray binaries.
An Algorithm for Radiation Magnetohydrodynamics Based on Solving the Time-dependent Transfer Equation
Jiang, Yan-Fei; Stone, James M.; Davis, Shane W.
We describe a new algorithm for solving the coupled frequency-integrated transfer equation and the equations of magnetohydrodynamics in the regime that light-crossing time is only marginally shorter than dynamical timescales. The transfer equation is solved in the mixed frame, including velocity-dependent source terms accurate to O(v/c). An operator split approach is used to compute the specific intensity along discrete rays, with upwind monotonic interpolation used along each ray to update the transport terms, and implicit methods used to compute the scattering and absorption source terms. Conservative differencing is used for the transport terms, which ensures the specific intensity (as well as energy and momentum) are conserved along each ray to round-off error. The use of implicit methods for the source terms ensures the method is stable even if the source terms are very stiff. To couple the solution of the transfer equation to the MHD algorithms in the ATHENA code, we perform direct quadrature of the specific intensity over angles to compute the energy and momentum source terms. We present the results of a variety of tests of the method, such as calculating the structure of a non-LTE atmosphere, an advective diffusion test, linear wave convergence tests, and the well-known shadow test. We use new semi-analytic solutions for radiation modified shocks to demonstrate the ability of our algorithm to capture the effects of an anisotropic radiation field accurately. Since the method uses explicit differencing of the spatial operators, it shows excellent weak scaling on parallel computers.