Polarized Synchrotron Emissivities and Absorptivities for Relativistic Thermal, Power-Law, and Kappa Distribution Functions

A. Pandya, Z. Zhang, M. Chandra, and C. F. Gammie

Synchrotron emission and absorption determine the observational appearance of many astronomical systems.  In this paper, we describe a numerical scheme for calculating synchrotron emissivities and absorptivities in all four Stokes parameters for arbitrary gyrotropic electron distribution functions, building on earlier work by Leung, Gammie, and Noble.  We use this technique to evaluate the emissivities and the absorptivities for a  thermal (Maxwell-J\”uttner), isotropic power-law, and isotropic kappa distribution function.  The latter  contains a power-law tail at high particle energies that smoothly merges with a thermal core at low energies, as is characteristic of observed particle spectra in collisionless plasmas. We provide fitting formulae and error bounds on the fitting formulae for use in codes that solve the radiative transfer equation. The numerical method and the fitting formulae are implemented in a compact C library called {\tt symphony}.  We find that: the kappa distribution has a source function that is indistinguishable from a thermal spectrum at low frequencies and transitions to the characteristic self-absorbed synchrotron spectrum, $\propto \nu^{5/2}$, at high frequency; the linear polarization fraction for a thermal spectrum is near unity at high frequency; and all distributions produce O(10\%) circular polarization at low frequency for lines of sight sufficiently close to the magnetic field vector.

The grim code, an implicit-explicit code for general relativistic nonideal MHD, will be released here.  Please see this site for animations, a description of the algorithm, tests, and related material.

Electron Thermodynamics in GRMHD Simulations of Low-Luminosity Black Hole Accretion

Simple assumptions made regarding electron thermodynamics often limit the extent to which general relativistic magnetohydrodynamic (GRMHD) simulations can be applied to observations of low-luminosity accreting black holes. We present, implement, and test a model that self-consistently evolves an electron entropy equation and takes into account the effects of spatially varying electron heating and relativistic anisotropic thermal conduction along magnetic field lines. We neglect the back-reaction of electron pressure on the dynamics of the accretion flow. Our model is appropriate for systems accreting at $\ll 10^{-5}$ of the Eddington rate, so radiative cooling by electrons can be neglected. It can be extended to higher accretion rates in the future by including electron cooling and proton-electron Coulomb collisions. We present a suite of tests showing that our method recovers the correct solution for electron heating under a range of circumstances, including strong shocks and driven turbulence. Our initial applications to axisymmetric simulations of accreting black holes show that (1)~physically-motivated electron heating rates yield electron temperature distributions significantly different from the constant electron to proton temperature ratios assumed in previous work, with higher electron temperatures concentrated in the coronal region between the disc and the jet; (2)~electron thermal conduction significantly modifies the electron temperature in the inner regions of black hole accretion flows if the effective electron mean free path is larger than the local scale-height of the disc (at least for the initial conditions and magnetic field configurations we study). The methods developed in this work are important for producing more realistic predictions for the emission from accreting black holes such as Sagittarius A* and M87; these applications will be explored in future work.

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.