# Variability Timescale and Spectral Index of Sgr A* in the Near Infrared: Approximate Bayesian Computation Analysis of the Variability of the Closest Supermassive Black Hole

Variability Timescale and Spectral Index of Sgr A* in the Near Infrared: Approximate Bayesian Computation Analysis of the Variability of the Closest Supermassive Black Hole

G. Witzel et al.

Sagittarius A* (Sgr A*) is the variable radio, near-infrared (NIR), and X-ray source associated with accretion onto the Galactic center black hole. We present an analysis of the most comprehensive NIR variability data set of Sgr A* to date: eight 24 hr epochs of continuous monitoring of Sgr A* at 4.5 μm with the IRAC instrument on the Spitzer Space Telescope, 93 epochs of 2.18 μm data from Naos Conica at the Very Large Telescope, and 30 epochs of 2.12 μm data from the NIRC2 camera at the Keck Observatory, in total 94,929 measurements. A new approximate Bayesian computation method for fitting the first-order structure function extracts information beyond current fast Fourier transformation (FFT) methods of power spectral density (PSD) estimation. With a combined fit of the data of all three observatories, the characteristic coherence timescale of Sgr A* is {τ }b={243}-57+82 minutes (90% credible interval). The PSD has no detectable features on timescales down to 8.5 minutes (95% credible level), which is the ISCO orbital frequency for a dimensionless spin parameter a = 0.92. One light curve measured simultaneously at 2.12 and 4.5 μm during a low flux-density phase gave a spectral index α s = 1.6 ± 0.1 ({F}ν \propto {ν }-{α s}). This value implies that the Sgr A* NIR color becomes bluer during higher flux-density phases. The probability densities of flux densities of the combined data sets are best fit by log-normal distributions. Based on these distributions, the Sgr A* spectral energy distribution is consistent with synchrotron radiation from a non-thermal electron population from below 20 GHz through the NIR.

# IPOLE – semi-analytic scheme for relativistic polarized radiative transport

IPOLE – semi-analytic scheme for relativistic polarized radiative transport

M. Moscibrodzka and C. Gammie

We describe IPOLE, a new public ray-tracing code for covariant, polarized radiative transport. The code extends the IBOTHROS scheme for covariant, unpolarized transport using two representations of the polarized radiation field: In the coordinate frame, it parallel transports the coherency tensor; in the frame of the plasma it evolves the Stokes parameters under emission, absorption, and Faraday conversion. The transport step is implemented to be as spacetime- and coordinate- independent as possible. The emission, absorption, and Faraday conversion step is implemented using an analytic solution to the polarized transport equation with constant coefficients. As a result, IPOLE is stable, efficient, and produces a physically reasonable solution even for a step with high optical depth and Faraday depth. We show that the code matches analytic results in flat space, and that it produces results that converge to those produced by Dexter’s GRTRANS polarized transport code on a complicated model problem. We expect IPOLE will mainly find applications in modelling Event Horizon Telescope sources, but it may also be useful in other relativistic transport problems such as modelling for the IXPE mission.

# 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 disk. 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 spatiotemporally variable. Energy spectra suggest an Alfvén-wave cascade at large scales and a kinetic-Alfvén-wave cascade at small scales, with strong small-scale density fluctuations and weak nonaxisymmetric density waves. Ions undergo nonthermal particle acceleration, their distribution accurately described by a κ distribution. These results have implications for the properties of low-collisionality accretion flows, such as that near the black hole at the Galactic center.

# Extended general relativistic magnetohydrodynamics: Formulation and application to black hole accretion

Extended general relativistic magnetohydrodynamics: Formulation and application to black hole accretion

Morampudi, Manichandra

One of the long standing problems in accretion disk theory is that concerning black holes that accrete at a rate much lower than the Eddington rate. The plasma that constitutes the disk is in a regime where the Coulomb mean free path is much larger than the disk, and the collision time scales are larger than the inflow time. Thus, the plasma is collisionless and is subject to a wide range of kinetic phenomena that are absent from current general relativistic ideal magnetohydrodynamic models. We exploit the gyro ordering of a collisionless magnetized plasma, and use Israel-Stewart formalism to derive a theory, called Extended General Relativistic Magnetohydrodynamics (EMHD), that accounts for up to second order anisotropic dissipative effects. Using detailed linear analysis, we show that the model is conditionally hyperbolic, causal and stable, and does not suffer from pathologies inherent in first order dissipative theories in general relativity. The dissipation in this theory is driven by spatio-temporal gradients of thermodynamic variables. This cannot be handled by current numerical schemes, which have been designed for ideal fluids. To address this, we formulate an algorithm to handle arbitrary hyperbolic theories, and implement this into a new computer code. The code {\tt grim} will allow for an exploration of the solution space of a broad range of relativistic fluid theories that incorporate sophisticated microphysics. It is designed to run on various computer architectures, and to achieve a significant fraction of machine peak. It exhibits near perfect scaling upto 4096 CPU cores, and 256 GPUs. We use it to integrate the EMHD theory in a Kerr space-time of a supermassive black hole, and show that kinetic effects have an O(1)O(1) effect on the structure of an accretion disk. These effects may have observational consequences for Sgr A*, the supermassive black hole at the center of the Milky Way, whose horizon scale dynamics will be imaged by the upcoming Event Horizon Telescope.

# Development and application of numerical techniques for general-relativistic magnetohydrodynamics simulations of black hole accretion

Development and application of numerical techniques for general-relativistic magnetohydrodynamics simulations of black hole accretion

White, Christopher Joseph

We describe the implementation of sophisticated numerical techniques for general-relativistic magnetohydrodynamics simulations in the Athena++ code framework. Improvements over many existing codes include the use of advanced Riemann solvers and of staggered-mesh constrained transport. Combined with considerations for computational performance and parallel scalability, these allow us to investigate black hole accretion flows with unprecedented accuracy. The capability of the code is demonstrated by exploring magnetically arrested disks.

# Time Domain Filtering of Resolved Images of Sgr A*

Time Domain Filtering of Resolved Images of Sgr A*

Shiokawa, Hotaka; Gammie, Charles F.; Doeleman, Sheperd S.

The goal of the Event Horizon Telescope (EHT) is to provide spatially resolved images of Sgr A*, the source associated with the Galactic Center black hole. Because Sgr A* varies on timescales short compared to an EHT observing campaign, it is interesting to ask whether variability contains information about the structure and dynamics of the accretion flow. In this paper, we introduce “time-domain filtering”, a technique to filter time fluctuating images with specific temporal frequency ranges, and demonstrate the power and usage of the technique by applying it to mock millimeter wavelength images of Sgr A*. The mock image data is generated from General Relativistic Magnetohydrodynamic (GRMHD) simulation and general relativistic ray-tracing method. We show that the variability on each line of sight is tightly correlated with a typical radius of emission. This is because disk emissivity fluctuates on a timescale of order the local orbital period. Time-domain filtered images therefore reflect the model dependent emission radius distribution, which is not accessible in time-averaged images. We show that, in principle, filtered data have the power to distinguish between models with different black hole spins, different disk viewing angles, and different disk orientations in the sky.

# The impact of non-thermal electrons on event horizon scale images and spectra of Sgr A*

The impact of non-thermal electrons on event horizon scale images and spectra of Sgr A*

Mao, S. Alwin; Dexter, Jason; Quataert, Eliot

Decomposing an arbitrary electron energy distribution into sums of Maxwellian and power-law components is an efficient method to calculate synchrotron emission and absorption. We use this method to study the effect of non-thermal electrons on submillimetre images and spectra of the Galactic Centre black hole, Sgr A*. We assume a spatially uniform functional form for the electron distribution function and use a semi-analytic radiatively inefficient accretion flow and a 2D general relativistic magnetohydrodynamic snapshot as example models of the underlying accretion flow structure. We develop simple analytic models that allow us to generalize from the numerical examples. A high-energy electron component containing a small fraction (few per cent) of the total internal energy (e.g. a ‘power-law tail’) can produce a diffuse halo of emission, which modifies the observed image size and structure. A population of hot electrons with a larger energy fraction (e.g. resulting from a diffusion in electron energy space) can dominate the emission, so that the observed images and spectra are well approximated by considering only a single thermal component for a suitable choice of the electron temperature. We discuss the implications of these results for estimating accretion flow or black hole parameters from images and spectra, and for the identification of the black hole ‘shadow’ in future millimetre-very long baseline interferometry data. In particular, the location of the first minimum in visibility profiles does not necessarily correspond to the shadow size as sometimes assumed.

# Kinetic simulations of the interruption of large-amplitude shear-Alfv\’en waves in a high-beta plasma

Kinetic simulations of the interruption of large-amplitude shear-Alfv\’en waves in a high-beta plasma

Squire, J.; Kunz, M. W.; Quataert, E.; Schekochihin, A. A.

Using two-dimensional hybrid-kinetic simulations, we explore the nonlinear “interruption” of standing and traveling shear-Alfv\’en waves in collisionless plasmas. Interruption involves a self-generated pressure anisotropy removing the restoring force of a linearly polarized Alfv\’enic perturbation, and occurs for wave amplitudes $\delta B_{\perp}/B_{0}\gtrsim \beta^{\,-1/2}$ (where $\beta$ is the ratio of thermal to magnetic pressure). We use highly elongated domains to obtain maximal scale separation between the wave and the ion gyroscale. For standing waves above the amplitude limit, we find that the large-scale magnetic field of the wave decays rapidly. The dynamics are strongly affected by the excitation of oblique firehose modes, which transition into long-lived parallel fluctuations at the ion gyroscale and cause significant particle scattering. Traveling waves are damped more slowly, but are also influenced by small-scale parallel fluctuations created by the decay of firehose modes. Our results demonstrate that collisionless plasmas cannot support linearly polarized Alfv\’en waves above $\delta B_{\perp}/B_{0}\sim \beta^{\,-1/2}$. They also provide a vivid illustration of two key aspects of low-collisionality plasma dynamics: (i) the importance of velocity-space instabilities in regulating plasma dynamics at high $\beta$, and (ii) how nonlinear collisionless processes can transfer mechanical energy directly from the largest scales into thermal energy and microscale fluctuations, without the need for a scale-by-scale turbulent cascade.

# Amplitude limits and nonlinear damping of shear-Alfvén waves in high-beta low-collisionality plasmas

Amplitude limits and nonlinear damping of shear-Alfvén waves in high-beta low-collisionality plasmas

Squire, J.; Schekochihin, A. A.; Quataert, E.

This work, which extends Squire et al (Astrophys. J. Lett. 2016 830 L25), explores the effect of self-generated pressure anisotropy on linearly polarized shear-Alfvén fluctuations in low-collisionality plasmas. Such anisotropies lead to stringent limits on the amplitude of magnetic perturbations in high-β plasmas, above which a fluctuation can destabilize itself through the parallel firehose instability. This causes the wave frequency to approach zero, ‘interrupting’ the wave and stopping its oscillation. These effects are explored in detail in the collisionless and weakly collisional ‘Braginskii’ regime, for both standing and traveling waves. The focus is on simplified models in one dimension, on scales much larger than the ion gyroradius. The effect has interesting implications for the physics of magnetized turbulence in the high-β conditions that are prevalent in many astrophysical plasmas.

# 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.