Chi-kwan Chan

VISCOUS, RESISTIVE MAGNETOROTATIONAL MODES

We carry out a comprehensive analysis of the behavior of the magnetorotational instability (MRI) in viscous, resistive plasmas. We find exact, nonlinear solutions of the nonideal magnetohydrodynamic (MHD) equations describing the local dynamics of an incompressible, differentially rotating background threaded by a vertical magnetic field when disturbances with wavenumbers perpendicular to the shear are considered. We provide a geometrical description of these viscous, resistive MRI modes and show how their physical structure is modified as a function of the Reynolds and magnetic Reynolds numbers. We demonstrate that when finite dissipative effects are considered, velocity and magnetic field disturbances are no longer orthogonal (as is the case in the ideal MHD limit) unless the magnetic Prandtl number is unity. We generalize previous results found in the ideal limit and show that a series of key properties of the mean Reynolds and Maxwell stresses also hold for the viscous, resistive MRI. In particular, we show that the Reynolds stress is always positive and the Maxwell stress is always negative. Therefore, even in the presence of viscosity and resistivity, the total mean angular momentum transport is always directed outward. We also find that, for any combination of the Reynolds and magnetic Reynolds numbers, magnetic disturbances dominate both the energetics and the transport of angular momentum and that the total mean energy density is an upper bound for the total mean stress responsible for angular momentum transport. The ratios between the Maxwell and Reynolds stresses and between magnetic and kinetic energy densities increase with decreasing Reynolds numbers for any magnetic Reynolds number; the lowest limit of both ratios is reached in the ideal MHD regime. The analytical results presented here provide new benchmarks for the various algorithms employed to solve the viscous, resistive MHD equations in the shearing box approximation.

PERSISTENT ASYMMETRIC STRUCTURE OF SAGITTARIUS A* ON EVENT HORIZON SCALES

The Galactic Center black hole Sagittarius A* (Sgr A*) is a prime observing target for the Event Horizon Telescope (EHT), which can resolve the 1.3 mm emission from this source on angular scales comparable to that of the general relativistic shadow. Previous EHT observations have used visibility amplitudes to infer the morphology of the millimeter-wavelength emission. Potentially much richer source information is contained in the phases. We report on 1.3 mm phase information on Sgr A* obtained with the EHT on a total of 13 observing nights over 4 years. Closure phases, the sum of visibility phases along a closed triangle of interferometer baselines, are used because they are robust against phase corruptions introduced by instrumentation and the rapidly variable atmosphere. The median closure phase on a triangle including telescopes in California, Hawaii, and Arizona is nonzero. This result conclusively demonstrates that the millimeter emission is asymmetric on scales of a few Schwarzschild radii and can be used to break 180-degree rotational ambiguities inherent from amplitude data alone. The stability of the sign of the closure phase over most observing nights indicates persistent asymmetry in the image of Sgr A* that is not obscured by refraction due to interstellar electrons along the line of sight.

FAST VARIABILITY AND MILLIMETER/IR FLARES IN GRMHD MODELS OF Sgr A* FROM STRONG-FIELD GRAVITATIONAL LENSING

We explore the variability properties of long, high cadence GRMHD simulations across the electromagnetic spectrum using an efficient, GPU-based radiative transfer algorithm. We focus on both disk- and jet-dominated simulations with parameters that successfully reproduce the time-averaged spectral properties of Sgr A ∗ and the size of its image at 1.3mm. We find that the disk-dominated models produce short timescale variability with amplitudes and power spectra that closely resemble those inferred observationally. In contrast, jet-dominated models generate only slow variability, at lower flux levels. Neither set of models show any X-ray flares, which most likely indicate that additional physics, such as particle acceleration mechanisms, need to be incorporated into the GRMHD simulations to account for them. The disk-dominated models show strong, short-lived mm/IR flares, with short (. 1hr) time lags between the mm and IR wavelengths, that arise from strong-field gravitational lensing of magnetic flux tubes near the horizon. Such events provide a natural explanation for the observed IR flares with no X-ray counterparts. Subject headings: accretion, accretion disks — black hole physics — Galaxy: center — radiative transfer

ON HYDROMAGNETIC STRESSES IN ACCRETION DISK BOUNDARY LAYERS

Detailed calculations of the physical structure of accretion disk boundary layers, and thus their inferred observational properties, rely on the assumption that angular momentum transport is opposite to the radial angular frequency gradient of the disk. The standard model for turbulent shear viscosity satisfies this assumption by construction. However, this behavior is not supported by numerical simulations of turbulent magnetohydrodynamic (MHD) accretion disks, which show that angular momentum transport driven by the magnetorotational instability (MRI) is inefficient in disk regions where, as expected in boundary layers, the angular frequency increases with radius. In order to shed light on physically viable mechanisms for angular momentum transport in this inner disk region, we examine the generation of hydromagnetic stresses and energy density in differentially rotating backgrounds with angular frequencies that increase outward in the shearing-sheet framework. We isolate the modes that are unrelated to the standard MRI and provide analytic solutions for the long-term evolution of the resulting shearing MHD waves. We show that, although the energy density of these waves can be amplified significantly, their associated stresses oscillate around zero, rendering them an inefficient mechanism to transport significant angular momentum (inward). These findings are consistent with the results obtained in numerical simulations of MHD accretion disk boundary layers and challenge the standard assumption of efficient angular momentum transport in the inner disk regions. This suggests that the detailed structure of turbulent MHD accretion disk boundary layers could differ appreciably from those derived within the standard framework of turbulent shear viscosity

GRMHD Simulations of Visibility Amplitude Variability for Event Horizon Telescope Images of Sgr A

Synthesis imaging of the black hole in the center of the Milky Way, Sgr A*, with the Event Horizon Telescope (EHT) rests on the assumption of a stationary image. We explore the limitations of this assumption using high-cadence GRMHD simulations of Sgr A*. We employ analytic models that capture the basic characteristics of the images to understand the origin of the variability in the simulated visibility amplitudes. We find that, in all simulations, the visibility amplitudes for baselines oriented perpendicular to the spin axis of the black hole typically decrease smoothly over baseline lengths that are comparable to those of the EHT. On the other hand, the visibility amplitudes for baselines oriented parallel to the spin axis show significant structure with one or more minima. This suggests that fitting EHT observations with geometric models will lead to reasonably accurate determination of the orientation of the black-hole on the plane of the sky. However, in the disk-dominated models, the locations and depths of the minima in the visibility amplitudes depend primarily on the width and asymmetry of the crescent-like images and are highly variable. In the jet-dominated models, the locations of the minima are determined by the separation of the two image components but their depths depend primarily on the relative brightness of the two components and are also variable. This suggests that using time-independent models to infer additional black-hole parameters, such as the shadow size or the spin magnitude, will be severely affected by the variability of the accretion flow.

OSCILLATIONS OF THE INNER REGIONS OF VISCOUS ACCRETION DISKS

Although quasi-periodic oscillations (QPOs) have been discovered in different X-ray sources, their origin is still a matter of debate. Analytical studies of hydrodynamic accretion disks have shown three types of trapped global modes with properties that appear to agree with the observations. However, these studies take only the linear effects into account. Moreover, observations suggest that resonances between modes play a crucial role. A systematic, numerical study of this problem is therefore needed. In this paper, we use a pseudo-spectral algorithm to perform a parameter study of the inner regions of hydrodynamic disks. By assuming α-viscosity, we show that steady state solutions rarely exist. The inner edges of the disks oscillate and excite axisymmetric waves, which provide a plausible explanation for the high-frequency QPOs observed from accreting black holes. In addition, the flows inside the inner edges are sometimes unstable to non-axisymmetric perturbations. One-armed, or even two-armed, spirals are developed. When the Reynolds numbers are above certain critical values, the inner disks go through some transient turbulent states characterized by strong trailing spirals; while large-scale leading spirals are developed in the outer disks. We compared our numerical results with standard thin disk oscillation models. Albeit the non-axisymmetric features have their analytical counterparts, more careful study is needed to explain the axisymmetric oscillations.

Variability in GRMHD Simulations of Sgr A* : Implications for EHT Closure Phase Observations

NSF GRFP [DGE 1144085]; NASA/NSF TCAN [NNX14AB48G]; NSF [TM6-17006X, AST 1312034, AST-1207752, 1228509]; John Simon Guggenheim Memorial Foundation; Radcliffe Institute for Advanced Study at Harvard University

A Class of Physically Motivated Closures for Radiation Hydrodynamics

Radiative transfer and radiation hydrodynamics use the relativistic Boltzmann equation to describe the kinetics of photons. It is difficult to solve the six-dimensional time-dependent transfer equation unless the problem is highly symmetric or in equilibrium. When the radiation field is smooth, it is natural to take angular moments of the transfer equation to reduce the degrees of freedom. However, low order moment equations contain terms that depend on higher order moments. To close the system of moment equations, approximations are made to truncate this hierarchy. Popular closures used in astrophysics include flux-limited diffusion and the M 1 closure, which are rather ad hoc and do not necessarily capture the correct physics. In this paper, we propose a new class of closures for radiative transfer and radiation hydrodynamics. We start from a different perspective and highlight the consistency of a fully relativistic formalism. We present a generic framework to approximate radiative transfer based on relativistic Grads moment method. We then derive a 14-field method that minimizes unphysical photon self-interaction.

On magnetohydrodynamic turbulence and angular momentum transport in accretion disk boundary layers

The physical modeling of the accretion disk boundary layer, the region where the disk meets the surface of the accreting star, usually relies on the assumption that angular momentum transport is opposite to the radial angular frequency gradient of the disk. The standard model for turbulent shear viscosity, widely adopted in astrophysics, satisfies this assumption by construction. However, this behavior is not supported by numerical simulations of turbulent magnetohydrodynamic (MHD) accretion disks, which show that angular momentum transport driven by the magnetorotational instability is inefficient in this inner disk region. I will discuss the results of a recent study on the generation of hydromagnetic stresses and energy density in the boundary layer around a weakly magnetized star. Our findings suggest that although magnetic energy density can be significantly amplified in this region, angular momentum transport is rather inefficient. This seems consistent with the results obtained in numerical simulations and suggests that the detailed structure of turbulent MHD boundary layers could differ appreciably from those derived within the standard framework of turbulent shear viscosity.