Stability of two-dimensional forced Navier-Stokes flow on a bounded circular domain

This research is concerned with the stability of a two-dimensional, electromagnetically forced, zonal flow on a circular domain. Flows like these are found in nature (e.g. shear flow in the atmosphere, Jovian disk) and experiment (e.g. plasma flow in a Fusion reactor) and a requirement for experiments is often that these types of flows remain stable and axi-symmetric. A numerical method is developed based on a spectral expansion into an infinite system of ordinary differential equations for velocity functions resulting from a Stokes eigenvalue problem. The system is truncated to gain a finite-dimensional system which is useful for computations of both equilibrium flows and strongly disturbed flows. Numerical results are compared to both finite difference method results and analytical results for the equilibrium basic flow. Both linear and nonlinear stability are explored for the Navier-Stokes equations on the circular domain and for the system of ordinary differential equations. Differences in stability and the evolution of perturbations are explained on the basis of discrepancies between infinite-dimensional partial differential equations like the Navier-Stokes equations and a finite-dimensional system of ordinary differential equations resulting from a Galerkin truncation. On the basis of both stability analyses a control system is developed which stabilizes the system of ordinary differential equations to stay in a desired equilibrium. It is argued that this control system is also usable for the control of the Navier-Stokes equations. This research is concerned with the stability of a two-dimensional, electromagnetically forced, zonal flow on a circular domain. Flows like these are found in nature (e.g. shear flow in the atmosphere, Jovian disk) and experiment (e.g. plasma flow in a Fusion reactor) and a requirement for experiments is often that these types of flows remain stable and axi-symmetric. A numerical method is developed based on a spectral expansion into an infinite system of ordinary differential equations for velocity functions resulting from a Stokes eigenvalue problem. The system is truncated to gain a finite-dimensional system which is useful for computations of both equilibrium flows and strongly disturbed flows. Numerical results are compared to both finite difference method results and analytical results for the equilibrium basic flow. Both linear and nonlinear stability are explored for the Navier-Stokes equations on the circular domain and for the system of ordinary differential equations. Differences in stability and the evolution of perturbations are explained on the basis of discrepancies between infinite-dimensional partial differential equations like the Navier-Stokes equations and a finite-dimensional system of ordinary differential equations resulting from a Galerkin truncation. On the basis of both stability analyses a control system is developed which stabilizes the system of ordinary differential equations to stay in a desired equilibrium. It is argued that this control system is also usable for the control of the Navier-Stokes equations

Plasmoid Instability in the Multiphase Interstellar Medium

The processes controlling the complex clump structure, phase distribution, and magnetic field geometry that develops across a broad range of scales in the turbulent interstellar medium remains unclear. Using unprecedentedly high resolution three-dimensional magnetohydrodynamic simulations of thermally unstable turbulent systems, we show that large current sheets unstable to plasmoid-mediated reconnection form regularly throughout the volume. The plasmoids form in three distinct environments: (i) within cold clumps, (ii) at the asymmetric interface of the cold and warm phases, and (iii) within the warm, volume-filling phase. We then show that the complex magneto-thermal phase structure is characterized by a predominantly highly magnetized cold phase, but that regions of high magnetic curvature, which are the sites of reconnection, span a broad range in temperature. Furthermore, we show that thermal instabilities change the scale dependent anisotropy of the turbulent magnetic field, reducing the increase in eddy elongation at smaller scales. Finally, we show that most of the mass is contained in one contiguous cold structure surrounded by smaller clumps that follow a scale free mass distribution. These clumps tend to be highly elongated and exhibit a size versus internal velocity relation consistent with supersonic turbulence, and a relative clump distance-velocity scaling consistent with subsonic motion. We discuss the striking similarity of cold plasmoids to observed tiny scale atomic and ionized structures and HI fibers, and consider how the prevalence of plasmoids will modify the motion of charged particles thereby impacting cosmic ray transport and thermal conduction in the ISM and other similar systems.Comment: 19 pages, 10 figures. For associated movies, see https://dfielding14.github.io/movies

Three-dimensional dynamics of strongly twisted magnetar magnetospheres: Kinking flux tubes and global eruptions

The origin of the various outbursts of hard X-rays from magnetars, highly magnetized neutron stars, is still unknown. We identify instabilities in relativistic magnetospheres that can explain a range of X-ray flare luminosities. Crustal surface motions can twist the magnetar magnetosphere by shifting the frozen-in footpoints of magnetic field lines in current-carrying flux bundles. Axisymmetric (2D) magnetospheres exhibit strong eruptive dynamics, as to say, catastrophic lateral instabilities triggered by a critical footpoint displacement of $\psi_{\rm crit}\gtrsim\pi$. In contrast, our new three-dimensional (3D) twist models with finite surface extension capture important non-axisymmetric dynamics of twisted force-free flux bundles in dipolar magnetospheres. Besides the well-established global eruption resulting (as in 2D) from lateral instabilities, such 3D structures can develop helical, kink-like dynamics, and dissipate energy locally (confined eruptions). Up to $25\%$ of the induced twist energy is dissipated and available to power X-ray flares in powerful global eruptions, with most of our models showing an energy release in the range of the most common X-ray outbursts, $\lesssim 10^{43}$erg. Such events occur when significant energy builds up deeply buried in the dipole magnetosphere. Less energetic outbursts likely precede powerful flares due to intermittent instabilities and confined eruptions of a continuously twisting flux tube. Upon reaching a critical state, global eruptions produce the necessary Poynting-flux-dominated outflows required by models prescribing the fast radio burst production in the magnetar wind, for example, via relativistic magnetic reconnection or shocks.Comment: 21 pages, 11 figures, submitted to ApJ

Black Hole Flares: Ejection of Accreted Magnetic Flux through 3D Plasmoid-mediated Reconnection

Magnetic reconnection can power bright, rapid flares originating from the inner magnetosphere of accreting black holes. We conduct extremely high-resolution (5376 × 2304 × 2304 cells) general-relativistic magnetohydrodynamics simulations, capturing plasmoid-mediated reconnection in a 3D magnetically arrested disk for the first time. We show that an equatorial, plasmoid-unstable current sheet forms in a transient, nonaxisymmetric, low-density magnetosphere within the inner few Schwarzschild radii. Magnetic flux bundles escape from the event horizon through reconnection at the universal plasmoid-mediated rate in this current sheet. The reconnection feeds on the highly magnetized plasma in the jets and heats the plasma that ends up trapped in flux bundles to temperatures proportional to the jet's magnetization. The escaped flux bundles can complete a full orbit as low-density hot spots, consistent with Sgr A* observations by the GRAVITY interferometer. Reconnection near the horizon produces sufficiently energetic plasma to explain flares from accreting black holes, such as the TeV emission observed from M87. The drop in the mass accretion rate during the flare and the resulting low-density magnetosphere make it easier for very-high-energy photons produced by reconnection-accelerated particles to escape. The extreme-resolution results in a converged plasmoid-mediated reconnection rate that directly determines the timescales and properties of the flare

General-relativistic Resistive Magnetohydrodynamics with Robust Primitive-variable Recovery for Accretion Disk Simulations

Recent advances in black hole astrophysics, particularly the first visual evidence of a supermassive black hole at the center of the galaxy M87 by the Event Horizon Telescope, and the detection of an orbiting "hot spot" nearby the event horizon of Sgr A* in the Galactic center by the Gravity Collaboration, require the development of novel numerical methods to understand the underlying plasma microphysics. Non-thermal emission related to such hot spots is conjectured to originate from plasmoids that form due to magnetic reconnection in thin current layers in the innermost accretion zone. Resistivity plays a crucial role in current sheet formation, magnetic reconnection, and plasmoid growth in black hole accretion disks and jets. We included resistivity in the three-dimensional general-relativistic magnetohydrodynamics (GRMHD) code BHAC and present the implementation of an implicit–explicit scheme to treat the stiff resistive source terms of the GRMHD equations. The algorithm is tested in combination with adaptive mesh refinement to resolve the resistive scales and a constrained transport method to keep the magnetic field solenoidal. Several novel methods for primitive-variable recovery, a key part in relativistic magnetohydrodynamics codes, are presented and compared for accuracy, robustness, and efficiency. We propose a new inversion strategy that allows for resistive-GRMHD simulations of low gas-to-magnetic pressure ratio and highly magnetized regimes as applicable for black hole accretion disks, jets, and neutron-star magnetospheres. We apply the new scheme to study the effect of resistivity on accreting black holes, accounting for dissipative effects as reconnection

SYMBA: An end-to-end VLBI synthetic data generation pipeline. Simulating Event Horizon Telescope observations of M 87

Context. Realistic synthetic observations of theoretical source models are essential for our understanding of real observational data. In using synthetic data, one can verify the extent to which source parameters can be recovered and evaluate how various data corruption effects can be calibrated. These studies are the most important when proposing observations of new sources, in the characterization of the capabilities of new or upgraded instruments, and when verifying model-based theoretical predictions in a direct comparison with observational data. Aims. We present the SYnthetic Measurement creator for long Baseline Arrays (SYMBA), a novel synthetic data generation pipeline for Very Long Baseline Interferometry (VLBI) observations. SYMBA takes into account several realistic atmospheric, instrumental, and calibration effects. Methods. We used SYMBA to create synthetic observations for the Event Horizon Telescope (EHT), a millimetre VLBI array, which has recently captured the first image of a black hole shadow. After testing SYMBA with simple source and corruption models, we study the importance of including all corruption and calibration effects, compared to the addition of thermal noise only. Using synthetic data based on two example general relativistic magnetohydrodynamics (GRMHD) model images of M 87, we performed case studies to assess the image quality that can be obtained with the current and future EHT array for different weather conditions. Results. Our synthetic observations show that the effects of atmospheric and instrumental corruptions on the measured visibilities are significant. Despite these effects, we demonstrate how the overall structure of our GRMHD source models can be recovered robustly with the EHT2017 array after performing calibration steps, which include fringe fitting, a priori amplitude and network calibration, and self-calibration. With the planned addition of new stations to the EHT array in the coming years, images could be reconstructed with higher angular resolution and dynamic range. In our case study, these improvements allowed for a distinction between a thermal and a non-thermal GRMHD model based on salient features in reconstructed images

First M87 Event Horizon Telescope Results. III. Data Processing and Calibration

We present the calibration and reduction of Event Horizon Telescope (EHT) 1.3 mm radio wavelength observations of the supermassive black hole candidate at the center of the radio galaxy M87 and the quasar 3C 279, taken during the 2017 April 5-11 observing campaign. These global very long baseline interferometric observations include for the first time the highly sensitive Atacama Large Millimeter/submillimeter Array (ALMA); reaching an angular resolution of 25 μas, with characteristic sensitivity limits of ∼1 mJy on baselines to ALMA and ∼10 mJy on other baselines. The observations present challenges for existing data processing tools, arising from the rapid atmospheric phase fluctuations, wide recording bandwidth, and highly heterogeneous array. In response, we developed three independent pipelines for phase calibration and fringe detection, each tailored to the specific needs of the EHT. The final data products include calibrated total intensity amplitude and phase information. They are validated through a series of quality assurance tests that show consistency across pipelines and set limits on baseline systematic errors of 2% in amplitude and 1° in phase. The M87 data reveal the presence of two nulls in correlated flux density at ∼3.4 and ∼8.3 Gλ and temporal evolution in closure quantities, indicating intrinsic variability of compact structure on a timescale of days, or several light-crossing times for a few billion solar-mass black hole. These measurements provide the first opportunity to image horizon-scale structure in M87