A Numerical Method for General Relativistic Magnetohydrodynamics

This paper describes the development and testing of a general relativistic magnetohydrodynamic (GRMHD) code to study ideal MHD in the fixed background of a Kerr black hole. The code is a direct extension of the hydrodynamic code of Hawley, Smarr, and Wilson, and uses Evans and Hawley constrained transport (CT) to evolve the magnetic fields. Two categories of test cases were undertaken. A one dimensional version of the code (Minkowski metric) was used to verify code performance in the special relativistic limit. The tests include Alfv\'en wave propagation, fast and slow magnetosonic shocks, rarefaction waves, and both relativistic and non-relativistic shock tubes. A series of one- and two-dimensional tests were also carried out in the Kerr metric: magnetized Bondi inflow, a magnetized inflow test due to Gammie, and two-dimensional magnetized constant-$l$ tori that are subject to the magnetorotational instability.Comment: 37 pages, 14 figures, submitted to ApJ. Animations can be viewed at http://www.astro.virginia.edu/~jd5v/grmhd/grmhd.htm

Transport of Large Scale Poloidal Flux in Black Hole Accretion

We report on a global, three-dimensional GRMHD simulation of an accretion torus embedded in a large scale vertical magnetic field orbiting a Schwarzschild black hole. This simulation investigates how a large scale vertical field evolves within a turbulent accretion disk and whether global magnetic field configurations suitable for launching jets and winds can develop. We find that a "coronal mechanism" of magnetic flux motion, which operates largely outside the disk body, dominates global flux evolution. In this mechanism, magnetic stresses driven by orbital shear create large-scale half-loops of magnetic field that stretch radially inward and then reconnect, leading to discontinuous jumps in the location of magnetic flux. In contrast, little or no flux is brought in directly by accretion within the disk itself. The coronal mechanism establishes a dipole magnetic field in the evacuated funnel around the orbital axis with a field intensity regulated by a combination of the magnetic and gas pressures in the inner disk. These results prompt a reevaluation of previous descriptions of magnetic flux motion associated with accretion. Local pictures are undercut by the intrinsically global character of magnetic flux. Formulations in terms of an "effective viscosity" competing with an "effective resistivity" are undermined by the nonlinearity of of the magnetic dynamics and the fact that the same turbulence driving mass motion (traditionally identified as "viscosity") can alter magnetic topology.Comment: 45 pages, 17 figures, 1 movie; ApJ accepted; updated version contains several new figures and a movie detailing the operation of the coronal mechanism. The movie and a version of the paper with high resolution figures can be found at http://www.astro.virginia.edu/~krb3u/0906.2784

Global General Relativistic Magnetohydrodynamic Simulations of Accretion Tori

This paper presents an initial survey of the properties of accretion flows in the Kerr metric from three-dimensional, general relativistic magnetohydrodynamic simulations of accretion tori. We consider three fiducial models of tori around rotating, both prograde and retrograde, and nonrotating black holes; these three fiducial models are also contrasted with axisymmetric simulations and a pseudo-Newtonian simulation with equivalent initial conditions to delineate the limitations of these approximations.Comment: Submitted to ApJ. 30 pages, 21 figures. Animations and high-resolution version of figures available at http://www.astro.virginia.edu/~jd5

Where is the Radiation Edge in Magnetized Black Hole Accretion discs?

General Relativistic (GR) Magnetohydrodynamic (MHD) simulations of black hole accretion find significant magnetic stresses near and inside the innermost stable circular orbit (ISCO), suggesting that such flows could radiate in a manner noticeably different from the prediction of the standard model, which assumes that there are no stresses in that region. We provide estimates of how phenomenologically interesting parameters like the ``radiation edge", the innermost ring of the disc from which substantial thermal radiation escapes to infinity, may be altered by stresses near the ISCO. These estimates are based on data from a large number of three-dimensional GRMHD simulations combined with GR ray-tracing. For slowly spinning black holes ($a/M<0.9$), the radiation edge lies well inside where the standard model predicts, particularly when the system is viewed at high inclination. For more rapidly spinning black holes, the contrast is smaller. At fixed total luminosity, the characteristic temperature of the accretion flow increases between a factor of $1.2-2.4$ over that predicted by the standard model, whilst at fixed mass accretion rate, there is a corresponding enhancement of the accretion luminosity which may be anywhere from tens of percent to order unity. When all these considerations are combined, we find that, for fixed black hole mass, luminosity, and inclination angle, our uncertainty in the characteristic temperature of the radiation reaching distant observers due to uncertainty in dissipation profile (around a factor of 3) is {\it greater} than the uncertainty due to a complete lack of knowledge of the black hole's spin (around a factor of 2) and furthermore that spin estimates based on the stress-free inner boundary condition provide an upper limit to $a/M$.Comment: 20 pages, 17 figures, accepted by MNRAS; major changes to original, including entirely new sections discussing characteristic temperature of black hole accretion flows and implications for measurements of black hole spin, along with substantially expanded conclusio

The study of a novel flat-topping resonator for more intense proton beams of better quality from cyclotrons

ABSTRACT The multi-disciplinary accelerator based facilities at iThemba LABS are used intensively for nuclear physics experiments, radiotherapy and the production of radioisotopes. To increase the beam intensity for radioisotope production and to improve the beam quality of the 66 MeV proton beam, a double-gap horizontal half-wave flat-topping resonator has been developed for the separated-sector cyclotron to operate at the associated fixed frequency. This type of flattopping resonator has never before been implemented in a cyclotron and this study is the first to show that it can be done, featuring a special characteristic not offered by other types. The resonator is reviewed against the other types of resonators that are already in use at other institutes around the world. The flat-topping voltage of the selected type has a sinusoidal half-wave distribution along a radial line in each of its acceleration gaps with the nodal points located on the injection and extraction orbits. The flat-topping voltage therefore progressively increases from zero at both of the two most critical orbits in a cyclotron to a maximum at about halfway between them. As a result will this resonator, apart from its basic function to reduce the energy spread in the beam, not decrease the orbit separation at the injection and extraction orbits in the cyclotron, as is the case with other types of flat-topping resonators. This advantageous feature implies that the beam pattern in the cyclotron is not affected in the regions of the delicate injection and extraction components and therefore will these components or the operational control of the beam not require any modification to accommodate the resonator. In order to design a resonator that will meet our requirements, the theory of the beam dynamics and resonator characteristics were studied to ascertain the expected improvement in beam quality and beam intensity when a flat-topping resonator is implemented with the cyclotron. All resonator types were considered and studied in terms of their power dissipation, voltage distribution, harmonic number, space requirements and influence on the beam. The horizontal half-wave resonator type, with two acceleration gaps, was selected as the most suitable for our application, because of its preferred electromagnetic characteristics and its geometric shape that permits the installation inside an existing vacuum chamber through an existing flange. Initially a half-scale resonator model was build to test the feasibility of such a resonator and also to verify the calculation methods. Transmission line methods and numerical field analysis in 3D were applied to determine the resonator characteristics. In the former method a computer program, POISSON, was used to calculate curvilinear squares on sections through a triangular-shaped transmission line and in the latter method a commercial computer program, SOPRANO, was used. SOPRANO is part of an internationally acclaimed suite of programs and the acquired knowledge and skill to use this state-of-the-art software for the studying and designing of such and other electromagnetic devices also put the institute amongst the front-runners in the world. The calculated characteristics of the half- and full-scale resonator models, the study of the different electromagnetic modes that resonate in close proximity to the required frequency, the heat transport modelling and the theory and implementation of the coupling and tuning devices are all in good agreement with their respective measured results and are reported in this document. This study lead the way to have the first-ever double-gap horizontal half-wave flat-topping resonator in a cyclotron successfully commissioned at iThemba LABS and the first tests with beam report very stable operation. Accelerator physicists now have another option to utilize for the establishing of flat-topped acceleration voltages

Magnetically Driven Accretion in the Kerr Metric III: Unbound Outflows

We have carried out fully relativistic numerical simulations of accretion disks in the Kerr metric. In this paper we focus on the unbound outflows that emerge self-consistently from the accretion flow. These outflows are found in the axial funnel region and consist of two components: a hot, fast, tenuous outflow in the axial funnel proper, and a colder, slower, denser jet along the funnel wall. Although a rotating black hole is not required to produce these unbound outflows, their strength is enhanced by black hole spin. The funnel-wall jet is excluded from the axial funnel due to elevated angular momentum, and is also pressure-confined by a magnetized corona. The tenuous funnel outflow accounts for a significant fraction of the energy transported to large distances in the higher-spin simulations. We compare the outflows observed in our simulations with those seen in other simulations.Comment: 33 pages, 8 figures, ApJ submitte

Dependence of inner accretion disk stress on parameters: the Schwarzschild case

We explore the parameter dependence of inner disk stress in black hole accretion by contrasting the results of a number of simulations, all employing 3-d general relativistic MHD in a Schwarzschild spacetime. Five of these simulations were performed with the intrinsically conservative code HARM3D, which allows careful regulation of the disk aspect ratio, H/R; our simulations span a range in H/R from 0.06 to 0.17. We contrast these simulations with two previously reported simulations in a Schwarzschild spacetime in order to investigate possible dependence of the inner disk stress on magnetic topology. In all cases, much care was devoted to technical issues: ensuring adequate resolution and azimuthal extent, and averaging only over those time-periods when the accretion flow is in approximate inflow equilibrium. We find that the time-averaged radial-dependence of fluid-frame electromagnetic stress is almost completely independent of both disk thickness and poloidal magnetic topology. It rises smoothly inward at all radii (exhibiting no feature associated with the ISCO) until just outside the event horizon, where the stress plummets to zero. Reynolds stress can also be significant near the ISCO and in the plunging region; the magnitude of this stress, however, depends on both disk thickness and magnetic topology. The two stresses combine to make the net angular momentum accreted per unit rest-mass 7-15% less than the angular momentum of the ISCO.Comment: Accepted for publication in ApJ, 52 pages, 38 figures, AASTEX. High-resolution versions can be found at the following links: http://ccrg.rit.edu/~scn/papers/schwarzstress.ps, http://ccrg.rit.edu/~scn/papers/schwarzstress.pd

The effects of the antenna power pattern uncertainty within a global 21 cm experiment

Experimental 21 cm cosmology aims to detect the formation of the first stars during the cosmic dawn and the subsequent epoch of reionization by utilizing the 21 cm hydrogen line transition. While several experiments have published results that begin to constrain the shape of this signal, a definitive detection has yet to be achieved. In this paper, we investigate the influence of uncertain antenna-sky interactions on the possibility of detecting the signal. This paper aims to define the level of accuracy to which a simulated antenna beam pattern is required to agree with the actual observing beam pattern of the antenna to allow for a confident detection of the global 21 cm signal. By utilising singular value decomposition, we construct a set of antenna power patterns that incorporate minor, physically motivated variations. We take the absolute mean averaged difference between the original beam and the perturbed beam averaged over frequency ($\Delta D$) to quantifying this difference, identifying the correlation between $\Delta D$ and antenna temperature. To analyse the impact of $\Delta D$ on making a confident detection, we utilize the REACH Bayesian analysis pipeline and compare the Bayesian evidence $\log \mathcal{Z}$ and root-mean-square error for antenna beams of different $\Delta D$ values. Our calculations suggest that achieving an agreement between the original and perturbed antenna power pattern with $\Delta D$ better than -35 dB is necessary for confident detection of the global 21 cm signal. Furthermore, we discuss potential methods to achieve the required high level of accuracy within a global 21~cm experiment

Charge-starved, relativistic jets and blazar variability

High energy emission from blazars is thought to arise in a relativistic jet launched by a supermassive black hole. The emission site must be far from the hole and the jet relativistic, in order to avoid absorption of the photons. In extreme cases, rapid variability of the emission suggests that structures of length-scale smaller than the gravitational radius of the central black hole are imprinted on the jet as it is launched, and modulate the radiation released after it has been accelerated to high Lorentz factor. We propose a mechanism which can account for the acceleration of the jet, and for the rapid variability of the radiation, based on the propagation characteristics of large-amplitude waves in charge-starved, polar jets. Using a two-fluid (electron-positron) description, we find the outflows exhibit a delayed acceleration phase, that starts at roughly 1pc, where the inertia associated with the wave currents becomes important. The time-structure imprinted on the jet at launch modulates photons produced by the accelerating jet provided the pair multiplicity in the black-hole magnetosphere is sufficiently small, suggesting that very rapid variability is confined to sources in which the electromagnetic cascade in the black-hole magnetosphere is not prolific.Comment: 8 pages, 1 figure. Momentum equation corrected. Conclusions unchanged. Erratum submitted to Ap