MHD Simulations of Relativistic Jets

In a series of time dependent numerical simulations we have performed a parameter study of magnetised relativistic jets. We have found that the impact of the magnetic field on the morphology of a jet depends strongly on the configuration of the field.     

MHD Models and Laboratory Experiments of Jets

Jet research has long relied upon a combination of analytical, observational and numerical studies to elucidate the complex phenomena involved. One element missing from these studies (which other physical sciences utilize) is the controlled experimental investigation of such systems. With the advent of high-power lasers and fast Z-pinch machines it is now possible to experimentally studysimilar systems in a laboratory setting. Such investigations can contribute in two useful ways. They can be used for comparison with numerical simulations as a means to validate simulation codes. More importantly, however, such investigations can also be used to complement other jet research, leading to fundamentally new knowledge. In the first part of this article, we analyze the evolution of magnetized wide-angle winds in a collapsing environment. We track the ambient and wind mass separately and describe a physical mechanism by which an ionized central wind can entrain the ambient gas giving rise to internal shells of molecular material on short time scales. The formation of internal shells in molecular outflows has been found to be an important ingredient in describing the observations of convex spurs in P-V diagrams (Hubble wedges in M-V diagrams).In the second part, we present astrophysically relevant experiments in which supersonic jets are created using a conical wire array Z-pinch. The conically convergent flow generates a standing shock around the axis which collimates the flow into a Mach ～ 30 jet. The jet formation process is closely related to the work of Cantó et al. (1988) for hydrodynamic jet collimation. The influence of radiative cooling on collimation and stability is studied by varying the wire material (Al, Fe, and W).     

3D Solar Null Point Reconnection MHD Simulations

Numerical MHD simulations of 3D reconnection events in the solar corona have improved enormously over the last few years, not only in resolution, but also in their complexity, enabling more and more realistic modeling. Various ways to obtain the initial magnetic field, different forms of solar atmospheric models as well as diverse driving speeds and patterns have been employed. This study considers differences between simulations with stratified and non-stratified solar atmospheres, addresses the influence of the driving speed on the plasma flow and energetics, and provides quantitative formulas for mapping electric fields and dissipation levels obtained in numerical simulations to the corresponding solar quantities. The simulations start out from a potential magnetic field containing a null-point, obtained from a Solar and Heliospheric Observatory (SOHO) Michelson Doppler Imager (MDI) magnetogram magnetogram extrapolation approximately 8?hours before a C-class flare was observed. The magnetic field is stressed with a boundary motion pattern similar to?–?although simpler than?–?horizontal motions observed by SOHO during the period preceding the flare. The general behavior is nearly independent of the driving speed, and is also very similar in stratified and non-stratified models, provided only that the boundary motions are slow enough. The boundary motions cause a build-up of current sheets, mainly in the fan-plane of the magnetic null-point, but do not result in a flare-like energy release. The additional free energy required for the flare could have been partly present in non-potential form at the initial state, with subsequent additions from magnetic flux emergence or from components of the boundary motion that were not represented by the idealized driving pattern.     

Numerical Simulations and Astrophysical Applications of Laboratory Jets at Omega

We have conducted experiments on the Omega laser at the University of Rochester that have produced jets of supersonic Ti impacting and being deflected by a ball of high density plastic. These mm-sized jets of dense plasma are highly complex, have large Reynolds numbers, and, given sufficient time and shear, should produce a fully turbulent flow. The experiments are diagnosed with a point-projection backlighter, resulting in a single image per shot. Simulations of the 3D hydrodynamics capture the large-scale features of the experimental data fairly well while missing some of the smaller scale turbulent-like phenomena. This is to be expected given the limited characterization of the targets as well as the finite resolution of the 3D simulations. If Euler scaling holds, these experiments should model larger astrophysical jets in objects such as HH 110 where an outflow can be seen colliding with a molecular cloud. However, Euler scaling demands that not only the isothermal internal Mach numbers of the two systems be similar but also that any dissipative mechanisms, such as radiative cooling or viscous dissipation, be of equal importance relative to each other. Similar equations of state are required as well. We discuss such issues in the context of these experiments and simulations.     

Virtual MHD Jets on Grids

As network performance has outpaced computational power and storage capacity, a new paradigm has evolved to enable the sharing of geographically distributed resources. This paradigm is known as Grid computing and aims to offer access to distributed resource irrespective of their physical location. Many national, European and international projects have been launched during the last years trying to explore the Grid and to change the way we are doing our everyday work. In Ireland, we have started the CosmoGrid project that is a collaborative project aimed to provide high performance super-computing environments. This will help to address complex problems such as magnetohydrodynamic outflows and jets in order to model and numerically simulate them. Indeed, the numerical modeling of plasma jets requires massive computations, due to the wide range of spatial-temporal scales involved. We present here the first jet simulations and their corresponding models that could help to understand results from laboratory experiments.     

Steady and Time-Dependent MHD Modelling of Jets

A brief review is given of some results of our work on the construction of (I) steady and (II) time-dependent MHD models for nonrelativistic and relativistic astrophysical outflows and jets, analytically and numerically. The only available exact solutions for MHD outflows are those in separable coordinates, i.e., with the symmetry of radial or meridional self-similarity. Physically accepted solutions pass from the fast magnetosonic separatrix surface in order to satisfy MHD causality. An energetic criterion is outlined for selecting radially expanding winds from cylindrically expanding jets. Numerical simulations of magnetic self-collimation verify the conclusions of analytical steady solutions. We also propose a two-component model consisting of a wind outflow from a central object and a faster rotating outflow launched from a surrounding accretion disk which plays the role of the flow collimator. We also discuss the problem of shock formation during the magnetic collimation of wind-type outflows into jets.     

On the MHD Acceleration of Astrophysical Jets

We present a 2.5D magnetohydrodynamic (MHD) simulation of the acceleration of a collimated jet from a magnetized accretion disk. We employ a MHD Adaptive Mesh Refinement (AMR) code (FLASH—University of Chicago). Thanks to this tool we can follow the evolution of the system for many dynamical timescales with a high-spatial resolution. Assuming an initial condition in which a Keplerian disk, thus with no accretion motions, is threaded by a uniform poloidal magnetic field, we show how both the accretion flow and the acceleration of the outflow occur, and we present in detail which are the forces responsible for the jet launching and collimation. Our simulation also shows how the collimating forces due to the self-generated toroidal magnetic field can produce some peculiar knotty features.     

How Can Jets Survive MHD Instabilities?

We present the main findings of two recent studies using high-resolution MHD simulations of supersonic magnetized shear flow layers. First, a strong large-scale coalescence effect partially countered by small-scale reconnection events is shown to dominate the dynamics in a two-dimensional layer subject to Kelvin-Helmholtz (KH) instabilities. Second, an interaction mechanism between two different types of instabilities (KH and current-driven modes) is shown to occur in a cylindrical jet configuration embedded in an helical magnetic field. Finally, we discuss the implications of these results for astrophysical jets survival.     

High-Resolution Simulations of Nonhelical MHD Turbulence

According to the kinematic theory of nonhelical dynamo action, the magnetic energy spectrum increases with wavenumber and peaks at the resistive cutoff wavenumber. It has previously been argued that even in the dynamical case, the magnetic energy peaks at the resistive scale. Using high resolution simulations (up to 1024³ meshpoints) with no large-scale imposed field, we show that the magnetic energy peaks at a wavenumber that is independent of the magnetic Reynolds number and about five times larger than the forcing wavenumber. Throughout the inertial range, the spectral magnetic energy exceeds the kinetic energy by a factor of two to three. Both spectra are approximately parallel. The total energy spectrum seems to be close to k ^?3/2, but there is a strong bottleneck effect and we suggest that the asymptotic spectrum is instead k ^?5/3. This is supported by the value of the second-order structure function exponent that is found to be ζ₂ = 0.70, suggesting a k ^?1.70 spectrum. The third-order structure function scaling exponent is very close to unity,—in agreement with Goldreich–Sridhar theory. Adding an imposed field tends to suppress the small-scale magnetic field. We find that at large scales the magnetic energy spectrum then follows a k ^?1 slope. When the strength of the imposed field is of the same order as the dynamo generated field, we find almost equipartition between the magnetic and kinetic energy spectra.     

MHD Simulations of Crab's Jet and Torus

The Crab nebula is regarded as one of the most important “cosmic laboratories” in astrophysics, which has made a bigger impact on the development of astronomy than any other single object beyond the solar system. The most intriguing recent result is the completely unexpected discovery of a peculiar “jet-torus” structure in the inner part of the nebula. Similar structures were found later in other Crab-like nebulae. This discovery clearly indicates significant anisotropy of the wind from the Crab pulsar which has been ignored so far in simplified theoretical models of the nebula. Fortunately, the impressive progress in computational relativistic magnetohydrodynamics in recent years has made possible to study the Crab nebula without making such a drastic simplification of the problem. In this paper we present the results of the first study of such kind. They provide a likely explanation of the jet-torus pattern and show that the flow in the nebula is much more complex than it has been widely believed.     

Simulating Astrophysical Jets in Laboratory Experiments

Pulsed-power technology and appropriate boundary conditions have been used to create simulations of magnetically driven astrophysical jets in a laboratory experiment. The experiments are quite reproducible and involve a distinct sequence. Eight initial flux tubes, corresponding to eight gas injection locations, merge to form the jet, which lengthens, collimates, and eventually kinks. A model developed to explain the collimation process predicts that collimation is intimately related to convection and pile-up of frozen-in toroidal flux convected with the jet. The pile-up occurs when there is an axial non-uniformity in the jet velocity so that in the frame of the jet there appears to be a converging flow of plasma carrying frozen-in toroidal magnetic flux. The pile-up of convected flux at this “stagnation region” amplifies the toroidal magnetic field and increases the pinch force, thereby collimating the jet.     

The Implications of 3D for Solar MHD Modelling

The effects of three-dimensionality on the modelling of solar magnetic fields are described. We focus on two processes that are believed to play an important role in coronal heating – the braiding of field lines by photospheric motions and the reconnection of colliding flux tubes. First, it is shown that a proper treatment of boundary conditions at the photosphere in 3D entails qualitatively new physical processes that are not present in 2D. The numerical resolution of even simple boundary velocity patterns in 3D leads to obstacles which have no counterpart in the 2D case. We conclude that adaptive mesh refinement is necessary for capturing the essential 3D physics of a braiding motion at the photosphere. Next, the effects of 3D on magnetic reconnection are discussed. Reconnection in 3D can lead to an evolution of interacting flux tubes, magnetic tunneling, that is not only impossible in lower dimensionality, but is strikingly counterintuitive. The implications of these results for the structure of the solar magnetic field and for coronal heating are described.     

Three-Dimensional Simulations of Jets from Keplerian Disks: Stability Issues

Three-dimensional simulations of the time-dependent evolution of non-relativistic outflows from the surface of Keplerian accretion disks are presented. We investigate the outflow that arises from a magnetized accretion disk that is initially in hydrostatic balance with its surrounding cold corona. Our simulations show that jets maintain their long-term stability through a self-limiting process wherein the average Alfvénic Mach number within the jet is maintained to order unity. This is accomplished in at least two ways. First, poloidal magnetic field is concentrated along the central axis of the jet forming a `backbone' in which the Alfvén speed is sufficiently high to reduce the average jet Alfvénic Mach number to unity. Second, the onset of higher order Kelvin-Helmholtz `flute' modes (m ≥ 2) reduce the efficiency with which the jet material is accelerated, and transfer kinetic energy of the out flow into the stretched, poloidal field lines of the distorted jet. This too has the effect of increasing the Alfvén speed and thereby reducing the Alfvénic Mach number. The jet is able to survive the onset of the more destructive m=1 mode in this way.     

Modeling Magnetic Tower Jets in the Laboratory

The twisting of magnetic fields threading an accretion system can lead to the generation on axis of toroidal field loops. As the magnetic pressure increases, the toroidal field inflates, producing a flow. Collimation is due to a background corona, which radially confines this axially growing “magnetic tower”. We investigate the possibility of studying in the laboratory the dynamics, confinement and stability of magnetic tower jets. We present two-dimensional resistive magnetohydrodynamic simulations of radial arrays, which consist of two concentric electrodes connected radially by thin metallic wires. In the laboratory, a radial wire array is driven by a 1 MA current which produces a hot, low density background plasma. During the current discharge a low plasma beta (β < 1), magnetic cavity develops in the background plasma (β is the ratio of thermal to magnetic pressure). This laboratory magnetic tower is driven by the magnetic pressure of the toroidal field and it is surrounded by a shock envelope. On axis, a high density column is produced by the pinch effect. The background plasma has >rsim1, and in the radial direction the magnetic tower is confined mostly by the thermal pressure. In contrast, in the axial direction the pressure rapidly decays and an elongated, well collimated magnetic-jet develops. This is later disrupted by the development of m = 0 instabilities arising in the axial column.     

Experimental Studies of Magnetically Driven Plasma Jets

We present experimental results on the formation of supersonic, radiatively cooled jets driven by pressure due to the toroidal magnetic field generated by the 1.5 MA, 250 ns current from the MAGPIE generator. The morphology of the jet produced in the experiments is relevant to astrophysical jet scenarios in which a jet on the axis of a magnetic cavity is collimated by a toroidal magnetic field as it expands into the ambient medium. The jets in the experiments have similar Mach number, plasma beta and cooling parameter to those in protostellar jets. Additionally the Reynolds, magnetic Reynolds and Peclet numbers are much larger than unity, allowing the experiments to be scaled to astrophysical flows. The experimental configuration allows for the generation of episodic magnetic cavities, suggesting that periodic fluctuations near the source may be responsible for some of the variability observed in astrophysical jets. Preliminary measurements of kinetic, magnetic and Poynting energy of the jets in our experiments are presented and discussed, together with estimates of their temperature and trapped toroidal magnetic field.     

太阳大气中磁重联的MHD数值模拟

回顾了近３０年太阳大气中磁重联过程的ＭＨＤ数值模拟工作取得的进展。着重描述了在验证理论模型,解释观测现象,以及研究各种因素对重联的影响三个方面的成果,如快速磁重联,太阳耀斑机制及色球,日冕中的各种爆发现象等。指出了在数值模拟中应注意的几个问题,并对该领域今后的发展作了简要的展望。     

Numerical Simulations of the Interaction of Jets with the Intracluster Medium

We study, by numerical simulations, the propagation of an axisymmetric supersonic jet in an isothermal King atmosphere and we analyse the evolution of the resulting X-ray properties and their dependence on the jet physical parameters. We show the existence of two distinct regimes of interaction, with strong and weak shocks. In the first case shells of enhanced X-ray emission are to be expected, whereas in the second case we expect deficit of X-ray emission coincident with the cocoon. Analysing the results of our simulations we find that the jet kinetic power is the main parameter controlling the transition between the two regimes. We also discuss, in the same scheme, the ICM heating induced by the jet propagation, considering its effects on the observed relations between the cluster X-ray luminosity and temperature and between cluster entropy and temperature.