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.     

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.     

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).     

Time-Dependent Synchrotron and Compton Spectra from Microquasar Jets

Jet models for the high-energy emission of Galactic X-ray binary sources have regained significant interest with detailed spectral and timing studies of the X-ray emission from microquasars, the recent detection by the HESS collaboration of very-high-energy γ-rays from the microquasar LS 5039, and the earlier suggestion of jet models for ultraluminous X-ray sources observed in many nearby galaxies. Here we study the synchrotron and Compton signatures of time-dependent electron injection and acceleration, and adiabatic and radiative cooling in the jets of Galactic microquasars.     

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.     

3D MHD Simulations of Laboratory Plasma Jets

Jets and outflows are thought to be an integral part of accretion phenomena and are associated with a large variety of objects. In these systems, the interaction of magnetic fields with an accretion disk and/or a magnetized central object is thought to be responsible for the acceleration and collimation of plasma into jets and wider angle flows. In this paper we present three-dimensional MHD simulations of magnetically driven, radiatively cooled laboratory jets that are produced on the MAGPIE experimental facility. The general outflow structure comprises an expanding magnetic cavity which is collimated by the pressure of an extended plasma background medium, and a magnetically confined jet which develops within the magnetic cavity. Although this structure is intrinsically transient and instabilities in the jet and disruption of the magnetic cavity ultimately lead to its break-up, a well collimated, “knotty” jet still emerges from the system; such clumpy morphology is reminiscent of that observed in many astrophysical jets. The possible introduction in the experiments of angular momentum and axial magnetic field will also be discussed.     

Linear MHD Wave Propagation in Time-Dependent Flux Tube

MHD waves and oscillations in sharply structured magnetic plasmas have been studied for static and steady systems in the thin tube approximation over many years. This work will generalize these studies by introducing a slowly varying background density in time, in order to determine the changes to the wave parameters introduced by this temporally varying equilibrium, i.e. to investigate the amplitude, frequency, and wavenumber for the kink and higher order propagating fast magnetohydrodynamic wave in the leading order approximation to the WKB approach in a zero-β plasma representing the upper solar atmosphere. To progress, the thin tube and over-dense loop approximations are used, restricting the results found here to the duration of a number of multiples of the characteristic density change timescale. Using such approximations it is shown that the amplitude of the kink wave is enhanced in a manner proportional to the square of the Alfvén speed, $V_{\mathrm{A}}^{2}$ . The frequency of the wave solution tends to the driving frequency of the system as time progresses; however, the wavenumber approaches zero after a large multiple of the characteristic density change timescale, indicating an ever increasing wavelength. For the higher order fluting modes the changes in amplitude are dependent upon the wave mode; for the m=2 mode the wave is amplified to a constant level; however, for all m≥3 the fast MHD wave is damped within a relatively small multiple of the characteristic density change timescale. Understanding MHD wave behavior in time-dependent plasmas is an important step towards a more complete model of the solar atmosphere and has a key role to play in solar magneto-seismological applications.     

Linear MHD Wave Propagation in Time-Dependent Flux Tube

The propagation of magnetohydrodynamic (MHD) waves is an area that has been thoroughly studied for idealised static and steady state magnetised plasma systems applied to numerous solar structures. By applying the generalisation of a temporally varying background density to an open magnetic flux tube, mimicking the observed slow evolution of such waveguides in the solar atmosphere, further investigations into the propagation of both fast and slow MHD waves can take place. The assumption of a zero-beta plasma (no gas pressure) was applied in Williamson and Erdélyi (Solar Phys. 2013, doi: 10.1007/s11207-013-0366-9 , Paper I) is now relaxed for further analysis here. Firstly, the introduction of a finite thermal pressure to the magnetic flux tube equilibrium modifies the existence of fast MHD waves which are directly comparable to their counterparts found in Paper I. Further, as a direct consequence of the non-zero kinetic plasma pressure, a slow MHD wave now exists, and is investigated. Analysis of the slow wave shows that, similar to the fast MHD wave, wave amplitude amplification takes place in time and height. The evolution of the wave amplitude is determined here analytically. We conclude that for a temporally slowly decreasing background density both propagating magnetosonic wave modes are amplified for over-dense magnetic flux tubes. This information can be very practical and useful for future solar magneto-seismology applications in the study of the amplitude and frequency properties of MHD waveguides, e.g. for diagnostic purposes, present in the solar atmosphere.     

Steady MHD Solutions for Collimated Winds

A convenient approach to model MHD steady axisymmetric outflows is the so-called self-similar technique wherein the physical variables are factorized and a scaling law is assumed along one of the coordinates. This scaling depends on the astrophysical process under investigation. In this note we summarize all possible self-similar MHD outflow solutions; furthermore, we briefly discuss the main properties of a class of solutions which are self-similar in the meridional direction and allow to analyse in simple terms the dynamical properties of an outflow close to its rotational axis. Special attention is focused on the asymptotic structure of collimated winds. It will be shown that different regimes are possible for jets, in particular they can be either thermally or magnetically confined, depending on the physical conditions of the flow. This analysis is complementary with the well known radial self-similar models which are invoked to study winds from accretion disks. This revised version was published online in July 2006 with corrections to the Cover Date.     

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.     

Recent Experimental Results and Modelling of High-Mach-Number Jets and the Transition to Turbulence

In recent years, we have carried out experiments at the University of Rochester’s Omega laser in which supersonic, dense-plasma jets are formed by the interaction of strong shocks in a complex target assembly (Foster et al., Phys. Plasmas 9 (2002) 2251). We describe recent, significant extensions to this work, in which we consider scaling of the experiment, the transition to turbulence, and astrophysical analogues. In new work at the Omega laser, we are developing an experiment in which a jet is formed by laser ablation of a titanium foil mounted over a titanium washer with a central, cylindrical hole. Some of the resulting shocked titanium expands, cools, and accelerates through the vacuum region (the hole in the washer) and then enters a cylinder of low-density foam as a jet. We discuss the design of this new experiment and present preliminary experimental data and results of simulations using AWE hydrocodes. In each case, the high Reynolds number of the jet suggests that turbulence should develop, although this behaviour cannot be reliably modelled by present, resolution-limited simulations (because of their low-numerical Reynolds number).     

The Origin of Jets from Young Stars: MHD Disk Wind Models Confronted to Observations

We discuss in this contribution constraints on the origin of mass-loss from young stars brought by recent observations at high angular resolution (0.1″ = 14 AU) of the inner regions of winds from T Tauri stars. Jet widths and collimation scales, the large extent of the velocity profile as well as the detection of rotation signatures agree with predictions from magneto-centrifugal disk wind ejection models. However dynamically cold disk wind solutions predict too large terminal velocities and too low jet densities and ionisation fractions, suggesting that thermal gradients (originating in an accretion heated disk corona for example) may play an important role in accelerating the flow.     

The Origin of Jets from Young Stars: Steady State Disk Wind Models Confronted to Observations

We discuss in this contribution constraints on the origin of mass-loss from young stars brought by recent observations at high angular resolution (0.1″ = 14 AU) of the inner regions of winds from T Tauri stars. Jet widths and collimation scales, the large extent of the velocity profile as well as the detection of rotation signatures agree with predictions from extended (R _e ≥ 1 AU) magneto-centrifugal disk wind ejection models. Detected poloidal and toroidal velocities imply large ejection efficiencies (ξ ? 0.05, λ ? 10), suggesting that thermal gradients (originating in an accretion heated disk corona for example) play an important role in accelerating the flow.     

Resonant Absorption of Nonlinear Slow MHD Waves in Isotropic Steady Plasmas - I. Theory

This paper considers driven resonant nonlinear slow magnetohydrodynamic (MHD) waves in dissipative steady plasmas. A theory developed by Ruderman, Hollweg, and Goossens (1997) is used and extended to study the effect of steady flows on the nonlinear resonant behaviour of slow MHD waves in slow dissipative layers. The method of matched asymptotic expansions is used to describe the behaviour of the wave variables in the slow dissipative layer. The nonlinear analogue of the connection formulae for slow MHD waves obtained previously by Goossens, Hollweg, and Sakurai (1992) and Erdélyi (1997) in linear MHD, are derived. The effect of an equilibrium flow results partly in a Doppler shift of the available frequency for slow resonance and partly in the modification of the width of the dissipative layer.     

Astrophysical Jets of Blazars and Microquasars

Some recent developments in the study of relativistic jets in active galactic nuclei and microquasars are reviewed. While it has been well established for some time that extragalactic jets found in radio galaxies, quasars, and BL Lac objects are the site of ultrarelativistic particle acceleration, the recent identification of the Galactic jet source and microquasar LS~5039 as a source of very-high-energy gamma-ray emission has underlined the striking similarity between the two types of astrophysical jet sources. In this paper, I will present an overview of the dominant radiation and particle acceleration processes and observational tests to distinguish between such processes. The wide-ranging analogies between Galactic and extragalactic jets, but also their distinct differences, in particular those caused by the presence of the companion star in Galactic microquasar systems, will be exposed.     

Entrainment and Deceleration of Relativistic Jets

Extragalactic radio sources are separated in two classes according to their specific luminosity: Fanaroff-Riley I and II. The origin of this dichotomy can be due either to intrinsec different properties of the AGN or to interaction of the jet with different enviroments. We assume that jets are always relativistic and supersonic close to their source, as recent observations suggest, and we explore the conditions in which the jets decelerate assuming FR I morphology. We have carried out high resolution 3D simulations for a set of parameters and in this paper we concentrate our discussion on two extreme cases.     

The Dynamics of Stellar Jets

This paper discusses the formation of two-shock working surfaces in Herbig-Haro (HH) jets. These working surfaces can be formed either at the leading edge of the jet flow, or inside the body of the jet beam (as a result of variabilities in the jet flow velocity), and depending on the parameters of the flow can be either massless or mass conserving. It is shown that observations might indicate that these two regimes actually occur in some HH jets. This revised version was published online in July 2006 with corrections to the Cover Date.