Dynamics of relativistic jets

We discuss the structure and relativistic kinematics that develop in three spatial dimensions when a moderately hot, supersonic jet propagates into a denser background medium and encounters resistance from an oblique magnetic field. Our simulations incorporate relativistic MHD in a four-dimensional spacetime and clearly show that (a) relatively weak, oblique fields (at 1/16 of the equipartition value) have only a negligible influence on the propagating jet and they are passively pushed away by the relativistically moving head; (b) oblique fields in equipartition with the ambient plasma provide more resistance and cause bending at the jet head, but the magnitude of this deflection and the associated backflow are small compared to those identified by previous studies. The new results are understood as follows: Relativistic simulations have consistently shown that these jets are effectively heavy and so they do not suffer substantial momentum losses and are not decelerated as efficiently as their nonrelativistic counterparts. In addition, the ambient magnetic field, however strong, can be pushed aside with relative ease by the beam, provided that the degrees of freedom associated with all three spatial dimensions are followed self-consistently during the simulations. The effect is analogous to pushing Japanese “noren” or vertical Venetian blinds out of the way while the slats are allowed to bend and twist in 3-D space. Applied to relativistic extragalactic jets from blazars, the new results are encouraging since superluminal outflows exhibit bending near their sources and their environments are profoundly magnetized – but observations do not provide support for irregular kinematics such as large-scale vortical motions and pronounced reverse flows near the points of origin.     

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.     

Magnetic-Tower Jet Solution for Launching Astrophysical Jets

In spite of the large number of global three-dimensional (3-D) magnetohydrodynamic (MHD) simulations of accretion disks and astrophysical jets, which have been developed since 2000, the launching mechanisms of jets is somewhat controversial. Previous studies of jets have concentrated on the effect of the large-scale magnetic fields permeating accretion disks. However, the existence of such global magnetic fields is not evident in various astrophysical objects, and their origin is not well understood. Thus, we study the effect of small-scale magnetic fields confined within the accretion disk. We review our recent findings on the formation of jets in dynamo-active accretion disks by using 3-D MHD simulations. In our simulations, we found the emergence of accumulated azimuthal magnetic fields from the inner region of the disk (the so-called magnetic tower) and also the formation of a jet accelerated by the magnetic pressure of the tower. Our results indicate that the magnetic tower jet is one of the most promising mechanisms for launching jets from the magnetized accretion disk in various astrophysical objects. We will discuss the formation of cosmic jets in the context of the magnetic tower model.     

Observations of the Blandford–Znajek process and the magnetohydrodynamic Penrose process in computer simulations of black hole magnetospheres

In this paper we report the results of axisymmetric relativistic magnetohydrodynamic (MHD) simulations for the problem of a Kerr black hole immersed in a rarefied plasma with 'uniform' magnetic field. The long-term solution shows properties that are significantly different from those of the initial transient phase studied recently by Koide. The topology of magnetic field lines within the ergosphere is similar to that of the split-monopole model with a strong current sheet in the equatorial plane. Closer inspection reveals a system of isolated magnetic islands inside the sheet and ongoing magnetic reconnection. No regions of negative hydrodynamic 'energy at infinity' are seen inside the ergosphere and the so-called MHD Penrose process does not operate. However, the rotational energy of the black hole continues to be extracted via the purely electromagnetic Blandford–Znajek mechanism. In spite of this, no strong relativistic outflows from the black hole are seen to be developing. Combined with results of other recent simulations, our results signal a potential problem for the standard MHD model of relativistic astrophysical jets should they be found at distances as small as a few tens of gravitational radii from the central black hole.     

wham: a WENO-based general relativistic numerical scheme – I. Hydrodynamics

Active galactic nuclei, X-ray binaries, pulsars and gamma-ray bursts are all believed to be powered by compact objects surrounded by relativistic plasma flows driving phenomena such as accretion, winds and jets. These flows are often accurately modelled by the relativistic magnetohydrodynamic (MHD) approximation. Time-dependent numerical MHD simulations have proven to be especially insightful, but one regime that remains difficult to simulate is when the energy scales (kinetic, thermal, magnetic) within the plasma become disparate. We develop a numerical scheme that significantly improves the accuracy and robustness of the solution in this regime. We use a modified form of the weighted essentially non-oscillatory (WENO) method to construct a finite-volume general relativistic hydrodynamics code called wham that converges at fifth order. We avoid (1) field-by-field decomposition by adaptively reducing down to two-point stencils near discontinuities for a more accurate treatment of shocks and (2) excessive reduction to low-order stencils, as in the standard WENO formalism, by maintaining high-order accuracy in smooth monotonic flows. Our scheme performs the proper surface integral of the fluxes, converts cell-averaged conserved quantities to point-conserved quantities before performing the reconstruction step, and correctly averages all source terms. We demonstrate that the scheme is robust in strong shocks, very accurate in smooth flows and maintains accuracy even when the energy scales in the flow are highly disparate.     

Linear Analysis of Axial Sheared Flow in Astrophysical Jets

A linear analysis of axial sheared flow in magnetohydrodynamic (MHD) jets with helical magnetic fields is presented. A linearized set of ideal MHD equations allows the investigation of plasmas with both magnetic shear and flow shear included in the equilibrium profile. These equations are integrated numerically by following the linear development in time of an initial seed perturbation. Global instability growth rates are obtained after the numerical solution converges to the fastest growing mode. It is shown that axial sheared flow reduces the growth of current-driven instabilities in plasma jets with constant magnetic pitch P = rB _z /B _θ.     

Simulating Magnetized Jets

A suitable model for the macroscopic behavior of accretion disk-jet systems is provided by the equations of MagnetoHydroDynamics (MHD). These equations allow us to perform scale-encompassing numerical simulations of multidimensional nonlinear magnetized plasma flows. For that purpose, we continue the development and exploitation of the Versatile Advection Code (VAC) along with its recent extension which employs dynamically controlled grid adaptation. In the adaptive mesh refinement AMRVAC code, modules for simulating any-dimensional special relativistic hydro- and magnetohydrodynamic problems are currently operational. Here, we review recent 3D MHD simulations of fundamental plasma instabilities, relevant when dealing with cospatial shear flow and twisted magnetic fields. Such magnetized jet flows can be susceptible to a wide variety of hydro (e.g. Kelvin-Helmholtz) or magnetohydrodynamic (e.g. current driven kink) instabilities. Recent MHD computations of 3D jet flows have revealed how such mutually interacting instabilities can in fact aid in maintaining jet coherency. Another breakthrough from computational magnetofluid modeling is the demonstration of continuous, collimated, transmagnetosonic jet launching from magnetized accretion disks. Summarizing, MHD simulations are rapidly gaining realism and significantly advance our understanding of nonlinear astrophysical magnetofluid dynamics.     

Does the plasma composition affect the long-term evolution of relativistic jets?

We study the influence of the matter content of extragalactic jets on their morphology, dynamics and emission properties. For this purpose we consider jets of extremely different compositions, including pure leptonic and baryonic plasmas. Our work is based on two-dimensional relativistic hydrodynamic simulations of the long-term evolution of powerful extragalactic jets propagating into a homogeneous environment. The equation of state used in the simulations accounts for an arbitrary mixture of electrons, protons and electron–positron pairs. Using the hydrodynamic models, we have also computed synthetic radio maps and the thermal bremsstrahlung X-ray emission from their cavities.
Although there is a difference of about three orders of magnitude in the temperatures of the cavities inflated by the simulated jets, we find that both the morphology and the dynamic behaviour are almost independent of the assumed composition of the jets. Their evolution proceeds in two distinct epochs. During the first one, multidimensional effects are unimportant and the jets propagate ballistically. The second epoch starts when the first larger vortices are produced near the jet head, causing the beam cross-section to increase and the jet to decelerate. The evolution of the cocoon and cavity is in agreement with a simple theoretical model. The beam velocities are relativistic  ( Γ ≃4)  at kiloparsec scales, supporting the idea that the X-ray emission of several extragalactic jets may be due to relativistically boosted CMB photons. The radio emission of all models is dominated by the contribution of the hotspots. All models exhibit a depression in the X-rays surface brightness of the cavity interior, in agreement with recent observations.     

Compressible turbulence in Hall Magnetohydrodynamics

By direct numerical simulations we investigate the nonlinear dynamics of a compressible Hall Magnetohydrodynamic (MHD) plasma. At small scales, where the Hall effect dominates, we found an increase of the compressibility of the system and the breakdown of the strong link between velocity and magnetic fields, typical of usual MHD. Moreover, we find that small-scale fluctuations are characterized by an anti-correlation between density and magnetic field intensity. These features characterize the excitation of a quasi-perpendicular magnetosonic turbulence that can be interpreted as the small-scale signature of the break-down of the MHD nonlinear energy cascade due to Hall effect. Fluctuations with the same properties, based on measurements by Cluster spacecraft in space plasma turbulence during different magnetopause crossings, have been recently observed.     

Simulations of nonthermal electron transport in multidimensional flows: synthetic observations of radio galaxies

We have applied an effective numerical scheme for cosmic-ray transport to 3D MHD simulations of jet flow in radio galaxies (see the companion paper by Jones et al. herein). The marriage of relativistic particle and 3D magnetic field information allows us to construct a rich set of ‘synthetic observations’ of our simulated objects. The information is sufficient to calculate the ‘true’ synchrotron emissivity at a given frequency using explicit information about the relativistic electrons. This enables us to produce synchrotron surface-brightness maps, including polarization. Inverse-Compton X-ray surface-brightness maps may also be produced. First results intended to explore the connection between jet dynamics and electron transport in radio lobes are discussed. We infer lobe magnetic field values by comparison of synthetically observed X-ray and synchrotron fluxes, and find these ‘inverse-Compton’ fields to be quite consistent with the actual RMS field averaged over the lobe. The simplest minimum energy calculation from the synthetic observations also seems to agree with the actual simulated source properties.     

A theoretical model of Fanaroff-Riley I jets

A fluid model of the jets in Fanaroff-Riley I class, for extended extragalactic radio sources, based on the idea that they are turbulent low Mach number supersonic flows consisting of relativistic and nonrelativistic plasma, has been developed. Mean flow approach and modified mixing length theory by Prandtl are used to obtain a corresponding mathematical tool. It is assumed that magnetic field is weak. Boundary conditions concerned the problem of the jet propagation through a non-uniform atmospheres of an elliptical galaxies are considered. Short discussion of the observational data determining the choice of the input parameters of the jets is given.     

Relativistic Jets from Accretion Disks

The jets observed to emanate from many compact accreting objects may arise from the twisting of a magnetic field threading a differentially rotating accretion disk which acts to magnetically extract angular momentum and energy from the disk. Two main regimes have been discussed, hydromagnetic jets, which have a significant mass flux and have energy and angular momentum carried by both matter and electromagnetic field and, Poynting jets, where the mass flux is small and energy and angular momentum are carried predominantly by the electromagnetic field. Here, we describe recent theoretical work on the formation of relativistic Poynting jets from magnetized accretion disks. Further, we describe new relativistic, fully electromagnetic, particle-in-cell (PIC) simulations of the formation of jets from accretion disks. Analog Z-pinch experiments may help to understand the origin of astrophysical jets.     

Jets from Young Stars and Compact Objects Environments

Several classes of cosmic objects, such as Young Stellar Objects, Active Galactic Nuclei, Micro-Quasars, Pulsars and probably Gamma Ray Bursts, display powerful winds and jets; for some of them the flow is even ultrarelativistic. For all these classes of objects, the magnetic field is supposed to play a major role in launching and collimating the flow, together with the angular momentum transfer. It probably plays an important role for the turbulent transport in accretion disks also. Regarding the high energy radiation of relativistic jets and the cosmic ray generation, the magnetic field is of course the acceleration agent and could produce the Ultra High Energy Cosmic Rays in some extragalactic objects. The main growth points of these topics are presented, mostly in the case of black hole environments; the case of Young Stellar Objects is more complicated because of the interaction of the stellar magnetosphere with the accretion disk, and the models for this interaction are not yet founded on a reliable theory.     

3-D Rpic Simulations of Relativistic Jets: Particle Acceleration, Magnetic Field Generation, and Emission

We have applied numerical simulations and modeling to the particle acceleration, magnetic field generation, and emission from relativistic shocks. We investigate the nonlinear stage of theWeibel instability and compare our simulations with the observed gamma-ray burst emission. In collisionless shocks, plasma waves and their associated instabilities (e.g., the Weibel, Buneman and other two-stream instabilities) are responsible for particle (electron, positron, and ion) acceleration and magnetic field generation. 3-D relativistic electromagnetic particle (REMP) simulations with three different electron-positron jet velocity distributions and also with an electron-ion plasma have been performed and show shock processes including spatial and temporal evolution of shocks in unmagnetized ambient plasmas. The growth time and nonlinear saturation levels depend on the initial jet parallel velocity distributions. Simulations show that the Weibel instability created in the collisionless shocks accelerates jet and ambient particles both perpendicular and parallel to the jet propagation direction. The nonlinear fluctuation amplitude of densities, currents, electric, and magnetic fields in the electron-positron shocks are larger for smaller jet Lorentz factor. This comes from the fact that the growth time of the Weibel instability is proportional to the square of the jet Lorentz factor. We have performed simulations with broad Lorentz factor distribution of jet electrons and positrons, which is assumed to be created by photon annihilation. Simulation results with this broad distribution show that the Weibel instability is excited continuously by the wide-range of jet Lorentz factor from lower to higher values. In all simulations the Weibel instability is responsible for generating and amplifying magnetic fields perpendicular to the jet propagation direction, and contributes to the electron’s (positron’s) transverse deflection behind the jet head. This small scale magnetic field structure contributes to the generation of “jitter” radiation from deflected electrons (positrons), which is different from synchrotron radiation in uniform magnetic fields. The jitter radiation resulting from small scale magnetic field structures may be important for understanding the complex time structure and spectral evolution observed in gamma-ray bursts or other astrophysical sources containing relativistic jets and relativistic collisionless shocks. The detailed studies of shock microscopic process evolution may provide some insights into early and later GRB afterglows.     

Self-similar solution of hot accretion flows with ordered magnetic field and outflow

Observations and numerical magnetohydrodynamic (MHD) simulations indicate the existence of outflows and ordered large-scale magnetic fields in the inner region of hot accretion flows. In this paper, we present the self-similar solutions for advection-dominated accretion flows (ADAFs) with outflows and ordered magnetic fields. Stimulated by numerical simulations, we assume that the magnetic field has a strong toroidal component and a vertical component in addition to a stochastic component. We obtain the self-similar solutions to the equations describing the magnetized ADAFs, taking into account the dynamical effects of the outflow. We compare the results with the canonical ADAFs and find that the dynamical properties of ADAFs such as radial velocity, angular velocity and temperature can be significantly changed in the presence of ordered magnetic fields and outflows. The stronger the magnetic field is, the lower the temperature of the accretion flow will be and the faster the flow rotates. The relevance to observations is briefly discussed.     

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.     

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.     

Dark matter distribution in the Draco dwarf from velocity moments

If the observed relativistic plasma outflows in astrophysical jets are magnetically collimated and a single-component model is adopted, consisting of a wind-type outflow from a central object, then a problem arises with the inefficiency of magnetic self-collimation to collimate a sizeable portion of the mass and magnetic fluxes in the relativistic outflow from the central object. To solve this dilemma, we have applied the mechanism of magnetic collimation to a two-component model consisting of a relativistic wind-type outflow from a central source and a non-relativistic wind from a surrounding disc. By employing a numerical code for a direct numerical solution of the steady-state problem in the zone of super-fast magnetized flow, which allows us to perform a determination of the flow with shocks, it is shown that in this two-component model it is possible to collimate into cylindrical jets all the mass and magnetic fluxes that are available from the central source. In addition, it is shown that the collimation of the plasma in this system is usually accompanied by the formation of oblique shock fronts. The non-relativistic disc-wind not only plays the role of the jet collimator, but it also induces the formation of shocks as it collides with the initially radial inner relativistic wind and also as the outflow is reflected by the system axis. Another interesting feature of this process of magnetic collimation is a sequence of damped oscillations in the width of the jet.     

Azimuthally symmetric magnetohydrodynamic and two-fluid equilibria with arbitrary flows

Magnetohydrodynamic (MHD) and two-fluid quasi-neutral equilibria with azimuthal symmetry, gravity and arbitrary ratios of (non-relativistic) flow speed to acoustic and Alfvén speeds are investigated. In the two-fluid case, the mass ratio of the two species is arbitrary, and the analysis is therefore applicable to electron–positron plasmas. The methods of derivation can be extended in an obvious manner to several charged species. Generalized Grad–Shafranov equations, describing the equilibrium magnetic field, are derived. Flux-function equations and Bernoulli relations for each species, together with Poisson's equation for the gravitational potential, complete the set of equations required to determine the equilibrium. These are straightforward to solve numerically. The two-fluid system, unlike the MHD system, is shown to be free of singularities. It is demonstrated analytically that there exists a class of incompressible MHD equilibria with magnetic field-aligned flow. A special subclass first identified by S. Chandrasekhar, in which the flow speed is everywhere equal to the local Alfvén speed, is compatible with virtually any azimuthally symmetric magnetic configuration. Potential applications of this analysis include extragalactic and stellar jets, accretion discs, and plasma structures associated with active late-type stars.