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.     

Subcritical dynamos in shear flows

Identifying generic physical mechanisms responsible for the generation of magnetic fields and turbulence in differentially rotating flows is fundamental to understand the dynamics of astrophysical objects such as accretion disks and stars. In this paper, we discuss the concept of subcritical dynamo action and its hydrodynamic analogue exemplified by the process of nonlinear transition to turbulence in non‐rotating wall‐bounded shear flows. To illustrate this idea, we describe some recent results on nonlinear hydrodynamic transition to turbulence and nonlinear dynamo action in rotating shear flows pertaining to the problem of turbulent angular momentum transport in accretion disks. We argue that this concept is very generic and should be applicable to many astrophysical problems involving a shear flow and non‐axisymmetric instabilities of shearinduced axisymmetric toroidal velocity or magnetic fields, such as Kelvin‐Helmholtz, magnetorotational, Tayler or global magnetoshear instabilities. In the light of several recent numerical results, we finally suggest that, similarly to a standard linear instability, subcritical MHD dynamo processes in high‐Reynolds number shear flows could act as a large‐scale driving mechanism of turbulent flows that would in turn generate an independent small‐scale dynamo. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Magnetohydrodynamic properties of extragalactic jets

The theory that magnetic fields are instrumental in the formation and propagation of jets in active galactic nuclei dates back four decades. Despite a recent growing consensus on this notion stemming from the results of numerical simulations of magnetohydrodynamic (MHD) flows near black holes, the precise dynamical role of magnetic fields in observed parsec and kiloparsec jets remains uncertain. Some of the unanswered fundamental questions about extragalactic jets include the location where the flow becomes relativistic and where acceleration and collimation terminate, as well as the specifics of how the flow interacts with the ISM. Such observed properties as superluminal motions and wiggled structures based on numerical simulations to constitute the foundation of an MHD paradigm for extragalactic jets. We particularly focus our attention to the M87 jet, which is one of the best candidates to investigate relativistic outflows in extragalactic system.     

Simulations of the axisymmetric magnetospheres of neutron stars

In this paper we present the results of time-dependent simulations of the dipolar axisymmetric magnetospheres of neutron stars carried out within the frameworks of both relativistic magnetohydrodynamics (MHD) and resistive force-free electrodynamics. The results of force-free simulations reveal the inability of our numerical method to accommodate the equatorial current sheets of pulsar magnetospheres, and raise a question mark about the robustness of this approach. On the other hand, the MHD approach allows us to make significant progress. We start with a non-rotating magnetically dominated dipolar magnetosphere and follow its evolution as the stellar rotation is switched on. We find that the time-dependent solution gradually approaches a steady state that is very close to the stationary solution of the pulsar equation found in 1999 by Contopoulos, Kazanas & Fendt. This result suggests that other stationary solutions that have the Y-point located well inside the light cylinder are unstable. The role of particle inertia and pressure on the structure and dynamics of MHD magnetospheres is studied in detail, as well as the potential implications of dissipative processes in the equatorial current sheet. We argue that pulsars may have differentially rotating magnetospheres which develop noticeable structural oscillations, and that this may help to explain the nature of the subpulse phenomena.     

Laboratory plasma dynamos, astrophysical dynamos and magnetic helicity evolution

The term 'dynamo' means different things to the laboratory fusion plasma and astrophysical plasma communities. To alleviate the resulting confusion and to facilitate interdisciplinary progress, we pinpoint conceptual differences and similarities between laboratory plasma dynamos and astrophysical dynamos. We can divide dynamos into three types: 1. magnetically dominated helical dynamos which sustain a large-scale magnetic field against resistive decay and drive the magnetic geometry towards the lowest energy state, 2. flow-driven helical dynamos which amplify or sustain large-scale magnetic fields in an otherwise turbulent flow and 3. flow-driven non-helical dynamos which amplify fields on scales at or below the driving turbulence. We discuss how all three types occur in astrophysics whereas plasma confinement device dynamos are of the first type. Type 3 dynamos require no magnetic or kinetic helicity of any kind. Focusing on Types 1 and 2 dynamos, we show how different limits of a unified set of equations for magnetic helicity evolution reveal both types. We explicitly describe a steady-state example of a Type 1 dynamo, and three examples of Type 2 dynamos: (i) closed volume and time dependent; (ii) steady state with open boundaries; (iii) time dependent with open boundaries.     

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.     

Magnetohydrodynamic behaviour of a finite amplitude disturbance in the solar magnetic field

In this paper, dynamic processes in the solar atmosphere are studied numerically from a complete set of MHD equations. Dynamic evolution of the non-linear magnetic field is produced by the finite amplitude of the azimuthai magnetic field at the base of the flux tube of the solar atmosphere. It is assumed that the initial configuration of the magnetic field is a force-free and potential field, the magnetic field is disturbed at the base, the plasma is driven and a part of the magnetic energy is transformed into the kinetic energy of the plasma.The compressed flow of the plasma has the features of fast MHD waves. The computation results give quantitatively the non-linear evolution of strong magnetic fields. These results could be used in an explanation of coronal transients, surge, spray and eruptive prominence events in the solar atmosphere, as well as in a modelling of plasma behaviour in high-β structure experiments in the laboratory.     

Numerical Simulation of the Creation of a Current Sheet During the Flare of 30 May 1991

Current-sheet creation in three dimensions above an active region is shown in a numerical experiment. The calculations are performed for the complex magnetic field of an active region. The PERESVET program solves the 3D resistive compressible MHD equations.     

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.     

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.     

Modeling the Resistive MHD by the Cese Method

In this paper, the Space–Time Conservation Element and Solution Element (CESE) method is applied to 2.5-dimensional resistive magnetohydrodynamics (MHD) equations in Cartesian coordinates, with the purpose of modeling the magnetic reconnection study. To show the validity and capacity of its application to MHD reconnection problem, spontaneous fast reconnection and magnetic reconnection in multiple heliospheric current sheets are studied, which show good consistency with those obtained formerly by other authors. In order to assess the ∇ ⋅ B = 0 constraint numerically, the contours and evolution of ∇ ⋅ B are analyzed. The numerical results tell us that the CESE numerical scheme not only has good numerical resolution but also can keep the divergence-free condition for magnetic fields in the reconnection problems during the evolutionary process without any special treatment.     

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.     

On the validity of quasi-linear kinematic mean-field electrodynamics in astrophysical flows

Mean-field theory in its kinematic form with the quasi-linear approximation is widely used for the modelling of the transport of weak magnetic fields in turbulent media. The validity of this approach to real astrophysical flows is discussed. Numerically evaluating the turbulent electromotive force using Lagrangian analysis for a set of simple, prescribed 2D flow patterns with a wide range of parameters, we find that quasi-linear expressions for the turbulent diffusivities and for the pumping velocities are correct within a factor of 2 for a wide variety of flow types with order of unity (or even higher) effective Strouhal numbers. The degree of the non-linear quenching of turbulent transport by a weak magnetic field is also discussed. We argue that, owing to the intermittency and small filling factors of magnetic fields in realistic astrophysical media, diffusivity and pumping effects are not quenched to order of magnitude, while a more moderate quenching of order 10 per cent is still present.     

Numerical construction of magnetosphere with relativistic two-fluid plasma flows

We present a numerical model in which a cold pair plasma is ejected with relativistic speed through a polar cap region and flows almost radially outside the light cylinder. Stationary axisymmetric structures of electromagnetic fields and plasma flows are self-consistently calculated. In our model, motions of positively and negatively charged particles are assumed to be determined by electromagnetic forces and inertial terms, without pair creation and annihilation or radiation loss. The global electromagnetic fields are calculated by the Maxwell's equations for the plasma density and velocity, without using ideal magnetohydrodynamic condition. Numerical result demonstrates the acceleration and deceleration of plasma due to parallel component of the electric fields. Numerical model is successfully constructed for weak magnetic fields or highly relativistic fluid velocity, i.e. kinetic energy dominated outflow. It is found that appropriate choices of boundary conditions and plasma injection model at the polar cap should be explored in order to extend present method to more realistic pulsar magnetosphere, in which the Poynting flux is dominated.     

Effects of finite resistivity on magnetorotational instabilities in a realistic accretion flow

A local perturbation analysis is performed on a realistic background accretion flow in a global magnetic field. The adopted background model is an analytic solution to the resistive MHD equations and describes magnetically-controlled advection-dominated accretion flows (ADAFs) with an accuracy to the first order in the resistive corrections. The results show that there are three independent wave modes, which may be called the Rayleigh, Balbus–Hawley and resistive modes. Within our resistive-MHD corrections to the ideal-MHD limit, a Balbus–Hawley-like criterion for the instability of axisymmetric perturbations appears as a consequence of the competition between damping due to magnetic diffusion and excitation due to shear flow. As for non-axisymmetric perturbations, the former two modes are likely to be unstable in the presence of shears because the magnetic diffusion acts as a stabilizer only to axisymmetric perturbations within our approximation.     

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.     

Dynamic evolution of a quasi-spherical general polytropic magnetofluid with self-gravity

In various astrophysical contexts, we analyze self-similar behaviours of magnetohydrodynamic (MHD) evolution of a quasi-spherical polytropic magnetized gas under self-gravity with the specific entropy conserved along streamlines. In particular, this MHD model analysis frees the scaling parameter n in the conventional polytropic self-similar transformation from the constraint of n+γ=2 with γ being the polytropic index and therefore substantially generalizes earlier analysis results on polytropic gas dynamics that has a constant specific entropy everywhere in space at all time. On the basis of the self-similar nonlinear MHD ordinary differential equations, we examine behaviours of the magnetosonic critical curves, the MHD shock conditions, and various asymptotic solutions. We then construct global semi-complete self-similar MHD solutions using a combination of analytical and numerical means and indicate plausible astrophysical applications of these magnetized flow solutions with or without MHD shocks.     

Nonresonant generation of MHD disturbances during supernova explosions in an inhomogeneous interstellar medium

We analyze the nonresonant generation of large-scale magnetic inhomogeneities near a shock front by accelerated particles. The MHD disturbances are generated by the electric current excited by relativistic particles in the preshock medium in the presence of weak large-scale density inhomogeneities. The MHD modes considered can be amplified by other resonant and nonresonant mechanisms related to the presence of relativistic particles. We estimate the magnetic fields and the energies to which charged particles can be accelerated in different phases of the interstellar medium by taking into account the random magnetic fields generated by the mechanism considered.     

Newtonian non-linear hydrodynamics and magnetohydrodynamics

We use covariant techniques to study the non-linear evolution of self-gravitating, non-relativistic media. The formalism is first applied to imperfect fluids, aiming at the kinematic effects of viscosity, before extended to inhomogeneous magnetized environments. The non-linear electrodynamic formulae are derived and successively applied to electrically resistive and to highly conductive fluids. By nature, the covariant equations isolate the magnetic effects on the kinematics and the dynamics of the medium, combining mathematical transparency and physical clarity. Employing the Newtonian analogue of the relativistic 1 + 3 covariant treatment also facilitates the direct comparison with the earlier relativistic studies and helps to identify the differences in an unambiguous way. The purpose of this work is to set the framework and take a first step towards the detailed analytical study of complex non-linear systems, like non-relativistic astrophysical plasmas and collapsing protogalactic clouds.