Jet simulations extending radially self-similar magnetohydrodynamics models

We perform a numerical simulation of magnetohydrodynamics (MHD) radially self-similar jets, whose prototype is the Blandford & Payne analytical example. The final steady state that is reached is valid close to the rotation axis and also at large distances above the disc where the classical analytical model fails to provide physically acceptable solutions. The outflow starts with a subslow magnetosonic speed, which subsequently crosses all relevant MHD critical points and corresponding magnetosonic separatrix surfaces. The characteristics are plotted together with the Mach cones and the superfast magnetosonic outflow satisfies MHD causality. The final solution remains close enough to the analytical one, which is thus shown to be topologically stable and robust for various boundary conditions.     

Solar coronal heating by magnetic cancellation – III. Thermodynamics

We present two-dimensional numerical magnetohydrodynamics simulations of a coronal X-ray bright point (XBP) caused by a cancelling magnetic feature (CMF). Cancellation is driven by converging motions of two magnetic bipolar sources. These sources are initially disconnected from each other so that both, the CMF and the associated reconnection/heating event (i.e. the XBP), are modelled in a self-consistent way. In the initial state, there is no X-point but two separatrices are present. Hence, the reconnection/heating and the cancellation phases have not yet started. Our numerical experiments end shortly after the converging magnetic bipole has fully cancelled. By this time, reconnection in the inner domain has ceased and occurs only at the base. Solving the energy equation with various heating and cooling terms included, and considering different bottom boundary conditions, reveals that the unrealistically high temperatures produced by Ohmic heating are reduced to more moderate temperatures of 1.5–2 MK consistent with observations of XBPs, if thermal conduction is included and density and temperature are fixed at the base.     

A constructing method for a self-consistent three-dimensional solution of the magnetohydrostatic equations using full-disk magnetogram data

A technique is proposed for constructing self-consistent 3-D solutions satisfying the magnetohydrostatic (MHS) equations, and fitting observations along the line of sight of the magnetic field at the photosphere. The technique is a generalization of a potential-field extrapolation method (Rudenko, 2001) using full-disk magnetogram data. The solution of the problem under consideration is based on representing the magnetic field in terms of a scalar function, with its subsequent harmonic expansion in terms of the functional basic set of spherical functions that satisfies the specified boundary conditions. It is expected that a numerical realization of the proposed method will make possible a real-time modeling of the three-dimensional magnetic field, temperature, pressure and density distributions.     

Reconstructing the IRAS Point Source Catalog Redshift Survey with a generalized PIZA

We study the influence of different magnetic boundary conditions on the generation of magnetic fields by turbulent convection. It is found that the structure and strength of the generated field in the vicinity of the boundary is strongly dependent on the choice of boundary conditions. In the convective interior, however, the solutions remain largely insensitive to the boundary conditions. In all cases the overall efficiency of the dynamo process remains high with a steady state magnetic energy density between 12 and 25 per cent of the turbulent kinetic energy, and peak field values exceeding the equipartition level. These results support the idea that the solar granulation may constitute a dynamo source for magnetic fields in the quiet photosphere.     

On the choice of boundary conditions when studying the turbulent diffusion of magnetic fields

In this paper, we present a discussion and results pertaining to the role of the choice of the boundary conditions in models that seek to address the form of the quenching of the turbulent magnetic diffusivity. We show that, for several natural choices of boundary conditions frequently selected in numerical investigations, 'weak' magnetic fields have a profound effect on the rate of diffusion. We go on to discuss further results that suggest a way by which such a catastrophic quenching may be avoided.     

General polytropic magnetofluid under self-gravity: Voids and shocks

We study the self-similar magnetohydrodynamics (MHD) of a quasi-spherical expanding void (viz. cavity or bubble) surrounding the centre of a self-gravitating gas sphere with a general polytropic equation of state. We show various analytic asymptotic solutions near the void boundary in different parameter regimes and obtain the corresponding void solutions by extensive numerical explorations. We find novel void solutions of zero density on the void boundary. These new void solutions exist only in a general polytropic gas and feature shell-type density profiles. These void solutions, if not encountering the magnetosonic critical curve (MCC), generally approach the asymptotic expansion solution far from the central void with a velocity proportional to radial distance. We identify and examine free-expansion solutions, Einstein–de Sitter expansion solutions, and thermal-expansion solutions in three different parameter regimes. Under certain conditions, void solutions may cross the MCC either smoothly or by MHD shocks, and then merge into asymptotic solutions with finite velocity and density far from the centre. Our general polytropic MHD void solutions provide physical insight for void evolution, and may have astrophysical applications such as massive star collapses and explosions, shell-type supernova remnants and hot bubbles in the interstellar and intergalactic media, and planetary nebulae.     

Viscosity alpha in rotating spherical shear flows with an external magnetic field

We study the turbulent behaviour induced by the magnetic shear instability for a magnetized, incompressible fluid in a spherical shell. A differential rotation that is decreasing outwards but hydrodynamically stable according to the Rayleigh criterion is prescribed, and an external, uniform magnetic field is imposed parallel to the rotation axis. Our main concern in this paper is the fully global treatment of this magnetohydrodynamical system, so we focus particular attention on the influence of the boundary conditions. Non-linear, steady solutions are presented for stress-free as well as for rigid boundary conditions for one specific model with a fixed strength of the external magnetic field and a fixed differential rotation rate. We calculate the eddy viscosity ν_T and the viscosity alpha α_SS resulting from the total stress tensor. These turbulence parameters turn out to differ drastically depending on the boundary conditions for the flow. An investigation of the radial structure of the viscosity alpha (whilst varying the differential rotation law) shows that the enhanced generation of turbulence takes place mainly in the boundary layers of the shell.     

Launching mechanisms of astrophysical jets

The combination of accretion disks and supersonic jets is used to model many active astrophysical objects, viz., young stars, relativistic stars, and active galactic nuclei. However, existing theories on the physical processes by which these structures transfer angular momentum and energy from disks to jets through viscous or magnetic torques are still relatively approximate. Global stationary solutions do not permit understanding the formation and stability of these structures; and global numerical simulations that include both the disk and jet physics are often limited to relatively short time scales and astrophysically out-of-range values of viscosity and resistivity parameters that are instead crucial to defining the coupling of the inflow/outflow dynamics. Along these lines we discuss self-consistent time-dependent simulations of the launching of supersonic jets by magnetized accretion disks, using high resolution numerical techniques. We shall concentrate on the effects of the disk physical parameters, and discuss under which conditions steady state solutions of the type proposed in the self-similar models of Blandford and Payne can be reached and maintained in a self-consistent nonlinear stationary state.     

Force-free magnetosphere of an aligned rotator with differential rotation of open magnetic field lines

Here we briefly report on results of self-consistent numerical modeling of a differentially rotating force-free magnetosphere of an aligned rotator. We show that differential rotation of the open field line zone is significant for adjusting of the global structure of the magnetosphere to the current density flowing through the polar cap cascades. We argue that for most pulsars stationary cascades in the polar cap can not support stationary force-free configurations of the magnetosphere.      

Invariant distributions and collisionless equilibria

This paper discusses the possibility of constructing time-independent solutions to the collisionless Boltzmann equation which depend on quantities other than global isolating integrals such as energy and angular momentum. The key point is that, at least in principle, a self-consistent equilibrium can be constructed from any set of time-independent phase-space building blocks which, when combined, generate the mass distribution associated with an assumed time-independent potential. This approach provides a way to justify Schwarzschild's method for the numerical construction of self-consistent equilibria with arbitrary time-independent potentials, generalizing thereby an approach developed by Vandervoort for integrable potentials. As a simple illustration, Schwarzschild's method is reformulated to allow for a straightforward computation of equilibria which depend only on one or two global integrals and no other quantities, as is reasonable, for example, for modelling axisymmetric configurations characterized by a non-integrable potential.     

MHD Simulation of Comets: The Plasma Environment of Comet Hale-Bopp

MHD simulation results of the interaction of the expanding atmosphere of comet Hale-Bopp with the magnetized solar wind are presented. At the upstream boundary a supersonic and superalfvénic solar wind enters into the simulation box 25 million km upstream of the nucleus. The solar wind is continuously mass loaded with cometary ions originating from the nucleus. The effects of photoionization, recombination and ion-neutral frictional drag are taken into account in the model. The governing equations are solved on an adaptively refined unstructured Cartesian grid using our MUSCL-type upwind numerical technique, MAUS-MHD (Multiscale Adaptive Upwind Scheme for MHD). The combination of the adaptive refinement with the MUSCL-scheme allows the entire cometary atmosphere to be modeled, while still resolving both the shock and the diamagnetic cavity of the comet. Detailed simulation results for the plasma environment of comet Hale-Bopp for slow and fast solar wind conditions are presented. We also calculate synthetic H₂O⁺, CO⁺ and soft x-ray images for observing conditions on April 11, 1997. This revised version was published online in July 2006 with corrections to the Cover Date.     

Magnetized centrifugal winds

It is argued that for steady, axisymmetric, non-relativistic magneto-centrifugal winds, not only the boundary and criticality conditions but also the current-closure condition are of crucial significance as global conditions in resolving the acceleration-collimation problem. In Sakurai's numerical models, the split-monopole field adopted at the surface of the source provided the most favourable condition for global collimation of the flow, by making the domain of anti -collimating flow with outgoing electric current degenerate into an infinitely thin boundary layer at the equator, and hence suppressing the explicit appearance of the current-closure condition.
For more general or realistic boundary conditions at the source, it is shown that the current-closure condition yields a two-component structure (with the return current at least in part in a volume current, not totally a sheet current) as a natural consequence of the transfield equation in the asymptotic domain. This equation, combined with the Bernoulli (and other) integrals, requires the wind to tend asymptotically to a 'quasi-conical' structure, as a natural consequence of the flow particles' becoming more and more ballistic as a result of the magnetohydrodynamic (MHD) acceleration. This is a result that the Poynting energy flux diminishes to zero along each field line. The criticality problem is solved for magneto-centrifugal winds, to give the eigenvalues of the Alfvénic distance and other quantities at the fast magnetosonic surface, situated somewhere between the subasymptotic and asymptotic domains.     

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.     

Dynamo theory and liquid metal MHD experiments

High values of magnetic Reynolds number R_m are characteristic not only to astrophysics, but also to other interesting objects, including liquid metal (LM) flows. Since sixties LM experiments have been performed illustrating important predictions of the dynamo theory, for example, about the existence and features of the α effect. Consideration of so called “laminar” dynamos provides a theoretical base for direct experimental realization and examination of the dynamo process. First step results, gathered at subcritical conditions, confirm the statement that self-excitation in LM experiments can be achieved practically today. In such devices as LM (sodium) cooled fast breeders R_m can reach values up to 50 and specific MHD phenomena have been observed in operating fast reactors. Cautions against crisis like processes have been expressed. It is important for the dynamo theory to understand what kind of perturbed motion is able to coexist with the generated magnetic field. Fundamentally new ideas here are issuing from the theory of 2D MHD turbulence. LM MHD served for the first direct proves, confirming, that the predicted surprising features of 2D turbulence can be observed in reality. It is worth incorporating these already not new ideas in the dynamo theory. In such a way a field for new solutions could be established.     

The global structure of the solar wind in June 1991

A numerical simulation of the global solar wind structure for Carrington rotation 1843 (31 May–28 June, 1991) is performed based on a fully three-dimensional, steady-state MHD model of the solar wind (Usmanov, 1993b). A self-consistent solution for 3-D MHD equations is constructed for the spherical shell extending from the solar photosphere up to 10 AU. Solar magnetic field observations are used to prescribe boundary conditions. The computed distribution of the magnetic field is compared with coronal hole observations and with the IMF measurements made by IMP-8 spacecraft at the Earth's orbit.     

Propagation of disturbances in the solar chromosphere and corona (II)

The first part of this article presents an analytic discussion of the linear properties of magnetohydrodynamic (MHD) wave propagation. Then, with a 2-dimensional, time-dependent, compressible MHD simulation subject to a self-consistent non-isothermal, non-uniform initial state, we study numerically the global propagation process following an initial pressure pulse applied at the base of the chromosphere. Our numerical results indicate that, if the pulse is applied near the pole, there are two modes, one fast, one slow of magnetoacoustic waves; whereas if the pressure pulse is applied near the equator, there is a fast mode and a standing disturbance located near the source. These results may help interpret the wave events observed by SOHO/EIT.     

A mathematical magnetospheric field model with independent physical parameters

A quantitative magnetospheric magnetic field model has been calculated in three dimensions. The model is based on an analytical solution of the Chapman-Ferraro problem. For this solution, the magnetopause was assumed to be an infinitesimally thin discontinuity with given geometry. The shape of the dayside magnetopause is in agreement with measurements derived from spacecraft boundary crossings.The magnetic field of the magnetopause currents can be derived from scalar potentials. The scalar potentials result from solutions of Laplace's equation with Neumann's boundary conditions. The boundary values and the magnetic flux through the magnetopause are determined by all magnetic sources which are located inside and outside the magnetospheric cavity. They include the Earth's dipole field, the fields of the equatorial ring current and tail current systems, and the homogeneous interplanetary magnetic field. In addition, the flux through the magnetopause depends on two constants of interconnection which provide the possibility of calculating static interconnection between magnetospheric and interplanetary field lines. Realistic numerical values for both constants have been derived empirically from observed displacements of the polar cusps which are due to changes in the orientation of the interplanetary field. The transition from a closed to an open magnetosphere and vice versa can be computed in terms of a change of the magnetic boundary conditions on the magnetopause. The magnetic field configuration of the closed magnetosphere is independent of the amount and orientation of the interplanetary field. In contrast, the configuration of the open magnetosphere confirms the observational finding that field line interconnection occurs primarily in the polar cusp and high latitude tail regions.The tail current system reflects explicitly the effect of dayside magnetospheric compression which is caused by the solar wind. In addition, the position of the plasma sheet relative to the ecliptic plane depends explicitly on the tilt angle of the Earth's dipole. Near the tail axis, the tail field is approximately in a self-consistent equilibrium with the tail currents and the isotropic thermal plasma.The models for the equatorial ring current depend on the D_st-parameter. They are self-consistent with respect to measured energy distributions of ring current protons and the axially symmetric part of the magnetospheric field.     

Cosmological dynamics of a non-minimally coupled bulk scalar field in DGP setup

We consider cosmological dynamics of a canonical bulk scalar field, which is coupled non-minimally to 5-dimensional Ricci scalar in a DGP setup. We show that presence of this non-minimally coupled bulk scalar field affects the jump conditions of the original DGP model significantly. Within a superpotential approach, we perform some numerical analysis of the model parameter space and consider bulk-brane energy exchange in this setup. Also we show that the normal, ghost-free branch of the DGP solutions in this case has the potential to realize a self-consistent phantom-like behavior and therefore explains late time acceleration of the universe in a consistent way.     

Magnetic fields and radio polarization of barred galaxies

In order to simulate evolution of a large-scale magnetic field in a barred galaxy possessing a gaseous halo we apply a three-dimensional (3D) MHD numerical model. We solve a induction equation using a time-dependent velocity field of molecular gas resulting from self-consistent 3D N-body simulations of a galactic disk. The gaseous halo rotates differentially co-rotating with the disk. In our model we introduce the dynamo process causing the amplification of the magnetic field as well as the formation of field structures high above the galactic disk. The simulated magnetic fields are used to construct the models of a high-frequency (Faraday rotation-free) polarized radio emission that accounts for effects of projection and limited resolution, and is thus suitable for direct comparison with observations. We found that the resultant magnetic field correctly reproduces the observed structures of polarization B-vectors, forming coherent patterns well aligned with spiral arms and with the bar. The process initializing a wave-like behavior of the magnetic field, which efficiently forms magnetic maxima between the spiral arms, is demonstrated. This revised version was published online in August 2006 with corrections to the Cover Date.