On the MHD effects on the force-free monopole outflow

The stationary axisymmetric outflow from a rotating sphere with a (split) monopole magnetic field is considered. The stream equation describing the outflow is linearized in terms of the Michel magnetization parameter σ⁻¹ ≪ 1, which allows a self-consistent analysis of the direct problem. It is shown that for a finite σ the fast magnetosonic surface is located at a finite distance ∼ σ^1/3 R _L ( R _L =  c /Ω_F is the light cylinder). We have also found that the particle energy at the fast surface is just equal to the Michel value γ ∼ 1/3σ. The particle acceleration and magnetic field collimation are shown to become ineffective outside the fast magnetosonic surface.     

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.     

Self-similar dynamics of a magnetized polytropic gas

In broad astrophysical contexts of large-scale gravitational collapses and outflows and as a basis for various further astrophysical applications, we formulate and investigate a theoretical problem of self-similar magnetohydrodynamics (MHD) for a non-rotating polytropic gas of quasi-spherical symmetry permeated by a completely random magnetic field. Within this framework, we derive two coupled nonlinear MHD ordinary differential equations (ODEs), examine properties of the magnetosonic critical curve, obtain various asymptotic and global semi-complete similarity MHD solutions, and qualify the applicability of our results. Unique to a magnetized gas cloud, a novel asymptotic MHD solution for a collapsing core is established. Physically, the similarity MHD inflow towards the central dense core proceeds in characteristic manners before the gas material eventually encounters a strong radiating MHD shock upon impact onto the central compact object. Sufficiently far away from the central core region enshrouded by such an MHD shock, we derive regular asymptotic behaviours. We study asymptotic solution behaviours in the vicinity of the magnetosonic critical curve and determine smooth MHD eigensolutions across this curve. Numerically, we construct global semi-complete similarity MHD solutions that cross the magnetosonic critical curve zero, one, and two times. For comparison, counterpart solutions in the case of an isothermal unmagnetized and magnetized gas flows are demonstrated in the present MHD framework at nearly isothermal and weakly magnetized conditions. For a polytropic index γ=1.25 or a strong magnetic field, different solution behaviours emerge. With a strong magnetic field, there exist semi-complete similarity solutions crossing the magnetosonic critical curve only once, and the MHD counterpart of expansion-wave collapse solution disappears. Also in the polytropic case of γ=1.25, we no longer observe the trend in the speed-density phase diagram of finding infinitely many matches to establish global MHD solutions that cross the magnetosonic critical curve twice.      

The effective acceleration of plasma outflow in the paraboloidal magnetic field

The problem of the efficiency of particle acceleration for a paraboloidal poloidal magnetic field is considered within the approach of steady axisymmetric magnetohydrodynamic (MHD) flow. For the large Michel magnetization parameter σ it is possible to linearize the stream equation near the force-free solution and to solve the problem self-consistently as was done by Beskin, Kuznetsova & Rafikov for a monopole magnetic field. It is shown that, on the fast magnetosonic surface (FMS), the particle Lorentz factor γ does not exceed the standard value  σ^1/3  . On the other hand, in the supersonic region, the Lorentz factor grows with the distance z from the equatorial plane as  γ≈ ( z / R _L)^1/2  up to the distance   z ≈σ² R _L  , where   R _L= c /Ω_F  is the radius of the light cylinder. Thus, the maximal Lorentz factor is  γ_max≈σ  , which corresponds to almost the full conversion of the Poynting energy flux into the particle kinetic one.     

Magnetized accretion flows: effects of gas pressure

We study how axisymmetric magnetohydrodynamic (MHD) accretion flows depend on γ adiabatic index in the polytropic equation of state. This work is an extension of Mościbrodzka & Proga, where we investigated the γ dependence of two-dimensional Bondi-like accretion flows in the hydrodynamical (HD) limit. Our main goal is to study if simulations for various γ can give us insights into the problem of various modes of accretion observed in several types of accretion systems, such as black hole binaries (BHBs), active galactic nuclei (AGN) and gamma-ray bursts. We find that for  γ≳ 4/3  , the fast-rotating flow forms a thick torus that is supported by rotation and gas pressure. As shown before for  γ= 5/3  , such a torus produces a strong, persistent bipolar outflow that can significantly reduce the polar funnel accretion of a slowly rotating flow. For low γ, close to 1, the torus is thin and is supported by rotation. The thin torus produces an unsteady outflow which is too weak to propagate throughout the polar funnel inflow. Compared to their HD counterparts, the MHD simulations show that the magnetized torus can produce an outflow and does not exhibit regular oscillations. Generally, our simulations demonstrate how the torus thickness affects the outflow production. They also support the notion that the geometrical thickness of the torus correlates with the power of the torus outflow. Our results, applied to observations, suggest that the torus ability to radiatively cool and become thin can correspond to a suppression of a jet as observed in the BHBs during a transition from a hard/low to soft/high spectral state and a transition from a quiescent to hard/low state in AGN.     

On the magnetohydrodynamic decollimation in compact objects

A simple analytical model of the particle-dominated outflow with zero total electric current from central rotating objects is considered. 'Exact' solutions for both relativistic and non-relativistic cases demonstrate the decollimation of the magnetic field lines in the region of the current closure. Such a decollimation can explain the presence of an energetic equatorial wind observed in many compact objects.     

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.     

Stability of magnetic equilibria in radio bubbles

Current-carrying flows, in the laboratory and in astrophysical jets, can form remarkably stable magnetic structures. Decades of experience show that such flows often build equilibria that reverse field directions, evolving to a magnetohydrodynamic (MHD) Taylor state, which has remarkable stability properties. We model jets and the magnetic bubbles they build as reversed-field pinch equilibria by assuming the driver current to be stiff in the MHD sense. Taking the jet current as rigid and a fixed function of position, we prove a theorem: that the same, simple MHD stability conditions guarantee stability, even after the jet turns off. This means that magnetic structures harbouring a massive inventory of magnetic energy can persist long after the building jet current has died away. These may be the relic radio 'fossils', 'ghost bubbles' or 'magnetic balloons' found in clusters. These equilibria, which are under magnetic tension, will evolve, retaining the stability properties from that state. The remaining fossil is not a disordered ball of magnetic fields, but a stable structure under tension, able to respond to the slings and arrows of outside forces. Typically their Alfvén speeds greatly exceed the cluster sound speed, and so they can keep out hot cluster plasma, leading to X-ray ghosts. Passing shocks cannot easily destroy them, but can energize and light them up anew at radio frequencies. Bubbles can rise in the hot cluster plasma, perhaps detaching from the parent radio galaxy but stable against Rayleigh–Taylor and other modes.     

新单极高速分子外向流源IRAS19282+1814

^12CoJ=1-0成图观测表明在IRAS19282 1814附近存在着一个蓝向单极高速分子外流，计算了其基本参量并进行了分析，它的成协红外源IRAS19282 1814可能是大质量年轻星体，其IRAS波段色指数表明该源深埋于气体和尘埃物质之中，由60-100μm流量密度获得尘埃温度为30K,它的附近没有其他的源，所以IRAS19282 1814可能是外向流的驱动源。     

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.     

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.     

MHD waves in the solar north polar coronal hole

The effects, hitherto not treated, of the temperature and the number density gradients, both in the parallel and the perpendicular direction to the magnetic field, of O VI ions, on the MHD wave propagation characteristics in the solar North Polar Coronal Hole are investigated. We investigate the magnetosonic wave propagation in a resistive MHD regime where only the thermal conduction is taken into account. Heat conduction across the magnetic field is treated in a non‐classical approach wherein the heat is assumed to be conducted by the plasma waves emitted by ions and absorbed at a distance from the source by other ions. Anisotropic temperature and the number density distributions of O VI ions revealed the chaotic nature of MHD standing wave, especially near the plume/interplume lane borders. Attenuation length scales of the fast mode is shown not to be smoothly varying function of the radial distance from the Sun (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

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.     

Wisps and knots in the central Crab nebula

The fast-spinning Crab pulsar (∼30 turn s⁻¹), which powers the massive expansion and synchrotron emission of the entire Crab nebula, is surrounded by quasi-stationary features such as fibrous arc-like wisps and bright polar knots in the radial range of 2×10¹⁶≲ r ≲2×10¹⁷ cm, as revealed by high-resolution (∼0.1 arcsec) images from the Wide Field and Planetary Camera 2 (WFPC2) on board the Hubble Space Telescope ( HST ). The spin-down energy flux (∼5×10³⁸ erg s⁻¹) from the pulsar to the luminous outer nebula, which occupies the radial range 0.1≲ r ≲2 pc, is generally believed to be transported by a magnetized relativistic outflow of an electron–positron e^± pair plasma. It is then puzzling that mysterious structures like wisps and knots, although intrinsically dynamic in synchrotron emission, remain quasi-stationary on time-scales of a few days to a week in the relativistic pulsar wind. Here we demonstrate that, as a result of slightly inhomogeneous wind streams emanating from the rotating pulsar, fast magnetohydrodynamic (MHD) shock waves are expected to appear in the pulsar wind at relevant radial distances in the forms of wisps and knots. While forward fast MHD shocks move outward with a speed close to the speed of light c , reverse fast MHD shocks may appear quasi-stationary in space under appropriate conditions. In addition, Alfvénic fluctuations in the shocked magnetized pulsar wind can effectively scatter synchrotron beams from gyrating relativistic electrons and positrons.     

A self-consistent model for the S140/L1204 region

Comparison of submillimetre continuum observations of the L1204/S140 complex with previous high resolution CS, NH₃ and CI observations provides evidence that, for the first time, demonstrates the PDR and outflow are intimately linked. The only scenario that is able to explain all of the available molecular and atomic emission line data and our submillimetre continuum data, is one in which the outflow has expanded towards the edge of the molecular cloud and the edge of the blueshifted outflow lobe is now bounded by the expanding HII region. The NH₃ and continuum emission emanate from the inner edge of the outflow lobe, shielded from the external UV field.     

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.     

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.     

Ballooning modes in the inner magnetosphere of the Earth

In this paper the low-frequency ideal MHD (magnetohydrodynamical) perturbations in the inner magnetosphere of the Earth are studied. The set of partial differential equations obtained from the MHD equations in the ballooning approximation and the dipole model of the geomagnetic field is used for this purpose. These equations describe both small-scale and large-scale perturbations in the magnetospheric plasmas. In the “cold” plasma approximation the obtained equations describe poloidal and toroidal standing Alfvén modes. The account of plasma pressure leads to the appearance of an additional type of oscillations—the slow magnetosonic modes. The stability of the magnetospheric plasma with respect to the ballooning perturbations was analyzed. We describe the ballooning perturbations taking into account a coupling between the poloidal Alfvén modes and the slow magnetosonic modes.     

Peculiarities of entropy and magnetosonic waves in optically thin cosmic plasma

The stability problem for small magnetohydrodynamic (MHD) perturbations in an optically thin, perfectly conducting uniform plasma with a cosmic abundance of elements is solved in the linear approximation. The electron heat conduction along the magnetic field and the proton heat conduction across the field are taken into account. We have shown for the first time that the entropy waves can grow exponentially, while the magnetosonic waves are damped in a wide range of physical conditions closest to the conditions in stellar coronae with the proper allowance for radiative losses. Slow magnetosonic waves are damped particularly rapidly. For the solar corona, the calculated damping decrement of slow magnetosonic waves agrees well with the averaged one in 11 quasi-periodic events observed from the TRACE satellite in extreme ultraviolet radiation. Other possible astrophysical applications of the results obtained are briefly discussed.