Energy, angular momentum and wave action associated with density waves in a rotating magnetized gas disc

Both fast and slow magnetohydrodynamic (MHD) density waves propagating in a thin rotating magnetized gas disc are investigated. In the tight-winding or WKBJ regime, the radial variation of MHD density-wave amplitude during wave propagation is governed by the conservation of wave action surface density which travels at a relevant radial group speed C _g. The wave energy surface density and the wave angular momentum surface density are related to by = and = m respectively, where is the angular frequency in an inertial frame of reference and the integer m , proportional to the azimuthal wavenumber, corresponds to the number of spiral arms. Consequently, both wave energy and angular momentum are conserved for spiral MHD density waves. For both fast and slow MHD density waves, net wave energy and angular momentum are carried outward or inward for trailing or leading spirals, respectively. The wave angular momentum flux contains separate contributions from gravity torque, advective transport and magnetic torque. While the gravity torque plays an important role, the latter two can be of comparable magnitudes to the former. Similar to the role of gravity torque, the part of MHD wave angular momentum flux by magnetic torque (in the case of either fast or slow MHD density waves) propagates outward or inward for trailing or leading spirals, respectively. From the perspective of global energetics in a magnetized gas sheet in rotation, trailing spiral structures of MHD density waves are preferred over leading ones. With proper qualifications, the generation and maintenance as well as transport properties of MHD density waves in magnetized spiral galaxies are discussed.     

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.     

Driven waves in a two-fluid plasma

We study the physics of wave propagation in a weakly ionized plasma, as it applies to the formation of multifluid, magnetohydrodynamics (MHD) shock waves. We model the plasma as separate charged and neutral fluids which are coupled by ion–neutral friction. At times much less than the ion–neutral drag time, the fluids are decoupled and so evolve independently. At later times, the evolution is determined by the large inertial mismatch between the charged and neutral particles. The neutral flow continues to evolve independently; the charged flow is driven by and slaved to the neutral flow by friction. We calculate this driven flow analytically by considering the special but realistic case where the charged fluid obeys linearized equations of motion. We carry out an extensive analysis of linear, driven, MHD waves. The physics of driven MHD waves is embodied in certain Green functions which describe wave propagation on short time-scales, ambipolar diffusion on long time-scales and transitional behaviour at intermediate times. By way of illustration, we give an approximate solution for the formation of a multifluid shock during the collision of two identical interstellar clouds. The collision produces forward and reverse J shocks in the neutral fluid and a transient in the charged fluid. The latter rapidly evolves into a pair of magnetic precursors on the J shocks, wherein the ions undergo force-free motion and the magnetic field grows monotonically with time. The flow appears to be self-similar at the time when linear analysis ceases to be valid.     

Compressible magnetohydrodynamic turbulence: mode coupling, scaling relations, anisotropy, viscosity-damped regime and astrophysical implications

We present numerical simulations and explore scalings and anisotropy of compressible magnetohydrodynamic (MHD) turbulence. Our study covers both gas-pressure-dominated (high β) and magnetic-pressure-dominated (low β) plasmas at different Mach numbers. In addition, we present results for super-Alfvénic turbulence and discuss in what way it is similar to sub-Alfvénic turbulence. We describe a technique of separating different magnetohydrodynamic modes (slow, fast and Alfvén) and apply it to our simulations. We show that, for both high- and low-β cases, Alfvén and slow modes reveal a Kolmogorov   k ^−5/3  spectrum and scale-dependent Goldreich–Sridhar anisotropy, while fast modes exhibit a   k ^−3/2  spectrum and isotropy. We discuss the statistics of density fluctuations arising from MHD turbulence in different regimes. Our findings entail numerous astrophysical implications ranging from cosmic ray propagation to gamma ray bursts and star formation. In particular, we show that the rapid decay of turbulence reported by earlier researchers is not related to compressibility and mode coupling in MHD turbulence. In addition, we show that magnetic field enhancements and density enhancements are marginally correlated. Addressing the density structure of partially ionized interstellar gas on astronomical-unit scales, we show that the viscosity-damped regime of MHD turbulence that we reported earlier for incompressible flows persists for compressible turbulence and therefore may provide an explanation for these mysterious structures.     

The impact of correlated noise on SuperWASP detection rates for transiting extrasolar planets

The evolution of the Alfvén turbulence due to three-wave interactions is discussed using kinetic theory for a collisionless, thermal plasma. There are three low-frequency modes, analogous to the three modes of compressible magnetohydrodynamics (MHD). When only Alfvén waves are considered, the known anisotropy of turbulence in incompressible MHD theory is reproduced. Inclusion of a fast mode wave leads to the separation of turbulence into two regimes: small wave numbers where three-wave processes involving a fast mode are dominant, and large wave numbers where the three Alfvén wave process is dominant. Possible application of the anisotropic Alfvén turbulence to the interstellar medium and dissipation of magnetic energy in magnetars are discussed.     

Superbubbles in magnetized interstellar media: blowout or confinement?

The importance of the interstellar magnetic field is studied in relation to the evolution of superbubbles with a three-dimensional (3D) numerical magnetohydrodynamical (MHD) simulation. A superbubble is a large supernova remnant driven by sequential supernova explosions in an OB association. Its evolution is affected by the density stratification in the galactic disc. After the superbubble size reaches 2–3 times the density scaleheight, it expands preferentially in the z -direction, until finally it can punch out a hole in the gas disc (blowout). On the other hand, the magnetic field running parallel to the galactic disc has the effect of preventing it from expanding in the direction perpendicular to the field. The density stratification and the magnetic fields have completely opposite effects on the evolution of the superbubble. We present results of a 3D MHD simulation in which both effects are included. As a result, it is concluded that when the magnetic field has a much larger scaleheight than the density, even for a model in which the bubble would blow out from the disc if the magnetic field were absent, a magnetic field with a strength of 5 μG can confine the bubble in | z |≲300 pc for ≃ 20 Myr (confinement). In a model in which the field strength decreases in the halo as B  ∝ ρ^1/2, the superbubble eventually blows out like a model with B  = 0 even if the magnetic field in the mid-plane is as strong as B  = 5 μG.     

Structures in a class of magnetized scale-free discs

We construct analytically stationary global configurations for both aligned and logarithmic spiral coplanar magnetohydrodynamics (MHD) perturbations in an axisymmetric background MHD disc with a power-law surface mass density  Σ₀∝ r ^−α  , a coplanar azimuthal magnetic field   B ₀∝ r ^−γ  , a consistent self-gravity and a power-law rotation curve   v ₀∝ r ^−β  , where v ₀ is the linear azimuthal gas rotation speed. The barotropic equation of state  Π∝Σ ⁿ   is adopted for both MHD background equilibrium and coplanar MHD perturbations where Π is the vertically integrated pressure and n is the barotropic index. For a scale-free background MHD equilibrium, a relation exists among  α, β, γ  and n such that only one parameter (e.g. β) is independent. For a linear axisymmetric stability analysis, we provide global criteria in various parameter regimes. For non-axisymmetric aligned and logarithmic spiral cases, two branches of perturbation modes (i.e. fast and slow MHD density waves) can be derived once β is specified. To complement the magnetized singular isothermal disc analysis of Lou, we extend the analysis to a wider range of  −1/4 < β < 1/2  . As an illustrative example, we discuss specifically the  β= 1/4  case when the background magnetic field is force-free. Angular momentum conservation for coplanar MHD perturbations and other relevant aspects of our approach are discussed.     

Excitation and kinematics in H2 bow shocks: near-infrared observations of HH 99 and VLA 1623A (HH 313)

We present a comprehensive near-infrared study of two molecular bow shocks in two protostellar outflows, HH 99 in R Coronae Australis and VLA 1623A (HH 313) in Rho Ophiuchi. New, high-resolution, narrow-band images reveal the well-defined bow shock morphologies of both sources. These are compared with two-dimensional MHD modelling of molecular bows from which we infer flow inclination angles, shock speeds and the magnetic field in the pre-shock gas in each system. With combined echelle spectroscopy and low-resolution K -band spectra we further examine the kinematics and excitation of each source. Bow shock models are used to interpret excitation (CDR) diagrams and estimate the extinction and, in the case of VLA 1623, the ortho–para ratio associated with the observed H₂ population. For the first time, morphology, excitation and kinematics are fitted with a single bow shock model.
Specifically, we find that HH 99 is best fitted by a C-type bow shock model (although a J-type cap is probably responsible for the [Fe  ii ] emission). The bow is flowing away from the observer (at an angle to the line of sight of ∼45°) at a speed of roughly 100 km s⁻¹. VLA 1623A is interpreted in terms of a C-type bow moving towards the observer (at an angle to the line of sight of ∼75°) at a speed of ∼80 km s⁻¹. The magnetic field associated with HH 99 is thought to be orientated parallel to the flow axis; in VLA 1623A the field is probably oblique to the flow axis, since this source is clearly asymmetric in our H₂ images.     

Protostellar evolution during time-dependent anisotropic collapse

The formation and collapse of a protostar involves the simultaneous infall and outflow of material in the presence of magnetic fields, self-gravity and rotation. We use self-similar techniques to self-consistently model the anisotropic collapse and outflow by using a set of angle-separated self-similar equations. The outflow is quite strong in our model, with the velocity increasing in proportion to radius, and material formally escaping to infinity in the finite time is required for the central singularity to develop.
Analytically tractable collapse models have been limited mainly to spherically symmetric collapse, with neither magnetic field nor rotation. Other analyses usually employ extensive numerical simulations, or either perturbative or quasistatic techniques. Our model is unique as an exact solution to the non-stationary equations of self-gravitating magnetohydrodynamics (MHD), which features co-existing regions of infall and outflow.
The velocity and magnetic topology of our model is quadrupolar, although dipolar solutions may also exist. We provide a qualitative model for the origin and subsequent evolution of such a state. However, a central singularity forms at late times, and we expect the late-time behaviour to be dominated by the singularity, rather than depend on the details of its initial state. Our solution may, therefore, have the character of an attractor among a much more general class of self-similarity.     

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.     

Helical fields and filamentary molecular clouds – I

We study the equilibrium of pressure truncated, filamentary molecular clouds that are threaded by rather general helical magnetic fields. We first apply the virial theorem to filamentary molecular clouds, including the effects of non-thermal motions and the turbulent pressure of the surrounding ISM. When compared with the data, we find that many filamentary clouds have a mass per unit length that is significantly reduced by the effects of external pressure, and that toroidal fields play a significant role in squeezing such clouds.
We also develop exact numerical MHD models of filamentary molecular clouds with more general helical field configurations than have previously been considered. We examine the effects of the equation of state by comparing 'isothermal' filaments, with constant total (thermal plus turbulent) velocity dispersion, with equilibria constructed using a logatropic equation of state.
Our theoretical models involve three parameters: two to describe the mass loading of the toroidal and poloidal fields, and a third that describes the radial concentration of the filament. We thoroughly explore our parameter space to determine which choices of parameters result in models that agree with the available observational constraints. We find that both equations of state result in equilibria that agree with the observational results. Moreover, we find that models with helical fields have more realistic density profiles than either unmagnetized models or those with purely poloidal fields; we find that most isothermal models have density distributions that fall off as r ^−1.8 to r ⁻², while logatropes have density profiles that range from r ⁻¹ to r ^−1.8. We find that purely poloidal fields produce filaments with steep radial density gradients that are not allowed by the observations.     

Photoionized Flows from Magnetized Globules

Low mass star formation may be triggered by the dynamical effects of radiation fields and winds from massive stars on nearby molecular material. The columns of neutral material observed at the edges of many Hii regions may be the tracers of this process. Magnetic fields are dynamically important in the molecular clouds from which new stars form, but their effect on the development of molecular columns has not been studied in detail. In this paper, I present initial MHD simulations of this process.     

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.     

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.     

The influence of gravitational acceleration on the supernova-driven Parker instability

Within a framework of 2D magnetohydrodynamic (MHD) simulations, we explore the dynamical regimes initiated by a supernova explosion in a magnetized stratified interstellar medium (ISM). We concentrate on the formation of large-scale magnetic structures and outflows connected with the Parker instability. For the sake of simplicity we only show models with a fixed explosion energy corresponding to a single supernova (SN) occurring in host galaxies with different fixed values of the gravitational acceleration g and different ratios of specific heats. We show that in general, depending on these two parameters, three different regimes are possible: a slowly growing Parker instability on time-scales much longer than the galactic rotation period for small g; the Parker instability growing at roughly the rotation period, which for ratios of specific heats larger than one is accompanied by an outflow resulting from the explosion for intermediate g; and a rapidly growing instability and a strong blow-out flow for large g . By means of numerical simulations and analytical estimates we show that the explosion energy and gravitational acceleration which separate the three regimes scale as Eg ²∼constant in the 2D case. We expect that in the 3D case this scaling law is Eg ³∼constant . Our simulations demonstrate furthermore that a single SN explosion can lead to the growth of multiple Parker loops in the disc and large-scale magnetic field loops in the halo, extending over 2–3 kpc horizontally and up to 3 kpc vertically above the mid-plane of the disc.     

On the meaning and inapplicability of the Zeldovich relations of magnetohydrodynamics

Considering a plasma with an initially weak large scale field subject to nonhelical turbulent stirring, Zeldovich (1957), for two‐dimensions, followed by others for three dimensions, have presented formulae of the form 〈b²〉 = f(R_M) . Such “Zeldovich relations” have sometimes been interpreted to provide steady‐state relations between the energy associated with the fluctuating magnetic field and that associated with a large scale or mean field multiplied by a function f that depends on spatial dimension and a magnetic Reynolds number R_M. Here we dissect the origin of these relations and pinpoint pitfalls that show why they are inapplicable to realistic, dynamical MHD turbulence and that they disagree with many numerical simulations. For 2D, we show that when the total magnetic field is determined by a vector potential, the standard Zeldovich relation applies only transiently, characterizing a maximum possible value that the field energy can reach before necessarily decaying. In 3D, we show that the standard Zeldovich relations are derived by balancing subdominant terms. In contrast, balancing the dominant terms shows that the fluctuating field can grow to a value independent of R_M and the initially imposed , as seen in numerical simulations. We also emphasize that these Zeldovich relations of nonhelical turbulence imply nothing about the amount mean field growth in a helical dynamo. In short, by re‐analyzing the origin of the Zeldovich relations, we highlight that they are inapplicable to realistic steady‐states of large R_M MHD turbulence. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Hypersonic Swizzle Sticks: Protostellar Turbulence, Outflows and Fossil Outflow Cavities

The expected lifetimes for molecular clouds has become a topic of considerable debate as numerical simulations have shown that MHD turbulence, the nominal means of support for clouds against self-gravity, will decay on short timescales. Thus it appears that either molecular clouds are transient features or they are resupplied with turbulent energy through some means. Jets and molecular outflows are recognized as a ubiquitous phenomena associated with star formation. Stars however form not isolation but in clusters of different density and composion. The ubiquity and high density of outflows from young stars in clusters make them an intriguing candidate for the source of turbulence energy in molecular clouds. In this contribution we present new studies, both observational and theoretical, which address the issue of jet/outflow interactions and their abilityto drive turbulent flows in molecular clouds. Our studies focus on scales associated with young star forming clusters. In particular we first show that direct collisions between active outflows are not effective at stirring the ambient medium. We then show that fossil cavities from “extinct” outflows may provide the missing link in terms of transferring momentum and energy to the cloud.     

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.     

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.