On the central core in MHD winds and jets

We analytically determine the structure of highly magnetized astrophysical jets at the origin in a region where the flow has been already collimated by an external medium, in both relativistic and non-relativistic regimes. We show that this can be achieved by solving a system of first-order ordinary differential equations that describe the transversal jet structure for a variety of external confining pressure profiles that collimate the jet to a near-cylindrical configuration. We obtain solutions for a central jet surrounded either by a self-similar wind or by an external pressure profile and derive the dependence of the velocity and the magnetic field strength along and across our jets. In particular, we find that the central core in a jet – the part of a flow with a nearly homogeneous magnetic field – must contain a poloidal field which is not much smaller than the critical value B _min. This allows us to determine the magnetic flux in a core which is much smaller than the total magnetic flux. We show that for such a small core flux the solutions with a magnetic field in a core much smaller than B _min are non-physical. For astrophysical objects the value of the critical magnetic field is quite large: 1 G for active galactic nuclei, 10¹⁰ G for gamma-ray bursts and 10⁻¹ G for young stellar objects. In a relativistic case for the core field greater than or of the order of B _min we show analytically that the plasma Lorentz factor must grow linearly with the cylindrical radius. For non-relativistic highly magnetized jets we propose that an oblique shock exists near the base of the jet so that the finite gas pressure plays an important role in force balance.     

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.     

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.     

Numerical simulations of astrophysical jets from Keplerian discs – III. The effects of mass loading

We present 2.5D time-dependent simulations of the non-linear evolution of non-relativistic outflows from the surface of Keplerian accretion discs. The gas is accelerated from the surface of the disc (which is a fixed platform in these simulations) into a cold corona in stable hydrostatic equilibrium. We explore the dependence of the resulting jet characteristics upon the mass loading of the winds. Two initial configurations of the threading disc magnetic field are studied: a potential field and a uniform vertical field configuration.
We show that the nature of the resulting highly collimated, jet-like outflows (steady or episodic) is determined by the mass load of the disc wind. The mass load controls the interplay between the collimating effects of the toroidal field and the kinetic energy density in the outflow. In this regard, we demonstrate that the onset of episodic behaviour of jets appears to be determined by the quantity     which compares the speed for a toroidal Alfvén wave to cross the diameter of the jet, with the flow speed v _p along the jet. This quantity decreases with increasing load. For sufficiently large N (small mass loads), disturbances appear to grow leading to instabilities and shocks. Knots are then generated and the outflow becomes episodic. These effects are qualitatively independent of the initial magnetic configuration that we employed and are probably generic to a wide variety of magnetized accretion disc models.     

Active galactic nuclei jet mass loading and truncation by stellar winds

Active galactic nuclei can produce extremely powerful jets. While tightly collimated, the scale of these jets and the stellar density at galactic centres implies that there will be many jet/star interactions, which can mass load the jet through stellar winds. Previous work employed modest wind mass outflow rates, but this does not apply when mass loading is provided by a small number of high mass-loss stars. We construct a framework for jet mass loading by stellar winds for a broader spectrum of wind mass-loss rates than has previously been considered. Given the observed stellar mass distributions in galactic centres, we find that even highly efficient (0.1 Eddington luminosity) jets from supermassive black holes of masses M _BH≲ 10⁴ M_⊙ are rapidly mass loaded and quenched by stellar winds. For  10⁴ M_⊙ < M _BH < 10⁸ M_⊙  , the quenching length of highly efficient jets is independent of the jet's mechanical luminosity. Stellar wind mass loading is unable to quench efficient jets from more massive engines, but can account for the observed truncation of the inefficient M87 jet, and implies a baryon-dominated composition on scales ≳2 kpc therein even if the jet is initially pair plasma dominated.     

Dynamic confinement of jets by magnetotorsional oscillations

Many quasars and active galactic nuclei (AGN) appear in radio, optical and X-ray maps as bright nuclear sources from which emerge single or double long, thin jets. When observed with high angular resolution, these jets show evidence of structure, with bright knots separated by relatively dark regions. High percentages of polarization, sometimes more then 50 per cent, indicate the non-thermal nature of the radiation, which is well explained as the synchrotron radiation of the relativistic electrons in an ordered magnetic field.
A strong collimation of jets is probably connected with ordered magnetic fields. The mechanism of magnetic collimation first suggested by Bisnovatyi-Kogan et al. was based on the initial charge separation, which led to the creation of an oscillating electrical current, which in turn produced an azimuthal magnetic field, preventing jet expansion and disappearance. Here we consider magnetic collimation associated with the torsional oscillations of a cylinder with an elongated magnetic field. Instead of initial blobs with charge separation, we consider a cylinder with a periodically distributed initial rotation around the cylinder axis. The stabilizing azimuthal magnetic field is created by torsional oscillations, meaning that charge separation is unnecessary. An approximate simplified model is developed, and an ordinary differential equation is derived and solved numerically, making it possible to estimate quantitatively the range of parameters for which jets may be stabilized by torsional oscillations.     

Cylindrical Jet—Wind interaction Model of Gamma—Ray Burst Afterglows

Observations on relativistic jets in radio galaxies, active galactic nuclei, and "microquasars" revealed that many of these outflows are cylindrical, not conical. So it is worthwhile to investigate the evolution of cylindrical jets in gamma-ray bursts. We discuss afterglows from cylindrical jets in a wind environment. Numerical results as well as analytic solutions in some special cases are presented. Our light curves are steeper compared to those in the homogeneous interstellar medium case, carefully considered by Cheng, Huang & Lu. We conclude that some afterglows, used to be interpreted as isotropic fireballs in a wind environment, can be fitted as well by cylindrical jets interacting with a wind.     

Jet confinement by magneto-torsional oscillations

Many quasars and active galactic nuclei (AGN) appear in radio, optical, and X-ray maps, as a bright nuclear sources from which emerge single or double long, thin jets. When observed with high angular resolution these jets show structure with bright knots separated by relatively dark regions. Nonthermal nature of a jet radiation is well explained as the synchrotron radiation of the relativistic electrons in an ordered magnetic field. We consider magnetic collimation, connected with torsional oscillations of a cylinder with elongated magnetic field, and periodically distributed initial rotation around the cylinder axis. The stabilizing azimuthal magnetic field is created here by torsional oscillations, where charge separation is not necessary. Approximate simplified model is developed. Ordinary differential equation is derived, and solved numerically, what gives a possibility to estimate quantitatively the range of parameters where jets may be stabilized by torsional oscillations.     

On the optical light curves of afterglows from jetted gamma-ray burst ejecta: effects of parameters

Owing to some refinements in the dynamics, we can follow the overall evolution of a realistic jet numerically until its bulk velocity is as small as c 10³ c . We find no obvious break in the optical light curve during the relativistic phase itself . However, an obvious break does exist at the transition from the relativistic phase to the non-relativistic phase, which typically occurs at time t 10⁶10^6.5 s (i.e. 1030 d). The break is affected by many parameters, such as the electron energy fraction _e, the magnetic energy fraction the initial half-opening angle ₀ and the medium number density n . Increasing any of them to a large enough value will make the break disappear. Although the break itself is parameter-dependent, afterglows from jetted GRB remnants are uniformly characterized by a quick decay during the non-relativistic phase, with power-law timing index 2.1. This is quite different from that of isotropic fireballs, and may be of fundamental importance for determining the degree of beaming in -ray bursts observationally.     

Collimation of astrophysical MHD outflows

We explain in simple terms why a rotating and magnetized outflow forms a core with a jet and show numerical simulations which substantiate this argument. The outflow from a solar-type inefficient magnetic rotator is found to be very weakly collimated while the outflow from a ten times faster rotating YSO is shown to produce a tightly collimated jet. This gives rise to an evolutionary scenario for stellar outflows. 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.     

Deflection of jets induced by jet–cloud and jet–galaxy interactions

The model first introduced by Raga & Cantó in which astrophysical jets are deflected on passing through an isothermal high‐density region is generalized by taking into account gravitational effects on the motion of the jet as it crosses the high‐density cloud. The problem is also generalized for relativistic jets in which gravitational effects induced by the cloud are neglected. Two further cases, classical and relativistic, are discussed for the cases in which the jet is deflected on passing through the interstellar gas of a galaxy in which a dark matter halo dominates the gravitational potential. The criteria for the stability of jets due to the formation of internal shocks are also discussed.     

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.     

The symbiotic star CH Cygni – I. Non-thermal bipolar jets

Very Large Array surface brightness and spectral index maps of the evolving extended emission of the triple symbiotic star CH Cygni are presented. These are derived from observations at 4.8, 8.4 and 14 GHz between 1985 and 1999. The maps are dominated by thermal emission around the central bright peak of the nebula, but we also find unambiguous non-thermal emission associated with the extended regions. Our observations confirm that this is a jet. The central region has been associated with the stellar components through Hubble Space Telescope imaging. If the jets are the result of ejection events at outburst, expansion velocities are consistent with those from other measurement methods. We propose that the non-thermal emission is caused by material ejected in the bipolar jets interacting with the circumstellar wind envelope. The resulting shocks lead to local enhancements in the magnetic field from the compact component of the order of 3 mG.     

Hydrodynamic simulations of molecular outflows driven by slow-precessing protostellar jets

We present hydrodynamic simulations of molecular outflows driven by jets with a long period of precession, motivated by observations of arc-like features and S-symmetry in outflows associated with young stars. We simulate images of not only H₂ vibrational and CO rotational emission lines, but also of atomic emission. The density cross-section displays a jaw-like cavity, independent of precession rate. In molecular hydrogen, however, we find ordered chains of bow shocks and meandering streamers which contrast with the chaotic structure produced by jets in rapid precession. A feature particularly dominant in atomic emission is a stagnant point in the flow that remains near the inlet and alters shape and brightness as the jet skims by. Under the present conditions, slow jet precession yields a relatively high fraction of mass accelerated to high speeds, as also attested to in simulated CO line profiles. Many outflow structures, characterized by HH 222 (continuous ribbon), HH 240 (asymmetric chains of bow shocks) and RNO 43N (protruding cavities), are probably related to the slow-precession model.     

A HED Laboratory Astrophysics Testbed Comes of Age: JET Deflection via Cross Winds

We present new data from High-Energy Density (HED) laboratory experiments designed to explore the interaction of a heavy hypersonic radiative jet with a cross wind. The jets are generated with the MAGPIE pulsed power machine where converging conical plasma flows are produced from a cylindrically symmetric array of inclined wires. Radiative hypersonic jets emerge from the convergence point. The cross wind is generated by ablation of a plastic foil via soft-X-rays from the plasma convergence region. Our experiments show that the jets are deflected by the action of the cross wind with the angle of deflection dependent on the proximity of the foil. Shocks within the jet beam are apparent in the data. Analysis of the data shows that the interaction of the jet and cross wind is collisional and therefore in the hydrodynamic regime. We consider the astrophysical relevance of these experiments applying published models of jet deflection developed for AGN and YSOs. We also present results of 3-D numerical simulations of jet deflection using a new astrophysical Adaptive Mesh Refinement code. These simulations show highly structured shocks occurring within the beam similar to what was observed in the experiments.     

The flat synchrotron spectra of partially self-absorbed jets revisited

Flat radio spectra with large brightness temperatures at the core of active galactic nuclei and X-ray binaries are usually interpreted as the partially self-absorbed bases of jet flows emitting synchrotron radiation. Here we extend previous models of jets propagating at large angles to our line of sight to self-consistently include the effects of energy losses of the relativistic electrons due to the synchrotron process itself and the adiabatic expansion of the jet flow. We also take into account energy gains through self-absorption. Two model classes are presented. The ballistic jet flows, with the jet material travelling along straight trajectories, and adiabatic jets. Despite the energy losses, both scenarios can result in flat emission spectra; however, the adiabatic jets require a specific geometry. No re-acceleration process along the jet is needed for the electrons. We apply the models to observational data of the X-ray binary Cygnus X-1. Both models can be made consistent with the observations. The resulting ballistic jet is extremely narrow with a jet opening angle of only 5 arcsec. Its energy transport rate is small compared to the time-averaged jet power and therefore suggests the presence of non-radiating protons in the jet flow. The adiabatic jets require a strong departure from energy equipartition between the magnetic field and the relativistic electrons. These models also imply a jet power of two orders of magnitude higher than the Eddington limiting luminosity of a  10-M_⊙  black hole. The models put strong constraints on the physical conditions in the jet flows on scales well below achievable resolution limits.     

On the structure of the inner Crab Nebula

Origin of the jet-like feature in the inner Crab Nebula is discussed. Because self-collimation processes in ultrarelativistic pulsar winds are extremely ineffective, it is suggested that the collimation occurs beyond the termination shock where the flow is already mildly (or non-) relativistic. It is argued that the shock shape is highly non-spherical because the energy flux in the pulsar wind decreases towards the axis. The shock near the axis should be much closer to the pulsar than at the equator and therefore the jet looks as if it originates directly from the pulsar.     

On the local magnetorotational instability of astrophysical jets

We present the local linear stability analysis of rotating jets confined by a toroidal magnetic field. Under the thin flux tube approximation, we derive the equation of motion for slender magnetic flux tubes. In addition to the terms responsible for the conventional instability of the toroidal magnetic field, a term related to the magnetic buoyancy and a term corresponding to the differential rotation become relevant for the stability properties. We find that the rigid rotation stabilizes while the differential rotational destabilizes the jet in a way similar to the Balbus–Hawley instability. Within the frame of our local analysis, we find that if the azimuthal velocity is of the order of or higher than the Alfvén azimuthal speed, the rigidly rotating part of the jet interior can be completely stabilized, while the strong shearing instability operates in the transition layer between the rotating jet interior and the external medium. This can explain the limb-brightening effect observed in several jets. However, it is still possible to find jet equilibria that are stable all across the jet, even in the presence of differential rotation. We discuss observational consequences of these results.