Doppler boosting, superluminal motion, and the kinematics of AGN jets

We discuss results from a decade long program to study the fine-scale structure and the kinematics of relativistic AGN jets with the aim of better understanding the acceleration and collimation of the relativistic plasma forming AGN jets. From the observed distribution of brightness temperature, apparent velocity, flux density, time variability, and apparent luminosity, the intrinsic properties of the jets including Lorentz factor, luminosity, orientation, and brightness temperature are discussed. Special attention is given to the jet in M87, which has been studied over a wide range of wavelengths and which, due to its proximity, is observed with excellent spatial resolution. Most radio jets appear quite linear, but we also observe curved non-linear jets and non-radial motions. Sometimes, different features in a given jet appear to follow the same curved path but there is evidence for ballistic trajectories as well. The data are best fit with a distribution of Lorentz factors extending up to γ∼30 and intrinsic luminosity up to ∼10²⁶ W Hz⁻¹. In general, gamma-ray quasars may have somewhat larger Lorentz factors than non gamma-ray quasars. Initially the observed brightness temperature near the base of the jet extend up to ∼5×10¹³ K which is well in excess of the inverse Compton limit and corresponds to a large excess of particle energy over magnetic energy. However, more typically, the observed brightness temperatures are ∼2×10¹¹ K, i.e., closer to equipartition.     

SS 433 — Again

The standard model for SS 433 encounters increasing difficulties, including geometrical and chemical irregularities, short-time correlations and the presence of circular polarization. It is argued that these difficulties disappear when one drops the assumption that the moving spectral lines are emitted by the (mapped) jets. All the spectral peculiarities can be blamed on (special) radiation from the inner accretion disk, at radius 10⁷ cm, around a young neutron star. The jets consist of relativistic pair plasma-like in all the other jet sources. A prediction is made for the center of the radio jets.     

Peculiar nature of hard X-ray eclipse in SS433 from INTEGRAL observations

The analysis of hard X-ray INTEGRAL observations (2003–2008) of superaccreting Galactic microquasar SS433 at precessional phases of the source with the maximum disc opening angle is carried out. It is found that the shape and width of the primary X-ray eclipse are strongly variable, suggesting additional absorption in dense stellar wind and gas outflows from the optical A7I component and the wind–wind collision region. The independence of the observed hard X-ray spectrum on the accretion disc precessional phase suggests that hard X-ray emission (20–100 keV) is formed in an extended, hot, quasi-isothermal corona, probably heated by interaction of relativistic jet with inhomogeneous wind outflow from the precessing supercritical accretion disc. A joint modelling of X-ray eclipsing and precessional hard X-ray variability of SS433 revealed by INTEGRAL by a geometrical model suggests the binary mass ratio   q = m_x / m _v ≃  0.25–0.5. The absolute minimum of joint orbital and precessional  χ²  residuals is reached at   q ≃ 0.3  . The found binary mass ratio range allows us to explain the substantial precessional variability of the minimum brightness at the middle of the primary optical eclipse. For the mass function of the optical star   f _v = 0.268 M_⊙  as derived from Hillwig & Gies data, the obtained value of   q ≃ 0.3  yields the masses of the components   m_x ≃ 5.3 M_⊙, m _v ≃ 17.7 M_⊙  , confirming the black hole nature of the compact object in SS433.     

On the physical conditions in AGN optical jets

The energy budget of all known optical jets is discussed. It is found that to power the extended radio lobes of radio galaxies, the jet bulk motion on kpc scales must be relativistic, on average. Based on various constraints, a “most probable” region centered around Γ_bulk∼7.5 and θ∼20° is found. Because of the consequent relativistic beaming, the rest frame magnetic field is lower and electron lifetimes longer. Combining the effects of time dilation and lower emission rate, the electron diffusion length becomes fully consistent with the deprojected jet length, without the need for reacceleration.     

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.     

Relativistic large-scale jets and minimum power requirements

The recent discovery, by the Chandra satellite, that jets of blazars are strong X-ray emitters at large scales     , lends support to the hypothesis that emitting plasma is still moving at highly relativistic speeds on these scales. In this case in fact the emission via inverse Compton scattering off cosmic background photons is enhanced and the resulting predicted X-ray spectrum accounts well for the otherwise puzzling observations. Here we point out another reason to favour relativistic large-scale jets, based on a minimum power argument: by estimating the Poynting flux and bulk kinetic powers corresponding to, at least, the relativistic particles and magnetic field responsible for the emission, one can derive the value of the bulk Lorentz factor for which the total power is minimized. It is found that both the inner and extended parts of the jet of PKS     satisfy such a condition.     

The power of blazar jets

We estimate the power of relativistic, extragalactic jets by modelling the spectral energy distribution of a large number of blazars. We adopt a simple one-zone, homogeneous, leptonic synchrotron and inverse Compton model, taking into account seed photons originating both locally in the jet and externally. The blazars under study have an often dominant high-energy component which, if interpreted as due to inverse Compton radiation, limits the value of the magnetic field within the emission region. As a consequence, the corresponding Poynting flux cannot be energetically dominant. Also the bulk kinetic power in relativistic leptons is often smaller than the dissipated luminosity. This suggests that the typical jet should comprise an energetically dominant proton component. If there is one proton per relativistic electrons, jets radiate around 2–10 per cent of their power in high-power blazars and 3–30 per cent in less powerful BL Lacs.     

3-D Rpic Simulations of Relativistic Jets: Particle Acceleration, Magnetic Field Generation, and Emission

We have applied numerical simulations and modeling to the particle acceleration, magnetic field generation, and emission from relativistic shocks. We investigate the nonlinear stage of theWeibel instability and compare our simulations with the observed gamma-ray burst emission. In collisionless shocks, plasma waves and their associated instabilities (e.g., the Weibel, Buneman and other two-stream instabilities) are responsible for particle (electron, positron, and ion) acceleration and magnetic field generation. 3-D relativistic electromagnetic particle (REMP) simulations with three different electron-positron jet velocity distributions and also with an electron-ion plasma have been performed and show shock processes including spatial and temporal evolution of shocks in unmagnetized ambient plasmas. The growth time and nonlinear saturation levels depend on the initial jet parallel velocity distributions. Simulations show that the Weibel instability created in the collisionless shocks accelerates jet and ambient particles both perpendicular and parallel to the jet propagation direction. The nonlinear fluctuation amplitude of densities, currents, electric, and magnetic fields in the electron-positron shocks are larger for smaller jet Lorentz factor. This comes from the fact that the growth time of the Weibel instability is proportional to the square of the jet Lorentz factor. We have performed simulations with broad Lorentz factor distribution of jet electrons and positrons, which is assumed to be created by photon annihilation. Simulation results with this broad distribution show that the Weibel instability is excited continuously by the wide-range of jet Lorentz factor from lower to higher values. In all simulations the Weibel instability is responsible for generating and amplifying magnetic fields perpendicular to the jet propagation direction, and contributes to the electron’s (positron’s) transverse deflection behind the jet head. This small scale magnetic field structure contributes to the generation of “jitter” radiation from deflected electrons (positrons), which is different from synchrotron radiation in uniform magnetic fields. The jitter radiation resulting from small scale magnetic field structures may be important for understanding the complex time structure and spectral evolution observed in gamma-ray bursts or other astrophysical sources containing relativistic jets and relativistic collisionless shocks. The detailed studies of shock microscopic process evolution may provide some insights into early and later GRB afterglows.     

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.     

Relativistic anisotropic pair plasmas

The properties of waves able to propagate in a relativistic pair plasma are at the basis of the interpretation of several astrophysical observations. For instance, they are invoked in relation to radio emission processes in pulsar magnetospheres and to radiation mechanisms for relativistic radio jets. In such physical environments, pair plasma particles probably have relativistic, or even ultrarelativistic, temperatures. Besides, the presence of an extremely strong magnetic field in the emission region constrains the particles to one-dimensional motion: all the charged particles strictly move along magnetic field lines.
We take anisotropic effects and relativistic effects into account by choosing one-dimensional relativistic Jűttner–Synge distribution functions to characterize the distribution of electrons and/or positrons in a relativistic, anisotropic pair plasma. The dielectric tensor, from which the dispersion relation associated with plane wave perturbations of such a pair plasma is derived, involves specific coefficients that depend on the distribution function of particles. A precise determination of these coefficients, using the relativistic one-dimensional Jűttner–Synge distribution function, allows us to obtain the appropriate dispersion relation. The properties of waves able to propagate in anisotropic relativistic pair plasmas are deduced from this dispersion relation. The conditions in which a beam and a plasma, both ultrarelativistic, may interact and trigger off a two-stream instability are obtained from this same dispersion relation. Two astrophysical applications are discussed.     

Observations of magnetic flux compression in jet impact experiments

The astrophysical jet experiment at Caltech generates a T=2–5 eV, n=10²¹–10²² m⁻³ plasma jet using coplanar disk electrodes linked by a poloidal magnetic field. A 100 kA current generates a toroidal magnetic field; the toroidal field pressure inflates the poloidal flux surface, magnetically driving the jet. The jet travels at up to 50 km/s for ∼20–25 cm before colliding with a cloud of initially neutral gas. We study the interaction of the jet and the cloud in analogy to an astrophysical jet impacting a molecular cloud. Diagnostics include magnetic probe arrays, a 12-channel spectroscopic system and a fast camera with optical filters. When a hydrogen plasma jet collides with an argon target cloud, magnetic measurements show the magnetic flux compressing as the plasma jet deforms. As the plasma jet front slows and the plasma piles up, the density of the frozen-in magnetic flux increases.     

Weakly relativistic solitary waves in multicomponent plasmas with electron inertia

Existence of compressive relativistic solitons is established in an arbitrary ξ-direction, inclining at an angle to the direction of the weak magnetic field (ω _pi ≫ω _Bi ) in this plasma compound with ions, relativistic electrons and relativistic electron beams. It is observed that the absolute linear growth of amplitudes of compressive solitons is due to inactive role of the weak magnetic field and the initial streaming speeds of relativistic electrons, electron beams, and Q _b (ion mass to electron beam mass). Besides, the small initial streaming of electrons is found to be responsible to generate relatively high amplitude compressive solitons. The non-relativistic ions in the background plasma, but in absence of electron-beam drift and in presence of weak magnetic field are the causing effect of interest for the smooth growth of soliton amplitudes in this model of plasma.     

The physics of E × B-drifting jets

E × B-drifting jets have been generally ignored for the past 25 years even though they may well describe all the astrophysical jet sources, both on galactic and stellar scales. Here we present closed-form solutions for their joint field-and-particle distribution, argue that the observed jets are near equipartition, with extremely relativistic, monoenergetic e^±-pairs of bulk Lorentz factor γ ≲ 10⁴, and are first-order stable. We describe plausible mechanisms for the jets’ (i) formation, (ii) propagation, and (iii) termination. Wherever a beam meets with resistance, its frozen-in Poynting flux transforms the delta-shaped energy distribution of the pairs into an almost white power law,E ² N _E ∼E ^−∫ with ∫ ≳ 0, via single-step falls through the huge convected potential.     

Acceleration of charged particles in the magnetosphere of a collapsing star and their nonthermal electromagnetic radiation

We investigate a transformation of a magnetic field and plasma in nonhomogeneous magnetospheres of collapsing stars with a dipole initial magnetic field and certain initial energy distributions of particles in the magnetosphere as the power low, relativistic Maxwell and Boltzmann. The betatron mechanism of the charged particles acceleration in a collapsing star’s magnetosphere is considered. When a magnetized star is compressed in the stage of the gravitational collapse, the magnetic field increases strongly. This variable magnetic field generates a vortical electric field. Our calculations show that this electric field will accelerate charged particles up to relativistic velocities. Thus, collapsing stars may be sources of high energy cosmic rays in our galaxy as in others. The acceleration of particles during the collapse happens mostly in polar regions of the magnetosphere that leads to polar relativistic streams (jets) formation. When moving in a magnetic field, these particles will generate nonthermal electromagnetic radiation in a broad electromagnetic wavelength band from radioto gamma rays. Thus, in the stage of the gravitational collapse, relativistic jets are formed in stellar magnetospheres. These jets are powerful sources of the nonthermal electromagnetic radiation.     

Relationship between the position angles of elongated structures and polarization vector of the compact radio source 3C84 AT 2, 4, and 6-cm wavelengths

The position angles (PA) of the elongated structure of the compact source 3C84 are compared with those of the E polarization vector of its 2, 4, and 6-cm emission. It is shown that during 1972–1984, the E vector had two preferred directions with PA = -10° and PA = +17°, which correspond to the directions of the two principal elongated structures of the radio source, which contain moderately relativistic subparsec-scale jets. The parallel directions of the polarization vector and radio jets for the source 3C84 agree with the model of magnetic field and relativistic electron cloud distributions in the moderately relativistic jets of the BL Lac objects examined by Grabusda et al. (1994). Translated fromAstrofizika, Vol. 40, No. 1, pp. 19–28, February, 1997     

Ejector and bipolar outflow of the radio galaxy M87

The superfine structure of the jet formation region in the radio galaxy M87 has been investigated. An accretion disk and high- and low-velocity jet and counterjet components have been identified. The high-velocity bipolar outflow is ejected from the central disk region, a nozzle 4 mpc in diameter, while the low-velocity one is ejected from a ring 60 mpc in diameter and 14 mpc in width. The low-velocity plasma flow is a hollow tube with a built-in helix. The observed helical structure of the high-velocity jet is determined by precession. The components of the structure, its disk and bipolar outflow, suggest solid-body rotation. Ring currents and aligned magnetic fields are generated in them under the action of an external magnetic field. The bipolar outflows are ejected coaxially but in opposite directions—along and opposite to the disk field. As a result, the jet flow accelerates, while the counterjet one decelerates. This causes the extent of the region of radiative cooling of the ejected relativistic electrons in the counterjet to decrease and maintains their “afterglow” at large distances in the jet. The high collimation of the rotating flows is determined by their interaction with the environment.     

Extragalactic jets on subpc and large scales

Jets can be probed in their innermost regions (d≲0.1 pc) through the study of the relativistically boosted emission of blazars. On the other extreme of spatial scales, the study of structure and dynamics of extragalactic relativistic jets received renewed impulse after the discovery, made by Chandra, of bright X-ray emission from regions at distances larger than hundreds of kpc from the central engine. At both scales it is thus possible to infer some of the basic parameters of the flow (speed, density, magnetic field intensity, power). After a brief review of the available observational evidence, I discuss how the comparison between the physical quantities independently derived at the two scales can be used to shed light on the global dynamics of the jet, from the innermost regions to the hundreds of kpc scale.     

Dynamics of relativistic jets

We discuss the structure and relativistic kinematics that develop in three spatial dimensions when a moderately hot, supersonic jet propagates into a denser background medium and encounters resistance from an oblique magnetic field. Our simulations incorporate relativistic MHD in a four-dimensional spacetime and clearly show that (a) relatively weak, oblique fields (at 1/16 of the equipartition value) have only a negligible influence on the propagating jet and they are passively pushed away by the relativistically moving head; (b) oblique fields in equipartition with the ambient plasma provide more resistance and cause bending at the jet head, but the magnitude of this deflection and the associated backflow are small compared to those identified by previous studies. The new results are understood as follows: Relativistic simulations have consistently shown that these jets are effectively heavy and so they do not suffer substantial momentum losses and are not decelerated as efficiently as their nonrelativistic counterparts. In addition, the ambient magnetic field, however strong, can be pushed aside with relative ease by the beam, provided that the degrees of freedom associated with all three spatial dimensions are followed self-consistently during the simulations. The effect is analogous to pushing Japanese “noren” or vertical Venetian blinds out of the way while the slats are allowed to bend and twist in 3-D space. Applied to relativistic extragalactic jets from blazars, the new results are encouraging since superluminal outflows exhibit bending near their sources and their environments are profoundly magnetized – but observations do not provide support for irregular kinematics such as large-scale vortical motions and pronounced reverse flows near the points of origin.     

Effects of dense medium surrounding galactic-sized radio sources

In this paper, I have analysed the subarcsecond polarization structure of two high-z compact steep-spectrum quasars. Morphology suggests that the jets are interacting strongly with intergalactic medium. Models of bending by ram pressure equilibrium in a cooling flow and alignment of magnetic field lines by jet-IGM shock suggest that the CSS jets are light, supersonic and mildly relativistic. Particle energy index variations along the jet suggests replenishment triggered by such interactions.     

Kinematical diagrams for conical relativistic jets

We present diagrams depicting the expected inter-dependences of two key kinematical parameters of radio knots in the parsec-scale jets of blazars, deduced from VLBI observations. The two parameters are the apparent speed (υ _app = cβ _app) and the effective Doppler boosting factor (δ _eff) of the relativistically moving radio knot. A novel aspect of these analytical computations of β-δ diagrams is that they are made for parsec-scale jets having a conical shape, with modest opening angles (ω up to 10°), in accord with the VLBI observations of the nuclei of the nearest radio galaxies. Another motivating factor is the recent finding that consideration of a conical geometry can have important implications for the interpretation of a variety of radio observations of blazar jets. In addition to uniform jet flows (i.e., those having a uniform bulk Lorentz factor, Γ), computational results are also presented for stratified jets where an ultra-relativistic central spine along the jet axis is surrounded by a slower moving sheath, possibly arising from a velocity shear.