We present numerical simulations of cold, axisymmetric, magnetically driven relativistic outflows. The outflows are initially sub-Alfvénic and Poynting flux-dominated, with total--to--rest-mass energy flux ratio up to $μ\sim 620$. To study the magnetic acceleration of jets we simulate flows confined within a funnel with rigid wall of prescribed shape, which we take to be $z\propto r^a$ (in cylindrical coordinates, with $a$ ranging from 1 to 2). This allows us to eliminate the numerical dissipative effects induced by a free boundary with an ambient medium. We find that in all cases they converge to a steady state characterized by a spatially extended acceleration region. For the jet solutions the acceleration process is very efficient - on the outermost scale of the simulation more than half of the Poynting flux has been converted into kinetic energy flux, and the terminal Lorentz factor approached its maximum possible value ($Γ_\infty \simeq μ$). The acceleration is accompanied by the collimation of magnetic field lines in excess of that dictated by the funnel shape. The numerical solutions are generally consistent with the semi-analytic self-similar jets solutions and the spatially extended acceleration observed in some astrophysical relativistic jets. In agreement with previous studies we also find that the acceleration is significantly less effective for wind solutions suggesting that pulsar winds may remain Poynting dominated when they reach the termination shock.
I review several central open questions concerning GRB Jets. 1) I discuss a new estimates of the beaming correction for the rate of GRBs ~ 75 +- 20. 2) I discuss the universal structured jet (USJ) model and conclude that while jets might be structured they are less likely to be universal. 3) I discuss recent observations of a sideways expansion of a GRB afterglow and compare these with current hydrodynamics simulations of jet evolution. 4) I discuss the implications of resent outliers to the energy-angle relation.
We calculate the time evolution of the flux, apparent size, and image centroid motion of gamma-ray burst (GRB) radio jets, and show that they can be resolved by the VLBA at distances of hundreds of Mpc. We find that GRB 030329 which showed spectroscopic evidence for an associated Type Ic supernova (SN) at a distance of $\approx$ 800 Mpc might just be resolvable by VLBA after several months. The prospects are much better for jets that are oriented sideways in similar SNe with no GRB counterpart; in particular, the motion of the flux centroid in such jets can be detected by VLBA up to $z\sim 1$ …
It is widely accepted that the Doppler deboosting effects exist in counter relativistic jets. However, people often neglect another important fact that both Doppler boosting and deboosting effects could happen in forward relativistic jets. Such effects might be used to explain some strange phenomena, such as the invisible gaps between the inner and outer jets of AGNs, and the rapid initial decays and re-brightening bumps in the light curves of GRBs.
There are several lines of evidence which suggest that the relativistic outflows in gamma-ray bursts (GRBs) are collimated into narrow jets. The jet structure has important implications for the true energy release and the event rate of GRBs, and can constrain the mechanism responsible for the acceleration and collimation of the jet. Nevertheless, the jet structure and its dynamics as it sweeps up the external medium and decelerates, are not well understood. In this review I discuss our current understanding of GRB jets, stressing their structure and dynamics.
High velocity highly collimated beams of plasma -- the jets -- are known as a general phenomenon among astrophysical sources of different energy and spatial scale. The common MHD scenario of astrophysical jet formation allows to describe the different jet sources by a scaling of the jet magnetization. In this paper we apply the MHD jet theory for GRB parameters and find indeed that main features as ultra-relativistic motion and strong collimation can be explained. Others, like GRB time-variability and the bi-modal GRB duration are (yet) beyond a MHD description.
Fireballs are huge isotropic explosions models widely believed to explain Gamma Ray Burst, GRBs (Piran,1999); ever-new versions consider wide beamed (10^o) Jet explosions hitting external shells. On the contrary, since 1994-1998, we argued (Fargion 1995-2000; see also Blackman et all.1996) that GRBs (as well as Soft Gamma Repeaters SGR) are spinning and precessing Gamma Jets, produced by collimated e^+,e^- Jet via Inverse Compton Scattering, in a very narrow (0.1^o) angles, blazing and flashing the observer. The Jet arises in Super-Nova (SN) explosions; its energy decays slowly from earliest S…
In several GRBs afterglows, rapid temporal decay is observed which is inconsistent with spherical (isotropic) blast-wave models. In particular, GRB 980519 had the most rapidly fading of the well-documented GRB afterglows, with t^{-2.05\pm 0.04} in optical as well as in X-rays. We show that such temporal decay is more consistent with the evolution of a jet after it slows down and spreads laterally, for which t^{-p} decay is expected (where p is the index of the electron energy distribution). Such a beaming model would relax the energy requirements on some of the more extreme GRBs by a factor of…
We investigate the effect that the structure of GRB jets has on the afterglow light curves for observers located at different viewing angles, $θ_{obs}$, from the jet symmetry axis. The largest uncertainty in the jet dynamics is the degree of lateral energy transfer. Thus, we use two simple models, that make opposite and extreme assumptions for this point, and calculate the light curves for an external density that is either homogeneous, or decreases as the square of the distance from the source. The Lorentz factor and kinetic energy per unit solid angle are initially taken to be power laws of …
Some progenitor models of gamma-ray bursts (GRBs) (e.g., collapsars) may produce anisotropic jets in which the energy per unit solid angle is a power-law function of the angle ($\proptoθ^{-k}$). We calculate light curves and spectra for GRB afterglows when such jets expand either in the interstellar medium or in the wind medium. In particular, we take into account two kinds of wind: one ($n\propto r^{-3/2}$) possibly from a typical red supergiant star and another ($n\propto r^{-2}$) possibly from a Wolf-Rayet star. We find that in each type of medium, one break appears in the late-time aftergl…
The central engine of gamma-ray bursts (GRBs) is believed to eject double-sided ultra-relativistic jets. For an observed GRB, one of the twin jets should point toward us, and is responsible for the prompt gamma-ray and subsequent afterglow emission. We consider in this Letter the other receding jet, which will give rise to late-time radio re-brightening (RRB) when it becomes non-relativistic (NR) and radiative isotropic. The RRB peaks at a time $5t_{NR}=2(E_{j,51}/n)^{1/3}$ yr after the GRB, where $t_{NR}$ is the observed NR timescale for the preceding jet, $E_j$ is the jet energy and $n$ is t…
(Abridged) SN 2002ap is an interesting event with broad spectral features like the famous SN 1998bw / GRB 980425. Here we examine the recently proposed jet hypothesis from SN 2002ap by a spectropolarimetric observation. We show that jets should be moving at about 0.23c with a jet kinetic energy of ~5 x 10^{50} erg, a similar energy scale to the GRB jets. The weak radio emission from SN 2002ap has been used to argue against the jet hypothesis, but we show that this problem can be avoided. However, the jet cannot be kept ionized because of adiabatic cooling without external photoionization or he…
We have made detailed calculations of the composition of magnetically driven jets ejected from collapsars, or rapidly rotating massive stars, based on long-term magnetohydrodynamic simulations of their core collapse with various distributions of magnetic field and angular momentum before collapse. We follow the evolution of the abundances of about 4000 nuclides from the collapse phase to the ejection phase and through the jet generation phase using a large nuclear reaction network. We find that the r-process successfully operates only in energetic jets (> 1e51 ergs), such that U and Th are syn…
We study the influence of jet structure on the curvature effect in a GRB-lightcurve. Using a simple model of jet emissivity, we numerically calculate lightcurves for a short flash from a relativistic outflow having various profiles of the Lorentz factor and outflowing energy density (gaussian, core+power-law). We find that for "on-beam" viewing geometry, with the line of sight passing through the bright core of the outflow, the shape of the lightcurve practically does not depend on the jet structure, initially following the temporal slope 2+delta, where delta is the spectral index. When the vi…
In this paper we report on the early evolution of core-collapse supernova explosion following the birth of a magnetar with the dipolar magnetic field of B=10^{15}G and the rotational period of 2ms, which was studied by means of axisymmetric general relativistic MHD simulations. The numerical models exhibit highly collimated magnetically-driven jets very early on. The jets are super-Alfvenic but remain sub-fast until the end of the simulations (t=0.2s). The power released in the jets is about 3x10^{50}erg/s which implies the spin-down time of ~37s. The total rotational energy of the magnetar, E…
A general formalism is developed for calculating the luminosity function and the expected number $N$ of observed GRBs above a peak photon flux $S$ for any GRB jet structure. This new formalism directly provides the true GRB rate without the need for a `correction factor'. We apply it to the uniform jet (UJ) and universal structured jet (USJ) models for the structure of GRB jets and perform fits to the observed log(N)-log(S) distribution from the GUSBAD catalog which contains 2204 BATSE bursts. A core angle $θ_c$ and an outer edge at $θ_{max}$ are introduced for the structured jet, and a finite…
There is now compelling evidence of a link between long-duration gamma-ray bursts (GRBs) and Type Ib/c supernovae (SNe). These core-collapse explosions are conjectured to radiate an anisotropic, beamed component associated with a decelerating, relativistic outflow and an unbeamed, isotropic component associated with the slowly expanding stellar debris. The anisotropic emission remains at a very low level until the Doppler cone of the beam intersects the observer's line of sight, making off-axis GRB jets directly detectable only at long wavelengths and late times. Circumstellar material, howeve…
We derive light curves of the afterglow emission from highly collimated jets if the power-law index ($p$) of the electron energy distribution is above 1 but below 2. We find (1) below the characteristic synchrotron frequency, the light curve index depends generally on $p$. (2) As long as the jet expansion is spherical, the light curve index above the characteristic frequency increases slowly as the spectral index of the emission increases. (3) Once the jet enters the spreading phase, the high-frequency emission flux decays as $\propto t^{-(p+6)/4}$ rather than $\propto t^{-p}$. All these resul…
Taking into account the recent suggestion that a short gamma-ray burst (GRB) looks like the first 1 sec of a long GRB, we propose that the jet of a GRB consists of multiple sub-jets or sub-shells (i.e., an inhomogeneous jet model). The multiplicity of the sub-jets along a line of sight n_s is an important parameter. If n_s is large (>> 1) the event looks like a long GRB, while if n_s is small (~1) the event looks like a short GRB. If our line of sight is off-axis to any sub-jets, the event looks like an X-ray flash or an X-ray rich GRB. The log-normal distribution of durations of short and lon…
It is now generally accepted that long gamma-ray bursts are associated with the final evolutionary stages of massive stars. As a consequence, their jets must propagate through the stellar progenitor and break out on their surface, before they can reach the photospheric radius and produce the gamma-ray photons. We investigate the role of the progenitor star in shaping the jet properties. We show that even a jet powered by a steady engine can develop a rich phenomenology at the stellar surface. We present special-relativistic simulations and compare the results to analytic considerations. We sho…
New two- and three-dimensional calculations are presented of relativistic jet propagation and break out in massive Wolf-Rayet stars. Such jets are thought responsible for gamma-ray bursts. As it erupts, the jet is surrounded by a cocoon of less energetic, but still highly relativistic ejecta that expands and becomes visible at much larger polar angles. These less energetic ejecta may be the origin of X-ray flashes and other high-energy transients which will be visible to a larger fraction of the sky, albeit to a shorter distance than common gamma-ray bursts. Jet stability is also examined in t…
We propose a method to estimate the pseudo jet opening half-angle of GRBs using the spectral peak energy ($\Ep$)--peak luminosity relation (so called Yonetoku relation) as well as the $\Ep$--collimation-corrected $γ$-ray energy relation (so called Ghirlanda relation). For bursts with known jet break times and redshifts, we compared the pseudo jet opening half-angle with the standard one and found that the differences are within a factor 2. We apply the method to 689 long GRBS. We found that the distribution function of the pseudo jet opening half-angle obeys $f(θ_j)\proptoθ_j^{-2.2 \pm 0.2}$ w…
After many years of speculation, recent observations have confirmed the association of gamma-ray bursts with core-collapse supernova explosions from massive stars. This association carries with it important consequences. The burst relativistic jet has to propagate through the cold dense stellar material before it reaches the transparency radius and the burst photons are produced. This propagation is likely to affect the initial properties of the jet, shaping it and changing its energy composition. The variability injected at the base of the jet is also likely to be erased by the jet-star inter…
Collapsars may be a source for the long Gamma Ray Bursts (GRBs) in the BATSE catalog. Collapsars may radiate gamma rays anisotropically by beamed jet emission close to the observer's line of sight. These jets must penetrate the radiation-dominated medium of their collapsar progenitor and break through its atmosphere in order to produce a GRB. We present a study of previously published, axisymmetric, collapsar jet simulations. Here we use the linearized, relativistic fluid equations to find the Kelvin-Helmholtz modes that are triggered by recollimation shocks within the jet. The modes will grow…
If Gamma-ray Bursts (GRBs) are generally associated with supernovae like 1998bw, a relatively wide intrinsic luminosity function is implied, which indicates the existence of a large amount of undetected dim bursts, and a much higher event-rate than is often assumed. If it is assumed that the intrinsic luminosity function of GRBs is a power-law: ${ϕ(L)} \propto {L^{-β}}$ ($β> 0$, $L_{min} \leq L \leq L_{max}$), data from the BATSE 4B catalog can be used to constrain slope index $β$ and the dynamic range width Log ${L_{max}\over L_{min}}$. Using a K-S test comparison with the observational Log $…
We consider the time-dependent evolution of a relativistic jet following its breakout through the surface of a massive compact star, as envisaged in the collapsar model of gamma-ray bursts. At breakout, the jet is tightly collimated by the pressure of its hot cocoon, which is created as the jet traverses the star. After breakout, the cocoon pressure drops and the jet expands toward its natural opening angle. We show that the evolving opening angle of the jet produces a stratification of the total energy with the off-axis angle, resulting in a universal morphology. The angular structure is larg…
We examine the propagation of 2-dimensional relativistic jets through the stellar progenitor in the collapsar model for gamma-ray bursts. In agreement with previous studies, we find that relativistic jets are collimated by their passage through the stellar mantle. Interaction of these jets with the star and their own cocoons also causes mixing that sporadically decelerates the flow. We speculate that this mixing instability is chiefly responsible for the variable Lorentz factor needed in the internal shock model and for the complex light curves seen in many GRBs. In all cases studied, the jet …
Long-duration gamma-ray bursts (GRBs) are thought to be connected to luminous and energetic supernovae (SNe), called hypernovae (HNe), resulting from the black-hole (BH) forming collapse of massive stars. For recent nearby GRBs~060505 and 060614, however, the expected SNe have not been detected. The upper limits to the SN brightness are about 100 times fainter than GRB-associated HNe (GRB-HNe), corresponding to the upper limits to the ejected $^{56}$Ni masses of $M({\rm ^{56}Ni})\sim 10^{-3}M_\odot$. SNe with a small amount of $^{56}$Ni ejection are observed as faint Type II SNe. HNe and faint…
Recent observations suggest that gamma ray bursts (GRBs) and their afterglows are produced in star formation regions in distant galaxies by highly relativistic jets that happen to point in our direction. Relativistic beaming collimates the emission from the highly relativistic jets into small solid angles along the jet direction. It implies that we are seeing only a small fraction of the events that produce GRBs. The observed GRB rate then requires an event rate which is comparable to the birth rate of neutron stars (NS). The highly relativistic jets sweep up ambient matter along their traject…
The steepening (break) of the power-law fall-off observed in the optical emission of some GRB afterglows at epoch ~1 day is often attributed to a collimated outflow (jet), undergoing lateral spreading. Wider opening GRB ejecta with a non-uniform energy angular distribution (structured outflows) or the cessation of energy injection in the afterglow can also yield light-curve breaks. We determine the optical and X-ray light-curve decay indices and spectral energy distribution slopes for 10 GRB afterglows with optical light-curve breaks (980519, 990123, 990510, 991216, 000301, 000926, 010222, 011…
I review the progress made on the physics of black hole systems in the context of the analogy between AGN and microquasars that was proposed one decade ago. If the emerging empirical correlations between the observational properties of stellar and supermassive black holes will become more robust, we will use them to determine the mass and spin of black holes, independently of theoretical models. Microquasars are fossils of sources of Gamma-ray bursts (GRBs) of long duration, and their kinematics provides observational clues on the physics of collapsars. If jets in GRBs, microquasars and AGN ar…
Growing observational evidence supports the proposition that gamma-ray bursts (GRBs) are powered by relativistic jets from massive helium stars whose cores have collapsed to black holes and an accretion disk (collapsars). We model the propagation of relativistic jets through the stellar progenitor and its wind using a two-dimensional special relativistic hydrodynamics code based on the PPM formalism. The jet emerges from the star with a plug in front and a cocoon surrounding it. During its propagation outside the star, the jet gains high Lorentz factor as its internal energy is converted into …
Gamma-Ray Bursts (GRBs) are now considered as relativistic jets. We analyze the gravitational waves from the acceleration stage of the GRB jets. We show that (i) the point mass approximation is not appropriate if the opening half-angle of the jet is larger than the inverse of the Lorentz factor of the jet, (ii) the gravitational waveform has many step function like jumps, and (iii) the practical DECIGO and BBO may detect such an event if the GRBs occur in Local group of galaxy. We found that the light curve of GRBs and the gravitational waveform are anti-correlated so that the detection of the…
It has been suggested that the peculiar properties of the luminous Type Ic supernova SN 1998bw and its low-energy gamma-ray burst GRB 980425 may be understood if they originated in a standard gamma-ray burst explosion viewed far from the axis of the relativistic jet. In this scenario, strong radio emission is predicted from the jet on a timescale 1 to 10 years after the explosion as it decelerates and spreads into our line of sight. To test this hypothesis we have carried out late-time radio observations of SN 1998bw at $t=5.6$ years, yielding upper limits which are consistent with the continu…
We present a relativistic-MHD numerical study of axisymmetric, magnetically driven jets with parameters applicable to gamma-ray burst (GRB) flows. We also present analytic expressions for the asymptotic jet shape and other flow parameters that agree very well with the numerical results. All current-carrying outflows exhibit self-collimation and consequent acceleration near the rotation axis, but unconfined outflows lose causal connectivity across the jet and therefore do not collimate or accelerate efficiently in their outer regions. Magnetically accelerated jets confined by an external pressu…
We model the radio, optical, and X-ray emission for the afterglows of GRB 980703, 990123, 990510, and 991216, within the framework of relativistic jets, to determine their physical parameters. The models that yield acceptable fits to the data have jet energies mostly between 10^{50} to 10^{51} erg and initial opening angles between 1 deg and 4 deg. The external medium density is uncertain by at least one order of magnitude in each case, being around 10^{-3}/cm^3 for GRB 980703 and 990123, ~0.1/cm^3 for GRB 990510, and ~3/cm^3 for GRB 991216. If the jets are uniform (i.e. there are no angular g…
Gamma ray bursts (GRB) occur at random points in the sky at cosmological distances. The spectra evolve through X-ray, optical region to possibly radio frequency. Though there are some models, the origin and time evolution of GRB are not well understood. Extragalactic radio sources also exhibit a baffling array of features that are poorly understood -- the core emission in ultraviolet region, lobes in RF range, transient gamma and X-ray emissions etc. These two phenomena appear to be very different, but the time evolution of the core emission of radio sources is essentially the same as GRBs, th…
Exact semianalytic solutions for GRB outflows were recently derived using the equations of special-relativistic ideal MHD (see Vlahakis & Konigl in these Proceedings for a summary). This contribution focuses on the implications of these results to various modeling and observational issues in GRB sources, including the baryon loading problem, polarization measurements of the prompt and reverse-shock emission, and the possible existence of a two-component outflow.
We extend our calculation of physical parameters of GRB jets by modeling the broadband emission of the afterglows 970508, 980519, 991208, 000926, 000418, and 010222. Together with 990123, 990510, 991216, and 000301c, there are ten well-observed afterglows for which the initial opening angle of the GRB jet can be constrained. The jet energies (after the GRB phase) obtained for this set of afterglows are within one decade around 5E50erg. With the exception of 000418, which requires a jet wider than 1/2 radians, the jet initial half-angle in the other cases ranges from 2 deg to 20 deg. We find th…
Comparing the properties AGN and Herbig-Haro jets can be a useful exercise for understanding the physical mechanisms at work in collimated outflows that propagate in such different environments. In the case of Herbig-Haro jets, the presence of emission lines in the spectra and the continuous evolution of the observation techniques greatly favor our knowledge of the physical parameters of the jets instead, for AGN jets, the process of constraining the jet parameters is hampered by the nature of the emission from these objects that is non-thermal. I will discuss how one cannot directly constrain…
A persistent, thin, micro-nano sr. beamed gamma jet, may be ejected from BH and Pulsars, powered by ultra-relativistic electron pairs. These jet while precessing and spinning are originated by Inverse Compton and-or Synchrotron Radiation at pulsars or micro-quasars sources. They are most powerful at Supernova birth, blazing, once on axis, to us and flashing GRB detector. The trembling of thin jets explains naturally the observed erratic multi-explosive structure of different GRBs. The jets are precessing and decaying on time scales of a few hours surviving as long as thousands of years, linkin…
Most powerful jets are observed to emanate from accreting black hole systems. Recent quasi-stationary radiative MHD calculations reveal that jet-launching start in the innermost region of a transition layer (:TL), which is located between the disk and the corona. The plasma in the TL is dominated by virial-hot protons, advective, highly magnetic-diffusive and rotates super-Keplerian. The amplified toroidal magnetic field (TMF) in the TL reach values beyond equipartition with respect to the electron thermal energy, thereby considerably enhancing the Poynting energy flux and yielding gravitation…
We argue the behavior of Poynting flux-dominated outflows from AGN in the galactic cluster systems by performing three-dimensional MHD simulations within the framework of the "magnetic tower" model. Of particular interests are the structure of MHD waves, the cylindrical radial force balance, the (de)collimation, and the stability properties of magnetic tower jets. Transition between the jet/lobe and the formation of wiggling jet by growing current-driven instability are discussed.
The role of kink instability in magnetically driven jets is explored through numerical one-dimensional steady relativistic MHD calculations. The instability is shown to have enough time to grow and influence the dynamics of Poynting-flux dominated jets. In the case of AGN jets, the flow becomes kinetic flux dominated at distances larger than ~1000 r_g because of the rapid dissipation of Poynting flux. When applied to GRB outflows, the model predicts more gradual Poynting dissipation and moderately magnetized flow at distances of ~10^{16} cm where the deceleration of the ejecta due to its inter…
The past year has witnessed a large increase in our knowledge of the polarization properties of Gamma-Ray Burst (GRB) radiation. In the prompt phase, the measurement (albeit highly debated) of a large degree of linear polarization in GRB 021206 has stimulated a deep theoretical study of polarization from GRB jets. The optical afterglow of GRB 030329, on the other hand, has been followed thoroughly in polarimetric mode, allowing for an unprecedented sampling of its polarization curve. I will review the present status of theories and observations of polarization in GRBs, focusing on how polarime…
We discuss a new VLBA program to investigate structural and polarization changes in the brightest AGN jets in the northern sky. Our study represents a significant improvement over previous surveys in terms of image fidelity, size, and completeness, and will serve to characterize the kinematics of AGN jets and determine how these are related to other source properties. We discuss several preliminary results from our program, including the detection of parsec-scale circularly polarized jet emission, enhanced magnetic field ordering at the sites of apparent bends, and intrinsic differences in the…
Compact relativistic jets in active galactic nuclei offer an effective tool for investigating the physics of nuclear regions in galaxies. The emission properties, dynamics, and evolution of jets in AGN are closely connected to the characteristics of the central supermassive black hole, accretion disk and broad-line region in active galaxies. Recent results from studies of the nuclear regions in several active galaxies with prominent outflows are reviewed in this contribution.
Most of energy carried by relativistic AGN jets remains undetected until hundreds of kiloparsecs where interaction with intergalactic medium produces hot spots. The jet's hidden energy is only partially dissipated at smaller scales, from parsecs to kiloparsecs. Several media may play the role of the ``prime mover'': ions, pairs or large scale magnetic fields. Analyzing VLBI polarization structures of relativistic parsec scale jets we conclude that large-scale magnetic fields can explain the salient polarization properties of parsec-scale AGN jets. This implies that large-scale magnetic fields …
Results of high-resolution simultaneous multi-frequency 8.1-15.4 GHz VLBA polarimetric observations of relativistic jets in active galactic nuclei (the MOJAVE-2 project) are analyzed. We compare characteristics of VLBI features with jet model predictions and test if adiabatic expansion is a dominating mechanism for the evolution of relativistic shocks in parsec-scale AGN jets. We also discuss magnetic field configuration, both predicted by the model and deduced from electric vector position angle measurements.
Velocities close to the speed of light are a robust observational property of the jets observed in microquasars and AGNs, and are expected to be behind much of the phenomenology of GRBs. Yet, the mechanism boosting relativistic jets to such large Lorentz factors is still essentially unknown. Building on recent general-relativistic, multidimensional simulations of progenitors of short GRBs, we discuss a new effect in relativistic hydrodynamics which can act as an efficient booster in jets. This effect is purely hydrodynamical and occurs when large velocities tangential to a discontinuity are pr…
