P. Hardee

WEIBEL INSTABILITY AND ASSOCIATED STRONG FIELDS IN A FULLY THREE-DIMENSIONAL SIMULATION OF A RELATIVISTIC SHOCK

Plasma instabilities (e.g., Buneman, Weibel and other two-stream instabilities) excited in collisionless shocks are responsible for particle (electron, positron, and ion) acceleration. Using a new 3-D relativistic particle-in-cell code, we have investigated the particle acceleration and shock structure associated with an unmagnetized relativistic electron-positron jet propagating into an unmagnetized electron-positron plasma. The simulation has been performed using a long simulation system in order to study the nonlinear stages of the Weibel instability, the particle acceleration mechanism, and the shock structure. Cold jet electrons are thermalized and slowed while the ambient electrons are swept up to create a partially developed hydrodynamic (HD) like shock structure. In the leading shock, electron density increases by a factor of 3.5 in the simulation frame. Strong electromagnetic fields are generated in the trailing shock and provide an emission site. We discuss the possible implication of our simulation results within the AGN and GRB context.

Acceleration Mechanics in Relativistic Shocks by the Weibel Instability

Plasma instabilities (e.g., Buneman, Weibel, and other two-stream instabilities) created in collisionless shocks may be responsible for particle (electron, positron, and ion) acceleration. Using a three-dimensional relativistic electromagnetic particle code, we have investigated long-term particle acceleration associated with relativistic electron-ion or electron-positron jet fronts propagating into an unmagnetized ambient electron-ion or electron-positron plasma. These simulations have been performed with a longer simulation system than our previous simulations in order to investigate the nonlinear stage of the Weibel instability and its particle acceleration mechanism. The current channels generated by the Weibel instability are surrounded by toroidal magnetic fields and radial electric fields. This radial electric field is quasi stationary and accelerates particles that are then deflected by the magnetic field. Whether particles are accelerated or decelerated along the jet propagation direction depends on the velocity of particles and the sign of × in the moving frame of each particle. For the electron-ion case the large-scale current channels generated by the ion Weibel instability lead to more acceleration near the jet head. Consequently, the accelerated jet electrons in the electron-ion jet have a significant hump above a thermal distribution. However, in the electron-positron case, accelerated jet electrons have a smoother, nearly thermal distribution. In the electron-positron case, initial acceleration occurs as current channels form and then continues at a much lesser rate as the current channels and corresponding toroidal magnetic fields generated by the Weibel instability dissipate.

A General Relativistic Magnetohydrodynamic Simulation of Jet Formation

We have performed a fully three-dimensional general relativistic magnetohydrodynamic (GRMHD) simulation of jet formation from a thin accretion disk around a Schwarzschild black hole with a free-falling corona. The initial simulation results show that a bipolar jet (velocity ~0.3c) is created, as shown by previous two-dimensional axisymmetric simulations with mirror symmetry at the equator. The three-dimensional simulation ran over 100 light crossing time units (τS = rS/c, where rS ≡ 2GM/c2), which is considerably longer than the previous simulations. We show that the jet is initially formed as predicted owing in part to magnetic pressure from the twisting of the initially uniform magnetic field and from gas pressure associated with shock formation in the region around r = 3rS. At later times, the accretion disk becomes thick and the jet fades resulting in a wind that is ejected from the surface of the thickened (torus-like) disk. It should be noted that no streaming matter from a donor is included at the outer boundary in the simulation (an isolated black hole not binary black hole). The wind flows outward with a wider angle than the initial jet. The widening of the jet is consistent with the outward-moving torsional Alfven waves. This evolution of disk-jet coupling suggests that the jet fades with a thickened accretion disk because of the lack of streaming material from an accompanying star.

Modeling the 3C 120 Radio Jet from 1 to 30 Milliarcseconds

In this paper we use the predicted spatial development of helical structures along an expanding jet to model observed structures and motions in the 3C 120 jet. New results of VLBI imaging of the parsec-scale radio jet in 3C 120 at 5 GHz are examined along with older long-term monitoring results at 5 GHz and older results obtained at 22 and 43 GHz. The high-frequency observations provide detailed information on motions and structure from 0.5 to 10 mas from the core and the lower frequency observations from 1 to 30 mas from the core. Proper motions of helical components associated with the pattern and of other components that move through the pattern provide estimates of flow and helical pattern speeds. Theoretical modeling of the motion and appearance of the helical pattern allows determination of sound speeds as a function of the jet viewing angle. The jet sound speed declines although probably not as fast as adiabatically. At a 12° viewing angle the most likely scenario involves a decline in jet sound speed from c/3 < aj < c/ at ~0.5 mas from the core to 0.1c < aj < 0.25c at ~25 mas from the core accompanied by some acceleration in the jet flow from Lorentz factor γ 5 to γ 7. The sound speed in the cocoon medium around the jet is less well determined but is less than the sound speed in the jet probably by a factor of 1.5-5. A largest possible viewing angle of 15° implies a jet sound speed at the upper limit of these estimates and somewhat higher flow Lorentz factors. However, jet morphology argues against viewing angles larger than 12°. At smaller viewing angles the jet sound speed is lower, and at a 6° viewing angle the jet sound speed is about a factor of 2 less, but the flow Lorentz factor is comparable. The decline in radio intensity is on the order of what would be associated with isothermal jet expansion. Knot-interknot intensity variations are greater than would be expected from adiabatic compressions associated with the helical twist, and we infer the presence of a shock along the leading edge of the helical twist in addition to shock or density structures flowing through the helical pattern. Our results imply that the macroscopic heating of the expanding jet fluid is less than the microscopic energization of the synchrotron radiating relativistic electrons.

Kinematics of the jet in M 87 on scales of 100-1000 Schwarzschild radii

Context. Very long baseline interferometry (VLBI) imaging of radio emission from extragalactic jets provides a unique probe of physical mechanisms governing the launching, acceleration, and collimation of relativistic outflows. Aims. VLBI imaging of the jet in the nearby active galaxy M 87 enables morphological and kinematic studies to be done on linear scales down to ~100 Schwarzschild radii ( R s ). Methods. The two-dimensional structure and kinematics of the jet in M 87 (NGC 4486) have been studied by applying the wavelet-based image segmentation and evaluation (WISE) method to 11 images obtained from multi-epoch Very Long Baseline Array (VLBA) observations made in January-August 2007 at 43 GHz ( λ = 7 mm). Results. The WISE analysis recovers a detailed two-dimensional velocity field in the jet in M 87 at sub-parsec scales. The observed evolution of the flow velocity with distance from the jet base can be explained in the framework of MHD jet acceleration and Poynting flux conversion. A linear acceleration regime is observed up to z obs ~ 2 mas. The acceleration is reduced at larger scales, which is consistent with saturation of Poynting flux conversion. Stacked cross correlation analysis of the images reveals a pronounced stratification of the flow. The flow consists of a slow, mildly relativistic layer (moving at β ~ 0.5 c ), associated either with instability pattern speed or an outer wind, and a fast, accelerating stream line (with β ~ 0.92, corresponding to a bulk Lorentz factor γ ~ 2.5). A systematic difference of the apparent speeds in the northern and southern limbs of the jet is detected, providing evidence for jet rotation. The angular velocity of the magnetic field line associated with this rotation suggests that the jet in M 87 is launched in the inner part of the disk, at a distance r 0 ~ 5 R s from the central engine. Conclusions. The combined results of the analysis imply that MHD acceleration and conversion of Poynting flux to kinetic energy play the dominant roles in collimation and acceleration of the flow in M 87.

A Magnetohydrodynamic Boost for Relativistic Jets

We have performed relativistic magnetohydrodynamic simulations of the hydrodynamic boosting mechanism for relativistic jets explored by Aloy & Rezzolla (2006) using the RAISHIN code. Simulation results show that the presence of a magnetic field may change the properties of the shock interface between the tenuous, overpressured jet (V(sub j) (sup z)) flowing tangentially to a dense external medium. Magnetic fields can lead to more efficient acceleration of the jet, in comparison to the pure-hydrodynamic case. A poloidal magnetic field (B(sup z)), tangent to the interface and parallel to the jet flow, produces both a stronger outward moving shock and inward moving rarefaction wave. This leads to a large velocity component normal to the interface in addition to acceleration tangent to the interface, and the jet is thus accelerated to a larger Lorentz factors than those obtained in the pure-hydrodynamic case. In contrast, a strong toroidal magnetic field (B(sup y)), tangent to the interface but perpendicular to the jet flow, also leads to stronger acceleration tangent to the shock interface relative to the pure-hydrodynamic case, but to a lesser extent than found for the poloidal case due to the fact that the velocity component normal to the shock interface is now much smaller. Overall, the acceleration efficiency in the toroidal case is less than that of the poloidal case but both geometries still result in higher Lorentz factors than the pure-hydrodynamic case. Thus, the presence and relative orientation of a magnetic field in relativistic jets can have a significant influence on the hydrodynamic boost mechanism studied by Aloy & Rezzolla (2006).

The role of Kelvin-Helmholtz instability in the internal structure of relativistic outflows. The case of the jet in 3C 273

Context. Relativistic outflows represent one of the best-suited tools to probe the physics of AGN. Numerical modelling of internal structure of the relativistic outflows on parsec scales provides important clues about the conditions and dynamics of the material in the immediate vicinity of the central black holes in AGN. Aims. We investigate possible causes of the structural patterns and regularities observed in the parsec-scale jet of the well-known quasar 3C 273. Methods. We present here the results from a 3D relativistic hydrodynamics numerical simulation based on the parameters given for the jet by Lobanov & Zensus (2001, Science, 294, 128), and one in which the effects of jet precession and the injection of discrete components have been taken into account. We compare the model with the structures observed in 3C 273 using very long baseline interferometry and constrain the basic properties of the flow. Results. We find growing perturbation modes in the simulation with similar wavelengths to those observed, but with a different set of wave speeds and mode identification. If the observed longest helical structure is produced by the precession of the flow, longer precession periods should be expected. Conclusions. Our results show that some of the observed structures could be explained by growing Kelvin-Helmholtz instabilities in a slow moving region of the jet. However, we point towards possible errors in the mode identification that show the need of more complete linear analysis in order to interpret the observations. We conclude that, with the given viewing angle, superluminal components and jet precession cannot explain the observed structures.

MAGNETOHYDRODYNAMIC EFFECTS IN PROPAGATING RELATIVISTIC JETS: REVERSE SHOCK AND MAGNETIC ACCELERATION

We solve the Riemann problem for the deceleration of an arbitrarily magnetized relativistic flow injected into a static unmagnetized medium in one dimension. We find that for the same initial Lorentz factor, the reverse shock becomes progressively weaker with increasing magnetization σ (the Poynting-to-kinetic energy flux ratio), and the shock becomes a rarefaction wave when σ exceeds a critical value, σ c , defined by the balance between the magnetic pressure in the flow and the thermal pressure in the forward shock. In the rarefaction wave regime, we find that the rarefied region is accelerated to a Lorentz factor that is significantly larger than the initial value. This acceleration mechanism is due to the strong magnetic pressure in the flow. We discuss the implications of these results for models of gamma-ray bursts and active galactic nuclei.

Radiation from relativistic shocks in turbulent magnetic fields

Using our new 3-D relativistic particle-in-cell (PIC) code parallelized with MPI, we investigated long-term particle acceleration associated with a relativistic electron–positron jet propagating in an unmagnetized ambient electron–positron plasma. The simulations were performed using a much longer simulation system than our previous simulations in order to investigate the full nonlinear stage of the Weibel instability and its particle acceleration mechanism. Cold jet electrons are thermalized and ambient electrons are accelerated in the resulting shocks. Acceleration of ambient electrons leads to a maximum ambient electron density three times larger than the original value as predicted by hydrodynamic shock compression. In the jet (reverse) shock behind the bow (forward) shock the strongest electromagnetic fields are generated. These fields may lead to time dependent afterglow emission. In order to calculate radiation from first principles that goes beyond the standard synchrotron model used in astrophysical objects we have used PIC simulations. Initially we calculated radiation from electrons propagating in a uniform parallel magnetic field to verify the technique. We then used the technique to calculate emission from electrons in a small simulation system. From these simulations we obtained spectra which are consistent with those generated from electrons propagating in turbulent magnetic fields with red noise. This turbulent magnetic field is similar to the magnetic field generated at an early nonlinear stage of the Weibel instability. A fully developed shock within a larger simulation system may generate a jitter/synchrotron spectrum. 2011 COSPAR. Published by Elsevier Ltd. All rights reserved.

Magnetic field generation in a jet-sheath plasma via the kinetic Kelvin-Helmholtz instability

Abstract. We have investigated the generation of magnetic fields associated with velocity shear between an unmagnetized relativistic jet and an unmagnetized sheath plasma. We have examined the strong magnetic fields generated by kinetic shear (Kelvin–Helmholtz) instabilities. Compared to the previous studies using counter-streaming performed by Alves et al. (2012), the structure of the kinetic Kelvin–Helmholtz instability (KKHI) of our jet-sheath configuration is slightly different, even for the global evolution of the strong transverse magnetic field. In our simulations the major components of growing modes are the electric field Ez, perpendicular to the flow boundary, and the magnetic field By, transverse to the flow direction. After the By component is excited, an induced electric field Ex, parallel to the flow direction, becomes significant. However, other field components remain small. We find that the structure and growth rate of KKHI with mass ratios mi/me = 1836 and mi/me = 20 are similar. In our simulations saturation in the nonlinear stage is not as clear as in counter-streaming cases. The growth rate for a mildly-relativistic jet case (γj = 1.5) is larger than for a relativistic jet case (γj = 15).