Distribution Of Lorentz Factors Research Articles

Jetsimpy: A Highly Efficient Hydrodynamic Code for Gamma-Ray Burst Afterglow

Gamma-ray burst (GRB) afterglows are emissions from ultrarelativistic blast waves produced by a narrow jet interacting with surrounding matter. Since the first multimessenger observation of a neutron star merger, hydrodynamic modeling of GRB afterglows for structured jets with smoothly varying angular energy distributions has gained increased interest. While the evolution of a jet is well described by self-similar solutions in both ultrarelativistic and Newtonian limits, modeling the transitional phase remains challenging. This is due to the nonlinear spreading of a narrow jet to a spherical configuration and the breakdown of self-similar solutions. Analytical models are limited in capturing these nonlinear effects, while relativistic hydrodynamic simulations are computationally expensive, which restricts the exploration of various initial conditions. In this work, we introduce a reduced hydrodynamic model that approximates the blast wave as an infinitely thin two-dimensional surface. Further assuming axial symmetry, this model simplifies the simulation to one dimension and drastically reduces the computational costs. We have compared our modeling to relativistic hydrodynamic simulations and semianalytic methods, and applied it to fit the light curve and flux centroid motion of GRB 170817A. These comparisons demonstrate good agreement and validate our approach. We have developed this method into a numerical tool, jetsimpy, which models the synchrotron GRB afterglow emission from a blast wave with arbitrary angular energy and Lorentz factor distribution. Although the code is built with GRB afterglow in mind, it applies to any relativistic jet. This tool is particularly useful in Markov Chain Monte Carlo studies and is provided to the community.

The signature of refreshed shocks in the afterglow of GRB 030329

ABSTRACT GRB 030329 displays one clear and, possibly, multiple less intense fast-rising (Δt/t ∼ 0.3) jumps in its optical afterglow light curve. The decay rate of the optical light curve remains the same before and after the flux jumps. This may be the signature of energy injection into the shocked material at the front of the jet. In this study, we model the Gamma-ray Burst (GRB) ejecta as a series of shells. We follow the dynamical evolution of the ejecta as it interacts with itself (i.e. internal shocks) and with the circumburst medium (i.e. external forward and reverse shocks), and calculate the emission from each shock event assuming synchrotron emission. We confirm the viability of the proposed model in which the jumps in the optical afterglow light curve of GRB 030329 are produced via refreshed shocks. The refreshed shocks may be the signatures of collisions between earlier ejected material with an average Lorentz factor $\bar{\Gamma }\gtrsim 100$ and later ejected material with $\bar{\Gamma } \sim 10$ once the early material has decelerated due to interaction with the circumburst medium. We show that even if the late material is ejected with a spread of Lorentz factors, internal shocks naturally produce a narrow distribution of Lorentz factors (ΔΓ/Γ ≲ 0.1), which is a necessary condition to produce the observed quick rise times of the jumps. These results imply a phase of internal shocks at some point in the dynamical evolution of the ejecta, which requires a low magnetization in the outflow.

Electron bunch dynamics and emission in particle-in-cell simulations of relativistic laser–solid interactions: On density artifacts, collisions, and numerical dispersion

Sub-optical-cycle dynamics of dense electron bunches in relativistic-intensity laser–solid interactions lead to the emission of high-order harmonics and attosecond light pulses. The capacity of particle-in-cell simulations to accurately model these dynamics is essential for the prediction of emission properties because the attosecond pulse intensity depends on the electron density distribution at the time of emission and on the temporal distribution of individual electron Lorentz-factors in an emitting electron bunch. Here, we show that in one-dimensional collisionless simulations, the peak density of the emitting electron bunch increases with the increase in the spatial resolution of the simulation grid. When collisions are added to the model, the peak electron density becomes independent of the spatial resolution. Collisions are shown to increase the spread of the peaks of Lorentz-factors of emitting electrons in time, especially in the regimes far from optimum generation conditions, thus leading to lower intensities of attosecond pulses as compared to those obtained in collisionless simulations.

Polarization of fast radio bursts: radiation mechanisms and propagation effects

ABSTRACT Fast radio bursts (FRBs) are observed to be highly polarized. Most have high linear polarization but a small fraction shows significant circular polarization. We systematically investigate a variety of polarization mechanisms of FRBs within the magnetar theoretical framework considering two emission sites inside and outside the magnetosphere. For each site, we discuss both intrinsic radiation mechanisms and propagation effects. Inside the magnetosphere, we investigate the polarization properties of both coherent curvature radiation and inverse Compton scattering by charged bunches and conclude that both mechanisms produce 100 per cent linear polarization at an on-axis geometry but can produce circular polarization if the viewing angle is off axis. The lack of circular polarization for the majority of bursts requires that the bunches have a large transverse dimension size. Resonant cyclotron absorption within magnetosphere may produce high circular polarization if electrons and positrons have an asymmetric Lorentz factor distribution. Outside the magnetosphere, the synchrotron maser emission mechanism in general produces highly linearly polarized emission. Circular polarization would appear at off-beam angles but the flux is greatly degraded and such bursts are not detectable at cosmological distances. Synchrotron absorption in a nebula with ordered magnetic field may reduce the circular polarization degree. Cyclotron absorption in a strongly magnetized medium may generate significant circular polarization. Faraday conversion in a medium with field reversal can convert one polarization mode to another. The two absorption processes require stringent physical conditions. Significant Faraday conversion may be realized in a magnetized dense environment involving binary systems or supernova remnants.

Density filamentation nonlinearly driven by the Weibel instability in relativistic beam plasmas

Density filamentation has been observed in many beam-plasma simulations and experiments. Because current filamentation is a pure transverse mode, charge density filamentation cannot be produced directly by the current filamentation process. To explain this phenomenon, several mechanisms are proposed such as the coupling of the Weibel instability to the two-stream instability, coupling to the Langmuir wave, differences in thermal velocities between the beam and return currents, the magnetic pressure gradient force, etc. In this paper, it is shown that the gradient of the Lorentz factor can, in fact, represent the nonlinear behavior of a plasma fluid and further that the nonuniform Lorentz factor distribution can give rise to electrostatic fields and density filaments. Simulation results together with theoretical analyses are presented.

Lorentz Factors of Compact Jets in Black Hole X-Ray Binaries

Abstract Compact, continuously launched jets in black hole X-ray binaries (BHXBs) produce radio to optical/IR synchrotron emission. In most BHXBs, an IR excess (above the disk component) is observed when the jet is present in the hard spectral state. We investigate why some BHXBs have prominent IR excesses and some do not, quantified by the amplitude of the IR quenching or recovery over the transition from/to the hard state. We find that the amplitude of the IR excess can be explained by inclination-dependent beaming of the jet synchrotron emission and the projected area of the accretion disk. Furthermore, we see no correlation between the expected and the observed IR excess for Lorentz factor 1, which is strongly supportive of relativistic beaming of the IR emission, confirming that the IR excess is produced by synchrotron emission in a relativistic outflow. Using the amplitude of the jet fade and recovery over state transitions and the known orbital parameters, we constrain for the first time the bulk Lorentz factor range of compact jets in several BHXBs (with all the well-constrained Lorentz factors lying in the range of Γ = 1.3–3.5). Under the assumption that the Lorentz factor distribution of BHXB jets is a power law, we find that . We also find that the very high amplitude IR fade/recovery seen repeatedly in the BHXB GX 339–4 favors a low inclination angle ( ) of the jet.

MOJAVE. XVII. Jet Kinematics and Parent Population Properties of Relativistically Beamed Radio-loud Blazars

Abstract We present results from a parsec-scale jet kinematics study of 409 bright radio-loud active galactic nuclei (AGNs) based on 15 GHz Very Long Baseline Array (VLBA) data obtained between 1994 August 31 and 2016 December 26 as part of the 2 cm VLBA survey and Monitoring Of Jets in Active galactic nuclei with VLBA Experiments (MOJAVE) programs. We tracked 1744 individual bright features in 382 jets over at least 5 epochs. A majority (59%) of the best-sampled jet features showed evidence of accelerated motion at the >3σ level. Although most features within a jet typically have speeds within ∼40% of a characteristic median value, we identified 55 features in 42 jets that had unusually slow pattern speeds, nearly all of which lie within 4 pc (100 pc deprojected) of the core feature. Our results, combined with other speeds from the literature, indicate a strong correlation between apparent jet speed and synchrotron peak frequency, with the highest jet speeds being found only in low-peaked AGNs. Using Monte Carlo simulations, we find best-fit parent population parameters for a complete sample of 174 quasars above 1.5 Jy at 15 GHz. Acceptable fits are found with a jet population that has a simple unbeamed power-law luminosity function incorporating pure luminosity evolution and a power-law Lorentz factor distribution ranging from 1.25 to 50 with slope −1.4 ± 0.2. The parent jets of the brightest radio quasars have a space density of 261 ± 19 Gpc−3 and unbeamed 15 GHz luminosities above ∼1024.5 W Hz−1, consistent with FR II class radio galaxies.

Observational constraints on the structure of gamma-ray burst jets

Motivated by GW170817 we examine constraints that observations put on the angular structure of long gamma-ray burst (GRB) jets. First, the relatively narrow observed distribution of $E_{X}/E_{\gamma}$ (the isotropic equivalent early X-ray afterglow to prompt $\gamma$-ray energy ratio) implies that at any angle that $\gamma$-rays are emitted the Lorentz factor must be high. Specifically, the Lorentz factor of $\gamma$-ray emitting material cannot drop rapidly with angle, and must be $\Gamma(\theta)\gtrsim 50$ even if there are angles for which the gamma-ray received energy is lower by three orders of magnitude compared to the jet core. Second, jets with an angular structure of the $\gamma$-ray emission that over-produce events with a $\gamma$-ray luminosity below the peak of the observed luminosity function are ruled-out. This eliminates models in which the $\gamma$-ray energy angular distribution isn't sufficiently steep and the Lorentz factor distribution isn't sufficiently shallow. Finally, models with a steep structure (e.g. Gaussian) which are detected away from the jet core generate afterglow light-curves that were never observed. We conclude that even if the jet kinetic energy distribution drops continuously with latitude, efficient $\gamma$-ray emission seems to be restricted to material with $\Gamma\gtrsim 50$ and is most likely confined to a narrow region around the core. While our study is confined to long GRBs, where the observed sample is larger and more complete, there are indications that similar conclusions may be applicable also to short GRBs. We discuss the possible implications to the $\gamma$-rays observed in GRB 170817A.

High-energy Neutrino Emission from Short Gamma-Ray Bursts: Prospects for Coincident Detection with Gravitational Waves

Abstract We investigate current and future prospects for coincident detection of high-energy neutrinos and gravitational waves (GWs). Short gamma-ray bursts (SGRBs) are believed to originate from mergers of compact star binaries involving neutron stars. We estimate high-energy neutrino fluences from prompt emission, extended emission (EE), X-ray flares, and plateau emission, and we show that neutrino signals associated with the EE are the most promising. Assuming that the cosmic-ray loading factor is ∼10 and the Lorentz factor distribution is lognormal, we calculate the probability of neutrino detection from EE by current and future neutrino detectors, and we find that the quasi-simultaneous detection of high-energy neutrinos, gamma-rays, and GWs is possible with future instruments or even with current instruments for nearby SGRBs having EE. We also discuss stacking analyses that will also be useful with future experiments such as IceCube-Gen2.

Low-Γ jets from Compact Binary Mergers as Candidate Electromagnetic Counterparts to Gravitational Wave Sources

AbstractCompact binary mergers, with neutron stars or neutron star and black-hole components, are thought to produce various electromagnetic counterparts: short gamma-ray bursts (GRBs) from ultra-relativistic jets followed by broadband afterglow; semi-isotropic kilonova from radioactive decay of r-process elements; and late time radio flares; etc. If the jets from such mergers follow a similar power-law distribution of Lorentz factors as other astrophysical jets then the population of merger jets will be dominated by low-Γ values. The prompt gamma-rays associated with short GRBs would be suppressed for a low-Γ jet and the jet energy will be released as X-ray/optical/radio transients when a shock forms in the ambient medium. Using Monte Carlo simulations, we study the properties of such transients as candidate electromagnetic counterparts to gravitational wave sources detectable by LIGO/Virgo. Approximately 78% of merger-jets result in failed GRB with optical peaks 14-22 magnitude and an all-sky rate of 2-3 per year.

Lorentz factor distribution of blazars from the optical Fundamental Plane of black hole activity

Blazar radiation is dominated by a relativistic jet which can be modeled at first approximation using just two intrinsic parameters - the Lorentz factor $\Gamma$ and the viewing angle $\theta$. Blazar jet observations are often beamed due to relativistic effects, complicating the understanding of these intrinsic properties. The most common way to estimate blazar Lorentz factors needs the estimation of apparent jet speeds and Doppler beaming factors. We present a new and independent method of constructing the blazar Lorentz factor distribution, using the optical fundamental plane of black hole activity. The optical fundamental plane is a plane stretched out by both the supermassive black holes and the X-ray binaries, in the 3D space provided by their [OIII] line luminosity, radio luminosity and black hole mass. We use the intrinsic radio luminosity obtained from the optical fundamental plane to constrain the boosting parameters of the VLBA Imaging and Polarimetry Survey (VIPS) blazar sample. We find a blazar bulk Lorentz factor distribution in the form of a power law as $N(\Gamma) \propto \Gamma^{-2.1 \pm 0.4}$ for the $\Gamma$ range of 1 to 40. We also discuss the viewing angle distribution of the blazars and the dependence of our results on the input parameters.

Population statistics of beamed sources – II. Evaluation of Doppler factor estimates

In a companion paper we presented a statistical model for the blazar population, consisting of distributions for the unbeamed radio luminosity function and the Lorentz factor distribution of each of the BL Lac and Flat Spectrum Radio Quasar (FSRQ) classes. Our model has been optimized so that it reproduces the MOJAVE distributions of apparent speeds and redshifts when the appropriate flux limit is applied and a uniform distribution of jet viewing angles is assumed for the population. Here we use this model to predict the Doppler factor distribution for various flux-limited samples for which Doppler factors have been estimated in a variety of ways (equipartition, variability + equipartition, inverse Compton dominance) on a blazar-by-blazar basis. By comparing the simulated and data-estimated Doppler factor distributions in each case, we evaluate the different methods of estimating blazar Doppler factors. We find that the variability Doppler factors assuming equipartition are the ones in the best agreement with our statistical model, whereas the inverse Compton Doppler factor method is only suitable for FSRQs. In the case of variability Doppler factors, we find that while random errors are relatively low ($\sim 30\%$), uncertainties are dominated by systematic effects. In the case of inverse Compton Doppler factors, random errors appear to dominate, but are significantly larger ($\sim 60\%$).

Prompt optical emission from gamma-ray bursts with multiple timescale variability of central engine activities

Complete high-resolution light curves of GRB 080319B observed by Swift present an opportunity for detailed temporal analysis of prompt optical emission. With a two-component distribution of initial Lorentz factors, we simulate the dynamical process of shells being ejected from the central engine in the framework of the internal shock model. The emitted radiations are decomposed into different frequency ranges for a temporal correlation analysis between the light curves in different energy bands. The resulting prompt optical and gamma-ray emissions show similar temporal profiles, with both showing a superposition of a component with slow variability and a component with fast variability, except that the gamma-ray light curve is much more variable than its optical counterpart. The variability in the simulated light curves and the strong correlation with a time lag between the optical and gamma-ray emissions are in good agreement with observations of GRB 080319B. Our simulations suggest that the variations seen in the light curves stem from the temporal structure of the shells injected from the central engine of gamma-ray bursts. Future observations with high temporal resolution of prompt optical emission from GRBs, e.g., by UFFO-Pathfinder and SVOM-GWAC, will provide a useful tool for investigating the central engine activity.

A “BOOSTED FIREBALL” MODEL FOR STRUCTURED RELATIVISTIC JETS

We present a model for relativistic jets which generates a particular angular distribution of Lorentz factor and energy per solid angle. We consider a fireball with specific internal energy E/M launched with bulk Lorentz factor \gamma_B. This "boosted fireball" model is motivated by the phenomenology of collapsar jets, but is applicable to a wide variety of relativistic flows. In its center-of-momentum frame the fireball expands isotropically, converting its internal energy into radially expanding flow with asymptotic Lorentz factor \eta_0 ~ E/M. In the lab frame the flow is beamed, expanding with Lorentz factor \Gamma = 2 \eta_0 \gamma_B in the direction of its initial bulk motion and with characteristic opening angle \theta_0 ~ 1/\gamma_B. The flow is jet-like with \Gamma \theta_0 ~ 2 \eta_0 such that jets with \Gamma > 1/\theta_0 are naturally produced. The choice \eta_0 ~ \gamma_B ~ 10 yields a jet with \Gamma ~ 200 on-axis and angular structure characterized by opening angle \theta_0 ~ 0.1 of relevance for cosmological GRBs, while \gamma_B >~ 1 may be relevant for low-luminosity GRBs. The model produces a family of outflows, of relevance for different relativistic phenomena with structures completely determined by \eta_0 and \gamma_B. We calculate the energy per unit solid angle for the model and use it to compute light curves for comparison with the widely used top-hat model. The jet break in the boosted fireball light curve is greatly subdued when compared to the top-hat model because the edge of the jet is smoother than for a top-hat. This may explain missing jet breaks in afterglow light curves.

Synchro-curvature self-Compton radiation of electrons in curved magnetic fields

In this paper, we present the spectrum of the synchro-curvature self-Compton radiation of relativistic electrons with a power-law distribution of Lorentz factors. We find that the resulting spectrum is significantly different from that of either the synchrotron self-Compton or the curvature self-Compton radiation if both the curvature radius of the magnetic field and the cyclotron radius of the electrons are within some proper ranges. The effects of electrons’ cooling and drifting, the low-energy self-absorption in seed spectra and the Klein–Nishina cut-off are also discussed in order to get an accurate picture. We take gamma-ray bursts (GRBs) as our example environment for discussions. The results would be considered as a universal approach of the self-Compton emission of relativistic electrons moving in curved magnetic fields and thus could be applied to many astrophysical phenomena, including GRBs, active galactic nuclei and pulsars.

MOJAVE: MONITORING OF JETS IN ACTIVE GALACTIC NUCLEI WITH VLBA EXPERIMENTS. VI. KINEMATICS ANALYSIS OF A COMPLETE SAMPLE OF BLAZAR JETS

We discuss the jet kinematics of a complete flux-density-limited sample of 135 radio-loud active galactic nuclei (AGNs) resulting from a 13 year program to investigate the structure and evolution of parsec-scale jet phenomena. Our analysis is based on new 2 cm Very Long Baseline Array (VLBA) images obtained between 2002 and 2007, but includes our previously published observations made at the same wavelength, and is supplemented by VLBA archive data. In all, we have used 2424 images spanning the years 1994–2007 to study and determine the motions of 526 separate jet features in 127 jets. The data quality and temporal coverage (a median of 15 epochs per source) of this complete AGN jet sample represent a significant advance over previous kinematics surveys. In all but five AGNs, the jets appear one-sided, most likely the result of differential Doppler boosting. In general, the observed motions are directed along the jet ridge line, outward from the optically thick core feature. We directly observe changes in speed and/or direction in one third of the well-sampled jet components in our survey. While there is some spread in the apparent speeds of separate features within an individual jet, the dispersion is about three times smaller than the overall dispersion of speeds among all jets. This supports the idea that there is a characteristic flow that describes each jet, which we have characterized by the fastest observed component speed. The observed maximum speed distribution is peaked at ∼10c, with a tail that extends out to ∼50c. This requires a distribution of intrinsic Lorentz factors in the parent population that range up to ∼50. We also note the presence of some rare low-pattern speeds or even stationary features in otherwise rapidly flowing jets that may be the result of standing re-collimation shocks, and/or a complex geometry and highly favorable Doppler factor.

OPTICAL AND γ-RAY EMISSIONS FROM INTERNAL FORWARD-REVERSE SHOCKS: APPLICATION TO GRB 080319B?

In the popular internal shock model for the prompt emission of gamma-ray bursts (GRBs), collisions between a series of relativistic shells generate lots of paired forward and reverse shocks. We show that the synchrotron emission produced by the forward and reverse shocks respectively could peak at two quite different energy bands if the Lorentz factors of these two types of shocks are significantly different with each other (e.g., one shock is relativistic and the other is Newtonian). We then investigate whether this scenario is applicable to the case of GRB 080319B and find that a bimodal distribution of the shell Lorentz factors, peaking at $\sim400$ and $\sim10^5$, is required. In addition, this scenario predicts an accompanying inverse-Compton (IC) GeV emission with a luminosity comparable to (not much higher than) that of the synchrotron MeV emission, which can be tested with future \textit{Fermi} observations.

X-ray flares, plateaus and chromatic breaks of GRB afterglows from up-scattered forward-shock emission

Scattering of the forward-shock synchrotron emission by a relativistic outflow located behind the leading blast wave may produce an X-ray emission brighter than that coming directly from the forward shock and may explain four features displayed by Swift X-ray afterglows: flares, plateaus (slow decays), chromatic light-curve breaks and fast post-plateau decays. For a cold scattering outflow, the reflected flux overshines the primary one if the scattering outflow is nearly baryon-free and highly relativistic. These two requirements can be relaxed if the scattering outflow is energized by weak internal shocks, so that the incident forward-shock photons are also inverse-Compton scattered, in addition to bulk scattering. Sweeping-up of the photons left behind by the forward shock naturally yields short X-ray flares. Owing to the boost in photon energy produced by bulk scattering, the reflected emission is more likely to overshine that coming directly from the forward shock at higher photon energies, yielding light-curve plateaus and breaks that appear only in the X-ray. The brightness, shape and decay of the X-ray light-curve plateau depend on the radial distribution of the scatterer's Lorentz factor and mass flux. Chromatic X-ray light-curve breaks and sharp post-plateau decays cannot be accommodated by the direct forward-shock emission and argue in favour of the scattering-outflow model proposed here. On the other hand, the X-ray afterglows without plateaus, those with achromatic breaks and those with very long lived power-law decays are more naturally accommodated by the standard forward-shock model. Thus, the diversity of X-ray light curves arises from the interplay of the scattered and direct forward-shock emissions.

Measuring the kinetic power of active galactic nuclei in the radio mode

We have studied the relationship among nuclear radio and X-ray power, Bondi rate and the kinetic luminosity of sub-Eddington active galactic nucleus (AGN) jets, as estimated from the pdV work done to inflate the cavities and bubbles observed in the hot X-ray-emitting atmospheres of their host galaxies and clusters. Besides the recently discovered correlation between jet kinetic and Bondi power, we show that a clear correlation exists also between Eddington-scaled kinetic power and bolometric luminosity, given by log(L kin /L Edd ) = (0.49 ± 0.07) log(L bol /L Edd )-(0.78±0.36). The measured slope suggests that these objects are in a radiatively inefficient accretion mode, and have been used to put stringent constraints on the properties of the accretion flow. Interestingly, we found no statistically significant correlations between Bondi power and bolometric AGN luminosity, apart from that induced by their common dependence on L kin , thus confirming the idea that most of the accretion power emerges from these systems in kinetic form. We have then analysed the relation between kinetic power and radio core luminosity. Combining the measures of jet power with estimators of the unbeamed radio flux of the jet cores as, for example, the so-called Fundamental Plane of active black holes, we are able to determine, in a statistical sense, both the probability distribution of the mean jet Lorentz factor, which peaks at Γ m ∼7, and the intrinsic relationship between kinetic and radio core luminosity (and thus the jet radiative efficiency), which we estimate as log L kin = (0.81 ± 0.11) log L R + 11.9 +4.1 -4.4 , in good agreement with theoretical predictions of synchrotron jet models. With the aid of these findings, quantitative assessments of kinetic feedback from supermassive black holes in the radio mode (i.e. at low dimensionless accretion rates) will be possible based on accurate determinations of the central engine properties alone, such as mass, radio core and/or X-ray luminosity. As an example, we suggest that Sgr A* may follow the same correlations of radio-mode AGN, based on its observed radiative output as well as on estimates of the accretion rate both at the Bondi radius and in the inner flow. If this is the case, the supermassive black hole in the Galactic Centre is the source of ∼5 x 10 38 erg s -1 of mechanical power, equivalent to about 1.5 supemovae every 10 5 yr.

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.