Distribution Of Lorentz Factors Research Articles

Observational Signatures of High‐Energy Emission during the Shallow Decay Phase of Gamma‐Ray Burst X‐Ray Afterglows

The widely existing shallow decay phase of the X-ray afterglows of gamma-ray bursts (GRBs) is generally accepted to be due to long-lasting energy injection. The outflows carrying the injecting energy, based on the component that is dominant in energy, fall into two possible types: baryon-dominated and lepton-dominated ones. The former type of outflow could be ejecta that is ejected during the prompt phase of a GRB and consists of a series of baryonic shells with a distribution of Lorentz factors, and the latter type could be an electron-positron pair wind that is driven by the postburst central engine. We here provide a unified description for the dynamics of fireballs based on these two types of energy injection and calculate the corresponding high-energy photon emission by considering synchrotron radiation and inverse Compton scattering (including synchrotron self-Compton and combined inverse Compton) of electrons. We find that, in the two energy-injection models, there is a plateau (even a hump) in high-energy light curves during the X-ray shallow decay phase. In particular, a considerable fraction of the injecting energy in the lepton-dominated model can be shared by the long-lasting reverse shock since it is relativistic. Furthermore, almost all of the energy of the reverse shock is carried by leptons, and thus, the inverse Compton emission is enhanced dramatically. Therefore, this model predicts more significant high-energy afterglow emission than the baryon-dominated model. We argue that these observational signatures would be used to discriminate between different energy-injection models in the upcoming Gamma-Ray Large Area Space Telescope (GLAST) era.

The Lorentz Factor Distribution and Luminosity Function of Relativistic Jets in AGNs

The observed apparent velocities and luminosities of the relativistic jets in AGNs are significantly different from their intrinsic values due to strong special relativistic effects. We adopt the maximum likelihood method to determine simultaneously the intrinsic luminosity function and the Lorentz factor distribution of a sample of AGNs. The values of the best estimated parameters are consistent with the previous results, but with much better accuracy. In previous study, it was assumed that the shape of the observed luminosity function of Fanaroff-Riley type II radio galaxies is the same with the intrinsic luminosity function of radio loud quasars. Our results prove the validity of this assumption. We also find that low and high redshift groups divided by z=0.1 are likely to be from different parent populations.

SwiftXRT Observations of the Afterglow of XRF 050416A

Swift discovered XRF 050416A with the BAT and began observing it with its narrow field instruments only 64.5 s after the burst onset. Its very soft spectrum classifies this event as an X-ray flash. The afterglow X-ray emission was monitored up to 74 days after the burst. The X-ray light curve initially decays very fast, subsequently flattens and eventually steepens again, similar to many X-ray afterglows. The first and second phases end about 172 and 1450 s after the burst onset, respectively. We find evidence of spectral evolution from a softer emission with photon index Gamma ~ 3.0 during the initial steep decay, to a harder emission with Gamma ~ 2.0 during the following evolutionary phases. The spectra show intrinsic absorption in the host galaxy. The consistency of the initial photon index with the high energy BAT photon index suggests that the initial phase of the X-ray light curve may be the low-energy tail of the prompt emission. The lack of jet break signatures in the X-ray afterglow light curve is not consistent with empirical relations between the source rest-frame peak energy and the collimation-corrected energy of the burst. The standard uniform jet model can give a possible description of the XRF 050416A X-ray afterglow for an opening angle larger than a few tens of degrees, although numerical simulations show that the late time decay is slightly flatter than expected from on-axis viewing of a uniform jet. A structured Gaussian-type jet model with uniform Lorentz factor distribution and viewing angle outside the Gaussian core is another possibility, although a full agreement with data is not achieved with the numerical models explored.

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.

Simulation study of jitter radiation associated with afterglows observed with Swift

Using a 3D Relativistic Particle-In-Cell (RPIC) code, we have investigated particle acceleration associated with a relativistic electron-positron jet front propagating into an ambient electron-positron plasma without initial magnetic fields in order to investigate the nonlinear stage of the Weibel instability. 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 tlie jet Lorentz factor. We have performed simulations with broad Lorentz factor distribution of jet electrons and positrons, which are assumed to be created by tlie photon annihilation. Simulation results show that tlie Weibel instability is responsible for generating and amplifying nonuniform, magnetic fields perpendicular to tlie jet propagation direction and contribute to the electron's (positron's) transverse deflection behind the jet head. This small-scale magnetic-field structure is appropriate to the generation of radiation from deflected electrons (positrons) as opposed to synchrotron radiation. The jitter radiation resulting from small-scale magnetic-field structures may be important for understanding the complex time structure anti spectral evolution observed in gamma-ray bursts or other astrophysical sources containing relativistic jets anti relativistic collisionless sliocks.

Physical Processes Shaping Gamma‐Ray Burst X‐Ray Afterglow Light Curves: Theoretical Implications from theSwiftX‐Ray Telescope Observations

With the successful launch of the Swift Gamma-Ray Burst Explorer, a rich trove of early X-ray afterglow data has been collected by its onboard X-Ray Telescope (XRT). Some interesting features are emerging, including a distinct rapidly decaying component preceding the conventional afterglow component in many sources, a shallow decay component before the more normal'' decay component observed in a good fraction of GRBs, and X-ray flares in nearly half of the afterglows. In this paper we systematically analyze the possible physical processes that shape the properties of the early X-ray afterglow light curves and use the data to constrain various models. We suggest that the steep decay component is consistent with the tail emission of the prompt gamma-ray bursts and/or the X-ray flares. This provides strong evidence that the prompt emission and afterglow emission are likely two distinct components, supporting the internal origin of the GRB prompt emission. The shallow decay segment observed in a group of GRBs suggests that very likely the forward shock keeps being refreshed for some time. This might be caused by either a long-lived central engine, or a wide distribution of the shell Lorentz factors, or else possibly the deceleration of a Poynting flux-dominated flow. X-ray flares suggest that the GRB central engine is very likely still active after the prompt gamma-ray emission is over, but with a reduced activity at later times. In some cases, the central engine activity even extends to days after the burst triggers. Analyses of early X-ray afterglow data reveal that GRBs are indeed highly relativistic events and that early afterglow data of many bursts, starting from the beginning of the XRT observations, are consistent with the afterglow emission from an ISM environment.

On the interpretation of spectral-energy correlations in long gamma-ray bursts

Context. Recently, Liang & Zhang found a tight correlation involving only observable quantities, namely the isotropic emitted energy E γ,iso , the energy of the peak of the prompt spectrum E' p , and the jet break time t' j of Gamma Ray Bursts. This phenomenological correlation can have a first explanation in the framework of jetted fireballs, whose semiaperture angle θ j is measured by the jet break time t' j . By correcting E γ,iso for he angle θ j one obtains the so-called Ghirlanda correlation, linking the collimation-corrected energy Ey and E' p . Aims. There are two ways to derive 0j from t' j in the standard scenario, corresponding to a homogeneous or to a wind-like circumburst medium. We compute and compare the E' p -E γ correlations derived in these two conditions and study the consistency of these model-dependent correlations with the empirical Liang & Zhang correlation. We consider the difference between the observed correlations and the ones in the comoving frame. Methods. We study 18 GRBs with firmly measured z, E peak and t break and discuss the differences with previously published samples. We compute the correlations accounting for the errors on all the relevant quantities. Results. We show that the Ghirlanda correlation with a wind-like circumburst medium is as tight as (if not tighter) than the Ghirlanda correlation for a homogeneous medium. These two Ghirlanda correlations are both consistent with the phenomenological Liang & Zhang relation. The wind-like Ghirlanda relation, which is linear, remains linear also in the comoving frame, independently of the distribution of bulk Lorentz factors. Instead, in the homogeneous density case, one is forced to assume the existence of a strict relation between the bulk Lorentz factor and the total energy, which in turn places constraints on the radiation mechanisms of the prompt emission. The wind-like Ghirlanda correlation, being linear, corresponds to different bursts having the same number of photons.

On the nature of X-ray flashes

We discuss the origin of X-Ray Flashes (XRFs), a recently discovered class of Gamma-Ray Bursts (GRBs). Using a simplified model for internal shocks we check if XRFs can be intrinsically soft due to some specific values of the parameters describing the relativistic outflow emerging from the central engine. We generate a large number of synthetic events and find that XRFs are obtained when the contrast $\Gamma_{\rm max}/\Gamma_{\rm min}$ of the Lorentz factor distribution is small while the average Lorentz factor $\bar \Gamma$ is large. A few XRFs may be GRBs at large redshifts but we exclude this possibility for the bulk of the population. If outflows with a small contrast are commonly produced, even a large population of XRFs could be explained. If conversely the Lorentz factor distribution within the wind is broad, one should then rely on extrinsic causes, such as viewing angle effects or high redshift.

Accurate Calorimetry of GRB 030329

We report late-time observations of the radio afterglow of GRB 030329. The light curves show a clear achromatic flattening at 50 days after the explosion. We interpret this flattening as resulting from the blast wave becoming trans-relativistic. Modeling of this transition enables us to make estimates of the energy content of the burst, regardless of the initial jet structure or the distribution of initial Lorentz factors of the ejecta. We find, in accordance with other events, that GRB 030329 is well-described by an explosion with total energy of a few times 10^51 erg expanding into a circumburst medium with a density of order unity.

Constraints on relativistic beaming from estimators of the unbeamed flux

We review the statistical properties of relativistic Doppler boosting relevant for studies of relativistic jets from compact objects based on radio--X-ray(--mass) correlations, such as that found in black-hole X-ray binaries in the low/hard state, or the ``fundamental plane'' of Merloni, Heinz, & DiMatteo. We show that the presence of only moderate scatter in such relations does not necessarily imply low Lorentz factors of the jets producing the radio emission in the samples under consideration. Applying Doppler beaming statistics to a large sample of XRBs and AGN, we derive a limit on the width of the Lorentz factor distribution of black holes with relativistic jets: If the X-rays are unbeamed (e.g., if they originate in the accretion disk or in the slower, innermost part of the jet), the width of the \beta\Gamma distribution should be about one order of magnitude or less. If the scatter about the ``fundamental plane'' is entirely dominated by relativistic beaming, a lower limit on the mean Lorentz factor > 5 can be derived. On the other hand, if the X-rays are boosted by the same factor as the radio emission, we show that the observed scatter cannot be reasonably explained by Doppler boosting alone.

Sub‐Milliarcsecond Imaging of Quasars and Active Galactic Nuclei. III. Kinematics of Parsec‐scale Radio Jets

We report the results of a 15 GHz (2 cm) multi-epoch VLBA program, begun in 1994 to study the outflow in radio jets ejected from quasars and active galaxies. The observed flow of 208 distinct features measured in 110 quasars, active galaxies, and BL Lac objects shows highly collimated relativistic motion with apparent transverse velocities typically between zero and about 15c, with a tail extending up to about 34c. Within individual jets, different features appear to move with a similar characteristic velocity which may represent an underlying continuous jet flow, but we also see some stationary and even apparently inward moving features which co-exist with the main features. Comparison of our observations with published data at other wavelengths suggests that there is a systematic decrease in apparent velocity with increasing wavelength, probably because the observations at different wavelengths sample different parts of the jet structure. The observed distribution of linear velocities is not consistent with any simple ballistic model. Either there is a rather broad range of Lorentz factors, a significant difference between the velocity of the bulk relativistic flow and the pattern speed of underlying shocks, or a combination of these options. Assuming a ballistic flow, comparison of observed apparent velocities and Doppler factors computed from the time scale of flux density variations is consistent with a steep power law distribution of intrinsic Lorentz factors, an isotropic distribution of orientations of the parent population, and intrinsic brightness temperatures about an order of magnitude below the canonical inverse Compton limit. It appears that the parent population of radio jets is not dominated by highly relativistic flows (abridged).

Altered Luminosity Functions of Relativistically Beamed Jet Populations

The intrinsic luminosity functions of extremely fast jets found in many active galaxies and gamma-ray bursts are difficult to measure since their apparent luminosities are strongly affected by relativistic beaming. Past studies have only provided analytical predictions for the beamed characteristics of populations in which all jets have the same Lorentz factor. However, the jets found in active galaxies are known to span a large range of speeds. Here we derive analytical expressions for the expected Doppler factor distributions and apparent (beamed) luminosity functions of randomly oriented, two-sided jet populations that have bulk Lorentz factors distributed according to a simple power law over a range [γ1, γ2]. We find that if a jet population has a uniform or inverted Lorentz factor distribution, its Doppler factor distribution and beamed luminosity function will be very similar to that of a jet population with Lorentz factors all equal to γ2. In particular, the beamed and intrinsic luminosity functions will have the same slope at high luminosities. In the case of a steep Lorentz factor distribution, the slopes at high luminosities will also be identical, but only up to an apparent luminosity equivalent to the upper cutoff of the intrinsic luminosity function. In addition, at very high apparent luminosities, the slope will be proportional to the power-law slope of the Lorentz factor distribution. At very low luminosities, the form of the apparent luminosity function is very sensitive to the lower cutoff and steepness of the Lorentz factor distribution. We discuss how it should be possible to recover useful information about the intrinsic luminosity functions of relativistic jets by studying flux-limited samples selected on the basis of beamed jet emission.

Dispersion of the Break Energy in the GRB Internal Shock Model

Abstract In order to investigate the dispersion of the spectral break energy in gamma-ray bursts, we simulate internal shocks, including effects of shell-splitting after shell collisions and the Thomson optical depth due to electron–positron pairs produced by synchrotron photons. We produce pseudo-observational data and estimate the break energy. If the distribution of initial Lorentz factors of shells has only one peak, many pulses with a break energy much lower than the typical observed value should be detected, while the effect of the Thomson optical depth reduces pulses with a break energy of $ \gt 1 \,\mathrm{MeV}$$ \gt 1 \,\mathrm{MeV}$. If the Lorentz factor distribution has multiple peaks, the distribution of the break energy can be consistent with observations.

Efficiency and Spectrum of Internal Gamma‐Ray Burst Shocks

We present an analysis of the Internal Shock Model of GRBs, where gamma-rays are produced by internal shocks within a relativistic wind. We show that observed GRB characteristics impose stringent constraints on wind and source parameters. We find that a significant fraction, of order 20 %, of the wind kinetic energy can be converted to radiation, provided the distribution of Lorentz factors within the wind has a large variance and provided the minimum Lorentz factor is higher than 10^(2.5)L_(52)^(2/9), where L=10^(52)L_(52)erg/s is the wind luminosity. For a high, >10 %, efficiency wind, spectral energy breaks in the 0.1 to 1 MeV range are obtained for sources with dynamical time R/c < 1 ms, suggesting a possible explanation for the observed clustering of spectral break energies in this range. The lower limit to wind Lorenz factor and the upper limit, around (R/10^7 cm)^(-5/6) MeV to observed break energies are set by Thomson optical depth due to electron positron pairs produced by synchrotron photons. Natural consequences of the model are absence of bursts with peak emission energy significantly exceeding 1 MeV, and existence of low luminosity bursts with low, 1 keV to 10 keV, break energies.

VLBA Observations of a Sample of Nearby FR I Radio Galaxies

We observed 17 nearby low luminosity FR I radio galaxies using the NRAO Very Long Baseline Array (VLBA) at 1.67 GHz, as part of a multi-wavelength study of a complete sample of 21 sources selected by radio flux density from the Uppsala General Catalogue of Galaxies. We detected radio emission from all 17 galaxies. At a FWHM resolution of ~ 10x4 mas, five galaxies show only an unresolved radio core, ten galaxies show core-jet structures, and two galaxies show twin-jet structures. Comparing these VLBA images with images previously obtained with the NRAO VLA, we find that all detected VLBA jets are well-aligned on parsec scales with the VLA jets on kilo parsec scales, and that the jet to counter-jet surface brightness ratios, or the sidedness, decreases systematically with increasing distance along the jet. We attribute the sidedness to the Doppler boosting effect and its decline to the deceleration of the jets. We show that a distribution of Lorentz factor centered near Gamma = 5 can reproduce our VLBA detection statistics for core, core-jet and twin-jet sources. We also note that the luminosity per unit length, L_j, of the VLBA jets drops quickly with distance, r, along the jet, approximately as L_j being proportional to r^(-2.0). We discuss three different mechanisms to explain this jet fading: (1) the decrease of Doppler boosting due to jet deceleration, (2) synchrotron losses, and (3) expansion losses in constant velocity but adiabatically spreading jets. Mechanisms (1) and (2) are inconsistent with the observations, while mechanism (3) is consistent with the observations provided the magnetic field lines in the jets are aligned perpendicular to the jet axis. This implies that the deceleration of the jets required by the Unified Scheme does not occur on the tens of parsec scales, but must occur on larger scales.

Power Density Spectra of Gamma-Ray Bursts in the Internal Shock Model

We simulate Gamma-Ray Bursts arising from internal shocks in relativistic winds, calculate their power density spectrum (PDS), and identify the factors to which the PDS is most sensitive: the wind ejection features, which determine the wind dynamics and its optical thickness, and the energy release parameters, which give the pulse 50-300 keV radiative efficiency. For certain combinations of ejection features and wind parameters the resulting PDS exhibits the features observed in real bursts. We found that the upper limit on the efficiency of conversion of wind kinetic energy into 50-300 keV photons is $\sim$ 1%. Winds with a modulated Lorentz factor distribution of the ejecta yield PDSs in accord with current observations and have efficiencies closer to $10^{-3}$, while winds with a random, uniform Lorentz factor ejection must be optically thick to the short duration pulses to produce correct PDSs, and have an overall efficiency around $10^{-4}$.

A Comparison of the Morphology and Stability of Relativistic and Nonrelativistic Jets

We compare results from a relativistic and a nonrelativistic set of two-dimensional axisymmetric jet simulations. For a set of five relativistic simulations that either increase the Lorentz factor or decrease the adiabatic index, we compute nonrelativistic simulations with equally useful power or thrust. We examine these simulations for morphological and dynamical differences, focusing on the velocity field, the width of the cocoon, the age of the jets, and the internal structure of the jet itself. The primary result of these comparisons is that the velocity field of nonrelativistic jet simulations cannot be scaled up to give the spatial distribution of Lorentz factors seen in relativistic simulations. Since the local Lorentz factor plays a major role in determining the total intensity for parsec-scale extragalactic jets, this suggests that a nonrelativistic simulation cannot yield the proper intensity distribution for a relativistic jet. Another general result is that each relativistic jet and its nonrelativistic equivalents have similar ages (in dynamical time units, ≡R/aa, where R is the initial radius of a cylindrical jet and aa is the sound speed in the ambient medium). Also, jets with a larger Lorentz factor have a smaller cocoon size. In addition to these comparisons, we have completed four new relativistic simulations to investigate the effect of varying thermal pressure on relativistic jets. The simulations confirm that faster (larger Lorentz factor) and colder jets are more stable, with smaller amplitude and longer wavelength internal variations. However, an exception to this occurs for the hottest jets, which appear the most stable. The apparent stability of these jets does not follow from linear normal mode analysis, which suggests that there are available growing Kelvin-Helmholtz modes. However, these modes are not excited because of a lack of perturbations able to couple to them. As an example of how these simulations can be applied to the interpretation of observations, we use our results to estimate some parameters of Cygnus A. Although none of these estimates alone can determine if the jets in Cyg A are relativistic or nonrelativistic, estimates for the age and the jet to ambient density ratio confirm values for these parameters estimated by other means.

Superluminal motions: the first 100 sources

First results from a large homogeneous superluminal motion survey are presented. The data do not show compelling evidence for the existence of intrinsically different populations of galaxies, BL Lac objects, or quasars. βapp in the range 1–5 h–1 occur with roughly equal frequency; higher values, up to βapp = 10 h–1, are rather more scarce than appeared to be the case from earlier work, which evidently concentrated on sources which are not representative of the general population. The βapp distribution suggests that there might be a skewed distribution of Lorentz factors over the sample, with a peak at γb ≈ 2 h–1 and a tail up to at least γb ≈ 10 h–1. There appears to be a clearly rising upper envelope to the βapp distribution when plotted as a function of observed 5 GHz luminosity; a combination of source counts and the apparent velocity statistics in a larger sample could provide much insight into the properties of radio jet sources.

Superluminal sources.

Predictions for the apparent velocity statistics under simple beaming models are presented and compared to the observations. The potential applications for tests of unification models and for cosmology (source counts, measurements of the Hubble constant H0 and the deceleration parameter q0) are discussed. First results from a large homogeneous survey are presented. The data do not show compelling evidence for the existence of intrinsically different populations of galaxies, BL Lacertae objects, or quasars. Apparent velocities betaapp in the range 1-5 h-1, where h = H0/100 km.s-1.Mpc-1 [1 megaparsec (Mpc) = 3.09 x 10(22) m], occur with roughly equal frequency; higher values, up to betaapp = 10 h-1, are rather more scarce than appeared to be the case from earlier work, which evidently concentrated on sources that are not representative of the general population. The betaapp distribution suggests that there might be a skewed distribution of Lorentz factors over the sample, with a peak at gammab approximately 2 h-1 and a tail up to at least gammab approximately 10 h-1. There appears to be a clearly rising upper envelope to the betaapp distribution when plotted as a function of observed 5-GHz luminosity; a combination of source counts and the apparent velocity statistics in a larger sample could provide much insight into the properties of radio jet sources.

Luminosity functions, relativistic beaming, and unified theories of high-luminosity radio sources

view Abstract Citations (201) References (55) Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS Luminosity Functions, Relativistic Beaming, and Unified Theories of High-Luminosity Radio Sources Padovani, P. ; Urry, C. M. Abstract If relativistically beamed emission dominates the observed radio flux from flat-spectrum radio quasars, as suggested by their rapid variability, polarization, and superluminal motion, then there must be counterpart sources whose emission is beamed at larger angles to the line of sight. We evaluate such unified schemes quantitatively, with steep- spectrum radio quasars and high-luminosity radio galaxies constituting the misaligned sources. Our procedure compares the number densities and luminosities of the separate populations, taking into account the strong selection effects introduced by relativistic beaming. First, we derive the local luminosity functions of high-luminosity (i.e., Fanaroff-Riley type II) radio galaxies, flat-spectrum quasars, and steep-spectrum quasars. Then we calculate the luminosity functions predicted by a relativistic beaming model and compare them to the observed ones. We find very good agreement both for flat- and steep- spectrum quasars for a distribution of Lorentz factors 5 <~γ <~40 (skewed toward lower values) that was estimated from the observed distribution of superluminal speeds for flat-spectrum quasars. Our model predicts that flat-spectrum quasars have their radio axes within θ~14^deg^ of the line of sight, steep-spectrum quasars are in the range 14^deg^ <~ θ <~ 40^deg^, and high-luminosity radio galaxies occupy the remaining angles. The alternative hypothesis that flat- spectrum quasars are simply the beamed version of steep-spectrum ones, with Fanaroff-Riley type II radio galaxies belonging to a separate class, does not give as good a fit to the data. Publication: The Astrophysical Journal Pub Date: March 1992 DOI: 10.1086/171098 Bibcode: 1992ApJ...387..449P Keywords: Galactic Nuclei; Quasars; Radio Galaxies; Radio Jets (Astronomy); Relativistic Plasmas; Stellar Luminosity; Brightness Distribution; Radio Emission; Unified Field Theory; Very Long Base Interferometry; Astrophysics; GALAXIES: JETS; GALAXIES: NUCLEI; GALAXIES: FUNDAMENTAL PARAMETERS; RADIO CONTINUUM: GALAXIES full text sources ADS | data products SIMBAD (3)