Population Of Relativistic Electrons Research Articles

XMM-Newton Detection of the Supernova Remnant G337.2+0.1

We report the first XMM-Newton detection of the SNR candidate G337.2+0.1 (=AX J1635.9-4719). The object shows centrally filled and diffuse X-ray emission. The emission peaks in the hard 3.0-10.0 keV band. A spatially resolved spectral study confirms that the column density of the central part of the SNR is about NH ~ 5.9(±1.5) × 1022 cm-2 and its X-ray spectrum is well represented by a single power law with a photon index Γ = 0.96 ± 0.56. The nondetection of line emission in the central spectrum is consistent with synchrotron radiation from a population of relativistic electrons. Detailed spectral analysis indicates that the outer region is highly absorbed and quite softer than the inner region, with NH ~ 16.2(±5.2) × 1022 cm-2 and kT = 4.4(±2.8) keV. Such characteristics are already observed in other X-ray plerions. On the basis of the morphological and spectral X-ray information, we confirm the SNR nature of G337.2+0.1 and suggest that the central region of the source is a pulsar wind nebula, originated by an energetic although yet undetected pulsar, that is currently losing energy at a rate of ~1036 ergs s-1.

Collective spectra of resonant inverse Compton scattering of fast electrons in a varied magnetic field

The resonant inverse Compton scattering (RICS) of the relativistic electrons in an intense magnetic field of a neutron star is an efficient mechanism for producing high-energy gamma-rays. For the purpose of practical applications of RICS, in this paper, we present a basic formula of the collective RICS spectrum produced by a population of relativistic electrons moving outwards along the directions of the magnetic and near-magnetic axes of a strongly magnetized neutron star or strange star. The derivation of the formula is based on a simple semiclassical quantum expression, describing the RICS spectral power of a single fast electron in a subcritical field B < B-cr = 4.413 x 10(13) G, given in our previous paper. As examples of application, by using this new formula, we calculated the collective RICS spectra in some typical ambient soft-photon fields around the neutron star. The obtained collective RICS spectra have simple analytical forms, which are convenient to compare with the observed spectra. Our calculations show that the RICS process is really a very efficient radiation mechanism in the hard X-ray and gamma-ray bands if the 'accommodation condition', presented in our previous paper, is satisfied. We show that the broken power-law form (different power indices in low- and high-frequency bands) is a common and proper feature of various collective RICS spectra, despite the initial forms of the ambient soft-photon field. Finally, we discuss the possible applications in high-energy astrophysics, e.g. in the exploration of the origins of radiation in the gamma-ray bursts (GRBs) and gamma-ray pulsars (GRPs), etc.

Radio emission of galaxy clusters

AbstractWe use a simplified numerical model for the relativistic electron population originating from hadronic proton decays inside a galaxy cluster to calculate its characteristic radio synchrotron emission under the influence of strong accretion and merger shocks. Earlier investigations showed that during structure formation the ICM magnetic field can be substantially magnified.We therefore expect the cluster dynamics to manifest itself in the observable synchrotron emission. Comparison to observations will help us gain better insight into the physics of cluster formation. (© 2006 WILEY‐VCH Verlag GmbH &amp; Co. KGaA, Weinheim)

High-energy γ-ray Emission from Microquasars: LS 5039 and LS I +61 303

The possible associations between the microquasars LS 5039 and LS I +61 303 and the EGRET sources 3EG J1824-1514 and 3EG J0241+6103 suggest that microquasars could also be sources of high-energy gamma-rays. In this work, we present a detailed numerical inverse Compton (IC) model, based on a microquasar scenario, that reproduces the high-energy gamma-ray spectra and variability observed by EGRET for the mentioned sources. Our model considers a population of relativistic electrons entrained in a cylindrical inhomogeneous jet that interact through IC scattering with both the radiation and the magnetic fields.

Parametric study of shock‐induced transport and energization of relativistic electrons in the magnetosphere

The sudden appearance of a new radiation belt consisting of electrons with energies greater than 13 MeV near 2.5 Earth radii (RE), was observed by CRRES (Combined Radiation and Release Experiment Satellite) on 24 March 1991. Li et al. (1993) showed that the cause was an electromagnetic pulse within the Earth's magnetosphere caused by an unusually strong, fast shock in the solar wind. Sudden shock‐induced injections of electrons with energies above 10 MeV to equatorial distances within 2.5 RE are extremely rare because of the intensity of the shock required. In the current study, the propagation velocity parameter and electric field amplitude of pulses within the magnetosphere in the Li et al. model were varied from 750 to 2500 km/s and 70 to 400 mV/m, respectively. It was found that a stronger electric field shifted the peak of the resultant relativistic electron population toward the Earth. Doubling the electric field amplitude from 120 to 240 mV/m moved the peak of the injected electrons with energies above 13 MeV from 2.8 to 2.4 RE. However, as the electric field pulse becomes even larger, the increase in response diminishes. This asympotic behavior shows that it is extremely difficult to produce energetic electron injections inside two Earth radii. The nominal propagation velocity (velocity parameter) is compared to the radial propagation velocities that would have been measured under this model and others and compared to observation. It is found that although the model radial velocity is smaller than the velocity parameter and decreasing with radial distance, it is faster than MHD results and observations. Decreasing the nominal propagation velocity of the pulse within the magnetosphere from 2500 km/s to 1400 km/s also moved the peak of the injected electrons with energies above 13 MeV slightly closer to the Earth. However, at velocities smaller than approximately 1200 km/s the number of electrons injected within 2.5 Earth radii with energies above 13 MeV greatly decreased. Halving the velocity from 2000 to 1000 km/s shifted the peak of electrons with energy greater than 13 MeV from L = 2.6 to L = 2.4 but produced a count rate reduced by a factor of more than 250, resulting in no significant new radiation belt. These results show that the typical large electromagnetic impulses caused by interplanetary shocks, with amplitudes of the order of 10 mV/m, are more than an order of magnitude too small to produce any significant new radiation belts within 2.5 Earth radii with energies of the order of 10 MeV. Contributing to the difficulty in producing such a new belt is the need for an already relativistic electron population with adequate flux beyond geosynchronous orbit. These results thus also help explain the rarity of events such as the 24 March 1991 injection.

The diamagnetic blob propeller in AE Aquarii and non-thermal radio to mid-infrared emission

This paper presents a qualitative investigation of the propeller mechanism in AE Aquarii within the framework of the magnetohydrodynamic (MHD) interaction between the fast rotating magnetosphere of the white dwarf and a blobby mass flow stream from the secondary star. It has been shown that the denser part of the mass flow can penetrate the fast rotating magnetosphere of the white dwarf to the circularization radius, before it is ejected from the system. It has been shown that the total MHD power dissipated on a volume of material equivalent to an orbiting ring of cross-sectional radius R stream ∼ 10 9 cm, at the circularization radius, is P MHD ∼ 10 34 erg s -1 , which is of the same order of magnitude as the inferred spin-down power of the white dwarf. Mixing of the magnetospheric field with a turbulent gas stream due to turbulent diffusion and Kelvin-Helmholtz instabilities, creating magnetic vortices in the flow, results in a transfer of mechanical energy to the stream, accelerating it like a slingshot to velocities exceeding the escape velocity over time-scales far too short for viscous spreading of the material into a disc. The diffusion of the field into the turbulent gas probably results in stripping of the magnetospheric field through fast reconnection as a result of the huge differential rotation, resulting in the creation of magnetized plasma clouds with fields of B cloud ≥ 300 G. It has been shown that the interaction of the white dwarf field with the magnetized blob can accelerate electrons to energies of at least ∈ e ∼ 130 MeV within the dominant energy-loss time-scales, which is high enough to account for the maximum electron energies of ∈ max ∼ 80 MeV, inferred from the latest detection of possible non-thermal emission at frequencies v ∼ 17 000 GHz and 25 000 GHz, using the Keck I Telescope in Hawaii. It has been shown that the efficiency of the MHD propeller in converting thermal electrons to relativistic electrons, energetic enough to drive the total observed non-thermal emission in AE Aquarii, is probably of the order of ∼0.1 per cent. This is consistent with the ratio (β ∼ 0.1 per cent) of the total observed radio to mid-infrared synchrotron emission to the total spin-down power of the white dwarf. Based upon energy arguments, it has been shown that magnetized synchrotron-emitting clouds with fields of B eq ∼ 300 G, which is similar to the magnetospheric field at the main interaction zone, i.e. the circularization radius, can confine a population of relativistic electrons that are able to power the total observed non-thermal radio to mid-infrared emission with luminosity L R-IR ∼ 10 31 ergs -1 .

Comparative study of outer‐zone relativistic electrons observed by Akebono and CRRES

Simultaneous observations by CRRES and Akebono in the near‐ and off‐equatorial inner magnetosphere are used to examine the pitch angle dependence of the relativistic electron variation in the outer zone during the period from 24 August to 17 September 1990. This period includes two interesting time intervals, namely, a magnetic storm interval with a net reduction of outer‐zone electron flux and a nonstorm interval with a gradual increase of the relativistic electron population. The Akebono and CRRES data show the coherent behavior of the relativistic electron fluxes between the two satellites in the region 4 &lt; L &lt; 6, consistent with the “global coherence” of the outer‐zone variation suggested by previous multisatellite observations. On the other hand, the electron fluxes in the region 3 &lt; L &lt; 4, corresponding to the center of the outer zone after the magnetic storm from 26 August 1990, show a remarkable difference between near‐ and off‐equatorial electron fluxes: at L = 3.25, during the storm recovery phase, the flux increase lasts longer at Akebono (which measures small equatorial pitch angles) than at CRRES (which measures larger equatorial pitch angles), and after the storm, the decay of relativistic electron fluxes is faster for the latter than the former. The former longer‐lasting flux increase at Akebono than at CRRES is explicable with pitch angle evolution from a pancake‐like to a more isotropic pitch angle distribution with a timescale of a few days. The latter difference in the decay timescale after the storm is caused by the energy‐dependent electron loss, i.e., faster decay for lower‐energy electrons in the 1–2.5 MeV energy range. These results indicate that evolution of the pitch angle distribution can violate the “global coherence” of relativistic electron behavior at least in some cases, depending on the wave mode(s) responsible for the pitch angle diffusion of electrons, and suggest the importance of equatorial observations in the center of the outer zone.

Unveiling the composition of radio plasma bubbles in galaxy clusters with the Sunyaev-Zel'dovich effect

The Chandra X-ray Observatory is finding a large number of cavities in the X-ray emitting intra-cluster medium which often coincide with the lobes of the central radio galaxy. We propose high-resolution Sunyaev-Zel'dovich (SZ) observations in order to infer the still unknown dynamically dominating component of the radio plasma bubbles. This work calculates the thermal and relativistic SZ emission of different compositions of these plasma bubbles while simultaneously allowing for the cluster's kinetic SZ effect. As examples, we present simulations of an Atacama Large Millimeter Array (ALMA) observation and of a Green Bank Telescope (GBT) observation of the cores of the Perseus cluster and Abell 2052. We predict a 5 sigma detection of the southern radio bubble of Perseus in a few hours with the GBT and ALMA while assuming a relativistic electron population within the bubble. In Abell 2052, a similar detection would require a few ten hours with either telescope, the longer exposures mainly being the result of the higher redshift and the lower central temperature of this cluster. Future high-sensitivity multi-frequency SZ observations will be able to infer the energy spectrum of the dynamically dominating electron population in order to measure its temperature or spectral characteristics. This knowledge can yield indirect indications for an underlying radio jet model.

Non-thermal emission from the intracluster medium

An important component of the intracluster medium in galaxy clusters is represented by a population of relativistic electrons, which are detected through their synchrotron diffuse radio emission. I will provide evidence that diffuse radio sources, and thus highly energetic relativistic electrons, can be present within the cluster volume on different scales, at different cluster locations and in clusters with different dynamical conditions. A connection is present between the relativistic and thermal plasma, as demonstrated by the correlation of radio power vs cluster X-ray luminosity (for halos and relics), or vs. cooling flow power (for mini-halos). Models for the origin and the reacceleration of the radio emitting electrons are briefly outlined.

Mergers and Non-Thermal Processes in Clusters

AbstractClusters of galaxies generally form by the gravitational merger of smaller clusters and groups. Mergers drive shocks in the intra-cluster gas which heat the intra-cluster gas. Mergers disrupt cluster cooling cores. Mergers produce large, temporary increases in the X-ray luminosities and temperatures of cluster; such merger boost may bias estimates of cosmological parameters from clusters. Chandra observations of the X-ray signatures of mergers, particularly “cold fronts,” will be discussed. X-ray observations of shocks can be used to determine the kinematics of the merger. As a result of particle acceleration in shocks and turbulent acceleration following mergers, clusters of galaxies should contain very large populations of relativistic electrons and ions. Observations and models for the radio, extreme ultraviolet, hard X-ray, and gamma-ray emission from non-thermal particles accelerated in these shocks are described.

MERGERS, COSMIC RAYS, AND NONTHERMAL PROCESSES IN CLUSTERS OF GALAXIES

Clusters of galaxies generally form by the gravitational merger of smaller clusters and groups. Major cluster mergers are the most energetic events in the Universe since the Big Bang. The basic properties of cluster mergers and their effects are discussed. Mergers drive shocks into the intracluster gas, and these shocks heat the intracluster gas. As a result of the impulsive heating and compression associated with mergers, there is a large transient increase in the X-ray luminosities and temperatures of merging clusters. These merger boost can affect X-ray surveys of clusters and their cosmological interpretation. Similar boosts occur in the strong lensing cross-sections and Sunyaev-Zeldovich effect in merging clusters. Merger shock and turbulence associated with mergers should also (re)accelerate nonthermal relativistic particles. As a result of particle acceleration in shocks and turbulent acceleration following mergers, clusters of galaxies should contain very large populations of relativistic electrons and ions. Observations and models for the radio, extreme ultraviolet, hard X-ray, and gamma-ray emission from nonthermal particles accelerated in these shocks will also be described. Gamma-ray observations with GLAST seem particularly promising.

The Highly Relativistic Kiloparsec‐Scale Jet of the Gamma‐Ray Quasar 0827+243

We present Chandra X-ray (0.2-8 keV) and Very Large Array radio (15 and 5 GHz) images of the γ-ray-bright, superluminal quasar 0827+243. The X-ray jet bends sharply—by ~90°, presumably amplified by projection effects—5'' from the core. Only extremely weak radio emission is detected between the nuclear region and the bend. The X-ray continuum spectrum of the combined emission of the knots is rather flat, with a slope of -0.4 ± 0.2, while the 5-15 GHz spectra are steeper for knots detected in the radio. These characteristics, as well as nondetection of the jet in the optical band by the Hubble Space Telescope, pose challenges to models for the spectral energy distributions (SEDs) of the jet features. The SEDs could arise from pure synchrotron emission from either a single or dual population of relativistic electrons only if the minimum electron energy per unit mass γmin 1000. In the case of a single population, the radiative energy losses of the X-ray-emitting electrons must be suppressed owing to inverse Compton scattering in the Klein-Nishina regime, as proposed by Dermer & Atoyan. Alternatively, the X-ray emission could result from inverse Compton scattering of the cosmic microwave background photons by electrons with Lorentz factors as low as γ ~ 15. In all models, the bulk Lorentz factor of the jet flow Γ 20 found on parsec scales must continue without substantial deceleration out to 800 kpc (deprojected) from the nucleus, and the magnetic field is very low, 2 μG, until the bend. Deceleration does appear to occur at and beyond the sharp bend, such that the flow could be only mildly relativistic at the end of the jet. Significant intensification of the magnetic field occurs downstream of the bend, where there is an offset between the projected positions of the X-ray and radio features.

Relativistic kinetic theory of pitch angle scattering, slowing down, and energy deposition in a plasma

The collisional dynamics of a relativistic electron population in a Lorentzian plasma are investigated and analyzed within the framework of kinetic theory. The relativistic Fokker-Planck equation describing both slowing down and pitch angle scattering is derived, analyzed, and solved. The analytical Green function is used to express the electron range, the range straggling, and the mean radial dispersion as a function of the plasma parameters. Compared to standard slowing down theories, the inclusion of the pitch angle scattering without any Gaussian approximation appears to be essential to calculate these quantities.

γ-ray emission from microquasars: A numerical model for LSI +61°303

We explore the possible association between the microquasar LSI +61 ◦ 303 and the EGRET source 2CG 135+01/3EG J0241+6103 by studying, with a detailed numerical model, whether this system can produce the emission and the variability detected by EGRET (>100 MeV) through inverse Compton (IC) scattering. Our numerical approach considers a population of relativistic electrons entrained in a cylindrical inhomogeneous jet, interacting with both the radiation and the magnetic fields, taking into account the Thomson and Klein-Nishina regimes of interaction. Our results reproduce the observed spectral characteristics and variability at γ-rays, thus strengthening the identification of LSI +61 ◦ 303 as a high-energy γ-ray source.

Collisions among Clouds inside Dusty Tori in Active Galactic Nuclei:Observational Consequences

A geometrically thick dusty torus in NGC 1068 has been unambiguously resolved by an infrared interferometry telescope. This implies that clouds composing the dusty torus are undergoing supersonic collisions with each other. We show that the collisions form strong nonrelativistic shocks, which accelerate populations of relativistic electrons. The torus reprocesses emission from the accretion disk into an infrared band. We show that the energy density of the infrared photons inside the torus is much higher than that of the magnetic field in the clouds, and the seed photons of inverse Compton scattering are mainly from the infrared. The maximum energy of the relativistic electrons can reach a Lorentz factor of 105. We calculate the spectrum of the synchrotron and inverse Compton scattering radiation from the electrons in the torus. The relativistic electrons in the torus radiate nonthermal emission from radio to γ-ray, which isotropically diffuses in the region of the torus. We find that the most prominent character is a peak at ~0.5-1 GeV. We apply this model to NGC 1068 and find that the observed radio emission from the core component S1 can be explained by the synchrotron emission from the relativistic electrons. We predict that there is γ-ray emission with a luminosity of 1040 ergs s-1 peaking at ~1 GeV from the torus, which could be detected by the Gamma-Ray Large-Array Space Telescope in the future. This will provide a new clue to understanding the physics in the torus. The nonthermal radiation from the dusty torus may explain the radio emission from Seyfert galaxies. The cosmological implications of the nonthermal emission to the γ-ray background radiation are also discussed.

Nonthermal Hard X‐Ray Emission in Galaxy Clusters Observed with theBeppoSAXPDS

We study the X-ray emission in a Sample of galaxy clusters using the BeppoSAX PDS instrument in the 20 - 80 keV energy band. We estimate the non-thermal hard X-ray cluster emission (HXR) by modeling the thermal contribution from the cluster gas and the non-thermal contamination from the unobscured AGN in the clusters. We also evaluate the systematic uncertainties due to the background fluctuations. Assuming negligible contamination from the obscured AGN, the resulting non-thermal component is detected at a 2 sigma level in approx. 50% of the non-significantly AGN-contaminated clusters: A2142, A2199, A2256, A3376, Coma, Ophiuchus and Virgo. The data are consistent with a scenario whereby relaxed clusters have no hard X-ray component of non-thermal origin, whereas merger clusters do. The co-added spectrum of the above clusters indicates a power-law spectrum for the HXR with a photon index of 2.8+0.3-0.4 in the 12 - 115 keV band, and we find indication that it has extended distribution. These indications argue against significant contamination from obscured AGN, which have harder spectra and centrally concentrated distribution. These results are supportive of the assumption of the merger shock acceleration of electrons in clusters, which has been proposed as a possible origin of the non-thermal hard X-ray emission models. Assuming that the Cosmic Microwave Background photons experience Inverse Compton scattering from the merger-accelerated relativistic electrons, and thus produce the observed HXR, the measured hard X-ray slope corresponds to a differential momentum spectra of the relativistic electrons with a slope of mu = 3.8 - 5.0. In presence of cluster magnetic fields this relativistic electron population produces synchrotron emission with a spectral index of 1.4 - 2.1, consistent with radio halo observations of merger clusters. Thus both hard X-ray and radio observations of merger clusters are consistent with the Inverse Compton model. The observed slope of HXR is also consistent with that predicted by the non-thermal bremsstrahlung, which chus cannot be ruled by the fit to the current data, even though this model requires an extreme, untenable cluster energetics. Assuming centrally concentrated distribution of HXR, the data requires a harder slope for the HXR spectrum, which is consistent with secondary electron models, but this model yields a worse fit to the PDS data and thus seems to be disfavored over the primary electron Inverse Compton model.

M 87 as a misaligned synchrotron-proton blazar

The giant radio galaxy M 87 is usually classified as a Fanaroff-Riley class I source, suggesting that M 87 is a mis- aligned BL Lac object. Its unresolved nuclear region emits strong non-thermal emission from radio to X-rays which has been interpreted as synchrotron radiation. In an earlier paper we predicted M 87 as a source of detectable gamma ray emission in the context of the hadronic Synchrotron-Proton Blazar (SPB) model. The subsequent tentative detection of TeV energy photons by the HEGRA-telescope array would, if confirmed, make it the first radio galaxy to be detected at TeV-energies. We discuss the emission from the unresolved nuclear region of M 87 in the context of the SPB model, and give examples of possible model rep- resentations of its non-simultaneous spectral energy distribution. The low-energy component can be explained as synchrotron radiation by a primary relativistic electron population that is injected together with energetic protons into a highly magnetized emission region. We find that the γ-ray power output is dominated either by µ ± /π ± synchrotron or proton synchrotron radiation depending on whether the primary electron synchrotron component peaks at low or high energies, respectively. The predicted γ-ray luminosity peaks at ∼100 GeV at a level comparable to that of the low-energy hump, and this makes M 87 a promis- ing candidate source for the newly-commissioned high-sensitivity low-threshold Cherenkov telescopes H.E.S.S., VERITAS, MAGIC and CANGAROO III. Because of its proximity, the high-energy spectrum of M 87 is unaffected by absorption in the cosmic infrared (IR) background radiation field, and could therefore serve as a template spectrum for the corresponding class of blazar if corrected for mis-alignment effects. This could significantly push efforts to constrain the cosmic IR radiation field through observation of more distant TeV-blazars, and could have a strong impact on blazar emission models. If M 87 is a mis- aligned BL-Lac object and produces TeV-photons as recently detected by the HEGRA-array, in the context of the SPB model it must also be an efficient proton accelerator.

A numerical model for the γ-ray emission of the microquasar LS 5039

The possible association between the microquasar LS 5039 and the EGRET source 3EG J1824-1514 suggests that microquasars could also be sources of high energy gamma-rays. In this paper, we explore, with a detailed numerical model, if this system can produce the emission detected by EGRET (>100 MeV) through inverse Compton (IC) scattering. Our numerical approach considers a population of relativistic electrons entrained in a cylindrical inhomogeneous jet, interacting with both the radiation and the magnetic fields, taking into account the Thomson and Klein-Nishina regimes of interaction. The computed spectrum reproduces the observed spectral characteristics at very high energy.

A New Solar Burst Spectral Component Emitting Only in the Terahertz Range

Solar flare energy manifestations were believed to be the result of the same kind of particle acceleration. It is generally accepted that a population of relativistic electrons accelerated during the impulsive phase of solar flares produces microwaves by synchrotron losses in the solar magnetic field and X-rays by collisions in denser regions of the solar atmosphere. We report the discovery of a new intense solar flare spectral radiation component, peaking somewhere in the shorter submillimeter to far-infrared range, identified during the 2003 November 4 large flare. The new solar submillimeter telescope, designed to extend the frequency range to above 100 GHz, detected this new component with increasing fluxes between 212 and 405 GHz. It appears along with, but is separated from, the well-known gyrosynchrotron emission component seen at microwave frequencies. The novel emission component had three major peaks with time, originated in a compact source whose position remained remarkably steady within 15''. Intense subsecond pulses are superposed with excess fluxes also increasing with frequency and amplitude increasing with the pulse repetition rate. The origin of the terahertz emission component during the flare impulsive phase is not known. It might be representative of emission due to electrons with energies considerably larger than the energies assumed to explain emission at microwaves. This component can attain considerably larger intensities in the far-infrared, with a spectrum extending to the white-light emission observed for that flare.

Brightness Suppression of Relativistic Radio Jets of Quasars: The Role of the Lower Electron Energy Cutoff

Although the possibility of a low-energy cutoff (LEC) of the relativistic electron population (Emin ~ 0.1 GeV) in the different components of radio galaxies has been discussed in the literature, from both theoretical and observational viewpoints, its possible role in causing a distinct spectral flattening, and thus reducing the apparent brightness temperature of the radio nucleus, has thus far not been explicitly discussed. Here we point out that such an effect may, in fact, be quite significant for the parsec-scale, superluminal emission regions associated with the inner radio jets. This is because the observed frequency of the spectral turnover arising from the LEC increases linearly with the bulk Doppler factor (δ) of the jet flow, whereas the frequency of synchrotron self-absorption (the well-known cause of spectral flattening and turnover at low frequencies) shows a mild decrease as δ rises. For an observationally relevant range of source parameters, we investigate here the role of the LEC. We argue that some statistical trends revealed by the recent very long baseline interferometry (VLBI) surveys can, in fact, be understood in terms of effects arising from LEC, including the faster superluminal motion found in the VLBI surveys at higher frequencies and the apparent inability of most radio cores to even attain the brightness temperatures consistent with the equipartition condition. We also point out some possible implications of the LEC for X-ray observations of kiloparsec-scale relativistic jets of quasars.