Bulk Lorentz Factor Research Articles

Prompt emission of high-energy photons from gamma ray bursts

Within the internal shock scenario, we consider different mechanisms of high-energy ( > 1 MeV) photon production inside a gamma ray burst (GRB ) fireball and derive the expected high-energy photon spectra from individual GRBs during the prompt phase. The photon spectra of leptonic and hadronic origins are compared within different sets of parameter regimes. Our results suggest that the high-energy emission is dominated by the leptonic component if the fraction of shock energy carried by electrons is not very small (e.g. ∈ e > 10 -3 ). For very small values of ∈ e , the hadronic emission component could be comparable to or even exceed the leptonic component in the GeV-TeV regime. However, in this case a much larger energy budget of the fireball is required to account for the same level of the observed sub-MeV spectrum. The fireballs are therefore extremely inefficient in radiation. For a canonical fireball bulk Lorentz factor (e.g. r = 400), emissions above ∼ 10 GeV are attenuated by two-photon pair production processes. For a fireball with an even higher Lorentz factor, the cut-off energy is higher, and emissions of 10 TeV-PeV due to 7r°-decay can also escape from the internal shocks. The flux level is, however, too low to be detected by current TeV detectors, and these photons also suffer attenuation by external soft photons. The GLAST Large Area Telescope can detect prompt emission of bright long GRBs above 100 MeV. For short GRBs, the prompt emission can be only barely detected for nearby bright ones with relatively 'long' durations (e.g. ∼1 s). With the observed high-energy spectrum alone, it appears that there is no clean picture to test the leptonic versus hadronic origin of the gamma rays. Such an issue may be, however, addressed by collecting both prompt and afterglow data. A moderate-to-high radiative efficiency would suggest a leptonic origin of high-energy photons, while a GRB with an extremely low radiative efficiency but an extended high-energy emission component would be consistent with (but not a proof for) the hadronic origin.

A New Method of Determining the Initial Size and Lorentz Factor of Gamma-Ray Burst Fireballs Using a Thermal Emission Component

In recent years increasing evidence has emerged for a thermal component in the gamma- and X-ray spectrum of the prompt emission phase in gamma-ray bursts. The temperature and flux of the thermal component show a characteristic break in the temporal behavior after a few seconds. We show here, that measurements of the temperature and flux of the thermal component at early times (before the break) allow the determination of the values of two of the least restricted fireball model parameters: the size at the base of the flow and the outflow bulk Lorentz factor. Relying on the thermal emission component only, this measurement is insensitive to the inherent uncertainties of previous estimates of the bulk motion Lorentz factor. We give specific examples of the use of this method: for GRB970828 at redshift z=0.9578, we show that the physical size at the base of the flow is r_0 = (2.9+-1.8)*10^8 Y_0^{-3/2} cm and the Lorentz factor of the flow is Gamma = (305\+-28) Y_0^{1/4}, and for GRB990510 at z=1.619, r_0=(1.7+-1.7)*10^8 Y_0^{-3/2} cm and Gamma=(384+-71) Y_0^{1/4}, where Y = 1 Y_0 is the ratio between the total fireball energy and the energy emitted in gamma- rays.

A simple test of the external shock model for the prompt emission in gamma-ray bursts

It is demonstrated here that if the prompt GRB emission is produced by the simplest version of the external shock model, a specific relation should prevail between the observed duration, isotropic equivalent energy, and photon peak energy. In essence, this relation arises because both the burst duration and the typical energy of the emitted synchrotron photons depend on the same combination of the, usually poorly constrained, external density at the deceleration radius, n dec, and initial bulk Lorentz factor, Γ 0. This has the fortunate consequence of making the relation independent of both Γ 0 and n dec. Unless the efficiency of electron acceleration is very low, synchrotron gamma-rays from the external shock would fail to meet the current observational constraints for the vast majority of GRBs, including those with a smooth, single peak temporal profile. This argues either against an external shock origin for the prompt emission in GRBs or for changes in our understanding of the microphysical and radiation processes occurring within the shocked region.

Resolving the innermost parsec of Centaurus A at mid-infrared wavelengths

We report the results of interferometric observations of Centaurus A with the MID-infrared Interferometer (MIDI) at ESO's VLTI telescope array. The interferometric measurements are spectrally resolved (R = 30) in the wavelength range 8 to 13 micron. Their spatial resolution reaches 15 mas at the shortest wavelengths. Supplementary observations were obtained in the near-infrared with the adaptive optics instrument NACO, and at mm wavelengths with SEST and JCMT. We find that he mid-infrared emission from the core of Centaurus A is dominated by an unresolved point source (<10 mas). Observations with baselines orientated perpendicular to the radio jet reveal an extended component which can be interpreted as a geometrically thin, dusty disk, the axis of which is aligned with the radio jet. Its diameter is about 0.6 pc. We argue, that the unresolved emission is dominated by a synchrotron source. Its overall spectrum is characterized by a \nu^{-0.36} power-law which cuts off exponentially towards high frequencies at 8x10^{13} Hz and becomes optically thick at \nu < 45 GHz. Based on a Synchrotron Self Compton (SSC) interpretation for the gamma-ray emission, we find a magnetic field strength of 26 microTesla and a maximum energy of relativistic electrons of \gamma_c = E_c/m_e c^2 = 8500. Near \gamma_c, the acceleration time scale is 4 days, in good agreement with the fastest X-ray variations. Our SSC model argues for an upper limit for the bulk Lorentz factor < 2.5, at variance with the concept of a mis-directed BL Lac object. We estimate a thermal core luminosity of 1.3x10^{34} W, intermediate between the values for highly efficiently accreting AGN (e.g. Seyfert galaxies) and those of typical FR I radio galaxies.

Influence of the jet opening angle on the derived kinematical parameters of blazar jets having uniform and stratified bulk motion

We present analytical modelling of conical relativistic jets, in order to evaluate the role of the jet opening angle on certain key parameters that are inferred from very long baseline interferometry (VLBI) radio observations of blazar nuclear jets. The key parameters evaluated are the orientation angle (i.e. the viewing angle) of the jet and the apparent speed and Doppler factor of the radio knots on parsec scales. Quantitative comparisons are made of the influence of the jet opening angle on the above parameters of the radio knots, as would be estimated for two widely discussed variants of relativistic nuclear jets, namely, those having uniform bulk speed and those in which the bulk Lorentz factor of the flow decreases with distance from the jet axis (a ‘spine–sheath’ flow). Our analysis shows that for both types of jet velocity distributions, the expectation value of the jet orientation angle at first falls dramatically with increases in the (central) jet Lorentz factor, but it levels off at a fraction of the opening angle for extremely relativistic jets. We also find that the effective values of the apparent speeds and Doppler factors of the knots always decline substantially with increasing jet opening angle, but this effect is strongest for ultra-relativistic jets with uniform bulk speed. We suggest that the paucity of highly superluminal parsec-scale radio components in TeV blazars can be understood if their jets are highly relativistic and, being intrinsically weaker, somewhat less well collimated, in comparison to the jets in other blazars.

Extragalactic MeV γ-ray emission from cocoons of young radio galaxies

Strong γ -ray emission from cocoons of young radio galaxies is predicted for the first time. Considering the process of adiabatic injection of the shock dissipation energy and mass of the relativistic jet in active nuclei into the cocoon, while assuming thermalizing electron plasma interactions, we find that the thermal electron temperature of the cocoon is typically predicted to be of the order of ∼ MeV, and is determined only by the bulk Lorentz factor of the relativistic jet. Together with the time-dependent dynamics of the cocoon expansion, we find that young cocoons can yield thermal bremsstrahlung emissions at energies ∼MeV.

"Late Prompt" Emission in Gamma-Ray Bursts?

The flat decay phase in the first 102-104 s of the X-ray light curve of gamma-ray bursts (GRBs) has not yet been convincingly explained. The fact that the optical and X-ray light curves are often different, with breaks at different times, makes problematic any explanation based on the same origin for both the X-ray and optical fluxes. We here assume that the central engine can be active for a long time, producing shells of decreasing bulk Lorentz factors Γ. We also assume that the internal dissipation of these late shells produces a continuous and smooth emission (power law in time), usually dominant in X-rays and sometimes in the optical. When Γ of the late shells is larger than 1/θj, where θj is the jet opening angle, we see only a portion of the emitting surface. Eventually, Γ becomes smaller than 1/θj, and the entire emitting surface is visible. Thus, there is a break in the light curve when Γ = 1/θj, which we associate with the time at which the plateau ends. After the steeply decaying phase that follows the early prompt, we see the sum of two emission components: the late-prompt emission (due to late internal dissipation), and the real afterglow emission (due to external shocks). A variety of different optical and X-ray light curves are then possible, explaining why the X-ray and the optical light curves often do not track each other (but sometimes do), and often they do not have simultaneous breaks.

Kinematical diagrams for conical relativistic jets

We present diagrams depicting the expected inter-dependences of two key kinematical parameters of radio knots in the parsec-scale jets of blazars, deduced from VLBI observations. The two parameters are the apparent speed (υ app = cβ app) and the effective Doppler boosting factor (δ eff) of the relativistically moving radio knot. A novel aspect of these analytical computations of β-δ diagrams is that they are made for parsec-scale jets having a conical shape, with modest opening angles (ω up to 10°), in accord with the VLBI observations of the nuclei of the nearest radio galaxies. Another motivating factor is the recent finding that consideration of a conical geometry can have important implications for the interpretation of a variety of radio observations of blazar jets. In addition to uniform jet flows (i.e., those having a uniform bulk Lorentz factor, Γ), computational results are also presented for stratified jets where an ultra-relativistic central spine along the jet axis is surrounded by a slower moving sheath, possibly arising from a velocity shear.

All the Astrophysical Jet Sources: Driven by Mono-energetic e ± Beams?

Gopal Krishna and I are now considering E × B-drifting jets since some 25 years, and are still convinced that they form the only consistent description of the huge body of observations. New is our 2004 tightening that (all) the jets consist of mono-energetic flows of extremely relativistic electron-positron pairs, of bulk Lorentz factor γ 104, moving in equipartition with their frozen-in magnetic and electric fields. Whenever their supersonic propagation gets blocked by some (heavy) obstacle, their frozen-in Poynting flux converts the delta-shaped particle-energy distribution into an almost white (in power) power law: E2NE ~ E− with 0.

Outflow Propagation in Collapsars: Collimated Jets and Expanding Outflows

We investigate the outflow propagation in the collapsar in the context of gamma-ray bursts (GRBs) with 2D relativistic hydrodynamic simulations. We vary the specific internal energy and bulk Lorentz factor of the injected out- flow from non-relativistic regime to relativistic one, fixing the power of the outflow to be 1051erg s−1. We observed the collimated outflow, when the Lorentz factor of the injected outflow is roughly greater than 2. To the contrary, when the velocity of the injected outflow is slower, the expanding outflow is observed. The transition from collimated jet to expanding outflow continuously occurs by decreasing the injected velocity. Different features of the dynamics of the outflows would cause the difference between the GRBs and similar phenomena, such as, X-ray flashes.

Dissipation of jet bulk kinetic energy in powerful blazars

We investigate the dissipation of the bulk kinetic energy of a relativistic jet at different distances from the central power--house and analyse in detail how the dissipated energy is radiated away. We assume that the location of the dissipation region is a function of the bulk Lorentz factor Gamma of the jet, being closer to the center for smaller Gamma. This assumption is naturally fulfilled in the internal shock scenario. The dissipated energy is partially used to accelerate electrons and to amplify the magnetic field. This process creates a source inside the jet (blob). Such blobs may efficiently produce synchrotron and inverse Compton emission. We find that even if the blobs or shells responsible for the blazar activity carry the same energy (in bulk kinetic form), the fact that they move at different Gamma can produce dramatic variations in different bands, even if the bolometric luminosity is instead very similar. This is due to the relative importance of the synchrotron, self-Compton and external Compton radiation processes, which greatly changes by changing Gamma and the compactness of the source, even if the total radiated energy is constant. We then find that the jet can produce most of its radiative output at small distances from the putative black-hole and its accretion disk, if this implies a low level of emitted MeV-GeV flux. Our findings, which we apply for illustrative purposes to the blazar 3C 454.3, will be easily testable by the coming gamma-ray satellite, such as AGILE and GLAST.

Bulk Comptonization spectra in blazars

We study the time dependent spectra produced via the bulk Compton process by a cold, relativistic shell of plasma moving (and accelerating) along the jet of a blazar, scattering on external photons emitted by the accretion disc and reprocessed in the broad line region. Bulk Comptonization of disc photons is shown to yield a spectral component contributing in the far UV band, and would then be currently unobservable. On the contrary, the bulk Comptonization of broad line photons may yield a significant feature in the soft X-ray band. Such a feature is time-dependent and transient, and dominates over the non thermal continuum only when: a) the dissipation occurs close to, but within, the broad line region; b) other competing processes, like the synchrotron self-Compton emission, yield a negligible flux in the X-ray band. The presence of a bulk Compton component may account for the X-ray properties of high redshift blazars that show a flattening (and possibly a hump) in the soft X-rays, previously interpreted as due to intrinsic absorption. We discuss why the conditions leading to a detectable bulk Compton feature might be met only occasionally in high redshift blazars, concluding that the absence of such a feature in the spectra of most blazars should not be taken as evidence against matter--dominated relativistic jets. The detection of such a component carries key information on the bulk Lorentz factor and kinetic energy associated to (cold) leptons.

Collimated Jet or Expanding Outflow: Possible Origins of Gamma‐Ray Bursts and X‐Ray Flashes

We investigate the dynamics of an outflow propagating in a progenitor in the context of the collapsar model for GRBs through two-dimensional axisymmetric relativistic hydrodynamic simulations. Initially, we locally inject an outflow near the center of a progenitor. We calculate 25 models, in total, by fixing its total input energy (1051 ergs s-1) and radius of the injected outflow (7 × 107 cm) while varying its bulk Lorentz factor, Γ0 = 1.05-5, and its specific internal energy, 0/c2 = 0.1-30 (with c being speed of light). We find a smooth but dramatic transition from a collimated jet to an expanding outflow among calculated models. The half opening angle of the outflow (θsim) is sensitive to Γ0; we find θsim < 2° for Γ0 ≳ 3. The maximum Lorentz factor is, on the other hand, sensitive to both Γ0 and 0: roughly Γmax ~ Γ0(1 + 0/c2). In particular, a very high Lorentz factor of Γmax ≳ 100 is achieved in one model. A variety of opening angles can arise by changing 0, even when the maximum Lorentz factor is fixed. The jet structure totally depends on Γ0. When Γ0 is high, high-pressure progenitor gas heated by the bow shock collimates the outflow to form a narrow, relativistic jet. When Γ0 is low, on the contrary, the outflow expands soon after the injection, since the bow shock is weak and thus the pressure of the progenitor gas is not high enough to confine the flow. Our finding will explain a smooth transition between the GRBs, X-ray-rich GRBs (XRRs), and X-ray flashes (XRFs) by the same model but with different 0 values.

Temporal Evolution of Pair Attenuation Signatures in Gamma‐Ray Burst Spectra

The spectra obtained above 100 MeV by the EGRET experiment aboard the Compton Gamma-Ray Observatory for a handful of gamma-ray bursts has given no indication of any spectral attenuation that might preclude detection of bursts at higher energies. With the discovery of optical afterglows and counterparts to bursts in the last few years, enabling the determination of significant redshifts for these sources, it is anticipated that profound spectral attenuation will arise in the Gamma-Ray Large Area Space Telescope (GLAST) energy band of 30 MeV-300 GeV for many if not most bursts. This paper explores time-dependent expectations for burst spectral properties in the EGRET/GLAST band, focusing on how attenuation of photons by pair creation internal to the source generates distinctive spectral signatures. The energy of spectral breaks and the associated spectral indices provide valuable information that constrains the bulk Lorentz factor of the GRB outflow at a given time. Moreover, the distinct temporal behavior that is present for internal attenuation is easily distinguished from extrinsic absorption due to intervening cosmic background fields. These characteristics define palpable observational goals for both spaced-based hard gamma-ray experiments such as GLAST, and ground-based Cherenkov telescopes, and strongly impact the observability of bursts above 300 MeV.

A Structured Leptonic Jet Model of the “Orphan” TeV Gamma‐Ray Flares in TeV Blazars

The emission spectra of TeV blazars extend up to tens of TeV, and the emission mechanism of the TeV γ-rays is explained by synchrotron self-Compton scattering in leptonic models. In these models the time variabilities of X-rays and TeV γ-rays are correlated. However, recent observations of 1ES 1959+65.0 and Mrk 421 have found the TeV γ-ray flares, i.e., TeV γ-ray flares without simultaneous X-ray flares. In this paper we propose a model for the orphan TeV γ-ray flares, employing an inhomogeneous leptonic jet model. After a primary flare that accompanies flare-up both in X-rays and TeV γ-rays, radiation propagates in various directions in the comoving frame of the jet. When a dense region in the jet receives the radiation, X-rays are scattered by relativistic electrons/positrons to become TeV γ-rays. These γ-ray photons are observed as an orphan TeV γ-ray flare. The observed delay time between the primary and orphan flares is about 2 weeks, and this is accounted for in our model for parameters such as Γ = 20, d = 4 × 1017 cm, α = 3, and η = 1, where Γ is the bulk Lorentz factor of the jet, d is the distance between the central black hole and the primary flare site, α/Γ is the angle between the jet axis and the direction of the motion of the dense region that scatters incoming X-rays produced by the primary flare, and η/Γ is the angle between the jet axis and the line of sight.

The milliarcsecond-scale jet of PKS 0735+178 during quiescence

We present polarimetric 5 GHz to 43 GHz VLBI observations of the BL Lacertae object PKS 0735+178, spanning March 1996 to May 2000. Comparison with previous and later observations suggests that the overall kinematic and structural properties of the jet are greatly influenced by its activity. Time intervals of enhanced activity, as reported before 1993 and after 2000 by other studies, are followed by highly superluminal motion along a rectilinear jet. In contrast the less active state in which we performed our observations, shows subluminal or slow superluminal jet features propagating through a twisted jet with two sharp bends of about 90° within the innermost three-milliarcsecond jet structure. Proper motion estimates from the data presented here allow us to constrain the jet viewing angle to values ≤ , and the bulk Lorentz factor to be between 2 and 4.

Bulk motion of ultrarelativistic conical blazar jets

Allowing for the conical shape of ultrarelativistic blazar jets with opening angles of a few degrees on parsec-scales we show that their bulk Lorentz factors and viewing angles can be much larger than the values usually inferred by combining their flux variability and proper motion measurements. This is in accord with our earlier finding that such ultrarelativistic (Lorentz factor, Gamma > 30) conical jets can reconcile the relatively slow apparent motions of VLBI knots in TeV blazars with the extremely fast flows implied by their rapid gamma-ray variability. This jet geometry also implies that de-projected jet opening angles will typically be significantly underestimated from VLBI measurements. In addition, de-projected jet lengths will be considerably overestimated if high Lorentz factors and significant opening angles are not taken into account.

General relativistic magnetohydrodynamic simulations of the jet formation and large-scale propagation from black hole accretion systems

The formation and large-scale propagation of Poynting-dominated jets produced by accreting, rapidly rotating black hole systems are studied by numerically integrating the general relativistic magnetohydrodynamic equations of motion to follow the self-consistent interaction between accretion disks and black holes. This study extends previous similar work by studying jets till $t\approx 10^4GM/c^3$ out to $r\approx 10^4GM/c^2$, by which the jet is super- fast magnetosonic and moves at a lab-frame bulk Lorentz factor of $\Gamma\sim 10$ with a maximum terminal Lorentz factor of $\Gamma_\infty\lesssim 10^3$. The radial structure of the Poynting-dominated jet is piece-wise self-similar, and fits to flow quantities along the field line are provided. Beyond the \alf surface at $r\sim 10$--$100GM/c^2$, the jet becomes marginally unstable to (at least) current-driven instabilities. Such instabilities drive shocks in the jet that limit the efficiency of magnetic acceleration and collimation. These instabilities also induce jet substructure with $3\lesssim\Gamma\lesssim 15$. The jet is shown to only marginally satisfy the necessary and sufficient conditions for kink instability, so this may explain how astrophysical jets can extend to large distances without completely disrupting. At large distance, the jet angular structure is Gaussian-like (or uniform within the core with sharp exponential wings) with a half-opening angle of $\approx 5^\circ$ and there is an extended component out to $\approx 27^\circ$. Unlike in some hydrodynamic simulations, the environment is found to play a negligible role in jet structure, acceleration, and collimation as long as the ambient pressure of the surrounding medium is small compared to the magnetic pressure in the jet.

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.

A Simple Two‐Parameter Characterization of Gamma‐Ray Burst Time Histories

A simple scheme delineates long GRBs with similar time histories using the internal luminosity function (ILF) power-law index and the spectral lag. Two generalizations are made about time history morphologies: (1) GRBs with long spectral lags contain fewer pulses that are broader than those found in bursts with short spectral lags, and (2) short-lag bursts with small ILF power-law indices have many narrow pulses and are highly variable, while long-lag bursts with small ILF power-law indices are characterized by broad, smooth pulses and have low variability. GRB time-history morphologies primarily identify intrinsic rather than extrinsic characteristics based on correlations with gamma-ray luminosity, afterglow luminosity, and number of pulses. These characteristics result because internal relativistic effects, due to bulk Lorentz factor, are larger than cosmological effects, and because the numbers and shapes of pulses indicate different efficiencies and forms of GRB energy release. Single-pulsed GRBs are characterized by either large ILF power indices (indicating a range of jet-opening angles and Lorentz factors with a FRED pulse shape), or long lags (large jet-opening angles with low Lorentz factors with either a FRED pulse shape or an unpeaked, smooth pulse shape). They also have lower luminosity afterglows than multipulsed GRBs. GRBs with simple time histories are often associated with Type Ibc supernovae. This suggests that some single-pulsed GRBs contain single, beamed blast waves that are similar to and have characteristics that overlap with those of many supernovae. Such a connection may not exist between multipulsed GRBs and supernovae.