Bulk Lorentz Factor Research Articles

DEVELOPMENT OF A GENERAL RELATIVISTIC MAGNETOHYDRODYNAMIC CODE AND ITS APPLICATION TO THE CENTRAL ENGINE OF LONG GAMMA-RAY BURSTS

In order to investigate the formation of relativistic jets at the center of a progenitor of a gamma-ray burst (GRB), we develop a two-dimensional general relativistic magnetohydrodynamic code. We show that the code passes many well-known test calculations, and confirm the reliability of the code. Then we perform a numerical simulation of a collapsar using a realistic progenitor model. It is shown that a jet is launched from the center of the progenitor. The structure of the jet is similar to the previous study: a Poynting flux jet is surrounded by the funnel-wall jet. Even at the final stage of the simulation, the bulk Lorentz factor of the jet is still low, and the total energy of the jet is still as small as 1048 erg. However, we find that the energy flux per unit rest-mass flux is as high as 102 at the bottom of the jet. Thus, we conclude that the bulk Lorentz factor of the jet can be potentially high when it propagates outward. Also, as long as the duration of the activity of the central engine is long enough, the total energy of the jet can be large enough to explain the typical explosion energy of a GRB (~1051 erg). It is shown that the outgoing Poynting flux exists at the horizon around the polar region, which proves that the Blandford-Znajek mechanism is really working. However, we conclude that the jet is mainly launched by the magnetic field amplified by the gravitational collapse and differential rotation around the black hole, rather than the Blandford-Znajek mechanism.

HYPERACCRETING NEUTRON STAR DISKS AND NEUTRINO ANNIHILATION

Newborn neutron stars surrounded by hyperaccreting and neutrino-cooled disks may exist in some gamma-ray bursts and/or supernovae. In this paper, we further study the structure of such a neutron star disk based on the two-region (i.e., inner and outer) disk scenario following our previous work, and calculate the neutrino annihilation luminosity from the disk in various cases. We investigate the effects of the viscosity parameter {alpha}, energy parameter {epsilon} (measuring the neutrino cooling efficiency of the inner disk), and outflow strength on the structure of the entire disk as well as the effect of emission from the neutron star surface boundary emission on the total neutrino annihilation rate. The inner disk satisfies the entropy-conservation self-similar structure for the energy parameter {epsilon} {approx_equal} 1 and the advection-dominated structure for {epsilon} < 1. An outflow from the disk decreases the density and pressure but increases the thickness of the disk. Moreover, compared with the black hole disk, the neutrino annihilation luminosity above the neutron star disk is higher, and the neutrino emission from the boundary layer could increase the neutrino annihilation luminosity by about one order of magnitude higher than the disk without boundary emission. The neutron star disk with the advection-dominatedmore » inner disk could produce the highest neutrino luminosity while the disk with an outflow has the lowest. Although a heavily mass-loaded outflow from the neutron star surface at early times of neutron star formation prevents the outflow material from being accelerated to a high bulk Lorentz factor, an energetic ultrarelativistic jet via neutrino annihilation can be produced above the stellar polar region at late times if the disk accretion rate and the neutrino emission luminosity from the surface boundary layer are sufficiently high.« less

LOOKING INTO THE FIREBALL: ROTSE-III ANDSWIFTOBSERVATIONS OF EARLY GAMMA-RAY BURST AFTERGLOWS

We report on a complete set of early optical afterglows of gamma-ray bursts (GRBs) obtained with the Robotic Optical Transient Search Experiment (ROTSE-III) telescope network from 2005 March through 2007 June. This set is comprised of 12 afterglows with early optical and Swift/X-Ray Telescope observations, with a median ROTSE-III response time of 45 s after the start of γ-ray emission (8 s after the GCN notice time). These afterglows span 4 orders of magnitude in optical luminosity, and the contemporaneous X-ray detections allow multi-wavelength spectral analysis. Excluding X-ray flares, the broadband synchrotron spectra show that the optical and X-ray emission originate in a common region, consistent with predictions of the external forward shock in the fireball model. However, the fireball model is inadequate to predict the temporal decay indices of the early afterglows, even after accounting for possible long-duration continuous energy injection. We find that the optical afterglow is a clean tracer of the forward shock, and we use the peak time of the forward shock to estimate the initial bulk Lorentz factor of the GRB outflow, and find 100 ≲ Γ_0 ≲ 1000, consistent with expectations.

Prompt optical emission and synchrotron self-absorption constraints on emission site of GRBs

We constrain the distance of the Gamma-Ray Burst (GRB) prompt emission site from the explosion centre, R, by determining the location of the electron's self absorption frequency in the GRB prompt optical-to-X/gamma-ray spectral energy distribution, assuming that the optical and the gamma-ray emissions are among the same synchrotron radiation continuum of a group of hot electrons. All possible spectral regimes are considered in our analysis. The method has only two assumed parameters, namely, the bulk Lorentz factor of the emitting source Gamma, and the magnetic field strength B in the emission region (with a weak dependence). We identify a small sample of 4 bursts that satisfy the following three criteria: (1) they all have simultaneous optical and gamma-ray detections in multiple observational time intervals; (2) they all show temporal correlations between the optical and gamma-ray light curves; and (3) the optical emission is consistent with belonging to the same spectral component as the gamma-ray emission. For all the time intervals of these 4 bursts, it is inferred that R \geq 10^{14} (Gamma/300)^{3/4} (B/10^5 Gauss)^{1/4} cm. For a small fraction of the sample, the constraint can be pinned down to R \approx 10^{14} - 10^{15} cm for Gamma ~ 300. For a second sample of bursts with prompt optical non-detections, only upper limits on R can be obtained. We find no inconsistency between the R-constraints for this non-detection sample and those for the detection sample.

Early afterglows from radially structured outflows and the application to X-ray shallow decays

In the fireball model, it is more physically realistic that gamma-ray burst (GRB) ejecta have a range of bulk Lorentz factors (assuming M α −S). The low Lorentz factor part of the ejecta will catch up with the high Lorentz factor part when the latter is decelerated by the surrounding medium to a comparable Lorentz factor. Such a process will develop a long-lasting weak reverse shock until the whole ejecta are shocked. Meanwhile, the forward shocked materials are gradually supplied with energy from the ejecta that are catching-up, and thus the temporal decay of the forward shock emission will be slower than that without an energy supply. However, the reverse shock may be strong. Here, we extend the standard reverse-forward shock model to the case of radially nonuniform ejecta. We show that this process can be classified into two cases: the thick shell case and the thin shell case. In the thin shell case, the reverse shock is weak and the temporal scaling law of the afterglow is the same as that in Sari & Mészáros (2000). However, in the thick shell case, the reverse shock is strong and thus its emission dominates the afterglow in the high energy band. Our results also show slower decaying behavior of the afterglow due to the energy supply by low Lorentz factor materials, which may help the understanding of the plateau observed in the early optical and X-ray afterglows.

PROMPT HIGH-ENERGY EMISSION FROM PROTON-DOMINATED GAMMA-RAY BURSTS

The prompt emission of gamma-ray bursts (GRBs) is widely thought to be radiation from accelerated electrons, but an appreciably larger amount of energy could be carried by accelerated protons, particularly if GRBs are the sources of ultra-high-energy cosmic rays (UHECRs). We model the expected photon spectra for such "proton-dominated" GRBs in the internal shock scenario through Monte Carlo simulations, accounting for various processes related to high-energy electrons and protons. Besides proton and muon synchrotron components, emission from photomeson-induced secondary pair cascades becomes crucial, generally enhancing the GeV–TeV and/or eV–keV photons and offering a signature of UHE protons. In some cases, it can overwhelm the primary electron component and result in GRBs peaking in the 10 MeV–1 GeV range, which may be relevant to some bursts discussed in a recent re-analysis of EGRET TASC data. The dependence of the spectra on key quantities such as the bulk Lorentz factor, magnetic field, and proton-to-electron ratio is nontrivial due to the nonlinear nature of cascading and the interplay of electron- and proton-induced components. Observations by Fermi, ground-based telescopes, and other facilities should test these expectations and provide critical constraints on the proton acceleration efficiency.

GRB 080916C: ON THE RADIATION ORIGIN OF THE PROMPT EMISSION FROM keV/MeV TO GeV

Fermi observations of high-energy gamma-ray emission from GRB 080916C shows that its spectrum is consistent with the Band function from MeV to tens of GeV. Assuming one single emission mechanism dominates in the whole energy range, we show that this spectrum is consistent with synchrotron origin by shock-accelerated electrons. The simple electron inverse-Compton model and the hadronic model are found to be less viable. In the synchrotron scenario, the synchrotron self-Compton scattering is likely to be in the Klein-Nishina regime and therefore the resulting high-energy emission is subdominant, even though the magnetic field energy density is lower than that in relativistic electrons. The Klein-Nishina inverse-Compton cooling may also affect the low-energy electron number distribution and hence results in a low-energy synchrotron photon spectrum $n(\nu)\propto\nu^{-1}$ below the peak energy. Under the framework of the electron synchrotron interpretation, we constrain the shock microphysical parameters and derive a lower limit of the upstream magnetic fields. The detection of synchrotron emission extending to about 70 GeV in the source frame in GRB 080916C favors the Bohm diffusive shock acceleration if the bulk Lorentz factor of the relativistic outflow is not significantly greater than thousands.

Refining a relativistic, hydrodynamic solver: Admitting ultra-relativistic flows

We have undertaken the simulation of hydrodynamic flows with bulk Lorentz factors in the range 10 2–10 6. We discuss the application of an existing relativistic, hydrodynamic primitive variable recovery algorithm to a study of pulsar winds, and, in particular, the refinement made to admit such ultra-relativistic flows. We show that an iterative quartic root finder breaks down for Lorentz factors above 10 2 and employ an analytic root finder as a solution. We find that the former, which is known to be robust for Lorentz factors up to at least 50, offers a 24% speed advantage. We demonstrate the existence of a simple diagnostic allowing for a hybrid primitives recovery algorithm that includes an automatic, real-time toggle between the iterative and analytical methods. We further determine the accuracy of the iterative and hybrid algorithms for a comprehensive selection of input parameters and demonstrate the latter’s capability to elucidate the internal structure of ultra-relativistic plasmas. In particular, we discuss simulations showing that the interaction of a light, ultra-relativistic pulsar wind with a slow, dense ambient medium can give rise to asymmetry reminiscent of the Guitar nebula leading to the formation of a relativistic backflow harboring a series of internal shockwaves. The shockwaves provide thermalized energy that is available for the continued inflation of the PWN bubble. In turn, the bubble enhances the asymmetry, thereby providing positive feedback to the backflow.

The bulk kinetic power of radio jets in active galactic nuclei

Based on the K\"onigl's inhomogeneous jet model, we estimate the jet parameters, such as bulk Lorentz factor $\Gamma$, viewing angle $\theta$ and electron number density $n_{\rm e}$ from radio VLBI and X-ray data for a sample of active galactic nuclei (AGNs) assuming that the X-rays are from the jet rather than the intracluster gas. The bulk kinetic power of jets is then calculated using the derived jet parameters. We find a strong correlation between the total luminosity of broad emission lines and the bulk kinetic power of the jets. This result supports the scenario that the accretion process are tightly linked with the radio jets, though how the disk and jet are coupled is not revealed by present correlation analysis. Moreover, we find a significant correlation between the bulk kinetic power and radio extended luminosity. This implies that the emission from the radio lobes are closely related with the energy flux transported through jets from the central part of AGNs.

Fast TeV variability in blazars: jets in a jet

Abstract The fast TeV variability of the blazars Mrk 501 and PKS 2155−304 implies a compact emitting region that moves with a bulk Lorentz factor of Γem∼ 100 towards the observer. The Lorentz factor is clearly in excess of the jet Lorentz factors Γj≲ 10 measured on sub-pc scales in these sources. We propose that the TeV emission originates from compact emitting regions that move relativistically within a jet of bulk Γj∼ 10. This can be physically realized in a Poynting flux-dominated jet. We show that if a large fraction of the luminosity of the jet is prone to magnetic dissipation through reconnection, then material outflowing from the reconnection regions can efficiently power the observed TeV flares through synchrotron-self-Compton emission. The model predicts simultaneous far-ultraviolet/soft X-ray flares.

Time-Evolution of Peak Energy and Luminosity Relation within Pulses for GRB 061007: Probing Fireball Dynamics

Abstract We performed a time-resolved spectral analysis of a bright, long gamma-ray burst GRB 061007 using Suzaku/WAM and Swift/BAT. Because of the large effective area of the WAM, we can investigate the time evolution of the spectral peak energy $E^{\rm t}_{ \rm peak}$ and the luminosity $L^{\rm t}_{\rm iso}$ with 1-s time resolution, and we find that the time-resolved pulses also satisfy the $E_{\rm peak}$–$L_{\rm iso}$ relation, which was found for the time-averaged spectra of other bursts, suggesting the same physical conditions in each pulse. Furthermore, the initial rising phase of each pulse could be an outlier of this relation with higher $E^{\rm t}_{ \rm peak}$ value by a factor of 2. This difference could suggest that the fireball radius expands by a factor of 2–4 and/or bulk Lorentz factor of the fireball is decelerated by a factor of $\sim$4 during the initial phase, providing a new probe of fireball dynamics in real time.

Prompt high-energy emission from gamma-ray bursts in the internal shock model

The prompt GRB emission is thought to arise from electrons accelerated in internal shocks propagating within a highly relativistic outflow. The launch of Fermi offers the prospect of observations with unprecedented sensitivity in high-energy (>100 MeV) gamma-rays. The aim is to explore the predictions for HE emission from internal shocks, taking into account both dynamical and radiative aspects, and to deduce how HE observations constrain the properties of the relativistic outflow. The emission is modeled by combining a time-dependent radiative code with a dynamical code giving the evolution of the physical conditions in the shocked regions.Synthetic lightcurves and spectra are compared to observations. The HE emission deviates significantly from analytical estimates, which tend to overpredict the IC component, when the time dependence and full cross-sections are included. The exploration of the parameter space favors the case where the dominant process in the BATSE range is synchrotron emission. The HE component becomes stronger for weaker magnetic fields. The HE lightcurve can display a prolonged pulse duration due to IC emission, or even a delayed peak compared to the BATSE range.Alternatively, having dominant IC emission in the BATSE range requires most electrons to be accelerated into a steep power-law distribution and implies strong 2nd order IC scattering. In this case, the BATSE and HE lightcurves are very similar. The combined dynamical and radiative approach allows a firm appraisal of GRB HE prompt emission. A diagnostic procedure is presented to identify from observations the dominant emission process and derive constrains on the bulk Lorentz factor, particle density and magnetic field of the outflow.

GAMMA-RAY BURST LIGHT CURVES IN THE RELATIVISTIC TURBULENCE AND RELATIVISTIC SUBJET MODELS

Randomly oriented relativistic emitters in a relativistically expanding shell provides an alternative to internal shocks as a mechanism for producing GRBs' variable light curves with efficient conversion of energy to radiation. In this model the relativistic outflow is broken into small emitters moving relativistically in the outflow's rest frame. Variability arises because an observer sees an emitter only when its velocity points towards him so that only a small fraction of the emitters are seen by a given observer. Models with significant relativistic random motions require converting and maintaining a large fraction of the overall energy into these motions. While it is not clear how this is achieved, we explore here, using two toy models, the constraints on parameters required to produce light curves comparable to the observations. We find that a tight relation between the size of the emitters and the bulk and random Lorentz factors is needed and that the random Lorentz factor determines the variability. While both models successfully produce the observed variability there are several inconsistencies with other properties of the light curves. Most of which, but not all, might be resolved if the central engine is active for a long time producing a number of shells, resembling to some extent the internal shocks model.

A turbulent model of gamma-ray burst variability

Abstract A popular paradigm to explain the rapid temporal variability observed in gamma-ray burst (GRB) light curves is the internal shock model. We propose an alternative model in which the radiating fluid in the GRB shell is relativistically turbulent with a typical eddy Lorentz factor γt. In this model, all pulses in the gamma-ray light curve are produced at roughly the same distance R from the centre of the explosion. The burst duration is ∼R/cΓ2, where Γ is the bulk Lorentz factor of the expanding shell, and the duration of individual pulses in the light curve is ∼R/cΓ2γ2t. The model naturally produces highly variable light curves with ∼γ2t individual pulses. Even though the model assumes highly inhomogeneous conditions, nevertheless the efficiency for converting jet energy to radiation is high.

Fermi Observations of High-Energy Gamma-Ray Emission from GRB 080916C

Gamma-ray bursts (GRBs) are highly energetic explosions signaling the death of massive stars in distant galaxies. The Gamma-ray Burst Monitor and Large Area Telescope onboard the Fermi Observatory together record GRBs over a broad energy range spanning about 7 decades of gammaray energy. In September 2008, Fermi observed the exceptionally luminous GRB 080916C, with the largest apparent energy release yet measured. The high-energy gamma rays are observed to start later and persist longer than the lower energy photons. A simple spectral form fits the entire GRB spectrum, providing strong constraints on emission models. The known distance of the burst enables placing lower limits on the bulk Lorentz factor of the outflow and on the quantum gravity mass.

The changing look of PKS 2149-306

<i>Aims. <i/> We study the blazar nature of the high-redshift Flat-Spectrum Radio Quasar PKS 2149-306 () by investigating its long-term behavior.<i>Methods. <i/>We analyzed all publicly available optical-to-X-ray observations performed by <i>XMM-Newton<i/>, <i>Swift<i/>, and <i>INTEGRAL<i/>.<i>Results. <i/>PKS 2149-306 is one of four blazars at that have been observed in the hard-X-ray regime with both the BAT and ISGRI instruments. Observations acquired almost 1 year apart in the keV energy band in the object rest frame, exhibit no noticeable change in spectral slope associated with a flux variation of more than a factor of two. <i>Swift<i/> data appear to show a roll-off below ~1 keV, which becomes increasingly evident during a ~3-day time-frame, that can be explained as the natural spectral break caused by the Inverse Compton onset. The broad-band spectra allow us to identify two different states. The SED modeling suggests that they can be interpreted by only a change in the bulk Lorentz factor of the jet.

High energy emission from AGN cocoons in clusters of galaxies

AbstractGamma‐ray emission from cocoons of young radio galaxies is predicted. Considering the process of adiabatic injection of the shock dissipation energy and mass of the relativistic jet into the cocoon, 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 jet. Together with the time‐dependent dynamics of the cocoon expansion, we find that young cocoons can yield thermal bremsstrahlung emissions at energies ∼MeV. Hotter cocoons (i.e., GeV) for younger sources are also discussed (© 2009 WILEY‐VCH Verlag GmbH &amp; Co. KGaA, Weinheim)

A structure and energy dissipation efficiency of relativistic reconfinement shocks

We present a semi-analytical hydrodynamical model for the structure of reconfinement shocks formed in astrophysical relativistic jets interacting with external medium. We take into account exact conservation laws, both across the shock front and in the zone of the shocked matter, and exact angular relations. Our results confirm a good accuracy of the approximate formulae derived by Komissarov & Falle (1997). However, including the transverse pressure gradient in the shocked jet, we predict an absolute size of the shock to be about about twice larger. We calculate the efficiency of the kinetic energy dissipation in the shock and show a strong dependence on both the bulk Lorentz factor and opening angle of the jet.

On the origin of ultra high energy cosmic rays: subluminal and superluminal relativistic shocks

Aims. The flux of ultra high energy cosmic rays (UHECRs) at E > 10 18.5 eV is believed to arise in plasma shock environments in extragalactic sources. In this paper, we present a systematic study of cosmic ray (CR) particle acceleration by relativistic shocks, in particular concerning the dependence on bulk Lorentz factor and the angle between the magnetic field and the shock flow. The contribution to the observed diffuse CR spectrum provided by the accelerated particles is discussed. Methods. For the first time, Monte Carlo simulations for super- and subluminal shocks are extended to boost factors up to Γ= 1000 and systematically compared. The source spectra derived are translated into the expected diffuse proton flux from astrophysical sources by folding the spectra with the spatial distribution of active galactic nuclei (AGN) and gamma ray bursts (GRBs). Results of these predictions are compared with UHECR data. Results. While superluminal shocks are shown to be inefficient at providing acceleration to the highest energies (E > 10 18.5 eV), subluminal shocks may provide particles up to 10 21 eV, limited only by the Hillas-criterion. In the subluminal case, we find that mildly-relativistic shocks, thought to occur in jets of AGN (Γ ∼ 10−30), yield energy spectra of dN/dE ∼ E −2 . Highly relativistic shocks expected in GRBs (100 < Γ < 1000), on the other hand, produce spectra as flat as ∼E −1.0 above 10 9.5 GeV. The model results are compared with the measured flux of CRs at the highest energies and it is shown that, while AGN spectra provide an excellent fit, GRB spectra are too flat to explain the observed flux. The first evidence of a correlation between the CR flux above 5.7 × 10 10 GeV and the distribution of AGN provided by Auger are explained by our model. Although GRBs are excluded as the principle origin of UHECRs, neutrino production is expected in these sources either in mildly or highly relativistic shocks. In particular, superluminal shocks in GRBs may be observable via neutrino and photon fluxes, rather than as protons.

An inhomogeneous jet model for the rapid variability of TeV blazars

Abstract We present a new time-dependent inhomogeneous jet model of non-thermal blazar emission, which reproduces the entire spectral energy distribution together with the rapid gamma-ray variability. Ultrarelativistic leptons are injected at the base of a jet and propagate along the jet structure. We assume continuous reacceleration and cooling, producing a relativistic quasi-maxwellian (or ‘pile-up’) particle energy distribution. The synchrotron and synchrotron self-Compton jet emissivity are computed at each altitude. Klein–Nishina effects as well as intrinsic gamma–gamma absorption are included in the computation. Due to the pair production optical depth, considerable particle density enhancement can occur, particularly during flaring states. Time-dependent jet emission can be computed by varying the particle injection, but due to the sensitivity of pair production process, only small variations of the injected density are required during the flares. The stratification of the jet emission, together with a pile-up distribution, allows significantly lower bulk Lorentz factors, compared to one-zone models. Applying this model to the case of PKS 2155-304 and its big TeV flare observed in 2006, we can reproduce simultaneously the average broad-band spectrum of this source as well as the TeV spectra and TeV light curve of the flare with bulk Lorentz factor lower than 15.