Jet Opening Angle Research Articles

The evolution of slab jets and self-similar models of extragalactic radio sources

Simple general arguments suggest that, like round jets, initially divergent hypersonic slab jets propagating through a uniform atmosphere are eventually recollimated by the high pressure of their cocoons and the subsequent evolution is approximately self-similar. Although slab jets are not directly relevant to astrophysical jets, they allow us to study the effects of enforced symmetry without resorting to expensive three-dimensional numerical simulations. In this paper we show that, although both jets with enforced mirror symmetry and those without eventually become self-similar, the flow depends significantly on the symmetry. In particular, the aspect ratio of the cocoon created by asymmetric jets seems to be independent of the initial jet opening angle for small opening angles, contrary to what is found for symmetric jets. This suggests that the hydrodynamics of the jet and its cocoon is much more complicated than has been assumed in current theoretical models of extragalactic radio sources and that results of two-dimensional axisymmetric numerical simulations can be rather misleading.

A Standard Kinetic Energy Reservoir in Gamma‐Ray Burst Afterglows

We present a comprehensive sample of X-ray observations of 41 γ-ray burst (GRB) afterglows, as well as jet opening angles, θj, for a subset with measured jet breaks. We show that there is a significant dispersion in the X-ray fluxes, and hence isotropic X-ray luminosities (LX,iso), normalized to t = 10 hr. However, there is a strong correlation between LX,iso and the beaming fractions, fb ≡ [1 - cos(θj)]. As a result, the true X-ray luminosity of GRB afterglows, LX = fbLX,iso, is approximately constant, with a dispersion of only a factor of 2. Since eEb ∝ LX, the strong clustering of LX directly implies that the adiabatic blast wave kinetic energy in the afterglow phase, Eb, is tightly clustered. The narrow distribution of LX also suggests that p ≈ 2, that inverse Compton emission does not in general dominate the observed X-ray luminosity, and that radiative losses at t < 10 hr are relatively small. Thus, despite the large diversity in the observed properties of GRBs and their afterglows, the energy imparted by the GRB central engine to the relativistic ejecta is approximately constant.

Gamma‐Ray Burst Energetics and the Gamma‐Ray Burst Hubble Diagram: Promises and Limitations

We present a complete sample of 29 gamma-ray bursts (GRBs) for which it has been possible to determine temporal breaks (or limits) from their afterglow light curves. We interpret these breaks within the framework of the uniform conical jet model, incorporating realistic estimates of the ambient density and propagating error estimates on the measured quantities. In agreement with our previous analysis of a smaller sample, the derived jet opening angles of those 16 bursts with redshifts result in a narrow clustering of geometrically corrected gamma-ray energies about γ = 1.33 × 1051 ergs; the burst-to-burst variance about this value is 0.35 dex, a factor of 2.2. Despite this rather small scatter, we demonstrate in a series of GRB Hubble diagrams that the current sample cannot place meaningful constraints upon the fundamental parameters of the universe. Indeed, for GRBs to ever be useful in cosmographic measurements, we argue the necessity of two directions. First, GRB Hubble diagrams should be based upon fundamental physical quantities such as energy, rather than empirically derived and physically ill-understood distance indicators (such as those based upon prompt burst time-profiles and spectra). Second, a more homogeneous set should be constructed by culling subclasses from the larger sample. These subclasses, although now first recognizable by deviant energies, ultimately must be identifiable by properties other than those directly related to energy. We identify a new subclass of GRBs ("f-GRBs") that appear both underluminous by factors of at least 10 and exhibit a rapid fading (fν ∝ t-2) at early times (t ≲ 0.5 day). About 10%-20% of observed long-duration bursts appear to be f-GRBs.

GRB afterglow light curves from uniform and non-uniform jets

It is widely believed that gamma-ray bursts are produced by a jet-like outflows directed towards the observer, and the jet opening angle (theta(j)) is often inferred from the time at which there is a break in the afterglow light curves. Here we calculate the GRB afterglow light curves from a relativistic jet as seen by observers at a wide range of viewing angles (theta(v)) from the jet axis, and the jet is uniform or non-uniform (the energy per unit solid angle decreases smoothly away from the axis epsilon(theta) proportional to (theta/theta(c))(-k)). We find that, for uniform jet (k = 0), the afterglow light curves for different viewing angles are somewhat different: in general, there are two breaks in the light curve, the first one corresponds to the time at which gamma similar to (theta(j) - theta(v))(-1), and the second one corresponds to the time when gamma similar to (theta(j) + theta(v))(-1). However, for non-uniform jet, the things become more complicated. For the case theta(v) = 0, we can obtain the analytical results, for k 8/(p + 4) there should be only one break corresponds to gamma similar to theta(c)(-1), and this provides a possible explanation for some rapidly fading afterglows whose light curves have no breaks since the time at which gamma similar to theta(c)(-1) is much earlier than our first observation time. For the case theta(v) not equal 0, our numerical results show that, the afterglow light curves are strongly affected by the values of theta(v), theta(c) and k. If theta(v) is close to theta(c) and k is small, then the light curve is similar to the case of k = 0, except the flux is somewhat lower. However, if the values of theta(v)/theta(c) and k are larger, there will be a prominent flattening in the afterglow light curve, which is quite different from the uniform jet, and after the flattening a very sharp break will be occurred at the time gamma similar to (theta(v) + theta(c))(-1).

X‐Ray Jet Emission from the Black Hole X‐Ray Binary XTE J1550−564 withChandrain 2000

We have discovered an X-ray jet due to material ejected from the black hole X-ray transient XTE J1550-564. The discovery was first reported in 2002 by Corbel and coworkers, and here we present an analysis of the three Chandra observations made between 2000 June and September. For these observations, a source is present that moves in an eastward direction away from the point source associated with the compact object. The separation between the new source and the compact object changes from 213 in June to 234 in September, implying a proper motion of 21.2 ± 7.2 mas day-1, a projected separation of 0.31-0.85 pc, and an apparent jet velocity between 0.34 ± 0.12 and 0.93 ± 0.32 times the speed of light for a source distance range of d = 2.8-7.6 kpc. These observations represent the first time that an X-ray jet proper-motion measurement has been obtained for any accretion-powered Galactic or extragalactic source. While this work deals with the jet to the east of the compact object, the western jet has also been detected in the X-ray and radio bands. The most likely scenario is that the eastern jet is the approaching jet and that the jet material was ejected from the black hole in 1998. Along with a 1998 VLBI proper-motion measurement, the Chandra proper motion indicates that the eastern jet decelerated between 1998 and 2000. There is evidence that the eastern jet is extended by ±2''-3'' in the direction of the proper motion. The upper limit on the source extension in the perpendicular direction is ±15, which corresponds to a jet opening angle of less than 75. The X-ray jet energy spectrum is well but not uniquely described by a power law with an energy index of α = -0.8 ± 0.4 (Sν ∝ να) and interstellar absorption. The eastern jet was also detected in the radio band during an observation made within 7.4 days of the June Chandra observation. The overall radio flux level is consistent with an extrapolation of the X-ray power law with α = -0.6. The 0.3-8 keV X-ray jet luminosity is in the range (3-24) × 1032 ergs s-1 for the June observation using the distance range above but is a factor of ~2-3 lower for the later observations. We cannot definitively determine the X-ray emission mechanism, but a synchrotron origin is viable and may provide the simplest explanation for the observations.

Reaching the jet engine with AMBER/VLTI

To understand star formation and its evolution, one needs to solve the problem of ejection and collimation mechanisms in jets from young stars. By measuring the jet opening angle at the ejection region we can test models for jet origin. However this very small region cannot be investigated with current monolithic telescopes. Only the AMBER near-IR instrument coupled with the VLTI provides enough resolution to reach the ejection region and enough spectral resolution/coverage to properly separate the emission line jet from the continuum. In this proposal we show that expected visibilities from jets can constrain the jet opening angle.

Emission lines in GRBs constrain the total energy reservoir

The emission features observed in the X{ray afterglow of Gamma Ray Bursts are extremely powerful. Since they last at least for several hours, they imply energies of the order of 10 49 ergs. This in turn implies that the energy contained in the illuminating continuum thought to be responsible of the line production must exceed 10 51 ergs. This is a strong lower limit to the energy reservoir of Gamma Ray Bursts, which is independent of collimation and beaming, and bears important consequences on the possible collimation of the reball radiation and the density of the medium surrounding the burst. The discovery that Gamma Ray Bursts (GRBs) are cos- mological implies large luminosities, but the exact value of the radiated luminosities and the kinetic power of the re- ball originating the emission are still uncertain by a large factor, since we do not know if the emission is isotropic or if it is instead collimated in a cone. The main tool to esti- mate the degree of collimation of the emission has been, so far, the presence of an achromatic break in the lightcurves of the afterglows. This is interpreted as due to the deceler- ation of the reball, whose bulk Lorentz factor becomes smaller than the inverse of the jet opening angle j (see e.g. Rhoads 1999). This allows to estimatej and to obtain the \true values of the emitted energy. Most notably, in this respect, is the nding of Frail et al. (2001) who found a remarkable \clustering of the reball energy, once they are corrected by the estimate of their degree of collima- tion. Since the total power and energy are obviously the main parameters for the construction of any model, the importance of these estimates is obvious. These in turn are based on a number of assumptions, such as the den- sity of the matter surrounding the burst site, which is responsible for the deceleration of the reball, and on the key observation of the presence of an achromatic break in the light curve of the afterglow. Independent estimates of the \true energy, or even limits on it, are called for. In this paper we point out that the observed emission features observed in the X{ray afterglow spectra of several bursts can indeed put a rm lower limit to the emitted luminosity of GRBs. This limit is at the same time simple, independent of the degree of

Discovery of a Tight Correlation between Pulse Lag/Luminosity and Jet‐Break Times: A Connection between Gamma‐Ray Bursts and Afterglow Properties

A correlation is presented between the pulse lag and the jet-break time for seven BATSE gamma-ray bursts (GRBs) with known redshifts. This is, to the best of our knowledge, the first known direct tight correlation between a property of the gamma-ray burst phase (the pulse lag) and the afterglow phase (the jet-break time). As pulse lag and luminosity have been found to be correlated, this also represents a correlation between peak luminosity and jet-break time. Observed timescales (variability or spectral lags), as well as peak luminosity, naturally have a strong dependence on the Lorentz factor of the outflow, so we propose that much of the variety among GRBs has a purely kinematic origin (the speed or direction of the outflow). We explore a model in which the variation among GRBs is due to a variation in jet opening angles and find that the narrowest jets have the fastest outflows. We also explore models in which the jets have similar morphology and size, and the variation among bursts is caused by variations in viewing angles and/or due to velocity profiles. The relations between luminosity, variability, spectral lag, and jet-break time can be qualitatively understood from models in which the Lorentz factor decreases as a function of angle from the jet axis. One expects to see high luminosities, short pulse lags, and high variability as well as an early jet-break time for bursts viewed on-axis, while higher viewing inclinations will yield lower luminosities, longer pulse lags, smoother bursts, and later jet-break times.

Off-Axis Afterglow Emission from Jetted Gamma-Ray Bursts

We calculate gamma-ray burst (GRB) afterglow light curves from a relativistic jet as seen by observers at various viewing angles, θobs, relative to the jet axis. We describe three increasingly more realistic models and compare the resulting light curves. An observer at θobs < θ0, where θ0 is the initial jet opening angle, should see a light curve very similar to that for an on-axis observer. An observer at θobs > θ0 sees a rising light curve at early times, peaking when the jet Lorentz factor is ~1/θobs, and approaching that seen by an on-axis observer, at later times. A strong linear polarization (≲40%) may occur near the peak in the light curve and slowly decay with time. We show that, if GRB jets have a universal energy, then orphan afterglows are detectable up to a maximum offset angle that is independent of the jet initial aperture and thus at a rate proportional to the true GRB rate. We also discuss the implications of the proposed connection between SN 1998bw and GRB 980425.

Orphan Gamma‐Ray Burst Radio Afterglows: Candidates and Constraints on Beaming

The number of orphan radio afterglows associated with gamma-ray bursts (GRBs) that should be detected by a flux-limited radio survey is calculated. It is shown that for jetted GRBs, this number is smaller for a smaller jet opening angle ?, contrary to naive expectation. For a beaming factor f ? (?2/2)-1 500, roughly the value inferred by Frail et al. from analysis of afterglow light curves, we predict that between several hundred to several thousand orphan radio afterglows should be detectable (over all sky) above 1 mJy at GHz frequencies at any given time. This orphan population is dominated by sources lying at distances of a few hundred Mpc and having an age of ~1 yr. A search for pointlike radio transients with flux densities greater than 6 mJy was conducted using the FIRST and NVSS surveys, yielding a list of nine orphan candidates. We argue that most of the candidates are unlikely to be radio supernovae. However, the possibility that they are radio-loud active galactic nuclei cannot be ruled out without further observation. Our analysis sets a conservative 95% CL upper limit for the all-sky number of radio orphans, which corresponds to a lower limit f > 13 on the beaming factor. Rejection of all candidates found in our search would imply f > 80. This, and the possibility that some candidates may indeed be radio afterglows, strongly motivate further observations of these transients.

Implications of the Lag‐Luminosity Relationship for Unified Gamma‐Ray Burst Paradigms

Spectral lags (tau(sub lag)) are deduced for 1437 long (T(sub 90) greater than 2 s) BATSE gamma-ray bursts (GRBs) with peak flux F(sub p) greater than 0.25 photons cm(sup -2)/s, near to the BATSE trigger threshold. The lags are modeled to approximate the observed distribution in the F(sub p)-T(sub lag) plane, realizing a noise-free representation. Assuming a two-branch lag-luminosity relationship, the lags are self-consistently corrected for cosmological effects to yield distributions in luminosity, distance, and redshift. The results have several consequences for GRB populations and for unified gamma-ray/afterglow scenarios which would account for afterglow break times and gamma-ray spectral evolution in terms of jet opening angle, viewing angle, or a profiled jet with variable Lorentz factor: A component of the burst sample is identified - those with few, wide pulses, lags of a few tenths to several seconds, and soft spectra - whose Log[N]-Log[F(sub p)] distribution approximates a -3/2 power-law, suggesting homogeneity and thus relatively nearby sources. The proportion of these long-lag bursts increases from negligible among bright BATSE bursts to approx. 50% at trigger threshold. Bursts with very long lags, approx. 1-2 less than tau(sub lag) (S) less than 10, show a tendency to concentrate near the Supergalactic Plane with a quadrupole moment of approx. -0.10 +/- 0.04. GRB 980425 (SN 1998bw) is a member of this subsample of approx. 90 bursts with estimated distances less than 100 Mpc. The frequency of the observed ultra-low luminosity bursts is approx. 1/4 that of SNe Ib/c within the same volume. If truly nearby, the core-collapse events associated with these GRBs might produce gravitational radiation detectable by LIGO-II. Such nearby bursts might also help explain flattening of the cosmic ray spectrum at ultra-high energies, as observed by AGASA.

Evidence for initial jet formation by an accretion disk in the radio galaxy M87

The nearby E0 galaxy M87 in the Virgo Cluster contains one of the nearest examples of a powerful non-thermal jet source. In addition, HST spectroscopy of its nucleus give strong evidence for the presence of a ≈3×10 9 M ⊙ central black hole (corresponding to Schwarzschild radius R s ∼0.0004 pc). These two facts together make M87 the best possible target for studying the initial jet formation and collimation process. Herein we report new 43 GHz VLBI observations of the nucleus of this galaxy, which clearly show the jet opening angle expanding rapidly as one approaches the core on scales ∼0.01 pc. We believe we have, for the first time, imaged the initial collimation region of a powerful extragalactic jet. We find significant collimation occurring on scales of 30–100 R s , and argue this is consistent with expectations for poloidal collimation by a rotating accretion disk.

What can we learn about extragalactic jets from galactic jets?

Jets are powerful features of extragalactic radio sources; yet jets are also seen in young stellar objects and X-ray binaries within our own galaxy. These occupy a very different parameter space from the extragalactic jets, and yet many are similar in appearance and nature to their powerful extragalactic cousins. In many cases far more information is available for the galactic jets, due to, e.g., rapid evolution and knowledge of emission line ratios and Doppler velocities. We review properties of galactic jets and speculate at implications they have for extragalactic ones. Specifically we consider central engine mass, jet opening angle and Mach number, the nature of the emission knots, the symmetry of the ejection process, and the source history.

The Difficulty in Using Orphan Afterglows to Measure Gamma‐Ray Burst Beaming

If gamma-ray burst (GRB) emission is strongly collimated, then GRBs occur throughout the universe at a rate much higher than is detected. Since the emission from the optical afterglow is thought to be more isotropic than the gamma-ray emission, it has been hypothesized that a search for orphan afterglows (those without the triggering GRB) would allow strong constraints to be placed on the degree of GRB collimation. In this paper we establish that, within the context of leading models of GRB jet evolution, measurement of the GRB beaming angle θjet using optical orphan searches is extremely difficult, perhaps impossible in practice. We show that this is because, in the leading model of GRB jets, the effective afterglow beaming angle scales with the jet angle, Ωopt ∝ Ωjet for small angles, and so the ratio of detected orphan afterglows to GRBs is independent of the jet opening angle. Thus, the number of expected afterglow detections is the same for moderate jet angles (~20°) as for arbitrarily small jet angles (≪01). For nearly isotropic GRB geometry, or for radio afterglow searches in which the jet has become nonrelativistic, the ratio of afterglows to GRBs may give information on collimation. However, using a simple model we estimate the expected number of orphan detections in current supernova surveys and find this number to be less than 1 for all jet opening angles. Even for future supernova surveys, the small detection rate and lack of dependence on collimation angle appear to ruin the prospects of determining GRB beaming by this method. Radio searches may provide the best hope to find the missing orphans.

Microlensing of Collimated Gamma‐Ray Burst Afterglows

We investigate the stellar microlensing of collimated gamma-ray burst afterglows. A spherical afterglow appears on the sky as a superluminally expanding thin ring (a "ringlike" image), which is maximally amplified as it crosses a lens. We find that the image of the collimated afterglow becomes quite uniform (a "disklike" image) after the jet-break time (after the Lorentz factor of the jet drops below the inverse of the jet opening angle). Consequently, the amplification peak in the light curve after the break time is lower and broader. Therefore, detailed monitoring of the amplification history will be able to test whether afterglows are jets or not, i.e., disklike or not, if lensing occurs after the break time. We also show that some proper motion and polarization is expected, peaking around the maximum amplification. The simultaneous detection of proper motion and polarization will indicate that the brightening of the light curve is due to microlensing.

On the Kinematics of GRB 980425 and Its association with SN 1998[CLC]bw[/CLC

In this paper I put forward a model in which GRB980425 is both associated with SN1998bw and is also a standard canonical (long; ~seconds) gamma-ray burst. Herein it is argued that if gamma-ray bursts are relativistic jets with the fastest moving material at the core, then the range of observed jet inclinations to the line-of-sight produces a range in the observed properties of GRBs, i.e. the lag-luminosity relationship. In particular, if the jet inclination is high enough, the observed emitter will move slowly enough to render relativistic beaming ineffective, thus distinguishing the jet from apparent isotropic emission. Thus we expect a break in the lag-luminosity relationship. I propose that GRB980425 defines that break. The position of this break gives important physical parameters such as the Lorentz factor (\gamma_max ~ 1000), the jet opening angle (~1 degree), and thus the beaming fraction (~10^-4). Estimates of burst rates are consistent with observation. If correct, this model is evidence in favor of the collapsar mode as the progenitor of cosmological, long gamma-ray bursts.

Collimating, relativistic, magnetic jets from rotating disks

The magnetic flux distribution is determined by the solution of the Grad-Shafranov equation. With differential rotation, i.e. the variation of the iso-rotation parameter, the shape of the light surface must be calculated in an iterative way. For the first time, we have calculated the force-free magnetic structure of truly two-dimensional, relativistic jets, anchored in a differentially rotating disk. Such an approach allows for a direct connection between parameters of the central source (mass, rotation) and the extension of the radio jet. We present an analytical estimate for the jet opening angle along the asymptotic branches of the light surface. In general, differential rotation of the iso-rotation parameter leads to an increase of the jet opening angle. Comparison to the M87 jet shows agreement in the collimation distance. We derive a light cylinder radius of the M87 jet of 50 Schwarzschild radii.

On the Kinematic Origin of the Luminosity–Pulse Lag Relationship in Gamma-Ray Bursts

This Letter presents an interpretation based on gamma-ray burst source kinematics for the relationship found by Norris et al. between peak luminosity and energy-dependent pulse lag. I argue that the correlation should instead be between number luminosity and pulse lag. This interpretation improves the least-squares fit of this correlation for the known bursts by 25% or more. It also suggests a distance estimation scheme. I propose that this relationship is due to the variation in line-of-sight velocity among bursts. This interpretation allows one to speculate on the range of gamma-ray burst expansion velocities or the size of their jet opening angles.

Steepening of Afterglow Decay for Jets Interacting with Stratified Media

We calculate light curves for gamma-ray burst afterglows when material ejected in the explosion is confined to a jet that propagates in a medium with a power-law density profile. The observed light-curve decay steepens by a factor of Γ2 when an observer sees the edge of the jet. In a uniform density medium, the increase in the power-law index (β) of the light curve as a result of this edge effect is ~0.7 and is completed over one decade in observer time. For a preejected stellar wind (ρ ∝ r-2), β increases by ~0.4 over two decades in time as a result of the edge effect, and the steepening of the light curve as a result of the jet sideways expansion takes about four decades in time. Therefore, a break in the light curve for a jet in a wind model is unlikely to be detected even for a very narrow opening angle of a few degrees or less, a case where the lateral expansion occurs at early times when the afterglow is bright. The light curve for the afterglow of GRB 990510, for which an increase in β of approximately 1.35 was observed on a timescale of 3 days, cannot be explained by only the sideways expansion and the edge effects in a jet in a uniform interstellar medium—the increase in β is too large and too rapid. However, the passage of the cooling or synchrotron peak frequencies through the observing band at about 0.1-1 day together with jet edge effect explains the observed data. The jet opening angle is found to be ~5°, and the energy in the explosion to be about 1051 ergs.

A Jet Model for the Afterglow Emission from GRB 000301C

We present broadband radio observations of the afterglow of GRB 000301C, spanning from 1.4 to 350 GHz for the period of 3-130 days after the burst. These radio data, in addition to measurements in the optical bands, suggest that the afterglow arises from a collimated outflow, i.e., a jet. To test this hypothesis in a self-consistent manner, we employ a global fit and find that a model of a jet expanding into a constant-density interstellar medium (ISM + jet) provides the best fit to the data. A model of the burst occurring in a wind-shaped circumburst medium (wind-only model) can be ruled out, and a wind + jet model provides a much poorer fit of the optical/IR data than the ISM + jet model. In addition, we present the first clear indication that the reported fluctuations in the optical/IR are achromatic, with similar amplitudes in all bands, and possibly extend into the radio regime. Using the parameters derived from the global fit, in particular a jet break time tjet ≈ 7.3 days, we infer a jet opening angle of θ0 ≈ 0.2 rad; consequently, the estimate of the emitted energy in the GRB itself is reduced by a factor of 50 relative to the isotropic value, giving E ≈ 1.1 × 1051 ergs.