Afterglow lightcurves, viewing angle and the jet structure of gamma-ray bursts

Gamma ray bursts are often modelled as jet-like outflows directed towards the observer; the cone angle of the jet is then commonly inferred from the time at which there is a steepening in the power-law decay of the afterglow. We consider an alternative model in which the jet has a beam pattern where the luminosity per unit solid angle (and perhaps also the initial Lorentz factor) decreases smoothly away from the axis, rather than having a well-defined cone angle within which the flow is uniform. We show that the break in the afterglow light curve then occurs at a time that depends on the viewing angle. Instead of implying a range of intrinsically different jets - some very narrow, and others with similar power spread over a wider cone - the data on afterglow breaks could be consistent with a standardized jet, viewed from different angles. We discuss the implication of this model for the luminosity function.Comment: Corrected typo in Eq. 1

Importance of an Astrophysical Perspective for Textbook Relativity

The importance of a teaching a clear definition of the ``observer'' in special relativity is highlighted using a simple astrophysical example from the exciting current research area of ``Gamma-Ray Burst'' astrophysics. The example shows that a source moving relativistically toward a single observer at rest exhibits a time ``contraction'' rather than a ``dilation'' because the light travel time between the source and observer decreases with time. Astrophysical applications of special relativity complement idealized examples with real applications and very effectively exemplify the role of a finite light travel time.Comment: 5 pages TeX, European Journal of Physics, in pres

Events in the life of a cocoon surrounding a light, collapsar jet

According to the collapsar model, gamma-ray bursts are thought to be produced in shocks that occur after the relativistic jet has broken free from the stellar envelope. If the mass density of the collimated outflow is less than that of the stellar envelope, the jet will then be surrounded by a cocoon of relativistic plasma. This material would itself be able to escape along the direction of least resistance, which is likely to be the rotation axis of the stellar progenitor, and accelerate in approximately the same way as an impulsive fireball. We discuss how the properties of the stellar envelope have a decisive effect on the appearance of a cocoon propagating through it. The relativistic material that accumulated in the cocoon would have enough kinetic energy to substantially alter the structure of the relativistic outflow, if not in fact provide much of the observed explosive power. Shock waves within this plasma can produce gamma-ray and X-ray transients, in addition to the standard afterglow emission that would arise from the deceleration shock of the cocoon fireball.Comment: 16 pages, 5 figures, slightly revised version, accepted for publication in MNRA

The Minimum Description Length Principle and Model Selection in Spectropolarimetry

It is shown that the two-part Minimum Description Length Principle can be used to discriminate among different models that can explain a given observed dataset. The description length is chosen to be the sum of the lengths of the message needed to encode the model plus the message needed to encode the data when the model is applied to the dataset. It is verified that the proposed principle can efficiently distinguish the model that correctly fits the observations while avoiding over-fitting. The capabilities of this criterion are shown in two simple problems for the analysis of observed spectropolarimetric signals. The first is the de-noising of observations with the aid of the PCA technique. The second is the selection of the optimal number of parameters in LTE inversions. We propose this criterion as a quantitative approach for distinguising the most plausible model among a set of proposed models. This quantity is very easy to implement as an additional output on the existing inversion codes.Comment: Accepted for publication in the Astrophysical Journa

Predictions for The Very Early Afterglow and The Optical Flash

According to the internal-external shocks model for $\gamma$-ray bursts (GRBs), the GRB is produced by internal shocks within a relativistic flow while the afterglow is produced by external shocks with the ISM. We explore the early afterglow emission. For short GRBs the peak of the afterglow will be delayed, typically, by few dozens of seconds after the burst. For long GRBs the early afterglow emission will overlap the GRB signal. We calculate the expected spectrum and the light curves of the early afterglow in the optical, X-ray and $\gamma$-ray bands. These characteristics provide a way to discriminate between late internal shocks emission (part of the GRB) and the early afterglow signal. If such a delayed emission, with the characteristics of the early afterglow, will be detected it can be used both to prove the internal shock scenario as producing the GRB, as well as to measure the initial Lorentz factor of the relativistic flow. The reverse shock, at its peak, contains energy which is comparable to that of the GRB itself, but has a much lower temperature than that of the forward shock so it radiates at considerably lower frequencies. The reverse shock dominates the early optical emission, and an optical flash brighter than 15th magnitude, is expected together with the forward shock peak at x-rays or $\gamma$-rays. If this optical flash is not observed, strong limitations can be put on the baryonic contents of the relativistic shell deriving the GRBs, leading to a magnetically dominated energy density.Comment: 23 pages including 4 figure

Cosmological Origin of the Stellar Velocity Dispersions in Massive Early-Type Galaxies

We show that the observed upper bound on the line-of-sight velocity dispersion of the stars in an early-type galaxy, sigma<400km/s, may have a simple dynamical origin within the LCDM cosmological model, under two main hypotheses. The first is that most of the stars now in the luminous parts of a giant elliptical formed at redshift z>6. Subsequently, the stars behaved dynamically just as an additional component of the dark matter. The second hypothesis is that the mass distribution characteristic of a newly formed dark matter halo forgets such details of the initial conditions as the stellar "collisionless matter" that was added to the dense parts of earlier generations of halos. We also assume that the stellar velocity dispersion does not evolve much at z<6, because a massive host halo grows mainly by the addition of material at large radii well away from the stellar core of the galaxy. These assumptions lead to a predicted number density of ellipticals as a function of stellar velocity dispersion that is in promising agreement with the Sloan Digital Sky Survey data.Comment: ApJ, in press (2003); matches published versio

Measuring the eccentricity of the Earth orbit with a nail and a piece of plywood

I describe how to obtain a rather good experimental determination of the eccentricity of the Earth orbit, as well as the obliquity of the Earth rotation axis, by measuring, over the course of a year, the elevation of the Sun as a function of time during a day. With a very simple "instrument" consisting of an elementary sundial, first-year students can carry out an appealing measurement programme, learn important concepts in experimental physics, see concrete applications of kinematics and changes of reference frames, and benefit from a hands-on introduction to astronomy.Comment: 12 pages, 6 figure

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.Comment: Discussion added on gamma-ray emission efficiency. Accepted for publication in Ap.J. Let

Radiation Front Sweeping the Ambient Medium of Gamma-Ray Bursts

Gamma-ray bursts (GRBs) are emitted by relativistic ejecta from powerful cosmic explosions. Their light curves suggest that the gamma-ray emission occurs at early stages of the ejecta expansion, well before it decelerates in the ambient medium. If so, the launched gamma-ray front must overtake the ejecta and sweep the ambient medium outward. As a result a gap is opened between the ejecta and the medium that surfs the radiation front ahead. Effectively, the ejecta moves in a cavity until it reaches a radius R_{gap}=10^{16}E_{54}^{1/2} cm where E is the isotropic energy of the GRB. At R=R_{gap} the gap is closed, a blast wave forms and collects the medium swept by radiation. Further development of the blast wave is strongly affected by the leading radiation front: the front plays the role of a precursor where the medium is loaded with e+- pairs and preaccelerated just ahead of the blast. It impacts the emission from the blast at R < R_{load}=5R_{gap} (the early afterglow). A spectacular observational effect results: GRB afterglows should start in optical/UV and evolve fast (< min) to a normal X-ray afterglow. The early optical emission observed in GRB 990123 may be explained in this way. The impact of the front is especially strong if the ambient medium is a wind from a massive progenitor of the GRB. In this case three phenomena are predicted: (1) The ejecta decelerates at R<R_{load} producing a lot of soft radiation. (2) The light curve of soft emission peaks at t_{peak}=40(1+z)E_{54}^{1/2}(Gamma_{ej}/100)^{-2} s where Gamma_{ej} is the Lorentz factor of the ejecta. Given measured redshift z and t_{peak}, one finds Gamma_{ej}. (3) The GRB acquires a spectral break at 5 - 50 MeV because harder photons are absorbed by radiation scattered in the wind.Comment: 20 pages, accepted to Ap

Rings and Jets around PSR J2021+3651: the `Dragonfly Nebula'

We describe recent Chandra ACIS observations of the Vela-like pulsar PSR J2021+3651 and its pulsar wind nebula (PWN). This `Dragonfly Nebula' displays an axisymmetric morphology, with bright inner jets, a double-ridged inner nebula, and a ~30" polar jet. The PWN is embedded in faint diffuse emission: a bow shock-like structure with standoff ~1' brackets the pulsar to the east and emission trails off westward for 3-4'. Thermal (kT=0.16 +/-0.02 keV) and power law emission are detected from the pulsar. The nebular X-rays show spectral steepening from Gamma=1.5 in the equatorial torus to Gamma=1.9 in the outer nebula, suggesting synchrotron burn-off. A fit to the `Dragonfly' structure suggests a large (86 +/-1 degree) inclination with a double equatorial torus. Vela is currently the only other PWN showing such double structure. The >12 kpc distance implied by the pulsar dispersion measure is not supported by the X-ray data; spectral, scale and efficiency arguments suggest a more modest 3-4 kpc.Comment: 22 pages, 5 figures, 3 tables, Accepted to Ap