Angular size and emission time scales of relativistic fireballs

The detection of delayed X-ray, optical and radio emission, ``afterglow,'' associated with gamma-ray bursts (GRBs) is consistent with models, where the bursts are produced by relativistic expanding blast waves, driven by expanding fireballs at cosmological distances. In particular, the time scales over which radiation is observed at different wave bands agree with model predictions. It had recently been claimed that the commonly used relation between observation time t and blast wave radius r, t=r/2\gamma^{2}c where \gamma(r) is the fluid Lorentz factor, should be replaced with t=r/16\gamma^{2}c due to blast wave deceleration. Applying the suggested deceleration modification would make it difficult to reconcile observed time scales with model predictions. It would also imply an apparent source size which is too large to allow attributing observed radio variability to diffractive scintillation. We present a detailed analysis of the implications of the relativistic hydrodynamics of expanding blast waves to the observed afterglow. We find that modifications due to shock deceleration are small, therefore allowing for both the observed afterglow time scales and for diffractive scintillation. We show that at time t the fireball appears on the sky as a narrow ring of radius h=r/\gamma and width 0.1h, where r and t are related by t=r/2\gamma^{2}c.Comment: Submitted to ApJL (11 pages, LaTeX

On the nature of gamma-ray burst time dilations

The recent discovery that faint gamma-ray bursts are stretched in time relative to bright ones has been interpreted as support for cosmological distances: faint bursts have their durations redshifted relative to bright ones. It was pointed out, however, that the relative time stretching can also be produced by an intrinsic correlation between duration and luminosity of gamma-ray bursts in a nearby, bounded distribution. While both models can explain the average amount of time stretching, we find a generic difference between them in the way the duration distribution of faint bursts deviates from that of bright ones. This allows us to distinguish between these two broad classes of model on the basis of the duration distributions of gamma-ray bursts, leading perhaps to an unambiguous determination of the distance scale of gamma-ray bursts. We apply our proposed test to the second BATSE catalog and conclude, with some caution, that the data favor a cosmological interpretation of the time dilation.Comment: 9 pages uuencoded compressed postscript including 2 figures, Princeton University Observatory preprint POP-567. Submitted to Astrophysical Journal Letters, 2 June 199

Microlensing of γ\gamma-Ray Burst Afterglows

The afterglow of a cosmological Gamma-Ray Burst (GRB) should appear on the sky as a narrow emission ring of radius 3x10^{16}cm(t/day)^{5/8} which expands faster than light. After a day, the ring radius is comparable to the Einstein radius of a solar mass lens at a cosmological distance. Thus, microlensing by an intervening star can modify significantly the lightcurve and polarization signal from a GRB afterglow. We show that the achromatic amplification signal of the afterglow flux can be used to determine the impact parameter and expansion rate of the source in units of the Einstein radius of the lens, and probe the superluminal nature of the expansion. If the synchrotron emission from the afterglow photosphere originates from a set of coherent magnetic field patches, microlensing would induce polarization variability due to the transient magnification of the patches behind the lens. The microlensing interpretation of the flux and polarization data can be confirmed by a parallax experiment which would probe the amplification peak at different times. The fraction of microlensed afterglows can be used to calibrate the density parameter of stellar-mass objects in the Universe.Comment: 12 pages, latex, 2 figures, submitted to ApJ

The Vela pulsar `jet': a companion-punctured bubble of fallback material

Markwardt and Oegelman (1995) used ROSAT to reveal a 12 by 45 arcmin structure in 1 keV X rays around the Vela pulsar, which they interpret as a jet emanating from the pulsar. We here present an alternative view of the nature of this feature, namely that it consists of material from very deep inside the exploding star, close to the mass cut between material that became part of the neutron star and ejected material. The initial radial velocity of the inner material was lower than the bulk of the ejecta, and formed a bubble of slow material that started expanding again due to heating by the young pulsar's spindown energy. The expansion is mainly in one direction, and to explain this we speculate that the pre-supernova system was a binary. The explosion caused the binary to unbind, and the pulsar's former companion carved a lower-density channel into the main ejecta. The resulting puncture of the bubble's edge greatly facilitated expansion along its path relative to other directions. If this is the case, we can estimate the current speed of the former binary companion and from this reconstruct the presupernova binary orbit. It follows that the exploding star was a helium star, hence that the supernova was of type Ib. Since the most likely binary companion is another neutron star, the evolution of the Vela remnant and its surroundings has been rather more complicated than the simple expansion of one supernova blast wave into unperturbed interstellar material.Comment: submitted to MNRAS; 6 pages laTeX, 3 figures (1 postscript, 2 gif files of images

The Dynamics and Light Curves of Beamed Gamma Ray Burst Afterglows

The energy requirements of gamma ray bursts have in past been poorly constrained because of three major uncertainties: The distances to bursts, the degree of burst beaming, and the efficiency of gamma ray production. The first of these has been resolved, with both indirect evidence (the distribution of bursts in flux and position) and direct evidence (redshifted absorption features in the afterglow spectrum of GRB 970508) pointing to cosmological distances. We now wish to address the second uncertainty. Afterglows allow a statistical test of beaming, described in an earlier paper. In this paper, we modify a standard fireball afterglow model to explore the effects of beaming on burst remnant dynamics and afterglow emission. If the burst ejecta are beamed into angle zeta, the burst remnant's evolution changes qualitatively once its bulk Lorentz factor Gamma < 1/zeta: Before this, Gamma declines as a power law of radius, while afterwards, it declines exponentially. This change results in a broken power law light curve whose late-time decay is faster than expected for a purely spherical geometry. These predictions disagree with afterglow observations of GRB 970508. We explored several variations on our model, but none seems able to change this result. We therefore suggest that this burst is unlikely to have been highly beamed, and that its energy requirements were near those of isotropic models. More recent afterglows may offer the first practical applications for our beamed models.Comment: 18 pages, uses emulateapj.sty, four embedded postscript figures. Submitted to The Astrophysical Journal, 199

Physical parameters of GRB 970508 and GRB 971214 from their afterglow synchrotron emission

We have calculated synchrotron spectra of relativistic blast waves, and find predicted characteristic frequencies that are more than an order of magnitude different from previous calculations. For the case of an adiabatically expanding blast wave, which is applicable to observed gamma-ray burst (GRB) afterglows at late times, we give expressions to infer the physical properties of the afterglow from the measured spectral features. We show that enough data exist for GRB970508 to compute unambiguously the ambient density, n=0.03/cm**3, and the blast wave energy per unit solid angle, E=3E52 erg/4pi sr. We also compute the energy density in electrons and magnetic field. We find that they are 12% and 9%, respectively, of the nucleon energy density and thus confirm for the first time that both are close to but below equipartition. For GRB971214, we discuss the break found in its spectrum by Ramaprakash et al. (1998). It can be interpreted either as the peak frequency or as the cooling frequency; both interpretations have some problems, but on balance the break is more likely to be the cooling frequency. Even when we assume this, our ignorance of the self-absorption frequency and presence or absence of beaming make it impossible to constrain the physical parameters of GRB971214 very well.Comment: very strongly revised analysis of GRB971214 and discussion, submitted to ApJ, 11 pages LaTeX, 4 figures, uses emulateapj.sty (included

Identifying the Environment and Redshift of GRB Afterglows from the Time-Dependence of Their Absorption Spectra

The discovery of Gamma-Ray Burst (GRB) afterglows revealed a new class of variable sources at optical and radio wavelengths. At present, the environment and precise redshift of the detected afterglows are still unknown. We show that if a GRB source resides in a compact (<100pc) gas-rich environment, the afterglow spectrum will show time-dependent absorption features due to the gradual ionization of the surrounding medium by the afterglow radiation. Detection of this time-dependence can be used to constrain the size and density of the surrounding gaseous system. For example, the MgII absorption line detected in GRB970508 should have weakened considerably during the first month if the absorption occurred in a gas cloud of size <100pc around the source. The time-dependent HI or metal absorption features provide a precise determination of the GRB redshift.Comment: 13 pages, 4 figures, submitted to ApJ