Evidence For and Against Collimation of Gamma Ray Bursts

The degree to which gamma ray bursts are collimated is now the dominant uncertainty in their energy requirements and event rates. In this review I begin with the reasons for studying GRB collimation, then discuss existing tests for collimation and their applications to date, and finally outline some possible future tests. The most important conclusions are that (1) mean collimation angles much tighter than 1 degree appear ruled out; (2) the collimation angle appears to vary from burst to burst (like most other GRB properties). Some alternative explanations of apparent collimation signatures remain, but it should be possible to distinguish them from true collimation with future data sets and may be possible already. New satellites, improved followup observations, and new tests for collimation all promise continued rapid progress in coming years.Comment: Invited review at Ninth Marcel Grossmann Meeting. 8 pages, uses World Scientific macros (included

Gamma Ray Burst Beaming Constraints from Afterglow Light Curves: GRB 970508

The beaming angle (zeta) is the main uncertainty in gamma ray burst energy requirements today. We summarize predictions for the light curves of beamed bursts, and model the R band light curve of GRB 970508 to derive zeta > 30 degrees. This yields an irreducible minimum energy requirement of 3.4 times 10^{49} ergs to power the afterglow alone.Comment: 2 pages, one embedded postscript figure. To appear in Astronomy and Astrophysics Supplement series (Rome conference proceedings issue). Uses "aa" documentclas

Afterglows as Diagnostics of Gamma Ray Burst Beaming

If gamma ray bursts are highly collimated, radiating into only a small fraction of the sky, the energy requirements of each event may be reduced by several (up to 4 - 6) orders of magnitude, and the event rate increased correspondingly. The large Lorentz factors (Gamma > 100) inferred from GRB spectra imply relativistic beaming of the gamma rays into an angle 1/Gamma. We are at present ignorant of whether there are ejecta outside this narrow cone. Afterglows allow empirical tests of whether GRBs are well-collimated jets or spherical fireballs. The bulk Lorentz factor decreases and radiation is beamed into an ever increasing solid angle as the burst remnant expands. It follows that if gamma ray bursts are highly collimated, many more optical and radio transients should be observed without associated gamma rays than with them. In addition, a burst whose ejecta are beamed into angle zeta undergoes a qualitative change in evolution when Gamma < 1/zeta: Before this, Gamma ~ r^{-3/2}, while afterwards, Gamma decays exponentially with r. This change results in a potentially observable break in the afterglow light curve. Successful application of either test would eliminate the largest remaining uncertainty in the energy requirements and space density of gamma ray bursters.Comment: 5 pages, LaTex, uses aipproc and psfig style files. To appear in the proceedings of the Fourth Huntsville Gamma Ray Burst Symposiu

Cosmic Ray Rejection by Linear Filtering of Single Images

We present a convolution-based algorithm for finding cosmic rays in single well-sampled astronomical images. The spatial filter used is the point spread function (approximated by a Gaussian) minus a scaled delta function, and cosmic rays are identified by thresholding the filtered image. This filter searches for features with significant power at spatial frequencies too high for legitimate objects. Noise properties of the filtered image are readily calculated, which allows us to compute the probability of rejecting a pixel not contaminated by a cosmic ray (the false alarm probability). We demonstrate that the false alarm probability for a pixel containing object flux will never exceed the corresponding probability for a blank sky pixel, provided we choose the convolution kernel appropriately. This allows confident rejection of cosmic rays superposed on real objects. Identification of multiple-pixel cosmic ray hits can be enhanced by running the algorithm iteratively, replacing flagged pixels with the background level at each iteration.Comment: Accepted for publication in PASP (May 2000 issue). An iraf script implementing the algorithm is available from the author, or from http://sol.stsci.edu/~rhoads/ . 16 pages including 3 figures. Uses AASTeX aaspp4 styl

The Volume Fraction of Ionized Intergalactic Gas at Redshift z=6.5

The observed number density of Lyman-alpha sources implies a minimum volume of the inter-galactic medium that must be ionized, in order to allow the Lyman-alpha photons to escape attenuation. We estimate this volume by assigning to each Lyman-alpha emitter the minimum Stromgren sphere that would allow half its Lyman-alpha photons to escape. This implies a lower limit to ionized gas volume fraction of 20-50% at redshift z=6.5. This is a lower limit in two ways: First, we conservatively assume that the Lyman-alpha sources seen (at a relatively bright flux limit) are the only ones present; and second, we assume the smallest Stromgren sphere volume that will allow the photons to escape. This limit is completely independent of what ionizing photon sources produced the bubbles. Deeper Lyman-alpha surveys are possible with present technology, and can strengthen these limits by detecting a higher density of Lyman-alpha galaxies.Comment: Submitted to ApJ Letter

Infrared Counterpart of the Gravitational Lens 1938+66.6

We report the detection of a very red source coincident with the gravitational lens 1938+66.6 (Patnaik et al. 1992) in K' (2.12 micron), H (1.6 micron), J (1.25 micron), and Thuan-Gunn r (0.65 micron) bands. 1938+66.6 has previously been detected as a partial radio ring indicating lensing. We find K'=17.1 +- 0.1 and r = 23.9 +- 0.2, making it a very red source with (r-K')=6.8 +- 0.25. We also observed in Thuan-Gunn g band (0.49 micron) and found g>24.5 at the 90% confidence level. We interpret our observations as a reddened gravitational lens on the basis of its optical-IR color and positional coincidence with the radio source.Comment: 8 pages, one PostScript figure; uses AAS LaTeX macros. Accepted for publication in The Astronomical Journa

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