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 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

Optimizing Air Force Depot Programming to Maximize Operational Capability

The Air Force wants to improve the link between resources and weapons system readiness by reducing costs, improving risk-based decision making, and balancing costs with performance. With that in mind, RAND Project Air Force developed a linear programming model linking Depot Purchased Equipment Maintenance to operational capability. This thesis examined that model, provided an alternate model, and then developed a new model that determined the minimum cost necessary to maintain the force structure. The utility of using the models using Weapon System Sustainment (WSS) and additional sources of data for aircraft and engine inventories was evaluated and critiqued. While every WSS requirement has a cost, the vast majority do not have quantities associated with them. Using the sources outlined for aircraft and engine inventories does not match up with WSS data. Aircraft inventory data is more specific than the WSS data requirements. Engine inventories are managed by engine type, not by aircraft. Many engines serve multiple aircraft, and many aircraft require multiple engines. The combined result is that using WSS data to process these models and obtain meaningful results is not possible at this time