Mathematics – Logic
Scientific paper
Dec 1993
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1993aas...183.0415g&link_type=abstract
American Astronomical Society, 183rd AAS Meeting, #04.15; Bulletin of the American Astronomical Society, Vol. 25, p.1295
Mathematics
Logic
Scientific paper
\over riptstyle\sim}} The detection of an echo of a gamma-ray burst (GRB) caused by gravitational lensing is the only means of directly confirming the cosmological nature of bursts. The echo should appear within the same positional error box on the sky as the original burst, but will occur at a later time. The echo will have the same light curve and spectrum, although it will have a different amplitude. We propose a statistical test for comparing noisy light curves. The method, based upon comparing the Fourier transforms of light curves in the low frequency regime where signal dominates over noise, can reliably distinguish the distinct origin of two bursts at 3\sigma confidence as long as the peak of each burst has S/N\gsim 2.5. As an example, we demonstrate the discriminatory power of this statistic on the burst GRB 910503 (trigger 143). Adopting a standard candle cosmological model for GRB, we consider the probability that light echoes, caused by the known population of galaxies, will be observed by BATSE. If the lensing galaxies are taken to be isothermal spheres, we predict that there are \sim 0.3\pm 0.2 double bursts per year. As with quasar lensing, elliptical galaxies dominate the lensing probability. If we modify the lens model for elliptical galaxies to include small, but finite, core radii, or if we use a finite mass lens model, which may be suitable if ellipticals do not have massive halos, the rate of double bursts is reduced by about a factor of 2. Due to BATSE's 34% duty cycle, only \sim 12%$ of double bursts should be observed. The odds improve if there are multiple echoes, such as from an elliptical lens. Simulations show, however, that the chance of detecting a lensing event increases only by about 10%. Our most optimistic to most pessimistic estimate ranges from about one double burst every 2 years to about one every 20 years. Even though these time scales are comparable to the expected lifetime of BATSE, the inefficient duty cycle means probably none will be seen, unless some other type of hypothetical lens (MACHOs) is important.
Grossman Scott A.
Nowak Michael
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