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The nature of the central ``engine'' of many cosmic X- and $\gamma$-ray sources is still a subject of considerable debate. Current speculation is that many of these sources are powered by the gravitational field of a black hole. Conclusive evidence of the existence of black holes would be another milestone in confirming Einstein's theory of gravitation.
This dissertation reports the results of my studies of high time-resolution data on Cygnus~X-1 collected by the OSSE instrument on board the Compton Gamma-Ray Observatory. Three major observations were performed from June, 1991 to June, 1993. Time series data were collected in several energy bands with a time resolution of 4 milliseconds. Using Fast Fourier Transforms and other time-series analysis techniques, this OSSE data was examined on various timescales for evidence of flares and other time structures, both periodicities and overlapping shots.
The results indicate that the high-energy variability occurs over timescales implying a much larger source region for high-energy photons than many models predict. It is also proposed that modeling of the inner accretion region around black holes might better be performed using kinetic theory rather than adopting the fluid approximation.
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