The aim of this research was to use the X-ray satellite Suzaku to establish a picture of a central engine that effectively converts the gravitational energy of accreting matter onto the supermassive black hole to a huge amount of radiation in an active galactic nucleus. Although the engine is known to consist of a Comptonizing corona and an accretion disk, its image has remained unclear because primary emissions, coming directly from the engine, cannot be identified in X-ray spectra without models. The book describes a technique of time variability assisted spectral decomposition to model-independently examine X-ray signals, and how this was applied to the Suzaku archive data of active galactic nuclei. As a result, at least three distinct primary X-ray components have been discovered in an X-ray from an active galactic nucleus, presumably indicating a novel picture that the engine is composed of multiple coronae with different physical properties in an accretion flow. Furthermore, the determination of the spectral shapes of the primary X-rays has a significant impact on estimations of black hole spins, because it is essential to quantify reprocessed X-ray spectra. The successful model-independent decomposition of X-ray spectral components with flux variations of active galactic nuclei is likely to be effective in future data analyses from the soon-to-be-launched Japanese X-ray satellite ASTRO-H, which is capable of achieving unprecedented fine spectros copy and broad energy band coverage.

This thesis brings together the various techniques of X-ray spectral analysis in order to examine the properties of black holes that vary in mass by several orders of magnitude. In all these systems it is widely accepted that the X-ray emission is produced by Compton up-scattering of lower energy seed photons in a hot corona or accretion flow, and here these processes are examined through a study of the X-ray spectral variability of each source. A new technique is introduced, in which models are fitted to over 2 million X-ray spectra on time-scales as short as 16 ms, and subsequently it is shown that the nature of the correlation between intensity and spectral index is strongly dependent upon the spectral state of the black hole. Finally, the results of an extensive survey of nearby galactic nuclei using the Chandra X-ray telescope are presented in the form of images and spectra, and these results are used along with data from the literature to search for Compton-thick nuclei.

The cosmic x-ray background is diffuse, uniform x-ray radiation originating from outside our galaxy. Over the past several decades since its discovery, much of it has been resolved into discrete sources. However, a fraction of the x-ray background still remains unresolved. This remaining fraction is composed of sources from the very early universe, and high energy processes from this time period have major impacts on the modern universe. We cannot observe these sources directly, but we can observe how the unresolved x-ray background varies over time. Sources such as active galactic nuclei are known to have variable fluctuations in brightness while galaxies do not, so by measuring the variability in brightness of individual x-ray background pixels over time, we can infer whether or not it is comprised of mostly active galactic nuclei or galaxies. We analyze x-ray images of the same area of sky taken at different points in time and measure the standard deviation of individual pixels in order to measure how they vary in brightness over time. We compare this to a mock dataset generated using the average pixel value of our experimental dataset following a random Poisson distribution that simulates a non-variable x-ray background. Our results indicate that the unresolved cosmic x-ray background is not variable, thus we infer that it is most likely primarily due to galaxies from the very early universe. This has significant cosmological implications because these are likely to be x-rays radiated from the very first generation of stars. Studying the unresolved cosmic x-ray background provides insight into what sort of high energy processes occurred in the early universe and how those processes shaped the universe that we observe today.