In this thesis we analyse X-ray data of accretion powered low mass and high mass X-ray binaries to understand the nature of their accretion mechanisms by searching for some clues of viscous time-scales of their accretion discs, if they have, in their low frequency power density spectra created from their long-term X-ray observations, or by doing pulse timing analysis with much shorter X-ray data to detect the effects of torque fluctuations caused by the accreting material on the pulsar. The low mass and high mass X-ray binaries we analysed have breaks in their power density spectra, which are attributed to the role of viscosity in the formation of accretion discs. Although, the time-scales corresponding to these break frequencies are smaller than the predictions of the Standard theory of accretion discs, the sources give consistent results among themselves by displaying the expected correlation between their break and orbital frequencies. The correlation curve of LMXBs implies thicker appearing accretion discs than those assumed by the theory. The dichotomy of the HMXBs on this curve points out the different origins of accretion that these sources may have, and offers a way to distinguish the stellar-wind fed systems from the Roche-lobe overflow systems. The timing and spectral analysis of Swift J1626.6-5156 reveal a correlation between the spin-up rate and the luminosity of the source implying that the pulsar is accretion-powered. This correlation together with the characteristics of the X-ray spectra enables us to estimate the magnetic field and the distance of the source. The AXP 1E 2259+586 does not display any signs of viscous time-scale in its low frequency power density spectra, and its pulse timing analysis gives a much smaller torque noise value than that expected from accretion powered pulsars. In addition, the analysis results presented in this thesis reveal magnetar-like glitches which differ than those of radio pulsars, due to the presence of the strong magnetic field of the pulsar. These results eliminate the possibility that the AXP is an accretion-powered pulsar.

In this thesis, RXTE observations of 4U 1907+09 are presented. Timing analysis of these data sets have yielded quasi periodic oscillations (QPOs) at orbital phases corresponding to the two flares in every orbital period. Known continuous spin down trend and QPO behaviour at the flares strongly suggest that a transient accretion disk occurs at the flares. Our findings strongly suggested that neutron star passes through the equatorial wind of Be companion star. During these passages a transient disk forms around Be neutron star.

In this thesis, X-ray spectral and pulse timing analysis of the high mass X-ray binary pulsar 4U 1907+09, based on the observations with Rossi X-ray Timing Explorer (RXTE) and International Gamma-Ray Astrophysics Laboratory (INTEGRAL), are presented. INTEGRAL (October 2005 - November 2007) and RXTE (June 2007 - December 2008) observations confirm that the luminosity of the source is highly variable such that, flaring and dipping activities are observed. The results of time-averaged energy spectra of RXTE and INTEGRAL observations are consistent with the previous studies. Orbital phase resolved spectroscopy with RXTE data, reveals that the Hydrogen column density varies through the orbit reaching to its maximum value just after periastron. This variation approves that the location of the absorbing material is the accretion flow. A slight spectral softening with increasing luminosity is aslo observed. 4U 1907+09 had been steadily spinning down for more than ~15 years with a rate of -3.54x10-14 Hz s-1. RXTE observations of the source in 2001 showed a ~60% decrease in the spin-down rate and INTEGRAL observations in 2003 showed a reversal to spin-up. The timing analysis presented in this thesis reveals a new spin-down episode with a rate of -3.59x10-14 Hz s-1, which is close to the previous steady spin-down rate. This result implies that a recent torque reversal before June 2007 has taken place. The reversal is a rare event for 4U 1907+09 and it indicates the variations in the mass accretion rate and/or geometry. Using RXTE observations, 24 new pulse periods are measured to demonstrate the period evolution. Energy resolved pulse profiles confirm that the profile has a double peak sinusoidal shape at energies below 20 keV, whereas the leading peak significantly loses its intensity above 20 keV. This energy dependence indicates that the physical circumstances of the two polar caps are different.

In this thesis, X-ray observations of four accretion powered pulsars are presented. Using RXTE observations of 4U 1907+09, we found three new pulse periods of the source. We found that the source spun-down almost at a constant rate of $dot nu$ = (-3.54 $pm 0.02) times 10^{-14}$ Hz s$^{-1}$ for more than 15 years. Using RXTE observations, X-ray flux related spectral and timing features in 2S 1417-62 were, in general, interpreted as a sign of a disc accretion with a similar geometry with a varying mass accretion rate, whereas spectral and timing features of the low X-ray flux regions were interpreted as a sign of possible temporary accretion geometry change prior to the next periastron. Using XMM-Newton and RXTE observations of SAX J2103.5+4545, we discovered quasi periodic oscillations around 0.044 Hz (22.7 sec) while the source was spinning-up with a rate of $(7.4pm0.9)times10^{-13}$Hz s$^{-1}$. In the X-ray spectrum, we also found a soft component consistent with a blackbody emission with ${rm{kT}}sim1.9$keV. Using RXTE observations, we also studied spectral evolution of Her X-1

This thesis concerns with the study of X-ray binaries which are gravitationally bound systems consisting of a compact object (either a neutron star or a black hole) and usually a non degenerate companion star, both rotating around the common centre of mass. The compact star shines brightly in the X-ray regime. Emission from these systems are powered by accretion which is the most radioactively efficient mechanism known in the universe by the release of gravitational potential energy when matter from the companion star falls on the compact object. Accretion onto high magnetic field neutron stars are special as the magnetic field plays a crucial role in governing the dynamics of gas flow and the flow of the matter close to the compact object. The radiation emitted from these systems are anisotropic and for a distant observer, the intensity is modulated at the spin period of the neutron star, hence these objects are called accretion powered pulsars. The angular pattern of the emitted radiation is also highly anisotropic and depends on the mass accreted and hence the luminosity. The beaming pattern commonly known as the pulse profiles exhibit a wide variety in the pulse shape and pulse fraction and vary with energy as well as intensity. They also exhibit cyclotron absorption features in their energy spectrum which are a direct probe to the magnetic field geometry of these systems. This thesis is dedicated to the study of the magnetic field and emission geometry of accretion powered pulsars through the pulse phase resolved studies of the cyclotron absorption features which are a direct probe of the magnetized plasma. In order to study these features in detail broadband continuum modeling of the energy spectrum is done, taking care of all other factors which may smear the pulse phase dependence. Another prerequisite for detailed continuum modeling is accounting for the low absorption dips in the pulse profiles of many these sources. The dips are presumably formed by phase locked accretion stream causing partial covering absorption when the stream is along our line of sight towards the emission region. Studying the pulse phase dependence of this partial covering absorber also provides us with important clues on the local environment of the neutron star and the structure of the accretion stream. All of these studies are performed with data from the broadband and most sensitive instruments onboard the Japanese satellite Suzuki. Lastly we provide estimates of the polarization expected to be detected from these sources by a Thomson scattering polarimeter being developed to observe the polarization of X-rays in the energy range of 5--30 keV. Along with the X-ray pulsars, we also make an estimate of the likelihood of detection of X-ray polarization from black hole X-ray binaries in different spectral states. This is a particularly interesting topic as it will play a crucial role in providing additional handles on the magnetic field geometry in accretion powered pulsars as well as constrain the fundamental parameters of a black hole like its spin.