Spectral Lags and Variability of Gamma-ray Bursts in the Swift Era

Gamma-ray bursts (GRBs) are thought to be the most concentrated and brightest explosions in the universe, making them observable to very great distances. Hence GRBs can be used to probe the early universe, including the re-ionization period as well as the intergalactic medium. GRBs may also be used to study the biggest mystery of our time: 'Dark Energy'. However, unlike Supernove 1a, GRBs as yet are not good standard candles. Hence, in order to use GRBs to connect luminosity and distance, we need GRB Luminosity Relations. Over the years people have proposed a number of GRB luminosity relations. Unfortunately, none of them are tight enough to be used individually to construct the GRB Hubble Diagram. However, by combining multiple GRB luminosity relations we can construct a GRB Hubble diagram that may be able to constrain cosmological parameters. Thus, it is important to study and improve existing GRB luminosity relations and perhaps discover new GRB luminosity relations. In addition to helping to improve our understanding of Dark Energy, these GRB luminosity relations are very useful to understand the underlying physics of GRBs. One major limiting factor in GRB luminosity relation studies is the low statistics. Before the Swift mission there were very few GRBs with measured redshifts. But now in the Swift era we have more than 150 GRBs with measured redshifts. In this work we have utilized this high-quality data set to study two GRB luminosity relations. In Part-I we extracted spectral lags and studied the lag-luminosity relation. The spectral lag is the time difference between the arrival of high-energy and low-energy photons. To quantify this lag we have developed an improved method based upon the cross correlation function. With this method we investigated the lag-luminosity relation over the entire Swift Burst Alert Telescope (BAT) energy range. Typically, a spectral lag is extracted in two arbitrary energy bands in the observer-frame. However, because of the redshift dependance of GRBs, the two energy bands can correspond to multiple energy bands in the source-frame. Thus, introducing a variable energy dependant factor into the lag-luminosity relation. We avoid this difficulty by defining two energy bands in the GRB source-frame and projecting these two bands into the observer-frame and extracting lags between them. This work has led to a significant improvement in the robustness of the lag-luminosity relation. In Part-II we studied the variability of GRBs using Fourier analysis and introduce a new GRB luminosity relation. We extract a maximum frequency at which there is still significant signal power and associate this threshold frequency with the isotropic luminosity of the burst. As a result of this study, we propose a potential correlation between isotropic peak luminosity and the extracted threshold frequency. In this investigation, we study in detail the potential observational biases in the frequency-luminosity relation. In Part-III we investigate long-term correlations and variability in GRB prompt emission light curves using the Hurst rescaled range analysis technique. As far as we know this is the first time this technique has been applied to GRBs. Based on this analysis, we present evidence indicating that the prompt emission of GRB light curves show anti-persistence