| Gamma-ray burst (GRB) is a kind of phenomenon that is the energy burst in gamma rays with a short duration. It was discovered for the first time by Vela satellite in 1976 by chance. In 1973, a paper including 16 bursts discovered by Vela was published in ApJL, which marks the official discovery of GRB. For GRB is characterized by short duration, complicated structure of light curves and a large quantity of energy output, which is even more than supernova explosion, it have caused a wide concern. Though many progresses have been made to date, some intrinsic issues haven't solved, such as what is the origin of GRB, how gamma rays are produced and so on. Recently, Swift is launched successfully, some new characters have been observed, which is the base for us to study the early afterglow properties and then understand the properties of GRB.In my thesis, the observational and theory progresses are reviewed, and some works including the problems of GRB efficiency , energetics and early afterglow properties are introduced during my pursuing PHD. This thesis consists of three parts. The first chapter is review, the second to the fourth ones are my works and the last chapter is the problems and prospects.In the second chapter, we study jet sideways expansion effect on estimating the GRB efficiency. Usually, the isotropic equivalent energy is calculated with the prompt emission and late afterglow data and the efficiency is derived. This is only valid for the case that jet opening angles are the same during the two phases. However, jet sideways expansion can exist during the outward expansion of jet. In this case, the usual method to estimate the GRB efficiency is not valid. We calculate the evolution of jet opening angles numerically and derive the collimation-corrected emission and kinetic energy. We find that with the typical parameters, the GRB efficiency is decreased by a factor of 1/2 (for the typical efficiency 0.1). If the circumburst is dense, this effect is more significant. We also take two pre-swift bursts (GRB 980703 and GRB 000926) for case studies, which confirm our previous results. So when the efficiency is derived with the late afterglow data, jet sideways expansion effect needs to be considered.In the third chapter, we use the numerical method to calculate the initial jet opening angle of GRB. The opening angle is usually derived with the afterglow light curve breaks through an analytical method with the assumption that the speed of expanding laterally is the light speed. This is only valid approximately. At the late time, the jet enters a phase of a moderate relativistic expansion, so this assumption is invalid. A more reasonable assumption is that the jet expands laterally at the comoving sound speed c_s. Using the hydrodynamic evolution equation group with the sideways expansion at the local sound speed derived by previous authors and the observed light curve breaks, we numerically derive the initial opening angles. With a new sample of GRB, we make a statistical study, and find that the energy clustering seems not to exist. We also test the E_p—E_γrelation, and find that the correlation improve slightly, while the power change from 0.71 to 0.64, which may provide constrain on model to interpret this relation in theory.In the fourth chapter, we consider a possible case that the GRB jet may travel in a curve line like the observed AGN jet. For a large Lorentz factor (7 > 100), a slight change of the view line angle will cause a significant light curve variation. Without knowing the mechanism of the bent of jet, we assume two relations between the view line angle and the observed time, and the light curve is calculated. We find some of the resulted light curves are similar to the observed ones. We argue that for some burst, the early X-ray afterglow may result from the bent of GRB jet.In the last chapter, we summarize the present problems in GRB. Some ideas are presented for some concrete problems. We also present a brief introduction to GLAST satellite and propose prospects.
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