Statistical Analysis Of The Observed Data Of Gamma-ray Bursts

Gamma-Ray Burst (GRB) is a phenomenon of short and intense pulses of gammarays occurred in space. GRBs were unexpected discovery in the late1960s by the Velasatellite, which caused widespread concern of astronomers and astrophysicists. In the lasttwo decades, some space missions---CGRO/BATSE, BeppoSAX, HETE II(High–Energy Transient Explorer), together with the ground–based optical, infrared, andradio observatories are changing our understanding of GRBs. GRBs are cosmologicalevents and accompanied with long–lasting afterglows. The Swift satellite dedicated tostudy the GRBs and the Fermi satellite covering large energy range, successfully launchedin2004and2008respectively, have taken us into a new era of GRB research.The main direction of this thesis is the correlation between Lorentz factor and meanisotropic luminosity/energy of GRBs, and interpretation with neutrino dominated accretionflow (NDAF) model of central engine of GRBs. This work involves the central engine ofGRB and data statistical analysis of observed quantities of GRBs. The thesis is structuredas follows: Chapter I is the review of GRBs, including the observations of promptradiation and afterglow of GRBs, radiation mechanisms, central engine of GRBs andsome important relations of GRBs. In Chapter II, we give the statistical fitting andtheoretical analysis with NDAF model between initial Lorentz factor and the isotropicequivalent luminosity or isotropic equivalent energy of GRBs. The initial Lorentz factor isa very important parameter to understand the physics of GRBs, especially forunderstanding the physical origin of the prompt GRB emission phase. We apply severalcommonly used methods to constrain the initial Lorentz factor of GRBs in Chapter II, andgive the details of NDAF model and the Lorentz factor statistics of51GRBs with knownredshifts. Chapter III is about the correlation studies between radio luminosity and X-rayluminosity of GRBs, and whether the relationship can be extended to the sun, cool starsand active galactic nuclei. Finally, we summarize the important findings of GRBs in thepast several years and the problems we hope to solve in future.This thesis provides detailed calculations of the initial Lorentz factor of gamma-ray burst, and gives the relationship between initial Lorentz factor and isotropic equivalentluminosity of GRBs, meanwhile it proposes an interpretation to the statistical correlationwithin the framework of a blackhole-NDAF disk GRB central engine model.