Grb Statistical Studies Of The Structural Model Of The Spectrum Of Nature And The Jets

The history and actuality of the observational and theoretical studies on gamma-ray bursts (GRBs) and their afterglows are reviewed. The theoretical models of this field are introduced in detail and some problems of these models are discussed. The statistical properties of the spectrum and the jet structure of GRBs are investigated.We investigate the global spectral behaviors of GRB population, including long GRB sample, short GRB sample, and X-ray flashes (XRFs), in a HR-Ep plane with BATSE and HETE-2 observations. Fitting the sequence by a universal Band function, we find that: (1) the long GRBs and the XRFs observed by HETE-2 seem to follow the same sequence in the HR-E_p plane, and the XRFs are in the low end of this sequence; (2) this sequence of long GRBs and the XRFs is mainly depicted by α , while β is numerically unstable; (3) the sequences of the long and short GRBs observed by BATSE in the HR-E_p plane are significantly different from that of the long GRBs. In the HR-E_p plane, most of the short GRBs are above the long GRB sequence, indicating that the short GRBs tend to have larger HR than the long GRBs at a given E_p; (4) a best-fit gives α =-0. 30 and β =-2. 05 for the BATSE long GRBs; (5)the α value of the short GRB sequence is significantly greater than that of the long GRBs.We test the viewing angle distributions of GRB predicted by the universal jet model with long-duration BATSE GRBs. Firstly, we assumingthat the observed GRB rate is proportional to the star formation rateincorporating with observational biases. Sencondly, we obtain P^ob(θ) and P^ob(θ, z) by a tight correlation of E_r-E_p. Finally, We test different universal structured jet (USJ) models by comparing model predictions, P^th(θ) and P^th(θ , z) with our empirical results. To make the comparison reasonable, an "effective" threshold is used when we derive the USJ model predictions. The comparisons show that single Gaussian jet and power-law jet can not give compatible consistency for both P^th(θ) and P^th(θ , z) with our empirical results; while a jet with two Gaussian components can yield acceptable consistency.