Doppler Effect Of Fireballs On The Light Curves Of Gamma-ray Bursts

We summarize the observational and theoretical results of Gamma-ray bursts (GRBs), and present in detail the results of our three researches on the Doppler effect of fireballs on the light curves of GRBs based on Qin model.The first is the prediction of there exists a reverse "S"-feature curve in the decay portion of the light curves of GRBs. we begin with the derived formulas of Qin model, and then two decay curves are given: one is the marginal decay curve which is associated with a local 6 function pulse with a monocolour radiation, another is the standard decay curve which is associated with a local 5 function pulse with a rest frame Band function radiation. Our theoretical analyses show that, light curves associated with local pulses without a decaying portion would bear the standard decay form in their decaying phase, whereas there would be a reverse "S" -feature deviation of the light curves arising from local pulses containing a decaying portion from the standard decay form, i.e., there is a "positive" deviation (over the standard form) of the light curves from the standard decay form within the range of fore-FWHM, and a "negative" deviation in the range of post-FWHM. Then we employ the sample of Kocevski, Ryde & Liang to check this prediction and find that the phenomenon of the reverse S-feature is common, when compared with both the standard decay form and the marginal decay curve. We accordingly propose to take the marginal decay curve (whose function is simple) as a criterion to check if an observed pulse could be taken as a candidate suffered from the Doppler effect.Secondly, we investigate the linear relationship between the full width at half-maximum (FWHM) and the rise width of the observed pulse found by Kocevski Ryde & Liang (2003). Our theoretical analyses show that, merely the Doppler effect could reproduce the relationship, and there exists a dead line in the rise width and full width of the observed pulse panel, which might be a criterion to check if the temporal behaviors of gamma-ray burst pulses do result from the contributions from the Doppler effect. The fact that both long and short...