Emission and absorption lines of gamma-ray bursts affected by the   relativistic motion of fireball ejecta
  We display by numerical calculation how rest frame spectral lines appear in the observed spectrum of gamma-ray bursts due to the Doppler effect in the fireball framework. The analysis shows that: a) in the spectrum of a relativistically expanding fireball, all rest frame lines would shift to higher energy bands and would be significantly smoothed; b) rest frame weak narrow emission lines as well as narrow absorption lines and absorption line forests would be smoothed and would hardly be detectable; c) the features of rest frame broad emission lines as well as both strong and weak broad absorption lines would remain almost unchanged and therefore would be easier to detect; d) deep gaps caused by rest frame broad absorption lines would be significantly filled; e) a rest frame emission line forest would form a single broad line feature; f) the observed relative width of the rest frame very narrow line would approach $ 0.162$; g) when the Lorentz factor $\Gamma $ is large enough, the observed line frequency $\nu_{line}$ and the rest frame line frequency $\nu_{0,line} $ would be related by $\nu_{line}\approx 2\Gamma \nu_{0,line}$. We also investigate the effect of time dependence of the line intensity and the effect of variation of $\Gamma $. We find that the feature of rest frame dimming narrow emission lines would disappear when $\Gamma $ is very large. The form of emission lines would be sharp on both edges when $\Gamma $ varies with time. This phenomenon depends not only on the initial Lorentz factor but also on the observation time. 
Yi-Ping Qin