Emission and absorption lines of gamma-ray bursts affected by the relativistic motion of fireball ejecta

Abstract

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 v(line) and the rest frame line frequency v(0,line) would be related by v(line) approximate to 2Gammav(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 varies with time. This phenomenon depends not only on the initial Lorentz factor but also on the observation time.