The lag and duration–luminosity relations of gamma-ray burst pulses

摘要

Context. Relations linking the temporal or/and spectralproperties of the prompt emission of gamma-ray bursts (hereafter GRBs)to the absolute luminosity are of great importance as they bothconstrain the radiation mechanisms and represent potential distanceindicators. Here we discuss two such relations: the lag-luminosityrelation and the newly discovered duration-luminosity relation ofGRBpulses. Aims. We aim to extend our previous work on the origin ofspectral lags, using the duration-luminosity relation recentlydiscovered by Hakkila etal. (2008, ApJ, 677, L81) to connect lagsand luminosity. We also present a way to test this relation which hasoriginally been established with a limited sample of only12pulses. Methods. We relate lags to the spectral evolution and shape ofthe pulses with a linear expansion of the pulse properties aroundmaximum. We then couple this first result to the duration-luminosityrelation to obtain the lag-luminosity and lag-duration relations. Wefinally use a Monte-Carlo method to generate a population of syntheticGRBpulses which is then used to check the validity of theduration-luminosity relation. Results. Our theoretical results for the lag andduration-luminosity relations are in good agreement with the data. Theyare rather insensitive to the assumptions regarding the burst spectralparameters. Our MonteCarlo analysis of a population of syntheticpulses confirms that the duration-luminosity relation must be satisfiedto reproduce the observational duration-peak flux diagram of BATSE GRBpulses. Conclusions. The newly discovered duration-luminosity relationoffers the possibility to link all three quantities: lag, duration andluminosity of GRB pulses in a consistent way. Some evidence for itsvalidity have been presented but its origin is not easy to explain inthe context of the internal shock model. Key words: gamma-rays bursts: general - radiation mechanisms: non-thermal