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

¹ Tirana University, Faculty of Natural Sciences, Tirana, Albania
² Institut d'Astrophysique de Paris, UMR 7095 Université Pierre et Marie Curie-Paris 6 – CNRS, 98bis boulevard Arago, 75014 Paris, France e-mail: mochko@iap.fr

Received: 25 January 2010
Accepted: 8 June 2010

Abstract

Context. Relations linking the temporal or/and spectral properties of the prompt emission of gamma-ray bursts (hereafter GRBs) to the absolute luminosity are of great importance as they both constrain the radiation mechanisms and represent potential distance indicators. Here we discuss two such relations: the lag–luminosity relation and the newly discovered duration–luminosity relation of GRB pulses.

Aims. We aim to extend our previous work on the origin of spectral lags, using the duration–luminosity relation recently discovered by Hakkila et al. (2008, ApJ, 677, L81) to connect lags and luminosity. We also present a way to test this relation which has originally been established with a limited sample of only 12 pulses.

Methods. We relate lags to the spectral evolution and shape of the pulses with a linear expansion of the pulse properties around maximum. We then couple this first result to the duration–luminosity relation to obtain the lag–luminosity and lag–duration relations. We finally use a Monte-Carlo method to generate a population of synthetic GRB pulses which is then used to check the validity of the duration–luminosity relation.

Results. Our theoretical results for the lag and duration–luminosity relations are in good agreement with the data. They are rather insensitive to the assumptions regarding the burst spectral parameters. Our Monte Carlo analysis of a population of synthetic pulses confirms that the duration–luminosity relation must be satisfied to reproduce the observational duration–peak flux diagram of BATSE GRB pulses.

Conclusions. The newly discovered duration–luminosity relation offers the possibility to link all three quantities: lag, duration and luminosity of GRB pulses in a consistent way. Some evidence for its validity have been presented but its origin is not easy to explain in the context of the internal shock model.