A simple theory of lags in gamma-ray bursts: Comparison to observations

Context. Lags observed between the light curves of a gamma-ray burst (GRB) seen in different energy bands are related to its spectral evolution. Moreover the lags have been found to correlate with burst luminosity, therefore providing a potential distance indicator. Aims. We want to quantify the nature of the link between lags and spectral evolution to better understand the origin of the lag-luminosity relation and evaluate its interest as a distance indicator. Methods. We directly relate the lag of a pulse to the spectral parameters (peak energy Ep, low and high energy indices, α and β, and their time derivatives) evaluated at pulse maximum. Then, using a Yonetoku-like relation we obtain a theoretical lag-luminosity relation that is confronted with data. Results. We first apply our model to the initial pulse of GRB 130427A, for which high quality data are available, to check quantitatively whether the measured lags are consistent with the observed spectral evolution. We then use a Monte Carlo approach to generate a sample of synthetic lags, which we compare to an observed sample of Swift bursts. The dispersion of both the observed and modelled lag-luminosity relations appears large, which questions the value of this relation as a reliable distance indicator