A bivariate luminosity model for GRB pulses and flares

We have fitted the complete Swift BAT and XRT light curves of 88 GRBs for which we have a redshift with a total of 331 pulses. For each GRB we also include an afterglow component to fit the plateau phase and the late decay seen in the XRT data. The combination of pulses and afterglow model all the emission detected, prompt plus afterglow, including late X-ray flares detected only in the XRT. Each pulse is described by a simple physical model which includes the spectrum at peak and the temporal characteristics of the pulse. We find that the pulse peak luminosity is correlated with both the mean photon energy in the bolometric band of the pulse spectrum at the peak, referred to as Ezbol, and the temporal parameter Tzf which is a measure of the pulse width. An empirical bivariate luminosity model set up with these parameters provides a good fit to the pulse luminosity. The analysis indicates that prompt pulses and X-ray flares are one and the same and arise from the same physical process and this physical process is responsible for the bivariate nature of the luminosity.