Photospheric emission from long-duration gamma-ray bursts powered by variable engines

We present the results of a set of numerical simulations of long-duration gamma-ray burst jets aimed at studying the effect of a variable engine on the peak frequency of the photospheric emission. Our simulations follow the propagation of the jet inside the progenitor star, its break-out, and the subsequent expansion in the environment out to the photospheric radius. A constant and two-step-function models are considered for the engine luminosity. We show that our synthetic light curves follow a luminosity-peak frequency correlation analogous to the Golenetskii correlation found in long-duration gamma-ray burst observations. Within the parameter space explored, it appears that the central engine luminosity profile does not have a significant effect on the location of a gamma-ray burst in the luminosity-peak frequency plane, bursts from different central engines being indistinguishable from each other.