Gamma-Ray bursts: Energetics and Prompt Correlations.

A model is presented here that is capable of simultaneously describing the luminosity function and the underlying joint population distribution of the prompt spectral and temporal parameters of Gamma-Ray Bursts (GRBs), subject to the detection threshold of gamma-ray instruments--in particular, BATSE and Fermi. Based on 2130 GRB prompt emission data in the BATSE catalog, I show that the population properties of the two classes of GRBs -- Long and Short durations -- bear striking similarities in the 4-dimensional space of prompt parameters: peak luminosity (Liso), total isotropic emission (Eiso), time-integrated spectral peak energy (Ep,z) and the prompt duration (T90,z). The two well-known Amati (Eiso-Ep,z) and Yonetoku (Liso-Ep,z) relations are shown to be highly affected by selection effects, undermining the legitimacy of their frequent uses in the studies of Dark Energy's equation of state and different cosmological models. In particular, I show that the slope of the Amati relation is likely in the range 0.2-0.3, corresponding to a Pearson's correlation strength of rho=0.58\pm0.04. This predicted slope is significantly (>16sigma) less than the value currently perceived by the GRB community (~0.56). I argue that similar Eiso-Ep,z and Liso-Ep,z relations with approximately same strength and significance should exist in the population of Short GRBs. Also predicted by the model is the strong positive correlation of the prompt emission duration (e.g., T90,z) with Eiso and Liso in both classes of Short and Long GRBs.