The Luminosity- E p Relation within Gamma-Ray Bursts and the Implications for Fireball Models

Abstract

Using a sample of 2408 time-resolved spectra for 91 BATSE gamma-ray bursts (GRBs) presented by Preece et al., we show that the relation between the isotropic-equivalent luminosity (L-iso) and the peak energy (E'(p)) of the nuF(nu) spectrum in the cosmological rest frame, L-iso proportional to E'(2)(p), holds within these bursts and also holds among these GRBs, assuming that the burst rate as a function of redshift is proportional to the star formation rate. The possible implications of this relation for the fireball models are discussed by defining a parameter omega = (L-iso/10(52) erg s(-1))(0.5)/(E'(p)/200 keV). It is found that omega is narrowly clustered in 0.1-1. We constrain some parameters for both the internal shock and external shock models from the requirement of omega similar to 0.1-1, assuming that these model parameters are uncorrelated. The distributions of the parameters suggest that if the prompt gamma rays are produced from kinetic-energy-dominated internal shocks, they may be radiated from a region around R similar to 10(12)-10(13) cm (or Lorentz factor similar to 130 - 410) with a combined internal shock parameter zeta(i)similar to0.1-1 during the prompt gamma-ray phase, which is consistent with the standard internal shock model; if the prompt gamma rays of these GRBs are radiated from magnetic-dissipation-dominated external shocks, the narrow cluster of omega requires sigma similar to 1-470, Gamma similar to216-511, E similar to 10(51)-10(54) ergs, n similar to 0.5-470 cm(-3), and zeta(e)similar to0.36-3.6, where sigma is the ratio of the cold to hot luminosity components, Gamma is the bulk Lorentz factor of the fireball, E is the total energy release in the gamma-ray band, n is the medium number density, and zeta(e) is a combined external shock parameter; these values are also in a good agreement with the fittings to the afterglow data. These results indicate that both the kinetic-energy-dominated internal shock model and the magnetic-dissipation - dominated external shock model can well interpret the L-iso proportional to E'(2)(p) relation and the value of omega.