Emission lines in GRBs constrain the total energy reservoir

Abstract

The emission features observed in the X{ray afterglow of Gamma Ray Bursts are extremely powerful. Since they last at least for several hours, they imply energies of the order of 10 49 ergs. This in turn implies that the energy contained in the illuminating continuum thought to be responsible of the line production must exceed 10 51 ergs. This is a strong lower limit to the energy reservoir of Gamma Ray Bursts, which is independent of collimation and beaming, and bears important consequences on the possible collimation of the reball radiation and the density of the medium surrounding the burst. The discovery that Gamma Ray Bursts (GRBs) are cos- mological implies large luminosities, but the exact value of the radiated luminosities and the kinetic power of the re- ball originating the emission are still uncertain by a large factor, since we do not know if the emission is isotropic or if it is instead collimated in a cone. The main tool to esti- mate the degree of collimation of the emission has been, so far, the presence of an achromatic break in the lightcurves of the afterglows. This is interpreted as due to the deceler- ation of the reball, whose bulk Lorentz factor becomes smaller than the inverse of the jet opening angle j (see e.g. Rhoads 1999). This allows to estimatej and to obtain the \true values of the emitted energy. Most notably, in this respect, is the nding of Frail et al. (2001) who found a remarkable \clustering of the reball energy, once they are corrected by the estimate of their degree of collima- tion. Since the total power and energy are obviously the main parameters for the construction of any model, the importance of these estimates is obvious. These in turn are based on a number of assumptions, such as the den- sity of the matter surrounding the burst site, which is responsible for the deceleration of the reball, and on the key observation of the presence of an achromatic break in the light curve of the afterglow. Independent estimates of the \true energy, or even limits on it, are called for. In this paper we point out that the observed emission features observed in the X{ray afterglow spectra of several bursts can indeed put a rm lower limit to the emitted luminosity of GRBs. This limit is at the same time simple, independent of the degree of