Empirical Constraints on Source Properties and Host Galaxies of Cosmological Gamma-Ray Bursts

Abstract

We discuss several constraints on the properties of gamma-ray bursts (GRBs) at cosmological distances. First we use the requirement that burst sources must be optically thin to a test photon for the process gamma + gamma --> e(+) + e(-) in order to produce the observed nonthermal spectra. In particular, we derive probability distributions for the minimum Lorentz expansion factor gamma(min), the radiation energy E(gamma), the maximum baryonic mass M(max) and the maximum surrounding gas density n(max) in the events, based on 254 events from the second BATSE catalog. In the case where the GRB spectrum cuts off at the highest observed energies (similar to 100 MeV), we obtain the mean values [gamma(min)] = 90, [E(gamma)] = 4 x 10(51) h(-2) ergs, and [M(max)] = 3 x 10(-5)xi(-1) M., where xi is the fraction of the total energy which is converted to gamma-rays. The distribution of burst energies ends at about 10(53) ergs, close to the binding energy of a neutron star.Second, the time variabilities of the bursts in the BATSE catalog are used to place an upper bound R(max) on the curvature radius of the emitting surfaces in the events. This is based on the requirement that the emitting region seen by the observer must be sufficiently small to produce the observed variability without violating causality. Using the 64 ms resolution of BATSE, we find that a significant number of bursts have R(max) approximate to 10(13)(gamma/10(2))(2) cm, where gamma is the Lorentz factor of the expansion. This limit should become stricter with finer time resolution.Finally, we discuss the association of cosmological GRBs with galaxies. We consider eight bright and well localized bursts detected by the Pioneer Venus Orbiter, whose positional error boxes contain no bright galaxies. Assuming that burst events occur in galaxies, we place upper limits on the luminosities of the host galaxies. Using the local luminosity function of galaxies, we calculate the probability for not seeing the GRB host galaxy. This probability tends to increase as the width of the GRB luminosity function increases. However, the allowed width of the GRB luminosity function is restricted by the burst peak flux distribution.