Empirical Constraints on Cosmological Gamma-Ray Bursts

Abstract

We place empirical constraints on the physical properties of $\gamma -$ray burst events at cosmological distances. In particular we derive probability distributions for the radiation energy $E_{\gamma }$, the minimum Lorentz factor ${\gamma }_{\min }$, the maximum baryonic mass $M_{\max }$ and the upper bound on the surrounding gas density $n_{\max }$ in the events, based on 169 bursts from the first BATSE catalog. Using peak flux as a distance indicator we probe bursts where the constraints are stronger than average. The resulting variance and skewness of the cosmological probability distributions are calculated in addition to their mean values: $⟨E_{\gamma }⟩=4\times 10^{51}{h}^{-2}\mathrm{erg}$, $⟨{\gamma }_{\min }⟩=5\times 10^2$, $⟨M_{\max }⟩=10^{-5}{\xi }^{-1}{M}_{\odot }$, and $\langle (γ/γ_{\rm min})^{-5} n_{\rm max}\rangle\lsim 10^{2} ξ^{-1}{\rm cm^{-3}}$, where $\xi$ is the fraction of the total energy which is converted to $\gamma -$rays. The distribution of burst energies ends at about $10^{53}\mathrm{erg}$, close to the binding energy of a neutron star.

13 pages, TEX, 2 figures can be obtained from [email protected]

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