A New Relation between GRB Rest-Frame Spectra and Energetics and Its Utility on Cosmology

We investigate the well-measured spectral and energetic properties of 19 gamma-ray bursts (GRBs) in their cosmological rest frames. We find a tight relation between the isotropic-equivalent γ-ray energy release Eiso, the local peak energy E ′ p of the νFν spectrum, and the local break time t ′ b of the GRB afterglow light curve, which is Eiso t ′ b ∝ E ′ 1.986±0.084 p (χ 2 ν = 1.42; ΩM = 0.27, ΩΛ = 0.73). Such a power-law relation can be understood via the high-energy radiation processes for the GRB prompt emission accompanying the beaming effects. We then consider this relation as an intrinsic one for the observed GRB sample, and obtain a constraint on the mass density ΩM = 0.26 +0.15 −0.13 (1σ) for a flat ΛCDM universe, and a χdof = 1.26 for ΩM ≈ 0.3 and ΩΛ ≈ 0.7. Ongoing GRB observations in the Swift era are expected to confirm this relation and make its cosmological utility progress much. Subject headings: gamma rays: bursts — cosmology: observations—cosmology: distance scale