Gamma-Ray Burst Energetics and the Gamma-Ray Burst Hubble Diagram: Promises and Limitations

We present a complete sample of 29 gamma-ray bursts (GRBs) for which it has been possible to determine temporal breaks (or limits) from their afterglow light curves. We interpret these breaks within the framework of the uniform conical jet model, incorporating realistic estimates of the ambient density and propagating error estimates on the measured quantities. In agreement with our previous analysis of a smaller sample, the derived jet opening angles of those 16 bursts with redshifts result in a narrow clustering of geometrically corrected gamma-ray energies about Script E_γ = 1.33 × 10^(51) ergs; the burst-to-burst variance about this value is 0.35 dex, a factor of 2.2. Despite this rather small scatter, we demonstrate in a series of GRB Hubble diagrams that the current sample cannot place meaningful constraints upon the fundamental parameters of the universe. Indeed, for GRBs to ever be useful in cosmographic measurements, we argue the necessity of two directions. First, GRB Hubble diagrams should be based upon fundamental physical quantities such as energy, rather than empirically derived and physically ill-understood distance indicators (such as those based upon prompt burst time-profiles and spectra). Second, a more homogeneous set should be constructed by culling subclasses from the larger sample. These subclasses, although now first recognizable by deviant energies, ultimately must be identifiable by properties other than those directly related to energy. We identify a new subclass of GRBs ("f-GRBs") that appear both underluminous by factors of at least 10 and exhibit a rapid fading (f_ν ∝ t^(-2)) at early times (t ≾ 0.5 day). About 10%-20% of observed long-duration bursts appear to be f-GRBs.