SIMBAD references

Most gamma-ray burst (GRB) models have predicted that the intrinsic isotropic energy is limited to below ∼10⁵³-10⁵⁴ ergs. Recently claimed high redshifts, correlation with supernovae, and connections to cosmic star formation activity point to a different energy requirement and source evolution history, possibly with strong beaming. We study the effects of the beaming-induced luminosity function on statistics of observed GRBs, assuming the cosmological scenario. We select and divide the BATSE 4B data into 588 long bursts (T₉₀>2.5 s) and 149 short bursts (T₉₀<2.5 s), and compare the statistics calculated in each subgroup. The <V/V_max> of the long bursts is 0.2901±0.0113, and that of the short bursts is 0.4178±0.0239. For luminosity function models, we consider a cylindrical beam and a conic beam. We take into account the spatial distribution of GRB sources as well. A broad luminosity function is naturally produced when one introduces beaming of GRBs. We calculate the maximum detectable redshift of GRBs, z_max. The estimated z_max for the cylindrical beam case is as high as ∼14 (α=1.0) and ∼6 (α=2.0) for the long bursts, and ∼3 (α=1.0) and ∼1.6 (α=2.0) for the short bursts, where α is the photon index. The large z_max value for the short bursts is rather surprising, in that the <V/V_max> for this subgroup is close to the so-called Euclidean value, 0.5. We calculate the fraction of bursts whose redshifts are larger than a certain redshift z', i.e., f_>z'. When we take z'=3.42 and apply the luminosity function derived for the cylindrical beam, the expected f_>z' is ∼75% (α=1.0) and ∼50% (α=2.0) for long bursts. When we increase the opening angle of the conic beam to Δθ=3°.0, f_>z' decreases to ∼20% (α=1.0) at z'=3.42. If we assume α=2.0, the conic beam with Δθ=3°.0 cannot explain the redshift distribution of the observed GRBs. We conclude that the beaming-induced luminosity functions are compatible with the redshift distribution of the observed GRBs, although the apparent ``Euclidean'' value of <V/V_max> might be explained by the standard model.