## Abstract

Most gamma-ray burst (GRB) models have predicted that the intrinsic isotropic energy is limited to below ∼10^{53}-10^{54} 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 (T_{90} > 2.5 s) and 149 short bursts (T_{90} < 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^{o}.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^{o}.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.

Original language | English |
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Pages (from-to) | 532-539 |

Number of pages | 8 |

Journal | Astrophysical Journal |

Volume | 548 |

Issue number | 2 PART 1 |

DOIs | |

State | Published - 20 Feb 2001 |

## Keywords

- Cosmology: theory
- Gamma rays: bursts
- Methods: statistical