Testing the Universal Structured Jet Models of Gamma-Ray Bursts by BATSE Observations

Abstract

Assuming that the observed gamma-ray burst (GRB) rate as a function of redshift is proportional to a corrected star formation rate, we derive the empirical distribution of the viewing angles of long BATSE GRBs, $P^{\mathrm{em}}(\theta )$, and the distribution of these bursts in the plane of $\theta$ against redshift, $P^{\mathrm{em}}(\theta ,z)$, by using a tight correlation between $E_{\gamma }$) and $E_{\mathrm{p}}^{{}^{\prime }}$). Our results show that $P^{\mathrm{em}}(\theta )$ is well fitted by a log-normal distribution centering at $\log \theta /\mathrm{rad}=-0.76$ with a width of ${\sigma }_{\log \theta }=0.57$. We test different universal structured jet models by comparing model predictions with our empirical results. To make the comparisons reasonable, an "effective" threshold, which corresponds to the sample selection criteria of the long GRB sample, is used. We find that the predictions of a two-Gaussian jet model are roughly consistent with our empirical results. A brief discussion shows that cosmological effect on the $E_{\gamma }-E_{\mathrm{p}}^{{}^{\prime }}$ relation does not significantly affect our results, but sample selection effects on this relationship might significantly influence our results.

5 pages, 6 figures, accepted for publication in AJ

References in corpus (40)

• The Physics of Gamma-Ray Bursts
• Gamma-Ray Bursts and the Fireball Model
• Intrinsic spectra and energetics of BeppoSAX Gamma-Ray Bursts with known redshifts
• Beaming in Gamma-Ray Bursts: Evidence for a Standard Energy Reservoir
• Jets in GRBs
• Gamma-Ray Bursts: Progress, Problems & Prospects
• Theories of Gamma-Ray Bursts
• The collimation--corrected GRB energies correlate with the peak energy of their $\nu F_{\nu }$ spectrum
• The BATSE Gamma-Ray Burst Spectral Catalog. I. High Time Resolution Spectroscopy of Bright Bursts using High Energy Resolution Data
• Afterglow lightcurves, viewing angle and the jet structure of gamma-ray bursts
• GRB Energetics and the GRB Hubble Diagram: Promises and Limitations
• Viewing Angle and Environment Effects in GRB: Sources of Afterglow Diversity
• A Common Origin for Cosmic Explosions Inferred from Fireball Calorimetry
• On the Association of Gamma-ray Bursts with Massive Stars: Implications for Number Counts and Lensing Statistics
• Gamma-ray burst beaming: a universal configuration with a standard energy reservoir?
• The prompt energy release of gamma-ray bursts using a cosmological k-correction
• The Propagation and Eruption of Relativistic Jets from the Stellar Progenitors of GRBs
• BATSE Observations of Gamma-Ray Burst Spectra. II. Peak Energy Evolution in Bright, Long Bursts -
• The Expected Redshift Distribution of Gamma-Ray Bursts
• Constraining ${\Omega }_M$ and Dark Energy with Gamma-Ray Bursts
• Quasi-universal Gaussian jets: a unified picture for gamma-ray bursts and X-ray flashes
• Testing the Gamma-Ray Burst Energy Relationships
• A Unified Jet Model of X-Ray Flashes, X-Ray-Rich Gamma-Ray Bursts, and Gamma-Ray Bursts: I. Power-Law-Shaped Universal and Top-Hat-Shaped Variable Opening-Angle Jet Models
• Rebrightening of XRF 030723: further evidence for a two-component jet in gamma-ray burst
• The bright optical afterglow of the nearby gamma-ray burst of 29 March 2003
• The Luminosity - E_p Relation within Gamma--Ray Bursts and Implications for Fireball Models
• BATSE Observations of Gamma-Ray Burst Spectra. IV. Time-Resolved High-Energy Spectroscopy
• GRB Afterglows from Anisotropic Jets
• Millimeter Observations of GRB 030329: Continued Evidence for a Two-Component Jet
• Formation Rate, Evolving Luminosity Function, Jet Structure, and Progenitors for Long Gamma-Ray Bursts
• On The Spectral Energy Dependence of Gamma-Ray Burst Variability
• Jets in GRBs: Tests and Predictions for the Structured Jet Model
• On the Structure of Quasi-Universal Jets for Gamma-Ray Bursts
• Gamma-Ray Bursts: Afterglows and Central Engines
• Is the Redshift Clustering of Long-Duration Gamma-Ray Bursts Significant?
• Testing the Predictions of the Universal Structured GRB Jet Model
• Global Test of a Quasi-Universal Gamma-Ray Burst Jet Model Through Monte-Carlo Simulations
• The Peak Energy Distribution of the nu F_nu Spectra and the Implications for the Jet Structure Models of Gamma-Ray Bursts
• Gamma Ray Burst Beaming Constraints from Afterglow Light Curves: GRB 970508
• Testing the Predictions of the Universal-Structured Jet Model of Gamma-Ray Bursts by Simulations

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