Selection Effects on the Observed Redshift Dependence of GRB Jet Opening Angles

Abstract

Apparent redshift dependence of the jet opening angles (${\theta }_{\mathrm{j}}$) of gamma-ray bursts (GRBs) is observed from current GRB sample. We investigate whether this dependence can be explained with instrumental selection effects and observational biases by a bootstrapping method. Assuming that (1) the GRB rate follows the star formation history and the cosmic metallicity history and (2) the intrinsic distributions of the jet-corrected luminosity ($L_{\gamma }$) and ${\theta }_{\mathrm{j}}$ are a Gaussian or a power-law function, we generate a mock {\em Swift}/BAT sample by considering various instrumental selection effects, including the flux threshold and the trigger probability of BAT, the probabilities of a GRB jet pointing to the instrument solid angle and the probability of redshift measurement. Our results well reproduce the observed ${\theta }_{\mathrm{j}}-z$ dependence. We find that in case of $L_{\gamma }\propto {\theta }_{\mathrm{j}}^2$ good consistency between the mock and observed samples can be obtained, indicating that both $L_{\gamma }$ and ${\theta }_{\mathrm{j}}$ are degenerate for a flux-limited sample. The parameter set $(L_{\gamma },{\theta }_{\mathrm{j}})=(4.9\times 10^{49}{\mathrm{erg}\mathrm{s}}^{-1},0.054\mathrm{rad})$ gives the best consistency for the current {\em Swift} GRB sample. Considering the beaming effect, the derived intrinsic local GRB rate accordingly is $2.85\times 10^2$ Gpc${}^{-3}$ yr${}^{-1}$, inferring that $\sim 0.59$ of Type Ib/c SNe may be accompanied by a GRB.

25pages, 7 figures. ApJ in press

References in corpus (18)

• Gamma-Ray Bursts: Progress, Problems & Prospects
• A Complete Catalog of Swift GRB Spectra and Durations: Demise of a Physical Origin for Pre-Swift High-Energy Correlations
• Making a Short Gamma-Ray Burst from a Long one: Implications for the Nature of GRB 060614
• A Comprehensive Analysis of Swift/XRT Data: III. Jet Break Candidates in X-ray and Optical Afterglow Lightcurves
• The First Swift BAT Gamma-Ray Burst Catalog
• Star Formation History up to z = 7.4: Implications for Gamma-Ray Bursts and the Cosmic Metallicity Evolution
• The redshift distribution of SWIFT Gamma-Ray Bursts: evidence for evolution
• The line-of-sight towards GRB 030429 at z = 2.66: Probing the matter at stellar, galactic and intergalactic scales
• Post-Launch Analysis of Swift's Gamma-Ray Burst Detection Sensitivity
• Peak energy of the prompt emission of long Gamma Ray Bursts vs their fluence and peak flux
• Enhanced Cosmological GRB Rates and Implications for Cosmogenic Neutrinos
• How common are long Gamma-Ray Bursts in the Local Universe?
• GRB 060605: multi-wavelength analysis of the first GRB observed using integral field spectroscopy
• GRB 090902B: afterglow observations and implications
• GRB 060206 and the quandary of achromatic breaks in afterglow light curves
• Gamma Ray Bursts from the early Universe: predictions for present-day and future instruments
• Gamma-Ray Bursts are Produced Predominately in the Early Universe
• Evidence for an anticorrelation between the duration of the shallow decay phase of GRB X-ray afterglows and redshift

Cited by in corpus (27)

• A test of the millisecond magnetar central engine model of GRBs with Swift data
• A Study of the Gamma-Ray Burst Fundamental Plane
• The long gamma-ray burst rate and the correlation with host galaxy properties
• Multi-color observations of short GRB afterglows: 20 events observed between 2007 and 2010
• Cosmological Tests Using GRBs, the Star Formation Rate and Possible Abundance Evolution
• A comprehensive statistical study on gamma-ray bursts
• Imprints of Electron-positron Winds on the Multi-wavelength Afterglows of Gamma-ray Bursts
• The Luminosity Function and Formation Rate of A Complete Sample of Long Gamma-Ray Bursts
• Statistical study of gamma-ray bursts with jet break feature in multi-wavelength afterglow emissions
• Testing black hole neutrino-dominated accretion discs for long-duration gamma-ray bursts
• New constraints on GRB jet geometry and relativistic shock physics
• Constraints on the Bulk Lorentz Factors of GRB X-Ray Flares
• Gamma-Ray Bursts: the Isotropic-Equivalent-Energy Function and the Cosmic Formation Rate
• Constraining the rate and luminosity function of Swift gamma-ray bursts
• Revisiting the luminosity and redshift distributions of long gamma-ray bursts
• A Comprehensive Study of Gamma-Ray Burst Optical Emission: III. Brightness Distributions and Luminosity Functions of Optical Afterglows
• Cosmic Evolution of Long Gamma-Ray Burst Luminosity
• The origin of the plateau and late rebrightening in the afterglow of GRB 120326A
• Gamma-ray burst cosmology: Hubble diagram and star formation history
• Testing Blandford-Znajek mechanism in black hole hyperaccretion flows for long-duration gamma-ray bursts
• Resolving the Excess of Long GRBs at low redshift in the Swift Era
• Magnetar central engines in gamma-ray busts follow the universal relation of accreting magnetic stars
• The Stellar-mass Function of Long Gamma-Ray Burst Host Galaxies
• Revisiting the Formation Rate and the Redshift Distribution of LGRBs
• Revisiting the Relationship between the Long GRB Rate and Cosmic Star Formation History Based on a Large Swift Sample
• Gamma-ray burst radio afterglows from Population III stars: Simulation methods and detection prospects with SKA precursors
• Exploring Jet Structure and Dynamics in Short Gamma Ray Bursts: A Case Study on GRB 090510