Gamma-Ray Burst Luminosity Functions Based On a Newly Discovered Correlation Between Peak Spectral Energy and V/V_max

Abstract

We have discovered a correlation between the observed peak spectral energy E_pk,obs and the average Euclidean value of V/V_max of gamma-ray bursts (GRBs). We present the evidence for the correlation in the GUSBAD catalog and use it to derive the luminosity function of GRBs without using any redshifts. The procedure involves dividing GUSBAD GRBs in five spectral classes based on their E_pk,obs. The overall luminosity function is derived assuming that each of the spectral classes contributes a gaussian luminosity function. Their central luminosity is derived from the average observed Euclidean V/V_max. We explore various forms for the GRB rate function GR(z) in predicting redshift distributions of GRBs detected by Swift. We find that GR(z) peaks at a higher redshift than the typical star formation history currently favored in the literature. We consider two examples of GR(z) that successfully predict the observed redshift distribution of Swift GRBs. With the luminosity functions in hand, we convert the E_pk,obs-V/V_max correlation into an E_pk,obs-L_iso correlation and a rest frame E_pk-L_iso correlation. In comparing the E_pk-L_iso correlation with a published correlation based on GRBs with known E_pk,obs and redshifts, we discuss the effect of Malmquist bias.

32 pages, 13 figures, two references added, others corrected

References in corpus (20)

• On the normalisation of the cosmic star formation history
• Intrinsic spectra and energetics of BeppoSAX Gamma-Ray Bursts with known redshifts
• Long gamma-ray bursts and core-collapse supernovae have different environments
• GRB Formation Rates inferred from the Spectral Peak Energy - Luminosity Relation
• On the evolution of star forming galaxies
• Connection Between Energy-dependent Lags And Peak Luminosity In Gamma-ray Bursts
• The Complete Spectral Catalog of Bright BATSE Gamma-Ray Bursts
• The Hubble Diagram to Redshift >6 from 69 Gamma-Ray Bursts
• A Complete Catalog of Swift GRB Spectra and Durations: Demise of a Physical Origin for Pre-Swift High-Energy Correlations
• Evolution of the Intergalactic Opacity: Implications for the Ionizing Background, Cosmic Star Formation, and Quasar Activity
• Outliers to the Isotropic Energy - Peak Energy Relation in GRBs
• Testing the Gamma-Ray Burst Energy Relationships
• Luminosity Function of Gamma-Ray Bursts Derived Without Benefit of Redshifts
• On the Redshift Distribution of Gamma Ray Bursts in the Swift Era
• Cosmological versus Intrinsic: The Correlation between Intensity and the Peak of the nu F_nu Spectrum of Gamma Ray Bursts
• Post-Launch Analysis of Swift's Gamma-Ray Burst Detection Sensitivity
• Probing the existence of the E_peak-E_iso correlation in long Gamma Ray Bursts
• Intrinsic properties of a complete sample of HETE-2 gamma-ray bursts. A measure of the GRB rate in the Local Universe
• Redshift Degeneracy in the Eiso-Epeak Relation of Gamma-Ray Bursts
• The GUSBAD Catalog of Gamma-Ray Bursts

Cited by in corpus (6)

• The Cosmic Rate, Luminosity Function and Intrinsic Correlations of Long GRBs
• The Optically Unbiased Gamma-Ray Burst Host (TOUGH) Survey. VII. The Host Galaxy Luminosity Function: Probing the Relationship Between GRBs and Star Formation to Redshift $\sim 6$
• Evidence for New Relations between Gamma Ray Burst Prompt and X-ray Afterglow Emission from 9 Years of Swift
• A Multivariate Fit Luminosity Function and World Model for Long GRBs
• The Fast Radio Burst Population Energy Distribution
• The Optical Luminosity Function of Gamma-ray Bursts deduced from ROTSE-III Observations