Cosmological Evolution and Luminosity Function Effects on Number Counts, Redshift and Time Dilation of Bursting Sources

Abstract

We present analytic formulae for the integral number count distribution of cosmological bursting or steady sources valid over the entire range of fluxes, including density evolution and either standard candle or a power law luminosity function. These are used to derive analytic formulae for the mean redshift, the time dilations and the dispersion of these quantities for sources within a given flux range for Friedmann models with $\Omega =1,\Lambda =0$ without K-corrections, and we discuss the extension to cases with $\Omega <1$ and inclusion of K-corrections. Applications to the spatial distribution of cosmological gamma ray burst sources are discussed, both with and without an intrinsic energy stretching of the burst time profiles, and the implied ranges of redshift $z$ are considered for a specific time dilation signal value. The simultaneous consideration of time dilation information and of fits of the number distribution versus peak flux breaks the degeneracy inherent in the latter alone, allowing a unique determination of the density evolution index and the characteristic luminosity of the sources. For a reported time dilation signal of 2.25 and neglecting [including] energy stretching we find that the proper density should evolve more steeply with redshift than comoving constant, and the redshifts of the dimmest sources with stretching would be very large. However, the expected statistical dispersion in the redshifts is large, especially for power law luminosity functions, and remains compatible with that of distant quasars. For smaller time dilation values of 1.75 and 1.35 the redshifts are more compatible with conventional ideas about galaxy formation, and the evolution is closer to a comoving constant or a slower evolution. More generally, we have considered a wide range of possible measured time dilation

Ap.J., in press, uuencoded .ps file, 33 pages plus 5 figures

Cited by in corpus (30)

• Gamma-Ray Bursts and the Fireball Model
• Cosmological Gamma-Ray Bursts and Evolution of Galaxies
• On the Redshift Distribution of Gamma Ray Bursts in the Swift Era
• An analysis of the durations of Swift Gamma-Ray Bursts
• 'On the difference between the short and long gamma-ray bursts'
• The Swift satellite and redshifts of long gamma-ray bursts
• Gamma-Ray Bursts are Produced Predominately in the Early Universe
• Constraining the rate and luminosity function of Swift gamma-ray bursts
• Testing the anisotropy in the angular distribution of $Fermi$/GBM gamma-ray bursts
• Gamma photometric redshifts for long gamma-ray bursts
• A redshift - observation-time relation for gamma-ray bursts: evidence of a distinct sub-luminous population
• Interpretations of gamma-ray burst spectroscopy. II. Bright BATSE bursts
• Constraints on the Redshift and Luminosity Distributions of Gamma Ray Bursts in an Einstein-de Sitter Universe
• Fourier Analysis of Gamma-Ray Burst Light Curves: Searching for Direct Signature of Cosmological Time Dilation
• Redshift distribution of gamma-ray bursts and star formation rate
• Cosmological effects on the observed flux and fluence distributions of gamma-ray bursts: Are the most distant bursts in general the faintest ones?
• An Oppositeness in the Cosmology: Distribution of the Gamma-Ray Bursts and the Cosmological Principle
• A viable varying speed of light model in the RW metric
• On the Reality of the Accelerating Universe
• Anisotropy in the angular distribution of the long gamma-ray bursts?
• Large-scale asymmetry between clockwise and counterclockwise galaxies revisited
• Review on the minimally extended varying speed of light model
• The significance of measuring cosmological time dilation in the Dark Energy Survey Supernova Program
• Constraints on the minimally extended varying speed of light model using the Pantheon+ dataset
• Cosmography of the minimally extended Varying Speed of Light Model
• Differential Source Count for Gamma Ray Bursts
• 3+1 formalism of the minimally extended varying speed of light model
• Revisiting Varying Speed of Light in Cosmology: Insights from the Friedmann-Lemaître-Robertson-Walker Metric
• Luminosity Selection for Gamma Ray Burst
• Gamma-ray bursts: A brief survey of the diversity