The Brightness Distribution of Bursting Sources in Relativistic Cosmologies

We present analytical solutions for the integral distribution of arbitrary bursting or steady source counts as a function of peak photon count rate within Friedmann cosmological models. We discuss both the standard candle and truncated power-law luminosity function cases with a power-law density evolution. While the analysis is quite general, the specific example discussed here is that of a cosmological gamma-ray burst distribution. These solutions show quantitatively the degree of dependence of the counts on the density and luminosity function parameters, as well as the the weak dependence on the closure parameter and the maximum redshift. An approximate comparison with the publicly available Compton Gamma Ray Observatory data gives an estimate of the maximum source luminosity and an upper limit to the minimum luminosity. We discuss possible ways of further constraining the various parameters.Comment: 16 pages plus one figure, uuencoded postscript file. to appear in Ap.J

Cosmological Brightness Distribution Fits of Gamma Ray Burst Sources

We discuss detailed fits of the BATSE and PVO gamma-ray burst peak-flux distributions with Friedman models taking into account possible density evolution and standard candle or power law luminosity functions. A chi-square analysis is used to estimate the goodness of the fits and we derive the significance level of limits on the density evolution and luminosity function parameters. Cosmological models provide a good fit over a range of parameter space which is physically reasonable.Comment: Ap.J. in press, uuencoded .ps file, 9 pages manuscript plus 5 figure

What is the Astrophysical Meaning of the Intermediate Subgroup of GRBs?

Published articles concerning the intermediate (third) subgroup of GRBs are surveyed. From a statistical perspective this subgroup may exist, however its significance depends on which data set is used. Its astrophysical meaning is unclear because the occurrence of this subgroup can also be an artificial selection effect. Hence, GRBs from this subgroup need not be given by a physically different phenomenon. The aim of this contribution is to search for the answer to the question in the title.Comment: journal: Proceedings of Science, Swift: 10 Years of Discovery; conference date: 2-5 December 2014; location: La Sapienza University, Rome, Italy; 6 pages, 4 figures, 1 table; accepted for publication in July 9 201

A Principal Component Analysis of the 3B Gamma-Ray Burst Data

We have carried out a principal component analysis for 625 gamma-ray bursts in the BATSE 3B catalog for which non-zero values exist for the nine measured variables. This shows that only two out of the three basic quantities of duration, peak flux and fluence are independent, even if this relation is strongly affected by instrumental effects, and these two account for 91.6% of the total information content. The next most important variable is the fluence in the fourth energy channel (at energies above 320 keV). This has a larger variance and is less correlated with the fluences in the remaining three channels than the latter correlate among themselves. Thus a separate consideration of the fourth channel, and increased attention on the related hardness ratio $H43$ appears useful for future studies. The analysis gives the weights for the individual measurements needed to define a single duration, peak flux and fluence. It also shows that, in logarithmic variables, the hardness ratio $H32$ is significantly correlated with peak flux, while $H43$ is significantly anticorrelated with peak flux. The principal component analysis provides a potentially useful tool for estimating the improvement in information content to be achieved by considering alternative variables or performing various corrections on available measurementsComment: Ap.J., accepted 12/9/97; revised version contains a new appendix, somewhat expanded discussion; latex, aaspp4, 15 page

A curious relation between the flat cosmological model and the elliptic integral of the first kind

The dependence of the luminosity distance on the redshift has a key importance in the cosmology. This dependence can well be given by standard functions for the zero cosmological constant. The purpose of this article is to present such a relation also for the non-zero cosmological constant, if the universe is spatially flat. A definite integral is used. The integration ends in the elliptic integral of the first kind. The result shows that no numerical integration is needed for the non-zero cosmological constant, if the universe is spatially flat.Comment: Accepted for publication in Astronomy & Astrophysics. 2 page

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

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 dilationComment: Ap.J., in press, uuencoded .ps file, 33 pages plus 5 figure