The Truncated Lognormal Distribution as a Luminosity Function for SWIFT-BAT Gamma-Ray Bursts

2019

IJAA

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The gamma function is a good approximation to the luminosity function of astrophysical objects, and a truncated gamma distribution would permit a more rigorous analysis. This paper examines the generalized gamma distribution (GG) and then introduces the scale and the new double truncation. The magnitude version of the truncated GG distribution with scale is adopted in order to fit the luminosity function (LF) for galaxies or quasars. The new truncated GG LF is applied to the five bands of SDSS galaxies, to the 2dF QSO Redshift Survey in the range of redshifts between 0.3 and 0.5, and to the COSMOS QSOs in the range of redshifts between 3.7 and 4.7. The average absolute magnitude versus redshifts for SDSS galaxies and QSOs of 2dF was modeled adopting a redshift dependence for the lower and upper absolute magnitude of the new truncated GG LF.

Section: Generalized Gamma Lfmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

New Probability Distributions in Astrophysics: I. The Truncated Generalized Gamma

2019

IJAA

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“…where we used 0 = 67.93km s −1 Mpc −1 , see Zaninetti (2016b). The differences between the two distances are the luminosity distance and the and the pseudo-Euclidean distance, which can be outlined in terms of a percentage difference: Δ.…”

Section: Luminosity Distancementioning

confidence: 99%

Filaments of galaxies and Voronoi diagrams

2018

Open Astronomy

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The intersections between a spherical shell and the faces of Voronoi's polyhedrons are numerically evaluated. The nodes of these intersections are the points that share the same distances from three nuclei. The nodes are assumed to be the places where we will find clusters of galaxies. The cosmological environment is given by the coupling between the number of galaxies as function of the redshift and the LCDM cosmology.

“…where x is the random variable, x l is the lower bound, x u is the upper bound, m is the scale parameter and σ is the shape parameter, see [10] for more details. Tables 3 and 4 report the four parameters of the TL for T 50 and T 90 respectively.…”

Section: The Fitmentioning

confidence: 99%

Classical and Relativistic Models for Time Duration of Gamma-Ray Bursts

2017

JHEPGC

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A classical model based on a power law assumption for the radius-time relationship in the expansion of a supernova (SN) allows to derive an analytical expression for the flow of mechanical kinetic energy and the time duration of gamma-ray burst (GRB). A random process based on the ratio of two truncated lognormal distributions for luminosity and luminosity distance allows to derive the statistical distribution for time duration of GRBs. The high velocities involved in the first phase of expansion of a SN require a relativistic treatment. The circumstellar medium is assumed to follow a density profile of Plummer type with eta = 6. A series solution for the relativistic flow of kinetic energy allows to derive in a numerical way the duration time for GRBs. Here we analyze two cosmologies: the standard cosmology and the plasma cosmology.