Abstract
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 requires 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 analyse two cosmologies: the standard cosmology and the plasma cosmology.
Highlights
The theoretical efforts for gamma-ray bursts (GRBs) analyze: 1) the different predictions between cannonball and fireball model, see [1] [2]; 2) the acceleration of ultrahigh-energy cosmic rays (UHECRs) at the afterglow phase, see [3]; 3) a possible connection with high-energy neutrinos (HEN) and gravitational waves (GW), see [4]; 4) the frames of hypersphere world-universe model (WUM), see [5]
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
Zaninetti reliability of time duration for GRBs along two astrophysical hypothesis: 1) the GRBs are generated in external galaxies; 2) the GRBs are connected with the light curve (LC) of a supernova (SN)
Summary
The theoretical efforts for gamma-ray bursts (GRBs) analyze: 1) the different predictions between cannonball and fireball model, see [1] [2]; 2) the acceleration of ultrahigh-energy cosmic rays (UHECRs) at the afterglow phase, see [3]; 3) a possible connection with high-energy neutrinos (HEN) and gravitational waves (GW), see [4]; 4) the frames of hypersphere world-universe model (WUM), see [5]. We briefly recall that the time duration for gamma-ray burst (GRB) is measured without the knowledge of the redshift, see as an example [6]. L. Zaninetti reliability of time duration for GRBs along two astrophysical hypothesis: 1) the GRBs are generated in external galaxies; 2) the GRBs are connected with the light curve (LC) of a supernova (SN).
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