The light curve in supernova modeled by a continuous radioactive decay of 56^{56}Ni

The UVOIR bolometric light curves are usually modeled by the radioactive decay. In order to model more precisely the absolute/apparent magnitude versus time relationship the continuous production of radioactive isotopes is introduced. A differential equation of the first order with separable variables is solved.Comment: 5 pages 2 figure

The relativistic three dimensional evolution of SN 1987A

The high velocities observed in supernovae require a relativistic treatment for the equation of motion in the presence of gradients in the density of the interstellar medium. The adopted theory is that of the thin layer approximation. The chosen medium is auto-gravitating with respect to an equatorial plane. The differential equation which governs the relativistic conservation of momentum is solved in numerically and by recursion. The asymmetric field of relativistic velocities as well the time dilation are plotted at the age of 1 yr for SN 1987A.Comment: 7 pages and 4 Figure

A classical and a relativistic law of motion for spherical supernovae

In this paper we derive some first order differential equations which model the classical and the relativistic thin layer approximations. The circumstellar medium is assumed to follow a density profile of Plummer type, or of Lane--Emden ($n=5$) type, or a power law. The first order differential equations are solved analytically, or numerically, or by a series expansion, or by recursion. The initial conditions are chosen in order to model the temporal evolution of SN 1993J over ten years and a smaller chi-squared is obtained for the Plummer case with eta=6. The stellar mass ejected by the SN progenitor prior to the explosion, expressed in solar mass, is identified with the total mass associated with the selected density profile and varies from $0.217$ to $0.402$ when the central number density is $10^7$ particles per cubic centimeter. The Full width at half maximum of the three density profiles, which can be identified with the size of the Pre-SN 1993J envelope, varies from 0.0071 pc to 0.0092 pc.Comment: 15 figures and 34 page

Three dimensional evolution of SN 1987A in a self-gravitating disk

The introduction of a exponential or power law gradient in the interstellar medium (ISM) allows to produce an asymmetric evolution of the supernova remnant (SNR) when the framework of the thin layer approximation is adopted. Unfortunately both the exponential and power law gradients for the ISM do not have a well defined physical meaning. The physics conversely is well represented by an isothermal self-gravitating disk of particles whose velocity is everywhere Maxwellian. . We derived a law of motion in the framework of the thin layer approximation with a control parameter of the swept mass. The photon's losses ,that are often neglected in the thin layer approximation, are modeled trough a velocity dependence. The developed framework is applied to SNR 1987A and the three observed rings are simulated.Comment: 11 pages and 9 figures. arXiv admin note: text overlap with arXiv:1109.401

Revisiting the Cosmological Principle in a Cellular Framework

The Cosmological Principle in it's various versions states that: (i) the Galaxy does not occupy a particular position, (ii) the Universe is homogeneous and isotropic. This statement does not agree with the recent astronomical observations in the range z lower than 0.05 which are in agreement with a cellular structure of the Universe. Here we present a local analysis of the inhomogeneity of the Universe. When z is greater than 0.05 our analysis cannot be applied because the astronomical sample of galaxies here processed is not complete. The two tools of the Poisson Voronoi tessellation (PVT) and the luminosity function for galaxies allow of building a new version of the local Cosmological Principle.Comment: 25 pages, 16 figure