Classical and relativistic evolution of an extra-galactic jet with back-reaction

We consider a turbulent jet which is moving in a Lane--Emden ($n=5$) medium. The conserved quantity is the energy flux, which allows finding, to first order, an analytical expression for the velocity and an approximate trajectory. The conservation of the relativistic flux for the energy allows deriving, to first order, an analytical expression for the velocity, and numerically determining the trajectory. The back-reaction due to the radiative losses for the trajectory is evaluated both in the classical and the relativistic case.Comment: 19 pages and 11 figure

Semi-analytical formulas for the Hertzsprung-Russell Diagram

The absolute visual magnitude as function of the observed colour (B-V), also named Hertzsprung-Russell diagram can be described through five equations; that in presence of calibrated stars means eight constants. The developed framework allows to deduce the remaining physical parameters that are mass, radius and luminosity. This new technique is applied to the first 10 pc, the first 50 pc, the Hyades and to the determination of the distance of a cluster. The case of the white dwarfs is analysed assuming the absence of calibrated data: our equation produces a smaller $\chi^2$ in respect to the standard colour-magnitude calibration when applied to the Villanova Catalog of Spectroscopically Identified White Dwarfs. The theoretical basis of the formulae for the colours and the bolometric correction of the stars are clarified through a Taylor expansion in the temperature of the Planck distribution.Comment: Pages 35, Figures 1

The relativistic equation of motion in turbulent jets

The turbulent jets are usually described by classical velocities. The relativistic case can be treated starting from the conservation of the relativistic momentum. The two key assumptions which allow to obtain a simple expression for the relativistic trajectory and relativistic velocity are null pressure and constant density.Comment: 2 figures 7 page

New formulae for the Hubble Constant in a Euclidean Static Universe

It is shown that the Hubble constant can be derived from the standard luminosity function of galaxies as well as from a new luminosity function as deduced from the mass-luminosity relationship for galaxies. An analytical expression for the Hubble constant can be found from the maximum number of galaxies (in a given solid angle and flux) as a function of the redshift. A second analytical definition of the Hubble constant can be found from the redshift averaged over a given solid angle and flux. The analysis of two luminosity functions for galaxies brings to four the new definitions of the Hubble constant. The equation that regulates the Malmquist bias for galaxies is derived and as a consequence it is possible to extract a complete sample. The application of these new formulae to the data of the two-degree Field Galaxy Redshift Survey provides a Hubble constant of $( 65.26 \pm 8.22 ) \mathrm{\ km\ s}^{-1}\mathrm{\ Mpc}^{-1}$ for a redshift lower than 0.042. All the results are deduced in a Euclidean universe because the concept of space-time curvature is not necessary as well as in a static universe because two mechanisms for the redshift of galaxies alternative to the Doppler effect are invoked.Comment: 27 pages 10 Figure

The Luminosity Function of Galaxies as modelled by the Generalized Gamma Distribution

Two new luminosity functions of galaxies can be built starting from three and four parameter generalized gamma distributions. In the astrophysical conversion, the number of parameters increases by one, due to the addition of the overall density of galaxies. A third new galaxy luminosity function is built starting from a three parameter generalized gamma distribution for the mass of galaxies once a simple nonlinear relationship between mass and luminosity is assumed; in this case the number of parameters is five because the overall density of galaxies and a parameter that regulates mass and luminosity are added. The three new galaxy luminosity functions were tested on the Sloan Digital Sky Survey (SDSS) in five different bands; the results always produce a "better fit" than the Schechter function. The formalism that has been developed allows to analyze the Schechter function with a transformation of location. A test between theoretical and observed number of galaxies as a function of redshift was done on data extracted from a two-degree field galaxy redshift survey.Comment: 14 Figures 24 page