arXiv subjects
Publications and source records attributed to Lorenzo Zaninetti.
A new analytical solution for the luminosity distance in flat $Λ$CDM cosmology is derived in terms of elliptical integrals of first kind with real argument. The consequent derivation of the distance modulus allows evaluating the Hubble constant, $H_0=69.77\pm 0.33$, $\om= 0.295\pm0.008$ and the cosmological constant, $Λ= (1.194 \pm 0.017)10^{-52} \frac{1}{m^2}$.
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.
The transition from ordered to disordered structures in Voronoi tessellation is obtained by perturbing the seeds that were originally identified with two types of lattice in 2D and one type in 3D. The area in 2D and the volume in 3D are modeled with the Kiang function. A new relationship that models the scaling of the Kiang function with a geometrical parameter is introduced. A first application models the local structure of sub- and supercritical ammonia as function of the temperature and a second application models the volumes of cosmic voids.
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.
The evaluation of the physical parameters or effects such as the luminosity function (LF) or the photometric maximum (PM) for galaxies is routinely modeled by their spectroscopic redshift. Here, we model LF and PM for galaxies by the photometric redshift as given by the Spitzer Wide-Area Infrared Extragalactic (SWIRE) catalog in the framework of a lognormal LF. In addition, we compare our model with the Schechter LF for galaxies. The adopted cosmological framework is that of the flat cosmology.
An enhancement in the number of galaxies as function of the redshift is visible on the SDSS Photometric Catalogue DR 12 at z=0.383. This over-density of galaxies is named the Great Wall. This variable number of galaxies as a function of the redshift can be explained in the framework of the luminosity function for galaxies. The differential of the luminosity distance in respect to the redshift is evaluated in the framework of the LCDM cosmology.
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 which can be exponential, Gaussian, Plummer-like, self-gravitating of Lane--Emden ($n=5$) type, or power law. The first order differential equations are solved analytically, or numerically, or by a series expansion, or by recursion, or by Padé approximation. The initial conditions are chosen in order to model the temporal evolution of SN 1993J over ten years. The Padé approximated equations of motion are applied to four SNRs: Tycho, Cas A, Cygnus loop, and SN~1006.
In order to model the Fermi bubbles we apply the theory of the superbubble (SB). A thermal model and a self-gravitating model are reviewed. We introduce a third model based on the momentum conservation of a thin layer which propagates in a medium with an inverse square dependence for the density. A comparison have been made between the sections of the three models and the section of an observed map of the Fermi bubbles. An analytical law for the SB expansion as function of the time and polar angle is deduced. We derive a new analytical result for the image formation of the Fermi bubbles in an elliptical framework.
Based on well known photometric rules for the number of galaxies as function of the distance in Mpc we model the so called "Great Wall" which is visible on the Cosmicflows-2 catalog. The gravitational field is evaluated at the light of the shell theorem and a finite value for the gravitational field is numerically derived.
The luminosity function (LF) for stars is here fitted by a Schechter function and by a Gamma probability density function. The dependence of the number of stars on the distance, both in the low and high luminosity regions, requires the inclusion of a lower and upper boundary in the Schechter and Gamma LFs. Three astrophysical applications for stars are provided: deduction of the parameters at low distances, behavior of the average absolute magnitude with distance, and the location of the photometric maximum as a function of the selected flux. The use of the truncated LFs allows to model the Malmquist bias.
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.
The spiral structure of the Milky Way can be simulated by adopting percolation theory, where the active zones are produced by the evolution of many supernova (SN). Here we assume conversely that the percolative process is triggered by superbubbles (SB), the result of multiple SNs. A first thermal model takes into account a bursting phase which evolves in a medium with constant density, and a subsequent adiabatic expansion which evolves in a medium with decreasing density along the galactic height. A second cold model follows the evolution of an SB in an auto-gravitating medium in the framework of the momentum conservation in a thin layer. Both the thermal and cold models are compared with the results of numerical hydro-dynamics. A simulation of GW~46.4+5.5, the Gould Belt, and the Galactic Plane is reported. An elementary theory of the image, which allows reproducing the hole visible at the center of the observed SB, is provided.
In this paper we present formulae for chord length distribution in the framework of Poissonian Voronoi Tessellation (PVT) and non Poissonian Voronoi Tessellation (NPVT). The introduction of the scale parameter in the obtained distributions allows us to model the chord for cosmic voids. A graphical comparison between cosmic voids visible on two catalogs of galaxies, 2dFGRS and VIPERS, and theoretical random chords is reported.
In this paper we derive three equations of motion for a supernova remnant (SNR) in the framework of the thin layer approximation using the Padé approximant. The circumstellar medium is assumed to follow a density profile of either an exponential type, a Gaussian type, or a Lane--Emden ($n=5$) type. The three equations of motion are applied to four SNRs: Tycho, Cas A, Cygnus loop, and SN~1006. The percentage error of the Padé approximated solution is always less than $10\%$. The theoretical decrease of the velocity over ten years for SNRs is evaluated.
A classical and a relativistic law of motion for a supernova remnant (SNR) are deduced assuming an inverse power law behavior for the density of the interstellar medium and applying the thin layer approximation. A third equation of motion is found in the framework of relativistic hydrodynamics with pressure, applying momentum conservation. These new formulas are calibrated against a decade of observations of \snr. The existing knowledge of the diffusive processes of ultrarelativistic electrons is reviewed in order to explain the behavior of the `U' shaped profile of intensity versus distance from the center of SN 1993J.
The voids between galaxies are identified with the volumes of the Poisson Voronoi tessellation. Two new survival functions for the apparent radii of voids are derived. The sectional normalized area of the Poisson Voronoi tessellation is modelled by the Kiang function and by the exponential function. Two new survival functions with equivalent sectional radius are therefore derived; they represent an alternative to the survival function of voids between galaxies as given by the self-similar distribution. The spatial appearance of slices of the 2dF Galaxy Redshift Survey is simulated.
Self-similar solutions to the problem of a special relativistic law of motion for thin shells of matter are calculated. These solutions represent the special relativistic generalization of momentum conservation for the thin layer approximation in classical physics. The analytical and numerical results are applied to Supernova Remnant 1987 A.
The asymmetric shape of the nebula around $η$-Carinae (Homunculus) can be explained by a spherical expansion in a non-homogeneous medium. Two models are analyzed: an exponential and an inverse power law dependence for the density as a function of distance from the equatorial plane. The presence of a medium with variable density along the polar direction progressively converts the original spherical shell into a bipolar nebula. In the case of the nebula around $η$-Carinae, we know the time elapsed since the great outburst in 1840. An exact match between observed radii and velocities can be obtained by fine tuning the parameters involved, such as initial radius, initial velocity and the typical scale that characterizes the gradient in density. The observed radius and velocity of the Homunculus as a function of the polar angle in spherical coordinates can be compared with the corresponding simulated data by introducing the efficiency in a single or multiple directions. Once the 3D spatial structure of the Homunculus is obtained, we can compose the image by integrating along the line of sight. In order to simulate the observed image, we have considered a bipolar nebula with constant thickness and an optically thin emitting layer. Some simulated cuts of the relative intensity are reported and may represent a useful reference for the astronomical cuts.