1,721,059 research outputs found
Emden-chandrasekhar axisymmetric, rigidly rotating polytropes III - Determination of equilibrium configurations by an improvement of Chandrasekhar's method
No full textThe author determines equilibrium configurations of Emden-Chandrasekhar axisymmetric, solid-body rotating polytropes, defined as EC polytropes, for polytropic indices ranging from 0 (homogeneous bodies) to 5 (Roche-type bodies). To this aim, he improves Chandrasekhar's method to determine equilibrium configurations in two respects: namely, (1) no distinction exists between undistorted and distorted terms in the expression of the potential, and (2) the comparison between the expressions of gravitational potential and its first derivatives inside and outside the body has to be made on the boundary of a sphere of radius ξ0 ≥ ΞE, which does not necessarily coincide with the undistorted Emden's sphere of radius ΞE. The author also allows different values of ξ0 for different physical parameters, and chooses a special set which fits more refined results (involving more complicated and more expensive computer codes) by James (1964)
Emden-Chandrasekhar axisymmetric, solid-body rotating polytropes II - Power series solutions to EC associated equations of degree 0 and 2
No full textAccording to the general results of a previous work (Caimmi, 1980), solutions to EC equation, which expresses a necessary and sufficient condition for equilibrium of Emden-Chandrasekhar axisymmetric solid-body rotating polytropes, are taken into account. The author extends the methods used by Seidov and Kuzakhmedov (1977), and Mohan and Al-Bayaty (1980), to construct power series related to the solid-body rotating configurations. Comparison between results of this paper and the accurate results by Linnell (1977, 1981) obtained using a different approach lead to a fair agreement
Emden-Chandrasekhar axisymmetric, rigid-body rotating polytropes IV - Exact configurations for n = 5
No full textIn connection with the basic theory reported in a previous paper for EC1 (rigidly rotating) polytropes, exact configurations are defined as configurations for which the equilibrium equation has solutions which are infinitely close to some analytical function and the related gravitational potential coincides, in fact, with the gravitational potential due to mass distribution, at any point not outside the system. The author restricts to the special case n = 5 and divides the related polytropes into two components, a massive body where each mass element has a finite (polytropic) distance from the centre, and a massless atmosphere where each mass element has an infinite (polytropic) distance from the centre. In the special case n = 0 it is shown that a particular configuration, the spheroidal one, is an exact configuration and evidence is given that spheroidal configurations are the most stable among all the allowed (axisymmetric) configurations. It is also pointed out that EC1 polytropes with n = 0 and incompressible Maclaurin spheroids belong to different sequences, even if they exhibit some common features
On bifurcation points in pseudo-barotropes
No full textStarting from the equations of hydrodynamics, which include both collisional and collisionless ideal fluids, the main properties of pseudo-barotropes are revisited and special attention is deserved to a necessary condition for equilibrium, i.e. the coincidence of the boundary with an isopotential (gravitational + centrifugal) surface. By use of the above condition, a new method is formulated to find bifurcation points from axisymmetric to triaxial pseudo-barotropic sequences
Chemical evolution of the Galaxy at the initial rapid-collapse phase
No full textThe dynamical and chemical evolution of the Galaxy are studied simultaneously in order to search for correlation between the phase of early collapse and the amount of metals produced by nucleosynthesis in newly formed stars. Simple equations are derived for the dynamical evolution, accounting for the experimental values of axial ratio and semimajor axis of the Galaxy. A particular stellar birth-rate function is adopted. The boundary condition is chosen that at the present time the birth-rate function should coincide with Salpeter's (1955). The resulting equations were solved numerically, and the effect of various parameters on gas density and metallicity is studied
The Arithmetic Mean Standard Deviation Distribution: A Geometrical Framework
Full text linkThe current attempt is aimed to outline the geometrical framework of a well known statistical problem, concerning the explicit expression of the arithmetic mean standard deviation distribution. To this respect, after a short exposition, three steps are performed as 1) formulation of the arithmetic mean standard deviation as a function of the errors which, by themselves, are statistically independent; 2) formulation of the arithmetic mean standard deviation distribution as a function of the errors; 3) formulation of the arithmetic mean standard deviation distribution as a function of the arithmetic mean standard deviation and the arithmetic mean rms error. The integration domain can be expressed in canonical form after a change of reference frame in the n-space, which is recognized as an infinitely thin n-cylindrical corona where the symmetry axis coincides with a coordinate axis. Finally, the solution is presented and a number of (well known) related parameters are inferred for sake of completeness
A generalized Schmidt star formation law: observational constraints. II
No full textThis paper aims to see whether the observed distribution of the Roberts time for different samples of late-type galaxies of a given class (normal, active) may be fitted by a single theoretical distribution, and what additional constraints are put on models obeying a generalized Schmidt star formation law. We find that an extended Poisson distribution with expected value k*=2.5Gyr and median value k‡=2.83Gyr is consistent with five different samples of normal galaxies, provided systems with Roberts time TR >7Gyr are excluded, and an extended Poisson distribution with expected value k*=0.05Gyr and median value k‡=0.52Gyr is consistent with both a sample of active galaxies and a sample of compact HII regions. In this view, active galaxies and ``normal'' galaxies with TR >7Gyr should be regarded as merger products in different stages of evolution. In dealing with a generalized Schmidt star formation law, we take into consideration closed, comoving models of chemical evolution. The history of a galaxy is described by two main phases: contraction (which produces the extended component) and equilibrium (which gives the disk). Negative values of the ratio of contraction time to age of a galaxy, Tc/T, relate with present-day, fractional star formation rates CD 5Gyr but, in general, the reverse is not true. Again, an extended Poisson distribution with expected value k*=2.5Gyr and median value k‡= 2.83Gyr is consistent with two different samples (for which total masses also are reported and then ratios Tc/T can be calculated) of normal galaxies, provided systems for which Tc/T 0 for normal galaxies; and Tc/T1011Msun) normal galaxies; a generalized Schmidt star formation law with an exponent n=~1 is favoured over one with n=~2. More precisely, 1<~n<~1.8 with a preferred value n=~1.2, which makes a generalized Schmidt star formation law with n=~1 consistent with the observations. Finally, a stochastic process of star formation, related to a Poisson distribution, is briefly outlined
The integral Newton's and MacLaurin's theorems in tensor form
No full textThe current paper deals with the investigation of the gravitational potential of heterogeneous ellipsoids and its extension to the tensor potential, since little attention has been given to this point in the last century. In this view, both integral Newton's and integral MacLaurin's theorems are formulated in tensor form. The generalization is extended to heterogeneous homeoids and focaloidally striated ellipsoids, respectively. A discontinuity in the tensor potential is found across a homogeneous, infinitely thin focaloid, which vanishes in the spherical limit. The potential-energy tensors related to focaloidally striated ellipsoids are expressed in integral form, depending on the density profile. All the results are particularized to the spherical limit, for which both Newton's and MacLaurin's theorems hold. With the aim of illustrating the procedure, an explicit calculation of the potential-energy tensors is outlined in the special case of homogeneous, spherical configurations. Finally, an application is made to the Coma cluster of galaxies
Il problema della misura
No full textI fondamenti della teoria degli errori sono presentati dal punto di vista della meccanica statistica, basandosi su un concetto primitivo (stato microscopico) e su un assioma (principio di indifferenza)
Anisotropy and rotation in homeoidally striated Jacobi ellipsoids
No full textIn this paper a unified theory of systematically rotating and peculiar motions is developed for homeoidally striated Jacobi ellipsoids, where both real and imaginary rotations are considered. The effect of positive or negative residual motion excess along the equatorial plane is considered to be equivalent either to an additional real or an imaginary rotation, respectively. The principle results consist of (i) the discovery that homeoidally striated Jacobi ellipsoids always admit an adjoint configuration i.e. a classical Jacobi ellipsoid of equal mass and axes; (ii) the establishment of further constraints on the amount of residual velocity anisotropy along the principal axes for triaxial configurations; (iii) the finding that bifurcation points from axisymmetric to triaxial configurations occur as in classical Jacobi ellipsoids, contrary to earlier findings. An interpretation of recent results from numerical simulations on stability is provided in the light of the model
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