A two-component model of a spherical stellar system

As a generalization of the King's widely-used model for a spherical stellar system containing stars of identical masses, a two-component model of an equilibrium stellar system consisting of stars of two different masses is built proceeding from a proper generalization of the distribution function. In such a system, the principle of thermal equilibrium, generally speaking, does not hold, i.e. equipartition of mean kinetic energy between light and heavy stars is absent.The radial distribution of partial density and velocity dispersion for each of the components and of the total density and velocity dispersion is obtained. The profiles of both the total density and velocity dispersion differ considerably from those given by the King's one-component model, especially in the centre of the system. In particular, the velocity dispersion of stars may there have a non-monotonous behaviour. The possibility of applying the many-component model for the explanation of the recently discovered luminosity cusps in the central regions of some elliptical galaxies is briefly discussed.     

Kinematic analysis of stellar radial velocities by the spherical harmonics

A method for a kinematic analysis of stellar radial velocities using spherical harmonics is proposed. This approach does not depend on the specific kinematic model and allows both low-frequency and high-frequency kinematic radial velocity components to be analyzed. The possible systematic variations of distances with coordinates on the celestial sphere that, in turn, are modeled by a linear combination of spherical harmonics are taken into account. Theoretical relations showing how the coefficients of the decomposition of distances affect the coefficients of the decomposition of the radial velocities themselves have been derived. It is shown that the larger the mean distance to the sample of stars being analyzed, the greater the shift in the solar apex coordinates, while the shifts in the Oort parameter A are determined mainly by the ratio of the second zonal harmonic coefficient to the mean distance to the stars, i.e., by the degree of flattening of the spatial distribution of stars toward the Galactic plane. The distances to the stars for which radial velocity estimates are available in the CRVAD-2 catalog have been decomposed into spherical harmonics, and the existing variations of distances with coordinates are shown to exert no noticeable influence on both the solar motion components and the estimates of the Oort parameter A, because the stars from this catalog are comparatively close to the Sun (no farther than 500 pc). In addition, a kinematic component that has no explanation in terms of the three-dimensional Ogorodnikov-Milne model is shown to be detected in the stellar radial velocities, as in the case of stellar proper motions.     

The dynamics of head-on collisions of spherical stellar systems

Energy changes in a head-on collision between two unequal Plummer model stellar systems (galaxies) are studied analytically under the impulsive approximation. The variation of the disruptive effects within and the mass escape from systems widely differing in mass and scalelength ratios are determined and some physical implications regarding the dynamical stability of the systems undergoing head-on collisions are indicated. It is found that if two systems differ considerably in size, both systems generally survive the collision if (i) the mass of the bigger is greater than about six times the mass of the smaller and (ii) the density of the smaller is more than about twenty-five times the entity of the bigger system, when the velocity at minimum separation is equal to the parabolic velocity of escape.     

Analysis of the three-dimensional stellar velocity field using vector spherical functions

We apply vector spherical functions to problems of stellar kinematics. Using these functions allows all of the systematic components in the stellar velocity field to be revealed without being attached to a specific physical model. Comparison of the theoretical decomposition coefficients of the equations for a particular kinematical model with observational data can provide precise information about whether the model is compatible with the observations and can reveal systematic components that are not described by this model. The formalism of vector spherical functions is particularly well suited for analyzing the present and future (e.g., GAIA) catalogs containing all three velocity vector components: the propermotions in both coordinates and the radial velocity. We show that there are systematic components in the proper motions of Hipparcos stars that cannot be interpreted in terms of the linear Ogorodnikov-Milne model. The same result is also confirmed by an analysis of the radial velocities for these stars.     

Strong spherical magnetogasdynamic shock waves in rotating stellar atmosphere

An analytic expression for the velocity of magnetogasdynamic shock wave, propagating in rotating inter stellar atmosphere has been obtained by using the method of characteristics and considering the effect of coriolis force. It has been shown that in the outer convective layer of the star Coriolis force and magnetic field both have significant effect on the shock velocity.     

Radially anisotropic models of collisionless spherical stellar systems without central singularity

A new class of the simplest equilibrium two-parameter distribution functions for spherical stellar systems with a radially anisotropic stellar velocity distribution is investigated. The models under consideration are a less singular counterpart of the so-called generalized polytropes, which in the past were among the most popular models in works on the equilibrium and stability of gravitating systems. In contrast to the well-known generalized polytropes, the proposed models have finite density and potential at the center. The absence of a singularity is necessary for a proper consideration of the radial orbit instability, which is the most important instability of spherical stellar systems. The main observed parameters of the proposed models (potential, density, anisotropy) are compared with those in well-known equilibrium models.     

The Zeeman effect in the Sobolev approximation: applications to spherical stellar winds

Modern spectropolarimeters are capable of detecting subkilogauss field strengths using the Zeeman effect in line profiles from the static photosphere, but supersonic Doppler broadening makes it more difficult to detect the Zeeman effect in the wind lines of hot stars. Nevertheless, the recent advances in observational capability motivate an assessment of the potential for detecting the magnetic fields threading such winds. We incorporate the weak-field longitudinal Zeeman effect in the Sobolev approximation to yield integral expressions for the flux of circularly polarized emission. To illustrate the results, two specific wind flows are considered: (i) spherical constant expansion with   v ( r ) = v _∞  and (ii) homologous expansion with   v ( r ) ∝ r   . Axial and split monopole magnetic fields are used to schematically illustrate the polarized profiles. For constant expansion, optically thin lines yield the well-known 'flat-topped' total intensity emission profiles and an antisymmetric circularly polarized profile. For homologous expansion, we include occultation and wind absorption to provide a more realistic observational comparison. Occultation severely reduces the circularly polarized flux in the redshifted component, and in the blueshifted component, the polarization is reduced by partially offsetting emission and absorption contributions. We find that for a surface field of approximately 100 G, the largest polarizations result for thin but strong recombination emission lines. Peak polarizations are approximately 0.05 per cent, which presents a substantial although not inconceivable sensitivity challenge for modern instrumentation.     

Physical and orbital properties of the stellar system HIP 43766

In this paper, we present the analysis of the stellar binary system HIP 43766 to determine its properties. We rely on dynamical modeling and atmospheric modeling with recent data to determine the orbital solution and the physical properties of the system. There is a consistency between observed and synthetic photometry obtained using atmospheric modeling. The calculated dynamical mass sum of the system ranged between 1.691 and 2.609 solar masses, while it ranges between 2.0 and 2.1 as estimated utilizing atmospheric modeling. This could be due to inaccuracy in estimating the orbit, which could be modified with future observations with more relative positional measurements. The parameters of the system and the position of the components on the evolutionary tracks show that the system consists of F5 and G5 subgiant stars, mostly formed by fragmentation. A dynamical mass sum is predicted for the system.     

Potentials for stationary point-axial stellar system models

Some potentials for a stationary stellar system model with point-axial symmetry and equatorial plane of symmetry that verifies Chandrasekhar's postulates have been obtained.Paper presented at the 12th European Astronomical Meetings of the IAU on European Astronomers Look to the Future, held 8–11 October, 1990, Davos, Switzerland.     

Trajectories of the local centroids in a two-component stellar system near the sun

In a stellar system in nonsteady states and according to Chandrasekhar's axially-symmetric model, the general trajectory of a local centroid is determined. In the neighbourhood of the Sun, a two-component stellar system is adopted to explain the kinematic behaviour of the stellar samples. Depending on the kinematic parameters of each subsystem, the trajectories of every local subcentroid are shown.Life is long for the wise stars but short for the giddy ones Some Seneca-like words about De breviate vitaePaper presented at the 11th European Regional Astronomical Meetings of the IAU on New Windows to the Universe, held 3–8 July, 1989, Tenerife, Canary Islands, Spain.     

Trends of stellar entropy along stellar evolution

This paper is devoted to discussing the difference in the thermodynamic entropy budget per baryon in each type of stellar object found in the Universe. We track and discuss the actual decrease of the stored baryonic thermodynamic entropy from the most primitive molecular cloud up to the final fate of matter in black holes, passing through evolved states of matter as found in white dwarfs and neutron stars.We then discuss the case of actual stars with different masses throughout their evolution, clarifying the role of the virial equilibrium condition for the decrease in entropy and related issues. Finally, we discuss the role of gravity in driving the composition and the structural changes of stars with different Main Sequence masses during their evolution up to the final product. Particularly, we discuss the entropy of a black hole in this context arguing that the dramatic increase in its entropy, differently from the other cases, is due to the gravitational field itself.     

Isolation of integrals for centroid orbits in stellar system models

In this paper we present two solutions for isolating integrals of the centroid motion in a non-stationary stellar system under the ellipsoidal hypothesis with point-axial symmetry.Paper presented at the 11th European Regional Astronomical Meetings of the IAU on New Windows to the Universe, held 3–8 July, 1989, Tenerife, Canary Islands, Spain.     

A calculation of structural parameters of spherical stellar systems by means of characteristic functions method. I. Theory

To calculate structural parameters of stellar systems such as an effective radius and central space (or surface) density, the method of characteristic functions is suggested. The characteristic function of the system is a Fourier image of their normalized space density profile f₃(r). In the case of spherical symmetry the probability distribution of r (Q₃(r) = (3/a³)r²f₃(r)) and its orthogonal projections have the same characteristic functions. This fact is used to calculate the effective radii of a few star cluster models (King law, Plummer model and Gausian profile). It is shown, that the characteristic function for King law clusters tends to a finite generalised function if the concentration parameter c is large. The expression for the effective radius (at c ≫ 1) is given. The formula of the effective radius in the Plummer model as well as the relation between the one-dimensional central velocity dispersion and the root mean square velocity are obtained. It is shown, that in the Gaussian model and for King law clusters the effective radius (half-mass visual radius) can differ from the effective (harmonic) radius a few times. This fact should be taken into account in estimating the mass-to-light ratio from the virial mass of such systems using the King radius.