Stellar structures with constant local adiabatic index under extreme relativistic conditions

Stellar structures with a constant local adiabatic index Γ have been discussed under the extreme relativistic condition (dP/dρ=1, at the center of the configuration). The equation of state,Pαρ^Γ, where ρ _r is the rest-mass density leads to the relations, (i)ρ=AP ^1/Γ?P/(Γ?1) between energy density and pressure, and (ii)e=NP between internal energy density and pressure, where the constantN may be called local polytropic index. The local adiabatic index, Γ, is found to be related to the adiabatic index, γ, through a simple relation, Γ=γ(1+P/ρ). The maximum value of surface redshift comes out to be 0.614 when σ=(P/ρ)₀=0.6. The structure are bound for σ≤0.83 and the maximum value of the binding coefficient is 0.181 at σ=0.4. For bound structures the central redshift z₀≤8.24. The maximum mass of neutron star based upon such a model comes out to be 2.39M _⊙ (for σ=0.4) and the maximum size comes out to be 13.7 km (for σ=0.2).     

Massive configurations with constant densities

Two new classes of solutions with constant observed proper and rest mass densities are described. Unlike the well-known solution of constant coordinate mass density, these solutions pertain to realistic physical situations. For these solutions, the various relevant parameters, viz. the redshifts (dP/d)₀ and binding coefficients have been calculated.     

Static cylindrically symmetric gravitational field with cosmological constant

We show that a class of solutions for a vacuum cylindrically symmetric gravitational field with nonvanishing cosmological constant reduce to the welknown Levi-Civita metric close to the axis. All the circular geodesics in this generalized vacuum are time like, null or space like depending on the relative magnitudes of the two parameters appearing in the solutions.For other particles moving inZ=constant plane there are some cases where the trapping of timelike and null trajectories occur, while in other cases some of the particles may orbit round the axis in a fixed zone bounded by two limiting radii.     

Homeoidally striated density profiles: sequences of virial equilibrium configurations with constant anisotropy parameters

The formulation of the tensor virial equations is generalized to unrelaxed configurations, where virial equilibrium does not coincide with dynamical (or hydrostatic) equilibrium. Homeoidally striated, Jacobi ellipsoids, which generalize classical Jacobi ellipsoids, are studied in detail. Further investigation is devoted to the generation of sequences of virial equilibrium configurations where the anisotropy parameters are left unchanged, including both flattened and elongated, triaxial configurations, and the determination of the related bifurcation points. An application is made to dark matter haloes hosting giant galaxies (M ≈ 10¹² m_⊙), with regard to assigned initial and final configuration, following and generalizing to many respects a procedure conceived by Thuan & Gott (1975). The dependence of the limiting axis ratios, below which no configuration is allowed for the sequence under consideration, on the change in mass, total energy, and angular momentum, during the evolution, is illustrated in some representative situations. The dependence of the axis ratios, ε₃₁ and ε₂₁, on a parameter, related to the initial conditions of the density perturbation, is analysed in connection with a few special cases. The same is done for the rotation parameters. Within the range of the rotation parameter, λ, deduced from high‐resolution numerical simulations, the shape of dark matter haloes is mainly decided by the amount of anisotropy in residual velocity distribution. On the other hand, the contribution of rotation has only a minor effect on the meridional plane, and no effect on the equatorial plane, as bifurcation points occur for larger values of λ. To this respect, dark matter haloes are found to resemble giant elliptical galaxies. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Fourier analysis of local Lyapunov characteristic exponents for satellite-type motions

For a binary star system with equal masses the transition from regular to stochastic motion has been determined by means of the Lyapunov Characteristic Numbers (LCN) in a paper of Gonczi and Froeschlé (1981), where the initial distance of the massless body to the second primary was used as parameter of integration. This time we analyse the Fourier spectra of the local LCNs (ln _k ⁱ ) of this system for different intervals of time.     

Static structure of general-relativistic degenerate configurations: Effects of a core

Models of spherically-symmetric static systems made up of self-gravitating, completely degenerate neutral fermions containing a core are constructed within the framework of general relativity and the effects of different core masses and compactness on the properties of the system are examined. For the specific case where the fermions are massive neutrinos (10 eV) we find, for example, that it is possible to have a neutrino halo with a normal Galaxy, or a cluster of galaxies, as the core, with the right values of mass and radius required of the invisible halo in the missing mass problem. The suggestive nature of these results calls for further studies using a more realistic equation of state.     

Gravitational collapse of a massive sphere of constant energy density

Gravitational collapse of a massive sphere of constant density has been studied from the point of view of a Keplerian observer. The asymptotic nature of collapse is attributed to the development of negative gravitational pressure acting radially outwards within the structure. The region of negative pressure asymptotically covers the entire interior asu=mass/radius tends to half.     

Static spherical configurations of cold matter in the Einstein-Cartan theory of gravitation

We investigate static, spherical configurations of cold catalized matter in the Einstein-Cartan theory of gravitation. Assuming that density of spin is proportional to the number density of baryonsn and using an equation of state of a degenerate, relativistic Fermi gas, we numerically integrated the relativistic equation of equilibrium. We have also studied the stability of those configurations. Configurations with central number densityn _c such that where is the effective pressure, are very similar to general relativistic configurations with the same central density. In the Einstein-Cartan theory there exists another disjoint family of equilibrium configurations for which but . Those configurations have very small masses 10^–6 g and raddi 10^–34 cm and are unstable.Supported in part by Research Grant MR-I-7.     

Stationary solutions and their characteristic exponents in the restricted three-body problem when the more massive primary is an oblate spheroid

This paper deals with the numerical investigations of the locations of the five equilibrium points by taking into consideration the effect of oblateness of the more massive primary for some systems of astronomical interest. This note is further concerned with the periodic solutions of the linearized equations of motion around the five equilibrium points. Interesting differences in the trends of the angular frequencies of these motions have been noticed.     

Some problems in constructing massive star models containing a chemically-inhomogeneous convective core with the local mixing-length theory

Some problems in constructing the massive star models which have a chemically-inhomogeneous convective core by using the local mixing-length theory are indicated. One problem is negative helium flux. Another one is a large discontinuity in velocity in the convective region. It does not seem easy to reconcile these problems with the present local mixing-length theory.     

An expanding Universe with constant pressure and no cosmological constant

Thanks to its fitting triumph, the ΛCDM paradigm is assumed to be the most powerful model, for describing the Universe dynamics, over much the myriad of cosmological models. Unfortunately, the quest of a self-consistent model remains not well explained, because it is not clear how to solve the problems of fine-tuning and coincidence, afflicting the ΛCDM framework; as a matter of fact, these theoretical drawbacks do not allow to consider the ΛCDM model, as the final picture of the modern cosmological scenario. Here, we show that the simplest model, which provides a constant equation of state for the pressure, leads to a generalization of ΛCDM, reducing to it in a particular case. Moreover, we highlight the physical mechanisms of this model, describing the thermodynamical reasons why a constant pressure should be negative in an expanding Universe. In addition, we fit the free parameters of our model by minimizing the chi square through the age differential method, involving a direct measurement of H.     

Einsteins' gravity with massive gravitons

Graviton may, in principle, have a small non-zero mass. In this paper the relevant theory of the massive graviton with six polarisations is developed. The drastic impact of a non-zero mass of the graviton on cosmology is also illustrated.     

Magnetic field configurations associated with fast solar wind

In this paper, we consider the implications of the observed inverse correlation between solar wind speed at Earth and the expansion rate of the Sun-Earth flux tube as it passes through the corona. We find that the coronal expansion rate depends critically on the large-scale photospheric field distribution around the footpoint of the flux tube, with the smallest expansions occurring in tubes that are rooted near a local minimum in the field. This suggests that the fastest wind streams originate from regions where large coronal holes are about to break apart and from the facing edges of adjacent like-polarity holes, whose field lines converge as they transit the corona. These ideas lead to the following predictions:

1. Weak holes and fragmentary holes can be sources of very fast wind.
2. Fast wind with steep latitudinal gradients may be generated where the field lines from the polar hole and a lower-latitude hole of like polarity converge to form a mid-latitude ‘apex’.
3. The fastest polar wind should occur shortly after sunspot maximum, when trailing-polarity flux converges onto the poles and begins to establish the new polar fields.

     

Quasi-spherical collapse with cosmological constant

The junction conditions between static and non-static space–times are studied for analysing gravitational collapse in the presence of a cosmological constant. We have discussed about the apparent horizon and their physical significance. We also show the effect of cosmological constant in the collapse and it has been shown that cosmological constant slows down the collapse of matter.     

Radio jet interactions with massive clouds

Three-dimensional simulations of light hydrodynamic jets are computed using the Zeus-3D code. We employ parameters corresponding to moderate to high power radio jets emerging through a galactic atmosphere or halo, and eventually crossing a tilted pressure matched interface with a hotter intracluster medium. These simulations aim the jets so that they hit massive dense clouds within the galactic halo. Such clouds are set up with radii several times that of the jet, and nominally correspond to giant molecular cloud complexes or small cannibalized galaxies. We find that powerful jets eventually disperse the clouds, but that, for the off-center collisions considered, non-axisymmetric instabilities are induced in those jets. Those instabilities grow faster for lower Mach number jets, and can produce disruptions substantially sooner than occurred in our earlier work on jets in the absence of collisions with massive clouds. Such interactions could be related to some Compact Steep Spectrum source morphologies. Very weak jets can be effectively halted by reasonably massive clouds, and this may have relevance for the paucity of radio jets in spiral galaxies. Slow, dense jets may be bent, yet remain stable for fairly extended times, thereby explaining some Wide-Angle-Tail and most “dog-leg” morphologies.     

Central configurations of the five-body problem with equal masses

In this paper we present a complete classification of the isolated central configurations of the five-body problem with equal masses. This is accomplished by using the polyhedral homotopy method to approximate all the isolated solutions of the Albouy-Chenciner equations. The existence of exact solutions, in a neighborhood of the approximated ones, is then verified using the Krawczyk method. Although the Albouy-Chenciner equations for the five-body problem are huge, it is possible to solve them in a reasonable amount of time.