A two-density neutron star model with continuity of density

Tolman's V solution has found wide application to the redshift problems in astrophysics but it has a drawback that there is singularity at the centre. We have developed a two-density model with a parabolic density distribution in the core ande r ²ⁿ in the envelope. The most distinctive feature of the model is that there is a continuity of all four variables (E, P, , and ) at the boundary. In other analytic core-envelope models the continuity of only three varaibles is possible. This two-density structure has been used to model neutron stars and their mass, size, and red shifts have been obtained.     

Static massive configurations with constant local adiabatic exponents

In this work an exhaustive study of static massive configurations with a constant local adiabatic exponent (₁) has been made under various physical conditions at the centre. The static parameters of these structures have been calculated at the extreme causality condition. These structures have been used to model neutron stars and the various neutron star parameters have been calculated. The radial pulsation and rotation of these configurations have also been discussed.     

A New Octahedrite from South Africa

Abstract Examination of an iron meteorite found in South Africa discloses it to be a coarse octahedrite containing 6.90 weight-percent nickel. The meteorite body contains several inclusions of troilite, or troilite plus graphite, and at least one of pure graphite veined with kamacite. Kamacite, cohenite, and phosphides are the other major constituents of the structure.     

Relativistic supermassive stars

A plausible scenario for the formation of a stable supermassive star in the relativistic regime has been discussed. The onset of the negativity of the `distribution function' in the stable sequences of the star clusters [the stability of star clusters is assured by using the variational method (Chandrasekhar, 1964a,b) for equivalent gas spheres] described by Tolman's type VII solution with vanishing surface density has been regarded as an indication of the conversion of the cluster structure into a supermassive star. For the critical values of the `adiabatic index', (4/3) < _crit (5/3) (forwhich a supermassive star represent neutrally stable system), the mass, and the size of this object comes out to be 6.87 × 10⁷ M M 1.7 × 10⁹M, and 2.74× 10¹⁴ cm a 1.43× 10¹⁵cm respectively, for the central temperature,T₀ = 6× 10⁷°K, which is sufficient for the release ofnuclear energy. The total energy released during their evolution rangesfrom 2.46× 10⁶⁰ - 3.18× 10⁶² erg, which is sufficient to power these objects at least for a period of 10⁶ - 10⁷years. These figures agrees quite well with those cited for Quasi Stellar Objects (QSOs) in the literature.     

Trapping of test particles in static and spherical space-time geometries

Estimates of the pulsation massesM _Q and of massesM _g=gR²/G (g is the surface gravity;R, the mean stellar radius; andG, the gravitational constant) of 89 Delta Scuti-variables have been obtained. An intercomparison of three kinds of masses —M _e, M_g, andM _Q — is performed; the evolutionary massesM _e of the same variables were estimated in a previous paper (Tsvetkov, 1986). It is pointed out that within the limits of the accuracy of determination, the three kinds of masses agree for the majority of the stars under study. For several varaibles, however, there is a considerable discrepancy between the estimates of the pulsation massesM _Q and the estimates of the massesM _e andM _g. Arguments are represented, which may alleviate or even remove this mass discrepancy for some of these stars. It is shown that the results from the comparison between the three kinds of masses of the considered Delta Scuti-stars are not very sensitive to the choice of the system of evolutionary tracks and the adopted chemical composition as well as to the evolutionary phases of the variables (core or shell hydrogen burning). The variations of the chemical composition in most of the stars under study are probably not very large.     

Homogeneous spheres with constant adriatic index

Compressible homogeneous spheres with constant adiabatic index γ were studied for their dynamical stability by Chandrasekhar and he found that for each value of u (≡ mass to size ratio), there is a value of γ = γ_c, such that for γ < γ_c, the configuration is dynamically unstable. On examining the properties of the Chandrasekhar's spheres (homogeneous spheres with constant γ) it is found that these spheres are non-isentropic, and the speed of sound within these spheres is finite. The authors find that (i) for the causality condition to be fulfilled throughout the configuration, the value of γ ≤ [2/(surface redshift)], (ii) for a given value of u, the binding coefficient, α_r = (M_r -M)/M, vanishes for some value of γ = γ_b and for all the values of γ < γ_b the configurations are unbound, and (iii) for u≤ (1/3), one can find configurations which are bound, dynamically stable, and the speed of sound is less than that of light throughout the configuration, whereas, for u >(1/3), the physically viable models of homogeneous density distribution are not possible. If the configuration is considered to be isentropic, then both γ and the speed of sound become infinite throughout the configuration. This revised version was published online in July 2006 with corrections to the Cover Date.     

Coastal dune conservation on an Irish commonage: community-based management or tragedy of the commons?

In Ireland 'commonage' refers to lands jointly owned by several individuals who have grazing rights. Commonage can provide the low-intensity grazing regime regarded as optimal for habitat conservation, and it is also unlikely to suffer the negative impacts of building development or coastal engineering. Today, however, the traditional control systems of coastal commonage are generally moribund, leading to habitat degradation. The only viable future management model is likely to be one based on local community control. Community management would have the legitimacy to counter the negative perceptions of external authority that generate environmental degradation.     

Polytropic spheres with isothermal cores

The paper deals with massive fluid spheres with an isothermal core (having finite central density) and a polytropic envelope in terms of the General Relativity. The matching of the solutions in the core and envelope has been done using Bondi's condition,H=0 and also without it. The study reveals that since this condition does not correspond to any particular physical situation the maximum values of fractional core size, fractional core mass and the redshift do not occur atH=0, but that they occur at some other point. Within the permissible physical conditions (dP/dρ≤1) the maximum values ofM _core/M,R _core/R and the surface redshift, for an isothermal coreP=ρ/3, are respectively 0.473, 0.554, and 0.565. Using the conditionH=0, it has been shown that for isothermal cores corresponding to the equation of the stateP≥0.6ρ, the configurations are pulsationally unstable.     

Physically realizable relativistic stellar structures

Relativistic stellar structures can be obtained both analytically and by computation, but all these models do not stand the tests of physical reality. It is shown that for a physically reasonable solution d/dr -r and d(e ^v /dr r near the centre, d(P/)/dr<-0 and (dP/d)>-(P/). If we change the variabler tox=Cr ², whereC is a constant, the field equations are reduced to a form which is easier to solve. A new set of exact solutions is obtained by consideringe ^v (1-x) ⁿ . Also, a method has been given to obtain generalized solution.It is shown that the solution discussed by Durgapal and Rawat (1980) is the only exact solution which in its most generalized form for a given density distribution stands all the tests of physical reality and for which both (P/) and (dP/d) decrase with increasing value ofr.Neutron star model is proposed by assuming >-2×10¹⁴g cm^–3. Two specific cases are considered, viz.,P<-1/3 and dP/d<-1, respectively. The structures are found to be bound and stable under radial perturbations. The models have been studied for slow rotation and the mass of the Crab pulsar has been estimated for different mechanisms.     

A non singular solution for spherical configuration with infinite central density

A non-singular exact solution with an infinite central density is obtained for the interior of spherically symmetric and static structures. Both the energy density and the pressure are infinite at the center but we have e ^λ(0)=1 and e ^ν(0)≠0. The solution admits the possibility of receiving signals from the region of infinite pressure.