Emulating the OPAL equation of state

The equation of state for the structure of the Sun and stars has to be precise to allow comparisons with observations, i.e., helioseismic inversions of thermodynamic quantities. Among the two of the most popular formalisms are (1) the OPAL equation of state developed at Livermore and (2) the Mihalas-Hummer-Däppen (MHD) equation of state. While OPAL has a solid theoretical foundation, and matches the observational data better, the MHD formalism is more intuitive, easy to realize, and has the possibility of adjustable parameters. Furthermore, it an open-source product in contrast to the proprietary OPAL. Recently a version of MHD has been obtained by including the so-called “Plank-Larkin partition function” and by adding scattering-state terms. The resulting formalism matches OPAL rather well. Here, we report on the next logical step, the implementation of this MHD upgrade into the simple and popular CEFF equation of state. Such an implementation will make it a flexible and convenient tool, allowing an approximative on-line implementation of OPAL in solar and stellar models.     

The structure of the planets Jupiter and Saturn

Planetary models for Jupiter and Saturn are computed using a fourth-order theory and a new molecular equation of state. The equation of state for the molecular hydrogen and helium planetary envelopes is taken from the Monte Carlo calculations of Slattery and Hubbard [Icarus 29, 187–192 (1976)]. Models for Jupiter are found that have a small amount of heavy elements either mixed with hydrogen and helium throughout the interior of the planet or concentrated in a small dense core. Saturn is modeled with a solar-composition hydrogen and helium envelope and a small derse core. We conclude that the molecular equation of state linked with suitable interior equations of state can produce Jovian models which satisfy the observational data. The planetary models show that the enrichment of heavy elements (relative to solar composition) is approximately 3 times for Jupiter and 10 times for Saturn.     

Stellar models with generalized polytropic equation of state

We find new classes of exact solutions to the Einstein field equations where the matter distribution satisfies a generalized polytropic equation of state. The matter distribution is uncharged with anisotropic pressures. Equations of state for polytropes and quark matter are contained as special cases. The matter variables and metric potentials can be obtained explicitly. Known solutions, for the choice of the gravitational potential made in this analysis, arise as special cases for particular choice of the equation of state parameters. A detailed physical analysis indicates that the model is well behaved.     

Constraining the cosmic equation of state from old galaxies at high redshift

New limits on the cosmic equation of state are derived from age measurements of three recently reported old high-redshift galaxies (OHRG). The results are based on a flat Friedmann–Robertson–Walker (FRW) type cosmological model driven by non-relativistic matter plus a smooth component parametrized by its equation of state p _x ωρ _x ( ω −1). The range of ω is strongly dependent on the matter density parameter. For Ω_M∼0.3, as indicated from dynamical measurements, the age estimates of the OHRG restrict the cosmic parameter to ω −0.27. However, if Ω_M is the one suggested by some studies of field galaxies, i.e., Ω_M≃0.5, only a cosmological constant ( ω =−1) may be compatible with these data.     

Behaviour of viscous fluid in string cosmological models in the framework of Lyra geometry

In this communication, we studied the aspects of bulk viscous fluid cosmological model with quadratic equation of state in the presence of strings loaded with particles in a higher dimensional (5- dimensional) Bianchi type-III geometry in Lyra’s Manifold (Lyra, 1951). Using physically plausible circumstances, an exact model of the universe is presented by obtaining the solutions of the Einstein’s field equations. Important geometrical and dynamical parameters of the model universes are premeditated and physical significance regarding their prospect in modern cosmology are discussed in details. Interestingly it is seen that both bulk viscosity and quadratic equation of state are acting crucial jobs throughout the evolution of the model which is expanding with acceleration so it represents dark energy model universe. Hence our model can be thought as a realistic universe.     

Stellar structure model in hydrostatic equilibrium in the context of f(R)-gravity

In this work we present a stellar structure model from the f(R)-gravity point of view capable of describing some classes of stars(white dwarfs, brown dwarfs, neutron stars, red giants and the Sun). This model is based on f(R)-gravity field equations for f(R) = R + f_2R~2, hydrostatic equilibrium equation and a polytropic equation of state. We compare the results obtained with those found by Newtonian theory. It has been observed that in these systems, where high curvature regimes emerge,stellar structure equations undergo modifications. Despite the simplicity of this model, the results are satisfactory. The estimated values of pressure, density and temperature of the stars are within those determined by observations. This f(R)-gravity model has proved to be necessary to describe stars with strong fields such as white dwarfs, neutron stars and brown dwarfs, while stars with weaker fields, such as red giants and the Sun, are best described by Newtonian theory.     

Molecular fluxes in the lunar atmosphere

The properties of a neutral lunar atmosphere are investigated theoretically. A non-uniformity is shown to result from the temperature variations and non-uniform gas source distribution on the surface of the Moon. An integral equation governing the distribution of molecular fluxes, in the steady state, is formulated. This equation is solved by computer and analytical methods. Solutions are obtained and discussed for mass numbers ranging from hydrogen to the heavy gases. Characteristic relaxation times for approach to the steady state are estimated and found generally to be a small fraction of the synodic period. It is concluded that in all cases a marked anisotropy of molecular fluxes can be expected. By measuring these fluxes conclusions can be drawn about the distribution of gas sources, the physical properties of the surface and the composition of the lunar atmosphere.     

Are Q-stars a serious threat for stellar-mass black hole candidates?

We examine the status of the threat posed to stellar-mass black hole candidates by the possible existence of Q-stars (compact objects with an exotic equation of state that might have masses well above the normally accepted maximum for standard neutron stars). We point out that Q-stars could be extremely compact (with radii less than 1.5 times the corresponding Schwarzschild radius) making it difficult to determine observationally that a given object is a black hole rather than a Q-star, unless there is direct evidence for the absence of a material surface. On the other hand, in order for a Q-star to have a mass as high as that inferred for the widely favoured black hole candidate V404 Cygni, it would be necessary for the Q-matter equation of state to apply already at densities an order of magnitude below that of nuclear matter and this might well be considered implausible on physical grounds. We also describe how rotation affects the situation and discuss the prospects for determining observationally that black hole candidates are not Q-stars.     

强磁场下中子星外壳的组分和状态方程

本文计算和讨论了强磁场下由冷的催化物质组成的中子星外壳的组份和状态方程。文中考虑了晶格能和强磁场下均匀电子气体的交换能的贡献.得出结论:(1)强磁场使低密度区的状态方程变软;(2)强磁场对高密度区的状态方程几乎没有影响;(3)核质量公式对外壳的组份影响较明显.     

The Fragmentation of Asteroids – A Synopsis of Analytical Methods (Mitteilungen der Universitäts-Sternwarte Jena Nr. 119)

Basing on the author's work a review of the possibilities as well as the limits of treating the problem of the collisional history of the asteroids by analytical methods is given. Using empirical data on rock fragmentation and general principles like symmetry and mass conservation the distribution function of the fragments arising from a single collision is analytically formulated. The size distribution of asteroids adjusting when crushing collisions have taken place a sufficiently long time can be obtained as the solution of an integrodifferential equation with partial derivatives (equation of fragmentation). Quasi-stationary solutions of the equation of fragmentation are discussed for particular cases. The problem of the steady state is reduced to the solution of a transcendental equation. The results obtained show that analytical methods already offer a good theoretical understanding of the observed size distribution of the asteroids. They should be, therefore, a useful basis of carrying out numerical calculations.     

Gravitational collapse of gas clouds with spherical,cylindrical or plane symmetry in the linear wave flow approximation

The equations of gas dynamics are solved, quasi-analytically by applying McVittie's method for spherical, cylindrical and plane configurations. The hypothesis of linear wave flow is applied and it is assumed that the final state of collapsing clouds is a hydrostatic equilibrium state, determined by complete polytropes. Complete analytical solutions are found when the generalized (to the three symmetries) Emden equation admits of analytical solutions. Otherwise the solutions are left in terms of the numerical solutions of the Emden equation. Numerical solutions to the Emden equation in the plane case are found and tabulated. A strong dependence of amplification, of density, pressure and temperature of the gas, on the symmetry is found. In addition, it is conclude that the flow remains subsonic, during the collapse, except toward the boundaries of the collapsing clouds.     

On the holographic dark energy in chameleon scalar-tensor cosmology

We study the holographic dark energy (HDE) model in generalized Brans-Dicke scenario with a non-minimal coupling between the scalar field and matter Lagrangian namely Chameleon Brans Dicke (CBD) mechanism. In this study we consider the interacting and non-interacting cases for two different cutoffs. The physical quantities of the model such as, equation of state (EoS) parameter, deceleration parameter and the evolution equation of dimensionless parameter of dark energy are obtained. We shall show that this model can describe the dynamical evolution of fraction parameter of dark energy in all epochs. Also we find the EoS parameter can cross the phantom divide line by suitable choices of parameters without any mines kinetic energy term.     

GPS定时噪声分析与控制

分析了选择可用性干扰的噪声特性,得到了选择可用干扰的数学模型。建立起时刻差方程的状态空间的描述,利用离散的状态方程,用卡尔曼滤波的方法减小ＳＡ干扰对校频,定时精度的影响。     

Newtonian hydrodynamics of the coalescence of black holes with neutron stars – IV. Irrotational binaries with a soft equation of state

We present the results of three-dimensional hydrodynamical simulations of the final stages of in-spiral in a black hole–neutron star binary, when the separation is comparable to the stellar radius. We use a Newtonian smooth particle hydrodynamics (SPH) code to model the evolution of the system, and take the neutron star to be a polytrope with a soft (adiabatic indices     and     equation of state and the black hole to be a Newtonian point mass. The only non-Newtonian effect we include is a gravitational radiation back reaction force, computed in the quadrupole approximation for point masses. We use irrotational binaries as initial conditions for our dynamical simulations, which are begun when the system is on the verge of initiating mass transfer and followed for approximately 23 ms. For all the cases studied we find that the star is disrupted on a dynamical time-scale, and forms a massive     accretion torus around the spinning (Kerr) black hole. The rotation axis is clear of baryons (less than 10⁻⁵ M_⊙ within 10°) to an extent that would not preclude the formation of a relativistic fireball capable of powering a cosmological gamma-ray burst. Some mass (the specific amount is sensitive to the stiffness of the equation of state) may be dynamically ejected from the system during the coalescence and could undergo r-process nucleosynthesis. We calculate the waveforms, luminosities and energy spectra of the gravitational radiation signal, and show how they reflect the global outcome of the coalescence process.     

The generalized second law for the interacting generalized Chaplygin gas model in non-flat universe enclosed by the apparent horizon

We investigate the validity of the generalized second law of gravitational thermodynamics in a non-flat FRW universe containing the interacting generalized Chaplygin gas with the baryonic matter. The boundary of the universe is assumed to be enclosed by the dynamical apparent horizon. We show that for the interacting generalized Chaplygin gas as a unified candidate for dark matter and dark energy, the equation of state parameter can cross the phantom divide. We also present that for the selected model under thermal equilibrium with the Hawking radiation, the generalized second law is always satisfied throughout the history of the universe for any spatial curvature, independently of the equation of state of the interacting generalized Chaplygin gas model.     

Phenomenological Nucleon-nucleon Potentials and the Equation of State of Neutron Star Matter

We have calculated the equation of state of the neutron star matter and some of its properties for a wide range of nucleon-nucleon potentials using the lowest order constrained variational (LOCV) method. It turns out that for the UV ₁₄+TNI potential, the proton fraction exhibits a peak and falls off at high densities. The equation of state with the UV ₁₄+TNI potential is seen to be much harder than those with other potentials. The polytropic behaviour of the neutron star matter with various potentials are discussed. Compared with the other methods, the LOCV results show good agreement for densities below 0.7 fm _-3. Above this density, however, the differences with other methods are appreciable.     

Virial oscillations of celestial bodies III. The solution of the evolutionary problem in non-newtonian time scale

Generalized Jacobi's equation is derived by introducing the friction force into the equations of motion of mass points constituting the system.The exact solution of the equation of virial oscillations of celestial bodies written for non-conservative systems is obtained using non-linear time scale in the course of the change of variables for a particular friction force law.The nature of the undamped virial oscillations of celestial bodies is though to be related to the system unstability near the state determined by the virial theorem. Thus, the friction force changes its sign near the unstable equilibrium state and due to dissipation of energy during evolution of the system the undamped virial oscillations can be described as self-exited oscillations.     

The comparative analysis of dense stellar models governed by quadratic and linear equations of state

In the present article we construct physically viable models of anisotropic charged compact stellar objects admitting quadratic equation of state and linear equation of state. We analyze the physical behavior of compact star models 4U1538-52, LMCX-4, and Vela X-1 with in the frame work of general relativity. Our stellar models are free from singularities, satisfy all energy conditions and exhibit physically admissible characters. The necessary stability criteria viz. Buchdhal condition, adiabatic index and causality condition all stand true for our charged anisotropic compact stellar models. We also inspect the physical characteristics of compact stars via Linear equation of state by applying slight changes in the parameters of the models pertaining to Quadratic equation of state and analyze the models in the perspective of both equations of state. We study the physical attributes of the model 4U1538-52 extensively by implementing analytical and graphical tools. The models retain their validity for both linear as well as quadratic equations of state, however there is a slight variation in few attributes of the models.     

Pseudo-Newtonian models for the equilibrium structures of rotating relativistic stars

We obtain equilibrium solutions for rotating compact stars, including special relativistic effects. The gravity is assumed to be Newtonian, but we use the active mass density, which takes into account all energies such as the motion of the fluid, internal energy and pressure energy in addition to the rest-mass energy, in computing the gravitational potential using Poisson's equation. Such a treatment could be applicable to neutron stars with relativistic motions or a relativistic equation of state. We applied Hachisu's self-consistent field (SCF) method to find spheroidal as well as toroidal sequences of equilibrium solutions. Our solutions show better agreement with general relativistic solutions than the Newtonian relativistic hydrodynamic approach, which does not take into account the active mass. Physical quantities such as the peak density and equatorial radii in our solutions agree with the general relativistic ones to within 5 per cent. Therefore our approach can be used as a simple alternative to the fully relativistic one when a large number of model calculations is necessary, as it requires much fewer computational resources.