Dynamic evolution model of isothermal voids and shocks

We explore self-similar hydrodynamic evolution of central voids embedded in an isothermal gas of spherical symmetry under the self-gravity. More specifically, we study voids expanding at constant radial speeds in an isothermal gas and construct all types of possible void solutions without or with shocks in surrounding envelopes. We examine properties of void boundaries and outer envelopes. Voids without shocks are all bounded by overdense shells and either inflows or outflows in the outer envelope may occur. These solutions, referred to as type void solutions, are further divided into subtypes and according to their characteristic behaviours across the sonic critical line (SCL). Void solutions with shocks in envelopes are referred to as type voids and can have both dense and quasi-smooth edges. Asymptotically, outflows, breezes, inflows, accretions and static outer envelopes may all surround such type voids. Both cases of constant and varying temperatures across isothermal shock fronts are analyzed; they are referred to as types and void shock solutions. We apply the ‘phase net matching procedure’ to construct various self-similar void solutions. We also present analysis on void generation mechanisms and describe several astrophysical applications. By including self-gravity, gas pressure and shocks, our isothermal self-similar void (ISSV) model is adaptable to various astrophysical systems such as planetary nebulae, hot bubbles and superbubbles in the interstellar medium as well as supernova remnants.      

On the peculiarities in the rotational frequency evolution of isolated neutron stars

The measurements of pulsar frequency second derivatives have shown that they are 10²−10⁶ times larger than expected for standard pulsar spin-down law, and are even negative for about half of pulsars. We explain these paradoxical results on the basis of the statistical analysis of the rotational parameters ν, and of the subset of 295 pulsars taken mostly from the ATNF database. We have found a strong correlation between and for both and , as well as between ν and . We interpret these dependencies as evolutionary ones due to being nearly proportional to the pulsars’ age. The derived statistical relations as well as “anomalous” values of are well described by assuming the long-time variations of the spin-down rate. The pulsar frequency evolution, therefore, consists of secular change of ν _ev(t), and according to the power law with n≈5, the irregularities, observed within a timespan as a timing noise, and the variations on the timescale larger than that—several decades. This work has been supported by the Russian Foundation for Basic Research (grant No 04-02-17555), Russian Academy of Sciences (program “Evolution of Stars and Galaxies”), and by the Russian Science Support Foundation. The authors would also like to thank the anonymous referee for valuable comments.     

The restricted two-body problem in constant curvature spaces

We perform the bifurcation analysis of the Kepler problem on and . An analog of the Delaunay variables is introduced. We investigate the motion of a point mass in the field of a Newtonian center moving along a geodesic on and (the restricted two-body problem). For the case of a small curvature, the pericenter shift is computed using the perturbation theory. We also present the results of numerical analysis based on an analogy with the motion of a rigid body.     

Modeling of the radial and transverse components of the albedo function

In this work, we shall confine ourselves to solve analytically the integrals called , for the two components of albedo radiation pressure on an Earth’s satellite. When the Earth’s albedo is variable, as far as we know, this case has not been dealt with analytically. We shall solve these two integrals when the satellite’ horizon is illuminated and when the sun lies on the equator. This approach will facilitate the evaluation of the mentioned two equations. We will also compare our results with previous works obtained numerically.     

Effect of dynamical cosmological constant in presence of modified Chaplygin gas for accelerating universe

In this paper we have considered the Universe to be filled with Modified Gas and the Cosmological Constant Λ to be time-dependent with or without the Gravitational Constant G to be time-dependent. We have considered various phenomenological models for Λ, viz., and . Using these models it is possible to show the accelerated expansion of the Universe at the present epoch. Also we have shown the natures of G and Λ over the total age of the Universe. Using the statefinder parameters we have shown the diagrammatical representation of the evolution of the Universe starting from radiation era to ΛCDM model.     

Earth’s precession–nutation motion: the error analysis of the theories IAU 2000 and IAU 2006 applying the VLBI data of the years 1984–2006

The long-term systematic errors of the analytical theories IAU 2000 and IAU 2006 of the Earth’s precession–nutational motion are studied making use of the VLBI data of 1984–2007. Several independent methods give indubitable evidence of the significant quadratic error in the IAU 2000 residuals of the precessional angle while the adopted value of the secular decrease /cy of the Earth’s ellipticity e (derived from Satellite Laser Ranging data) should manifest itself in the residuals of as the negative quadratic trend . The problem with the precession of the IAU 2006 theory adopted as a new international standard and based on the precession model P03 (Capitaine et al., Astron Astrophys 432:355–367, 2005) appears to be even more serious because the above mentioned quadratic term has already been incorporated into the P03 precession. Our analysis of the VLBI data demonstrates that the quadratic trend of the IAU 2006 residuals does amount to the expected value (30.0 ± 3) mas/cy². It means, first, that the theoretical precession rate of IAU 2006 should be augmented by the large secular correction and, second, that the available VLBI data have potentiality of estimating the rate . And indeed, processing these data by the numerical theory ERA of the Earth’s rotation (Krasinsky, Celest Mech Dyn Astron 96:169–217, 2006, Krasinsky and Vasilyev, Celest Mech Dyn Astron 96:219–237, 2006) yields the estimate /cy statistically in accordance with the satellite-based . On the other hand, applying IAU 2000/2006 models, the positive value /cy is found which is incompatible with the SLR estimate and, evidently, has no physical meaning. The large and steadily increasing error of the precession motion of the IAU 2006 theory makes the task of replacing IAU 2006 by a more accurate model be most pressing.     

Monte Carlo Simulation of Solar Active-Region Energy

A Monte Carlo approach to solving a stochastic-jump transition model for active-region energy (Wheatland and Glukhov: Astrophys. J. 494, 858, 1998; Wheatland: Astrophys. J. 679, 1621, 2008) is described. The new method numerically solves the stochastic differential equation describing the model, rather than the equivalent master equation. This has the advantages of allowing more efficient numerical solution, the modeling of time-dependent situations, and investigation of details of event statistics. The Monte Carlo approach is illustrated by application to a Gaussian test case and to the class of flare-like models presented in Wheatland (Astrophys. J. 679, 1621, 2008), which are steady-state models with constant rates of energy supply, and power-law distributed jump transition rates. These models have two free parameters: an index (δ), which defines the dependence of the jump transition rates on active-region energy, and a nondimensional ratio ( ) of total flaring rate to rate of energy supply. For the nondimensional mean energy of the active-region satisfies , resulting in a power-law distribution of flare events over many decades of energy. The Monte Carlo method is used to explore the behavior of the waiting-time distributions for the flare-like models. The models with δ≠0 are found to have waiting times that depart significantly from simple Poisson behavior when . The original model from Wheatland and Glukhov (Astrophys. J. 494, 858, 1998), with δ=0 (i.e., no dependence of transition rates on active-region energy), is identified as being most consistent with observed flare statistics.     

Back reaction and Hawking radiation from a Vaidya black hole

Using Damour-Ruffini’s and Hamilton-Jacobi’s methods, Hawking radiation from a Vaidya black hole is investigated. Due to non-stationary black holes, the event horizon r _H and the entropy S are all related to both the mass m(υ) and . When the back-reaction of particles’s energy to space-time is considered, we get the emission probability. It is found that the result is different from that of the stationary Schwarzschild black hole, because is the function of mass m(υ).      

On the gravitational radiation of gravitating objects

In the framework of unifying gravity and electromagnetism, we have shown that accelerating objects emit gravitational wave as those determined by Larmor formula for the accelerating charged particle. We have found new formulae for the power of Gravitational waves radiated by spinning and orbiting objects. The minimum wavelength of the gravitational wave emitted by an object of mass m and radius R is .     

Dynamical dark energy from extra dimensions

We consider multidimensional cosmological model with a higher-dimensional product manifold M = R × × /Γ, where is d _o-dimensional Ricci-flat external (our) space and /Γ is d ₁-dimensional compact hyperbolic internal space. M2-brane solution for this model has the stage of accelerating expansion of the external space. We apply this model to explain the late time acceleration of our Universe. Recent observational data (the Hubble parameter at the present time and the redshift when the deceleration parameter changes its sign) fix fully all free parameters of the model. As a result, we find that considered model has too big size of the internal space at the present time and variation of the effective four-dimensional fine structure constant strongly exceeds the observational limits. The article is published in the original.     

Limits on the changes in the gravitational constant from nucleosynthesis

Due to the recent all-sky, high-precision measurement of microwave background anisotropies by WMAP, a value for baryon-to-photon ratio η was obtained. At the WMAP value for η, the ⁴HE abundance was predicted. In this article we use a simple semi-analytical method with ⁴He predicted and measured values to place a limit on the variation of the gravitational constant G. We find using a conservative range for the measured values for Y _p , that ΔG/G is constrained between −0.26 and 0.15. If we assume a monotonic power law time dependence G∼t ^−β then β values is constrained between −0.008 and 0.0038, which translate into . This compares well with results obtained by others using full numerical analysis.      

Synchronization features of the magnetic nova V1500 Cyg

An analysis of an eleven-year photometric study of the first magnetic nova V1500 Cyg from observations made at the Crimean Observatory is presented. The data indicate the existence of a beat period caused by rotational-orbital asynchronization as well as its increase with time. The current rotational period of the primary component — a magnetic white dwarf — was calculated for each year by using the current values of the beat period and a constant value for the orbital period. It is shown that rapid synchronization of the components has not occurred uniformly with time: the rate of increase of the rotational period of the white dwarf was during 1977–1979 and over the next ten years. This would lead to synchronization of the rotational and orbital periods over about 230 year if remains constant at 2.7 · 10^–8.Translated fromAstrofizika, Vol. 39, No. 2, pp. 193–199, April–June, 1996.     

Completely Integrable Systems Connected with Lie Algebras

In a recent paper Ballersteros and Ragnisco (1998) have proposed a new method of constructing integrable Hamiltonian systems. A new class of integrable systems may be devised using the following sequence: , where A is a Lie algebra is a Lie–Poisson structure on R ₃, C is a Casimir for is a reduced Poisson bracket and (A, ▵) is a bialgebra. We study the relation between a Lie-Poisson stucture Λ and a reduced Poisson bracket , which is a key element in using the Lie algebra A to constructing this sequence. New examples of Lie algebras and their related integrable Hamiltonian systems are given. This revised version was published online in July 2006 with corrections to the Cover Date.     

The Evolution of Dilatonic Universe with a Double Exponential Potential

In this paper, dilaton in Weyl-Scaled induced gravitational theory is regarded as a candidate of dark energy. When the potential of dilaton field is taken as the form of a double exponential , we find that there exist attractor solutions in dilatonic dark energy model, and these attractors correspond to an equations of state and a cosmic density parameter , which are important features for a dark energy model that can meet the current observations. We find out the sufficient condition of the existence of a late time de Sitter attractor.     

Periodic solutions for resonance 4/3: Application to the construction of an intermediary orbit for Hyperion’s motion

The motion of Hyperion is an almost perfect application of second kind and second genius orbit, according to Poincaré’s classification. In order to construct such an orbit, we suppose that Titan’s motion is an elliptical one and that the observed frequencies are such that 4n _H−3n _T+3n _ω=0, where n _H, n _T are the mean motions of Hyperion and Titan, n _ω is the rate of rotation of Hyperion’s pericenter. We admit that the observed motion of Hyperion is a periodic motion such as . Then, .N _H, N _T, k∈ N ⁺. With that hypothesis we show that Hyperion’s orbit tends to a particular periodic solution among the periodic solutions of the Keplerian problem, when Titan’s mass tends to zero. The condition of periodicity allows us to construct this orbit which represents the real motion with a very good approximation. This revised version was published online in July 2006 with corrections to the Cover Date.     

Absolute dimensions of TT Hydrae

The photometric elements of the Algol type binary TT Hydrae derived by the authors from theirUBV observations during 1973–77 have been combined with the spectroscopic elements given by Sanford (1937) and Sahade and Cesco (1946) to obtain the absolute dimensions of the system. It is found that the spectroscopic orbital elements given by Sanford represent the evolutionary status of the secondary component better than those of Sahade and Cesco. The primary appears to be an Al v main sequence star of mass and radius ∼2.3R _⊙. The secondary fills its Roche lobe; it can be represented by a K0iii star of mass and radius ∼6.0R _⊙. Better spectroscopic data are needed for confirmation of these results.