Self-Interacting Dark Matter in the SU(3)C⊗ SU(3)L ⊗ U(1)N models

We present the gauge models based on SU(3)_C⊗ SU(3)_L ⊗ U(1)_N (3-3-1) group which contain particles satisfying conditions for dark matter. There are two such models: one with exotic positive charged lepton and a variant with right-handed neutrinos. The scalar self-interacting dark matters are stable without imposing of new symmetry and should be weak-interacting. PACS Nos: 95.35.+d, 12.60.Fr, 14.80.Cp     

Bianchi Type I string dust cosmological model with magnetic field in general relativity

Bianchi Type I string dust cosmological models in presence and absence of magnetic field following the techniques used by Letelier and Stachel, are investigated. To get the deterministic solution, we have assumed that σ ₁¹ is proportional to the expansion (θ) where σ ₁¹ is the eigen value of shear tensor (σ _i ^j ) and which leads to A=N(BC)⁻ⁿ , n>0 where A,B,C are metric potentials and , N and ℓ are constants. The behaviour of the models in presence and absence of magnetic field are discussed. The other physical and geometrical aspects of the model are also discussed.     

Isotropization by scalar field driven inflation and the cosmological quantum boundary

We derive the Wheeler-de Witt equation for the scalar field of mass m > 0 in a Bianchi-type I universe. We argue that classical trajectories become possible at h² ⩽ αt_p^-2, h being the mean Hubble value and t_p the Planck time. We feel justified to set the numerical constant α ≈︁ 1. We discuss this condition in geometrically invariant quantities and compare it with ⩽t_p^-4. The proposed quantum boundary of classical trajectories represents a 3-dimensional sphere in the 4-space of the dynamical system. Equipartition of the initial energy over field (m < m_p) and shear variables at the quantum boundary will cause inflation with a probability p of the order p = 1 - m/m_p thus, p = 1 - 10^-4 for m taken from GUT. In the course of the inflationary stage the initially arbitrarily large shear-anisotropy exponentially decays.     

Molecular Hydrogen in high redshift Damped Lyman-α systems

I describe briefly the status of an ongoing mini-survey for molecular hydrogen in high-redshift Damped Lyman-α systems using UVES at the VLT. H₂ is detected in about 30% of the cases. When H2 is not detected the molecular fraction f = 2N(H₂)/(2N(H₂)+N(HI) is smaller than 10^-5. Therefore, most of the DLA systems arise in warm (T > 3000 K) and diffuse neutral gas embedded in a strong UV flux. The very recent detection of HD molecules in a Damped Lyman-α system at z _abs = 2.337 demonstrates the possibility to discuss the high redshift chemistry. This revised version was published online in September 2006 with corrections to the Cover Date.     

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.     

On the interpretation of the observed angular-size-flux-density relation for extragalactic radio sources

The interpretation of the observed relation between median angular sizes (θ _m) of extragalactic radio sources and flux density at 408 MHz has been examined. The predictedθ _m-S relations based on well-observed strong sources in parent samples selected at 178 and 1400 MHz, and existing models of the evolving radio luminosity function can be made to fit the observed relation only by invoking cosmological evolution in linear sizes even for theq ₀ = 0 universe. Predictions based on a parent sample at 2.7 GHz are shown to overestimate the contribution of steep-spectrum, compact (SSC) sources in low-frequency samples unless the downward curvature in the spectra of such sources is taken into account. When approximate corrections are made for this effect, predictions based on the 2.7 GHz parent sample cannot obviate the need for linear size evolution as claimed in the literature.     

Robe’s problem: its extension to 2+2 bodies

In the problem of 2+2 bodies in the Robe’s setup, one of the primaries of mass m^*₁m^{*}_{1} is a rigid spherical shell filled with a homogeneous incompressible fluid of density ρ ₁. The second primary is a mass point m ₂ outside the shell. The third and the fourth bodies (of mass m ₃ and m ₄ respectively) are small solid spheres of density ρ ₃ and ρ ₄ respectively inside the shell, with the assumption that the mass and the radius of third and fourth body are infinitesimal. We assume m ₂ is describing a circle around m^*₁m^{*}_{1}. The masses m ₃ and m ₄ mutually attract each other, do not influence the motion of m^*₁m^{*}_{1} and m ₂ but are influenced by them. We also assume masses m ₃ and m ₄ are moving in the plane of motion of mass m ₂. In the paper, the equations of motion, equilibrium solutions, linear stability of m ₃ and m ₄ are analyzed. There are four collinear equilibrium solutions for the given system. The collinear equilibrium solutions are unstable for all values of the mass parameters μ,μ ₃,μ ₄. There exist an infinite number of non collinear equilibrium solutions each for m ₃ and m ₄, lying on circles of radii λ,λ′ respectively (if the densities of m ₃ and m ₄ are different) and the centre at the second primary. These solutions are also unstable for all values of the parameters μ,μ ₃,μ ₄, φ, φ′. Such a model may be useful to study the motion of submarines due to the attraction of earth and moon.     

Asymptotic orbits in the (<Emphasis Type="Italic">N</Emphasis>+1)-body ring problem

In this paper we study the asymptotic solutions of the (N+1)-body ring planar problem, N of which are finite and ν=N−1 are moving in circular orbits around their center of masses, while the Nth+1 body is infinitesimal. ν of the primaries have equal masses m and the Nth most-massive primary, with m ₀=β m, is located at the origin of the system. We found the invariant unstable and stable manifolds around hyperbolic Lyapunov periodic orbits, which emanate from the collinear equilibrium points L ₁ and L ₂. We construct numerically, from the intersection points of the appropriate Poincaré cuts, homoclinic symmetric asymptotic orbits around these Lyapunov periodic orbits. There are families of symmetric simple-periodic orbits which contain as terminal points asymptotic orbits which intersect the x-axis perpendicularly and tend asymptotically to equilibrium points of the problem spiraling into (and out of) these points. All these families, for a fixed value of the mass parameter β=2, are found and presented. The eighteen (more geometrically simple) families and the corresponding eighteen terminating homo- and heteroclinic symmetric asymptotic orbits are illustrated. The stability of these families is computed and also presented.     

Unified structure of analytical solutions for radiative transfer problems in plane-parallel,homogeneous media

The basic concepts for developing a system of analytic solutions for the standard problems of radiative transfer theory are discussed. These solutions, which are found using Ambartsumyan’s layer addition method in Sobolev’s probabilistic interpretation for radiative diffusion problems, are maximally compact and easily used in numerical computations. New expressions are obtained for the resolvents and the resolvent functions, as well as a unified structure for the form of an integral representation for solving different radiative transfer problems in semi-infinite media and in finite layers. Block diagrams of the sequence of stages for solving these problems are provided, where the Ambartsumyan function φ(η) (more precisely, 1/φ(η)) plays a fundamental role in the case of semi-infinite media while the functions a(η, τ₀ ) and b(η, τ₀) play an analogous role for finite layers.     

Stability of strange dwarfs II. Computational results

The stability of strange dwarfs for quark cores with M _0core /M _⨀ = 10⁻⁴, has been studied by calculating, in each individual case, a series of strange dwarfs with configurations in which 5 ⋅ 10⁻⁴, 10⁻³, 5 ⋅ 10⁻³, 10⁻², 1.31 ⋅ 10⁻², 1.6 ⋅ 10⁻², 1.7 ⋅ 10⁻², 2 ⋅ 10⁻², ranges from the values in white dwarfs to ρ _drip = 4.3 ⋅ 10¹¹ g/cm³, at which free neutrons are produced in the crust. For the series with M _0core /M _⨀ < 0.0131, stability is lost when ρ _tr < ρ _drip . For the series with M _0core /M _⨀ > 0.0131, the equality ρ _tr = ρ _drip is reached before the strange dwarf attains its maximum mass. Although the frequency of the radial pulsations in the fundamental mode obeys ω₀² > 0 for these configurations, they are unstable with respect to transitions into a strange star state with the same total number of baryons and a radius on the order of that of neutron stars. An energy on the order of the energy in a supernova explosion is released during these transitions. It is shown that the gravitational red shift of white and strange dwarfs are substantially different for low and limiting (high) masses.     

Restricted Three-Body Problem: An Approximation of its General Solution – Part One – the Manifold of Symmetric Periodic Solutions

This paper gives the results of a programme attempting to exploit ‘la seule bréche’ (Poincaré, 1892, p. 82) of non-integrable systems, namely to develop an approximate general solution for the three out of its four component-solutions of the planar restricted three-body problem. This is accomplished by computing a large number of families of ‘solutions précieuses’ (periodic solutions) covering densely the space of initial conditions of this problem. More specifically, we calculated numerically and only for μ = 0.4, all families of symmetric periodic solutions (1st component of the general solution) existing in the domain D:(x ₀ ∊ [−2,2],C ∊ [−2,5]) of the (x ₀, C) space and consisting of symmetric solutions re-entering after 1 up to 50 revolutions (see graph in Fig. 4). Then we tested the parts of the domain D that is void of such families and established that they belong to the category of escape motions (2nd component of the general solution). The approximation of the 3rd component (asymmetric solutions) we shall present in a future publication. The 4th component of the general solution of the problem, namely the one consisting of the bounded non-periodic solutions, is considered as approximated by those of the 1st or the 2nd component on account of the `Last Geometric Theorem of Poincaré' (Birkhoff, 1913). The results obtained provoked interest to repeat the same work inside the larger closed domain D:(x ₀ ∊ [−6,2], C ∊ [−5,5]) and the results are presented in Fig. 15. A test run of the programme developed led to reproduction of the results presented by Hénon (1965) with better accuracy and many additional families not included in the sited paper. Pointer directions construed from the main body of results led to the definition of useful concepts of the basic family of order n, n = 1, 2,… and the completeness criterion of the solution inside a compact sub-domain of the (x ₀, C) space. The same results inspired the ‘partition theorem’, which conjectures the possibility of partitioning an initial conditions domain D into a finite set of sub-domains D i that fulfill the completeness criterion and allow complete approximation of the general solution of this problem by computing a relatively small number of family curves. The numerical results of this project include a large number of families that were computed in detail covering their natural termination, the morphology, and stability of their member solutions. Zooming into sub-domains of D permitted clear presentation of the families of symmetric solutions contained in them. Such zooming was made for various values of the parameter N, which defines the re-entrance revolutions number, which was selected to be from 50 to 500. The areas generating escape solutions have being investigated. In Appendix A we present families of symmetric solutions terminating at asymptotic solutions, and in Appendix B the morphology of large period symmetric solutions though examples of orbits that re-enter after from 8 to 500 revolutions. The paper concludes that approximations of the general solution of the planar restricted problem is possible and presents such approximations, only for some sub-domains that fulfill the completeness criterion, on the basis of sufficiently large number of families.     

Shear-free homogeneous cosmological model with heat flux

We present the condition of vanishing shear in a spatially homogeneous spacetime in terms of the Ricci rotation co-efficients corresponding to an orthonormal tetrad (ν ^α. _A η ^α) (whereν ^α is the unit vector along the time axis and _A η ^α are the three independent reciprocal group vectors). Assuming that the velocity vector can be expanded in the direction ofν ^α and any one of the _A η ^α’s it is shown that shear-free motion is possible only in case of some special Bianchi types, and these cases are studied assuming the velocity vector to be geodetic and that there may be a nonvanishing heat flux term.     

Spectroscopy and photometry of the protoplanetary nebula candidate stHα62 = IRAS 07171+1823

We present the results of spectroscopic and photometric observations for the B star StHα62 with an IR excess, a post-AGB candidate identified with the IR source IRAS 07171+1823. High-resolution spectroscopy has allowed the λ4330–7340 Å spectrum of the star to be identified: it contains absorption lines of an early B star and emission lines of a gaseous shell. The residual line intensities have been measured. The heliocentric radial velocities measured from absorption lines of the star and emission lines of the shell are 〈V _r 〉 = +45 ± 1 and +52 ± 1 km s^?1, respectively. The line-of-sight velocities of gas-dust clouds determined from the interstellar Na I lines are 12 and 33 km s^?1. The He I λ5876 Å line exhibits a P Cyg profile, which is indicative of an ongoing mass loss by the star. The expansion velocity of the outer shell estimated from forbidden lines is 12–13 km s^?1. Quantitative classification gives the spectral type B0.51 for the star. The parameters of the gaseous shell have been determined: N _e = 3.1 × 10³ cm^?3 and T _e ～ 21 000 K. Over 4 years of its observations, the star showed rapid irregular light variations with the amplitudes ΔV = We present the results of spectroscopic and photometric observations for the B star StHα62 with an IR excess, a post-AGB candidate identified with the IR source IRAS 07171+1823. High-resolution spectroscopy has allowed the λ4330–7340 ? spectrum of the star to be identified: it contains absorption lines of an early B star and emission lines of a gaseous shell. The residual line intensities have been measured. The heliocentric radial velocities measured from absorption lines of the star and emission lines of the shell are 〈V _r 〉 = +45 ± 1 and +52 ± 1 km s⁻¹, respectively. The line-of-sight velocities of gas-dust clouds determined from the interstellar Na I lines are 12 and 33 km s⁻¹. The He I λ5876 ? line exhibits a P Cyg profile, which is indicative of an ongoing mass loss by the star. The expansion velocity of the outer shell estimated from forbidden lines is 12–13 km s⁻¹. Quantitative classification gives the spectral type B0.51 for the star. The parameters of the gaseous shell have been determined: N _e = 3.1 × 10³ cm⁻³ and T _e ∼ 21 000 K. Over 4 years of its observations, the star showed rapid irregular light variations with the amplitudes ΔV = , ΔB = , and ΔU = and no color-magnitude correlation. We estimate the total extinction for the star from our photometric observations as A _v = . Near-IR observations have revealed dust radiation with a temperature of ∼1300 K. We estimate the distance to StHα62 to be r = 5.2 ± 1.2 kpc by assuming that the star is a low-mass (M = 0.55 ± 0.05 M _⊙) protoplanetary nebula. Original Russian Text ? V.P. Arkhipova, V.G. Klochkova, E.L. Chentsov, V.F. Esipov, N.P. Ikonnikova, G.V. Komissarova, 2006, published in Pis’ma v Astronomicheskiĭ Zhurnal, 2006, Vol. 32, No. 10, pp. 737–747.     

Perfect Fluid Lrs Bianchi I With Time Varying Constants

It is investigated the behaviour of the “constants” G, c and Λ in the framework of a perfect fluid LRS Bianchi I cosmological model. It has been taken into account the effects of a c-variable into the curvature tensor. Two exact cosmological solutions are investigated, arriving t the conclusion that if q < 0 (deceleration parameter) then G, c are growing functions on time t while Λ is a negative decreasing function on time.     

Formation of a mass distribution of objects. ii. mergings in a two-component set of particles

The random quantity ξ, the number of pairwise mergings for a two-component sample N = N₁ + N₂, N₂≤ N₁, is found under the assumption that mergings only between particles of different types are possible. Let T₀,T₁,T₂,..., T_m, ... be a sequence of times. We then have a discrete approximation of the process of mergings by a uniform Markov chain. Translated from Astrofizika, Vol. 43, No. 1, pp. 137-142, January–March, 2000.     

On most general exact solution for Vaidya-Tikekar isentropicsuperdense star

The energy density of Vaidya-Tikekar isentropic superdense star is found to be decreasing away from the center, only if the parameter K is negative. The most general exact solution for the star is derived for all negative values of K in terms of circular and inverse circular functions. Which can further be expressed in terms of algebraic functions for K = 2-(n/δ)² < 0 (n being integer andδ = 1,2,3 4). The energy conditions 0 ≤ p ≤ αρc ², (α = 1 or 1/3) and adiabatic sound speed conditiondp dρ ≤ c ², when applied at the center and at the boundary, restricted the parameters K and α such that .18 < −K −2287 and.004 ≤ α ≤ .86. The maximum mass of the star satisfying the strong energy condition (SEC), (α = 1/3) is found to be3.82 Mq_· at K=−2/3, while the same for the weak energy condition (WEC), (α =1) is 4.57 M_ _⊙ atK=−>5/2. In each case the surface density is assumed to be 2 × 10¹⁴ gm cm^-3. The solutions corresponding to K>0 (in fact K>1) are also made meaningful by considering the hypersurfaces t= constant as 3-hyperboloid by replacing the parameter R ² by −R² in Vaidya-Tikekar formalism. The solutions for the later case are also expressible in terms of algebraic functions for K=2-(n/δ² > 1 (n being integer or zero and δ =1,2,3 4). The cases for which 0 < K < 1 do not possess negative energy density gradient and therefore are incapable of representing any physically plausible star model. In totality the article provides all the physically plausible exact solutions for the Buchdahl static perfect fluid spheres. This revised version was published online in July 2006 with corrections to the Cover Date.     

Stability of motion in the Sitnikov 3-body problem

We study the stability of motion in the 3-body Sitnikov problem, with the two equal mass primaries (m ₁ = m ₂ = 0.5) rotating in the x, y plane and vary the mass of the third particle, 0 ≤ m ₃ < 10⁻³, placed initially on the z-axis. We begin by finding for the restricted problem (with m ₃ = 0) an apparently infinite sequence of stability intervals on the z-axis, whose width grows and tends to a fixed non-zero value, as we move away from z = 0. We then estimate the extent of “islands” of bounded motion in x, y, z space about these intervals and show that it also increases as |z| grows. Turning to the so-called extended Sitnikov problem, where the third particle moves only along the z-axis, we find that, as m ₃ increases, the domain of allowed motion grows significantly and chaotic regions in phase space appear through a series of saddle-node bifurcations. Finally, we concentrate on the general 3-body problem and demonstrate that, for very small masses, m ₃ ≈ 10⁻⁶, the “islands” of bounded motion about the z-axis stability intervals are larger than the ones for m ₃ = 0. Furthermore, as m ₃ increases, it is the regions of bounded motion closest to z = 0 that disappear first, while the ones further away “disperse” at larger m ₃ values, thus providing further evidence of an increasing stability of the motion away from the plane of the two primaries, as observed in the m ₃ = 0 case.     

Cosmological model with a conformally coupled scalar field

Modern concepts of the universe support the assumed existence of a nongravitational source, known as dark energy, for which ε + 3 P < 0 (where ε is the energy density and P is the pressure). This ensures accelerated expansion of the universe. This paper examines a tensor-scalar variant of the theory of gravitation with a conformally coupled scalar field. Various cosmological models are examined and the possible evolutionary development of the universe with accelerated expansion is discussed. Translated from Astrofizika, Vol. 51, No. 4, pp. 653–661 (November 2008).     

Radiative cooling flows of self-gravitating filamentary clouds

We study the dynamics of a self-gravitating cooling filamentary cloud using a simplified model. We concentrate on the radial distribution and restrict ourselves to quasi-hydrostatic, cylindrically symmetric cooling flows. For a power-law dependence of cooling function on the temperature, self-similar solutions which describe quasi-hydrostatic cooling flows are derived. We consider obtically thin filaments with a constant mass per unit length and the solutions are parameterized by their line masses. There is no polytropic relation between the density and the pressure. The filament experiences radiative condensation, irrespective of the γ,the gas specific heat ratio. So, the filament becomes denser due to the quasi-hydrostatic flows and the density at the center (ρ_c) increases in proportion to (t ₀-t)^-1, where t denotes the time. The term,t ₀, denotes an epoch at which the central density increases infinitely. We also found that the radius of the filament (r _c) decreases in proportion to (t ₀-t)^1/2. This revised version was published online in July 2006 with corrections to the Cover Date.