On the meaning and inapplicability of the Zeldovich relations of magnetohydrodynamics

Considering a plasma with an initially weak large scale field subject to nonhelical turbulent stirring, Zeldovich (1957), for two‐dimensions, followed by others for three dimensions, have presented formulae of the form 〈b²〉 = f(R_M) . Such “Zeldovich relations” have sometimes been interpreted to provide steady‐state relations between the energy associated with the fluctuating magnetic field and that associated with a large scale or mean field multiplied by a function f that depends on spatial dimension and a magnetic Reynolds number R_M. Here we dissect the origin of these relations and pinpoint pitfalls that show why they are inapplicable to realistic, dynamical MHD turbulence and that they disagree with many numerical simulations. For 2D, we show that when the total magnetic field is determined by a vector potential, the standard Zeldovich relation applies only transiently, characterizing a maximum possible value that the field energy can reach before necessarily decaying. In 3D, we show that the standard Zeldovich relations are derived by balancing subdominant terms. In contrast, balancing the dominant terms shows that the fluctuating field can grow to a value independent of R_M and the initially imposed , as seen in numerical simulations. We also emphasize that these Zeldovich relations of nonhelical turbulence imply nothing about the amount mean field growth in a helical dynamo. In short, by re‐analyzing the origin of the Zeldovich relations, we highlight that they are inapplicable to realistic steady‐states of large R_M MHD turbulence. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Fluctuations in helium nuclear reaction-diffusion systems

In this paper the question about the space correlation of the fluctuation in helium nuclear reaction diffusion system has been analysed. We have introduced the diffusion term into master equation of the probability distribution function of density. The spectrum of fluctuation waves in helium nuclear reaction system have been obtained. There is a series of waves which described the propagation of the fluctuation moments of the local density. The instability of helium combustion at its beginning for the star which mass satisfyingM<2M may be related with those increasing fluctuation waves. We also use the bifurcation theory to deal with the partial differential equation of helium nuclear reaction system. The expression of supercritical ordinary bifurcation is obtained.     

Multi-dimensional cosmological models in effective string gravitation. I

We consider multi-dimensional cosmological models in the low-energy field theory of strings with a boson gravitational sector containing a metric, dilaton field, and antisymmetric Kalb-Ramon field. We study the conformal properties of the action and show that in the general conformal representation the theory is equivalent to a generalized scalar-tensor theory with a Lagrangian of nongravitating matter dependent on the dilaton. We find exact solutions of the flat homogeneous anisotropic model with structure R×M¹×...×Mⁿ and with equation of state p_i=a_i in the space Mⁱ. We discuss the picture of cosmological evolution in different conformal representations.Translated fromAstrofizika, Vol. 38, No. 2, 1995.     

A model of the Algol type close binary TT hydrae

UBV photometric observations and elements of TT Hydrae obtained by Kulkarni and Abhyankar (1980) are combined with the radial velocity curve of Popper (1979, personal communication) to derive the absolute dimensions and. a model of this important Algol system. While the photometric ratios of radii inV andB are in agreement givingk = 0.3812 for a limb darkening coefficient ofx = 0.6, application of Irwin’s (1947) method givesx = 0.4 forU. The primary is found to be a main sequence Al V star of mass 2.61M _⊙ and radius 2.01 R_⊙, and the secondary is classified as a Kl III star of mass 0.70M _⊙ and radius 5.33R _⊙. The observed Fourier coefficients for the light outside the eclipse agree with those calculated from theory for the reflection and ellipticity effects. The system shows an ultraviolet excess of 0.5 to 0.6 magnitudes during primary eclipse, which is attributed to an asymmetric circumstellar distribution of matter around the primary. The evolutionary status of the secondary, which does not appear to fill its Roche lobe completely, is discussed.     

Effects of local thermodynamics and of stellar mass ratio on accretion disc stability in close binaries

Inflow kinematics at the inner Lagrangian point L1, gas compressibility, and physical turbulent viscosity play a fundamental role on accretion disc dynamics and structure in a close binary (CB). Physical viscosity supports the accretion disc development inside the primary gravitational potential well, developing the gas radial transport, converting mechanical energy into heat. The Stellar‐Mass‐Ratio (SMR) between the compact primary and the secondary star (M₁/M₂) is also effective, not only in the location of the inner Lagrangian point, but also in the angular kinematics of the mass transfer and in the geometry ofthe gravitational potential wells. In this work we pay attention in particular to the role ofthe SMR, evaluating boundaries, separating theoretical domains in compressibility‐viscosity graphs where physical conditions allow a well‐bound disc development, as a function ofmass transfer kinematic conditions. In such domains, the lower is the gas compressibility (the higher the polytropic index γ), the higher is the physical viscosity (α) requested. In this work, we show how the boundaries of such domains vary as a function of M₁/M₂. Conclusions as far as dwarf novae outbursts are concerned, induced by mass transfer rate variations, are also reported. The smaller M₁/M₂, the shorter the duration of the active‐to‐quiet and vice‐versa transitional phases. Time‐scales are of the order of outburst duration of SU Uma, OY Car, Z Cha and SS Cyg‐like objects. Moreover, conclusions as far as active‐quiet‐active phenomena in a CB, according to viscous‐thermal instabilities, in accordance to such domains, are also reported (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Chaotic Motions in The Field of Two Fixed Black Holes

We study the chaotic motions in the field of two fixed black holes M₁, M₂ by calculating (a) the asymptotic curves from the main unstable periodic orbits, (b) the asymptotic orbits, with particular emphasis οn the homoclinic and heteroclinic orbits, and (c) the basins of attraction of the two black holes. The orbits falling on M₁and M₂form fractal sets. The asymptotic curves consist of many arcs, separated by gaps. Every gap contains orbits falling on a black hole. The sizes of various arcs decrease as the mass ofM₁ increases. The basins of attraction of the black holes M₁, M₂consist of large compact regions and of thin filaments. The relative area of the basin M₂ tends to 100 as M₁ → 0, and it decreases as M₁ increases. The total area of the basins is found analytically, while the relative area of the basin M₂ is given by an empirical formula. Further empirical formulae give the exponential decrease of the number of asymptotic orbits that have not yet reached a black hole after n iterations.     

The action of the satellite 1981 S13, and the optical depth profile of the Encke-gap ringlet in the Saturn A ring

The radial optical depth profile of the Encke ringlet obtained by the occultation experiment of the Voyager photopolarimeter (PPS data) is explained to be caused by the gravitational action of the recently discovered stallite 1981 S13 and a second smaller moonlet orbiting near one of its either libration points — L₄ or L₅. To this aim the results of previous and new numerical particle simulations as well as an extension of the scattering theory concerning a single moonlet to a pair of satellites have been used leading to a triple-peaked ringlet near the orbits of the moonlets. The width and the shape of that ringlet and its separate peaks depend on the mass ratio of both moonlets and on their orbital eccentricites. The best resemblance between the PPS data and the theoretical profile is obtained if the mass ratio of the either moonlets takes M₂/M_1981S13 ≈ (0.8 … 3.0) × 10⁻² and the eccentricities hold: e_1981S13 < h_1981S13; e₂ ≈ h₂ (the values h are the Hill scales of either moonlets defined by h_1981S13/2 ≈ (M_1981S13/2/3M_h)^1/3, M_h = Saturn mass). Furthermore, our results yield a size of 1981 S13 of < 15 km in diameter.     

Composite spectra: XX. 45 Cancri

From accurate radial‐velocity measurements covering 11 circuits of the orbit of the composite‐spectrum binary 45 Cnc, together with high‐resolution spectroscopy spanning nearly 3 circuits, we have (i) isolated cleanly the spectrum of the early‐type secondary, (ii) classified the component spectra as G8 III and A3 III, (iii) derived the first double‐lined orbit for the system and a mass ratio (M₁/M₂) of 1.035 ± 0.01, and (iv) extracted physical parameters for the component stars, deriving the masses and (log) luminosities of the G star and A star as 3.11 and 3.00 M_⊙, and 2.34 and 2.28 L_⊙, respectively, with corresponding uncertainties of ±0.10 M_⊙ and ±0.09 L_⊙. Since the mass ratio is close to unity, we argue that the more evolved component is unlikely to have been a red giant long enough to have made multiple ascents of the RGB, an argument that is supported somewhat by the rather high eccentricity of the orbit (e = 0.46) and the evolutionary time‐scales of the two components, but chiefly by the presence of significant Li I in the spectrum of the cool giant. (© 2015 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Some new exact solutions with finite central parameters and?uniform radial motion of sound

We present three new categories of exact and spherically symmetric Solutions with finite central parameters of the general relativistic field equations. Two well behaved solutions in curvature coordinates first category are being studied extensively. These solutions describe perfect fluid balls with positively finite central pressure, positively finite central density; their ratio is less than one and causality condition is obeyed at the centre. The outmarch of pressure, density, pressure-density ratio and the adiabatic speed of sound is monotonically decreasing for these solutions. Keeping in view of well behaved nature of these solutions, one of the solution (I₁) is studied extensively. The solution (I₁) gives us wide range of Schwarzschild parameter u (0.138≤u≤0.263), for which the solution is well behaved hence, suitable for modeling of Neutron star. For this solution the mass of Neutron star is maximized with all degree of suitability and by assuming the surface density ρ _b =2×10¹⁴ g/cm³. Corresponding to u=0.263, the maximum mass of Neutron star comes out to be 3.369 M _Θ with linear dimension 37.77 km and central and surface redshifts are 4.858 and 0.4524 respectively. We also study some well known regular solutions (T-4, D-1, D-2, H, A, P) of Einstein’s field equations in curvature coordinates with the feature of constant adiabatic sound speed. We have chosen those values of Schwarzschild parameter u for which, these solutions describe perfect fluid balls realistic equations of state. However, except (P) solution, all these solutions have monotonically non-decreasing feature of adiabatic sound speed. Hence (P) solution is having a well behaved model for uniform radial motion of sound. Keeping in view of well behaved nature of the solution for this feature and assuming the surface density; ρ _b =2×10¹⁴ g/cm³, the maximum mass of Neutron star comes out to be 1.34 M _Θ with linear dimension 28.74 km. Corresponding central and surface redshifts are 1.002 and 0.1752 respectively.     

Fractal Dimensions as Chaos Indicators

The correlation dimension D ₂ is used to develop a method of classification for phase space orbits. D ₂ depends only on the mutual distances of the orbits points, therefore the time development of the orbit is reflected in the time development of the correlation dimension approximants. It is shown, that this technique allows to investigate the dynamical properties of a phase space orbit, a classification of chaotic and regular orbits and a detection of sticky orbits.     

Equations of motion of the restricted problem of (2 + 2) bodies when primaries are magnetic dipoles and minor bodies are taken as electric dipoles

In this problem of the restricted (2 + 2) bodies we have considered two magnetic dipoles of masses M ₁ and M ₂(M ₁ > M ₂) moving in circular Keplarian orbit about their centre of mass. Two minor bodies of masses m ₁, m ₂(m _j< M ₂) are taken as electric dipoles in the field of rotating magnetic dipoles. These minor bodies interact with each other but do not perturb the primaries.We have found equations of motions which differ from that of Goudas and Petsagouraki's (1985).     

Charged analogues of Schwarzschild interior solution in terms of pressure

Recently, Bijalwan (Astrophys. Space Sci., doi:, 2011a) discussed charged fluid spheres with pressure while Bijalwan and Gupta (Astrophys. Space Sci. 317, 251–260, 2008) suggested using a monotonically decreasing function f to generate all possible physically viable charged analogues of Schwarzschild interior solutions analytically. They discussed some previously known and new solutions for Schwarzschild parameter u( = \fracGMc²a ) ￡ 0.142u( =\frac{GM}{c^{2}a} ) \le 0.142, a being radius of star. In this paper we investigate wide range of u by generating a class of solutions that are well behaved and suitable for modeling Neutron star charge matter. We have exploited the range u≤0.142 by considering pressure p=p(ω) and f = ( f₀(1 - \fracR²(1 - w)a²) +f_a\fracR²(1 - w)a² )f = ( f_{0}(1 - \frac{R^{2}(1 - \omega )}{a^{2}}) +f_{a}\frac{R^{2}(1 - \omega )}{a^{2}} ), where w = 1 -\fracr²R²\omega = 1 -\frac{r^{2}}{R^{2}} to explore new class of solutions. Hence, class of charged analogues of Schwarzschild interior is found for barotropic equation of state relating the radial pressure to the energy density. The analytical models thus found are well behaved with surface red shift z _s ≤0.181, central red shift z _c ≤0.282, mass to radius ratio M/a≤0.149, total charge to total mass ratio e/M≤0.807 and satisfy Andreasson’s (Commun. Math. Phys. 288, 715–730, 2009) stability condition. Red-shift, velocity of sound and p/c ² ρ are monotonically decreasing towards the surface while adiabatic index is monotonically increasing. The maximum mass found to be 1.512 M _Θ with linear dimension 14.964 km. Class of charged analogues of Schwarzschild interior discussed in this paper doesn’t have neutral counter part. These solutions completely describe interior of a stable Neutron star charge matter since at centre the charge distribution is zero, e/M≤0.807 and a typical neutral Neutron star has mass between 1.35 and about 2.1 solar mass, with a corresponding radius of about 12 km (Kiziltan et al., [astro-ph.GA], 2010).     

A new class of charged analogues of Vaidya–Tikekar type super-dense star

First ever closed form solution for charged fluid sphere expressed by a space time with its hypersurfaces t= constant as spheroid is obtained for the case 0<K<1. The same is utilized to construct a superdense star with surface density 2×10¹⁴ gm/cm³. The star is seen to satisfy the reality and causality conditions for 0<K≤0.045 and possesses maximum mass and radius to be 0.065216M _Θ and 1.137496 km respectively. Moreover the interior of the star satisfy strong energy condition. However in the absence of the causality condition, the reality conditions are valid for a wider range 0<K≤0.13. The maximum mass and radius for the later case are 1.296798M _Θ and 2.6107 km respectively for the strong energy condition, while the said parameters for the weak energy condition read as 1.546269M _Θ and 2.590062 km respectively.     

Catalog of nearby isolated galaxies in the volume <Emphasis Type="Italic">z</Emphasis> < 0.01

We present a catalog of 520 most isolated nearby galaxies with angular velocities V _LG < 3500 km/s, covering the entire sky. This population of “space orphans” makes up 4.8% among 10 900 galaxies with measured radial velocities. We describe the isolation criterion used to select our sample, called the “Local Orphan Galaxies”(LOG), and discuss their basic optical and HI properties. A half of the LOG catalog is occupied by the Sdm, Im and Ir morphological type galaxies without a bulge. The median ratio M _gas/M _star in the LOG galaxies exceeds 1. The distribution of the catalog galaxies on the sky looks uniform with some signatures of a weak clustering on the scale of about 0.5 Mpc. The LOG galaxies are located in the regions where the mean local density of matter is approximately 50 times lower than the mean global density. We indicate a number of LOG galaxies with distorted structures, which may be the consequence of interaction of isolated galaxies with massive dark objects.     

Gravitation and inertia; a rearrangement of vacuum in gravity

We address gravitation and inertia in the framework of a general gauge principle (GGP) which accounts for the gravitation gauge group G _R generated by a hidden local internal symmetry implemented on the flat space. Following the method of phenomenological Lagrangians, we connect the group G _R to a non-linear realization of the Lie group of the distortion G _D of the local internal properties of six-dimensional flat space, M ₆, which is assumed as a toy model underlying four-dimensional Minkowski space. We study the geometrical structure of the space of parameters and derive the Maurer–Cartan’s structure equations. We treat distortion fields as Goldstone fields, to which the metric and connection are related, and we infer the group invariants and calculate the conserved currents. The agreement between the proposed gravitational theory and available observational verifications is satisfactory. Unlike the GR, this theory is free of fictitious forces, which prompts us to address separately the inertia from a novel view point. We construct a relativistic field theory of inertia, which treats inertia as a distortion of local internal properties of flat space M ₂ conducted under the distortion inertial fields. We derive the relativistic law of inertia (RLI) and calculate the inertial force acting on the photon in a gravitating system. In spite of the totally different and independent physical sources of gravitation and inertia, the RLI furnishes a justification for the introduction of the Principle of Equivalence. Particular attention is given to the realization of the group G _R by the hidden local internal symmetry of the abelian group U ^loc=U(1) _Y ×diag[SU(2)], implemented on the space M ₆. This group has two generators, the third component T ³ of isospin and the hypercharge Y, implying Q ^d =T ³+Y/2, where Q ^d is the distortion charge operator assigning the number −1 to particles, but +1 to anti-particles. This entails two neutral gauge bosons that coupled to T ³ and Y. We address the rearrangement of the vacuum state in gravity resulting from these ideas. The neutral complex Higgs scalar breaks the vacuum symmetry leaving the gravitation subgroup intact. The resulting massive distortion field component may cause an additional change of properties of the spacetime continuum at huge energies above the threshold value.     

On the restricted circular three-charged-body problem

Two-charged bodiesM ₁ andM ₂ revolve round their centre of mass in circular orbits under Newton's inverse-square law and the so similar Coulomb's law. A third-charged-bodyM, without mass and charge (i.e., such that it is attracted or repulsed byM ₁ andM ₂, but does not influence their motion), moves in a field with a force function, namely $$U = {\text{ }}\frac{{q - \mu }}{{r_1 }}{\text{ }} + {\text{ }}\frac{{\mu - q}}{{r_2 }}$$ , which is created byM ₁ andM ₂. In what follows, the existence and location of the collinear and equilateral Lagrangian points or solutions with be discussed and the interpretation of them will be given. This work is a generalization of the classical restricted circular three-body problem.     

Dynamics of binary compact massive objects in galactic nuclei during interactions with globular clusters

The migration of binary systems of compact massive objects in galactic nuclei owing to encounters with globular clusters is studied. A binary moves in the field of a galactic bulge with a fixed potential. An empirical relationship between the masses of the binary and bulge of the form M _b = 1000(M ₁+M ₂) is used, where M ₁ and M ₂ are the masses of the components of the binary. The amplitude of the drift of the binary components is found as a function of the initial binary orbit parameters, the size of the bulge, and the initial velocity and mass of the globular cluster. It is shown that the amplitude of the drift depends to a greater extent on the parameters of the cluster, while the magnitude of the perturbation in the binary orbit depends weakly on the bulge size and the eccentricity and major semiaxis of the binary orbit. The amplitude of the drift of the center of mass also decreases on the average as the difference between the masses of the components becomes larger.     

Preliminary results on the fundamental parameters of the eclipsing binary V398 Lacertae

The Hipparcos Space Astrometry Mission photometric observations of V398 Lac, led to the discovery of its variability, allowing to classify it as an eclipsing binary with an orbital period of about 5.4 days. This prompted us to acquire highresolution échelle spectra with the aim of performing accurate radial velocity measurements and to determine the main physical parameters of the system's components. We present, for the first time, a double‐lined radial velocity curve and determine the orbital and physical parameters of the two components, that can be classified both as late B‐type stars. In particular, we obtained an orbital inclination i ∼ 85°. With this value of the inclination, we deduced masses M₁ = 3.83±0.35 M_⊙ andM₂ = 3.29±0.32 M_⊙, and radii R₁ = 4.89±0.18 R_⊙ and R₂ = 2.45±0.11 R_⊙ for the more massive and less massive components, respectively. Both components are well inside their own Roche lobes. The mass ratio is M₂/M₁ ∼ 0.86. We derived also the projected rotational velocities as v₁ sin i = 79±2 km s^–1 and v² sin i = 19±2 km s^–1. Our measurements indicate that the rotation of the primary star is essentially pseudo‐synchronized with the orbital velocity at the periastron, while the secondary appears to rotate very slowly and has not yet attained synchronization. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Restricted quantum-mechanical three-body problems

The Schrödinger equation is solved if an electron moves in the field of chargesZ ₁ andZ ₂ which are fixed in space. The wave function is expanded in power series, the eigenvalues are given graphically and partly in tabular form. The asymptotic behaviour of the eigenvalues is discussed when the distance of the two fixed charges is small and large. Some consequences are drawn on hydrogen line broadening, shift andgrenzkontinua. Further utilization of the calculations is indicated. The mathematical appendix helps to clarify some technical details of the calculations.     

Low-Mass Quark Stars or Quark White Dwarfs

An equation of state is considered that, in superdense nuclear matter, results in a phase transition of the first kind from the nucleon state to the quark state with a transition parameter > 3/2 ( = _Q /( _N + P ₀/c ²)). A calculation of the integrated parameters of superdense stars on the basis of this equation of state shows that on the stable branch of the dependence of stellar mass on central pressure (dM/dP _c > 0), in the low-mass range, following the formation of a tooth-shaped break (M = 0.08 M , R = 200 km) due to quark formation, a new local maximum with M _max = 0.082 M and R = 1251 km is also formed. The mass and radius of the quark core of such a star turn out to be M _core = 0.005 M and R _core = 1.7 km, respectively. Mass accretion in this model can result in two successive transitions to a neutron star with a quark core, with energy release like supernova outbursts.