Evidence for a disaggregation of the universe

Combining the kinematical definitions of the two dimensionless parameters, the deceleration q(x) and the Hubble t ₀ H(x), we get a differential equation (where x=t/t ₀ is the age of the universe relative to its present value t ₀). First integration gives the function H(x). The present values of the Hubble parameter H(1) [approximately t ₀ H(1)≈1], and the deceleration parameter [approximately q(1)≈−0.5], determine the function H(x). A second integration gives the cosmological scale factor a(x). Differentiation of a(x) gives the speed of expansion of the universe. The evolution of the universe that results from our approach is: an initial extremely fast exponential expansion (inflation), followed by an almost linear expansion (first decelerated, and later accelerated). For the future, at approximately t≈3t ₀ there is a final exponential expansion, a second inflation that produces a disaggregation of the universe to infinity. We find the necessary and sufficient conditions for this disaggregation to occur. The precise value of the final age is given only with one parameter: the present value of the deceleration parameter [q(1)≈−0.5]. This emerging picture of the history of the universe represents an important challenge, an opportunity for the immediate research on the Universe. These conclusions have been elaborated without the use of any particular cosmological model of the universe.     

Comparing maps to symplectic integrators in a galactic type Hamiltonian

We obtain thex - p _xPoincare phase plane for a two dimensional, resonant, galactic type Hamiltonian using conventional numerical integration, a second order symplectic integrator and a map based on the averaged Hamiltonian. It is found that all three methods give good results, for small values of the perturbation parameter, while the symplectic integrator does a better job than the mapping, for large perturbations. The dynamical spectra are used to distinguish between regular and chaotic motion.     

Mosaic and gradient SiGe single crystals for gamma ray Laue lenses

Both Ge_1−x Si _x mosaic crystals and Si_1−x Ge _x crystals with gradient of composition could be grown using the modified Czochralski technique to produce the diffracting elements for the MAX gamma ray telescope. Although many elements cut from the mosaic crystal and used before for CLAIRE gamma ray telescope had an efficiency up to 20%, the overall efficiency of the lens was about 8.1 ± 0.7 %, which is more than twice lower than the theoretically predicted efficiency. Some causes of this behaviour are discussed. In addition to mosaic crystals, the growth of Si_1−x Ge _x crystals with a gradient of composition and their properties are analysed. Such composition-gradient crystals could be a promising way to improve the diffraction efficiency of Laue lens for MAX.     

“Stickiness” in mappings and dynamical systems

We present results of a study of the so-called “stickiness” regions where orbits in mappings and dynamical systems stay for very long times near an island and then escape to the surrounding chaotic region. First we investigated the standard map in the form x_i+1 = x_i+y_i+1 and y_i+1 = y_i+K/2π · sin(2πx_i) with a stochasticity parameter K = 5, where only two islands of regular motion survive. We checked now many consecutive points—for special initial conditions of the mapping—stay within a certain region around the island. For an orbit on an invariant curve all the points remain forever inside this region, but outside the “last invariant curve” this number changes significantly even for very small changes in the initial conditions. In our study we found out that there exist two regions of “sticky” orbits around the invariant curves: A small region I confined by Cantori with small holes and an extended region II is outside these cantori which has an interesting fractal character. Investigating also the Sitnikov-Problem where two equally massive primary bodies move on elliptical Keplerian orbits, and a third massless body oscillates through the barycentre of the two primaries perpendicularly to the plane of the primaries—a similar behaviour of the stickiness region was found. Although no clearly defined border between the two stickiness regions was found in the latter problem the fractal character of the outer region was confirmed.     

Programmed motion in the presence of homogeneity

In the framework of the inverse problem of dynamics, we face the following question with reference to the motion of one material point: Given a region T_orb of the xy plane, described by the inequality g (x, y) ≤ c₀, are there potentials V = V (x, y) which can produce monoparametric families of orbits f (x, y) = c (also to be found) lying exclusively in the region T_orb? As the relevant PDEs are nonlinear, an answer to this question (generally affirmative, but not with assurance) can be given by the procedure of the determination of certain constants specifying the pertinent functions. In this paper we ease the mathematics involved by making certain simplifying assumptions referring to the homogeneity of both the function g (x, y) (describing the boundary of T_orb) and of the slope function γ(x, y) = f_y/f_x (representing the required family f (x, y) = c). We develop the method to treat the so formulated problem and we show that, even under these restrictive assumptions, an affirmative answer is guaranteed provided that two algebraic equations have in common at least one solution (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

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.     

On the adjustment of outer solar layer models

Using the electron density n _e as an independent variable agreement between the models of the convective zone, photosphere, chromosphere, corona and solar wind is obtained. As a base the known data about the mean models of the individual layers of the quiet Sun are taken (i.e. without taking account of inhomogeneities and deviations from spherical symmetry). The chromospheric region is the exclusion. Here the run of T _e (n _e ) is revised anew to provide a smooth transition from temperature minimum to the corona and to satisfy the observed intensity distribution in the shortwave radio emission spectrum.A plot of the gas density versus n _e permits to get a clear representation about the rate of change of the degree of ionization x and to evaluate quickly the numerical values of x.     

Hamiltonian Stability of Spin–Orbit Resonances in Celestial Mechanics

The behaviour of ‘resonances’ in the spin-orbit coupling in celestial mechanics is investigated in a conservative setting. We consider a Hamiltonian nearly-integrable model describing an approximation of the spin-orbit interaction. The continuous system is reduced to a mapping by integrating the equations of motion through a symplectic algorithm. We study numerically the stability of periodic orbits associated to the above mapping by looking at the eigenvalues of the matrix of the linearized map over the full cycle of the periodic orbit. In particular, the value of the trace of the matrix is related to the stability character of the periodic orbit. We denote by ε_* (p/q) the value of the perturbing parameter at which a given elliptic periodic orbit with frequency p/q becomes unstable. A plot of the critical function ε_* (p/q) versus the frequency at different orbital eccentricities shows significant peaks at the synchronous resonance (for low eccentricities) and at the synchronous and 3:2 resonances (at higher eccentricities) in good agreement with astronomical observations. This revised version was published online in July 2006 with corrections to the Cover Date.     

Variation of stellar coronal activity with age

We investigate the variation in coronal activity of late-type stars with age. We determine the age of the star from the colour-colour diagram (U-B vsB-V). We show that the ratio of X-ray luminosity (L _x) to bolometric luminosity (L _bol) is well correlated with age over several orders of magnitude variations. We find thatL _x/L _bol) decreases with age with a power of –1.55. This is consistant with the expected results from the studies of the variation of the corona with chromosphere and the dependence of chromosophere on age.     

Some properties of an intrinsically degenerate Hamiltonian system

Using theoretical arguments we study some properties of a time independent, two-dimensional Hamiltonian system in the 1:1 resonance case. In particular we find the frequency of the oscillation near the elliptic points, the ratio of the semiaxes of the ellipses surrounding them and the inclination angle of the asymptotes of the hyperbolic orbits in the original variablesx–p _x. The results are in satisfactory agreement with those given by numerical integration of the equations of motion. Some possible applications for the motion of stars in elliptical galaxies are also discussed.     

Dark energy and flatness from observational H(z)+WMAP constraint

We analyse the dark energy problem using observational H(z) data plus the curvature constraint given by WMAP. After a non-parametric statistical study covering the most probable range of Ω _m0 and H ₀ from different combination of data, we investigate the possibility of having the dark energy EoS parameter ω _x ≠−1. In order to keep strict flatness (1% of deviation from Ω=1), our results point out this is the case for 0.20≲Ω _m0≲0.23 and H ₀≈67 km/s/Mpc, with ω _x ≈−0.55. However, if we admit a 10% deviation from the flatness condition, ω _x may have any value in the range [−1.2,−0.5] for 0.20≲Ω _m0≲0.35 and 67≲H ₀≲74 km/s/Mpc.     

The accuracy of supermassive black hole masses determined by the single-epoch spectrum (Dibai) method

The first set of supermassive black hole mass estimates, published from 1977 to 1984 by E.A. Dibai, are shown to be in excellent agreement with recent reverberation-mapping estimates. Comparison of the masses of 17 AGNs covering a mass range from about 10⁶ to 10⁹ M _⊙ shows that the Dibai mass estimates agree with reverberation-mapping mass estimates to significantly better than ±0.3 dex and were, on average, only 0.14 dex (∼40%) systematically lower than masses obtained from reverberation mapping. This surprising agreement with the results of over a quarter of a century ago has important implication for the structure and kinematics of AGNs and implies that type-1 AGNs are very similar. Our results give strong support to the use of the single-epoch-spectrum (Dibai) method for investigating the co-evolution of supermassive black holes and their host galaxies. The article was translated by the authors.     

Ion composition and chemistry in the coma of Comet 1P/Halley—A comparison between Giotto's Ion Mass Spectrometer and our ion-chemical network

In order to understand the cometary plasma environment it is important to track the closely linked chemical reactions that dominate ion evolution. We used a coupled MHD ion-chemistry model to analyze previously unpublished Giotto High Intensity Ion Mass Spectrometer (HIS-IMS) data. In this way we study the major species, but we also try to match some minor species like the CH_x and the NH_x groups. Crucial for this match is the model used for the electrons since they are important for ion-electron recombination. To further improve our results we included an enhanced density of supersonic electrons in the ion pile-up region which increases the local electron impact ionization. In this paper we discuss the results for the following important ions: C⁺, CH⁺, CH⁺₂, CH⁺₃, N⁺, NH⁺, NH⁺₂, NH⁺₃, NH⁺₄, O⁺, OH⁺, H₂O⁺, H₃O⁺, CO⁺, HCO⁺, H₃CO⁺, and CH₃OH⁺₂. We also address the inner shock which is very distinctive in our MHD model as well as in the IMS data. It is located just inside the contact surface at approximately 4550 km. Comparisons of the ion bulk flow directions and velocities from our MHD model with the data measured by the HIS-IMS give indication for a solar wind magnetic field direction different from the standard Parker angle at Halley's position. Our ion-chemical network model results are in a good agreement with the experimental data. In order to achieve the presented results we included an additional short lived inner source for the C⁺, CH⁺, and CH⁺₂ ions. Furthermore we performed our simulations with two different production rates to better match the measurements which is an indication for a change and/or an asymmetric pattern (e.g. jets) in the production rate during Giotto's fly-by at Halley's comet.     

Solution of Lambert's problem for short arcs

Approximation formulas are found for and , wherex(t) satisfies ,x(0)=x ₀,x(1)=x ₁. The results are applied to an example of two-body motion.     

The existence of three-dimensional symmetric orbits in the magnetic-binary problem

We study the existence of three-dimensional symmetric orbits in a magnetic-binary system. We point out that only two kinds of such orbits exist, depending on the orientation of both magnetic momentsM _i,i=1, 2; one with respect to the plane,y=0 and one with respect to thex-axis of the rotating-coordinate system.     

Discovery of a Giant Radio Halo in a Massive Merging Cluster at z?=?0.443

We have discovered a giant radio halo in the massive merging cluster MACSJ0417.5-1154. This cluster, at a redshift of 0.443, is one of the most X-ray luminous galaxy cluster in the MAssive Cluster Survey (MACS) with an X-ray luminosity in the 0.1–2.4 keV band of 2.9×10⁴⁵ erg s^− 1. Recent observations from GMRT at 230 and 610 MHz have revealed a radio halo of ∼ 1.2 × 0.3 Mpc² in extent. This halo is elongated along the North-West, similar to the morphology of the X-ray emission from Chandra. The 1400 MHz radio luminosity (L _r) of the halo is ∼2 × 10²⁵ W Hz^− 1, in good agreement with the value expected from the L _x − L _r correlation for cluster halos.     

Distribution of stars perpendicular to the plane of the galaxy

We present here rigorous analytical solutions for the Boltzmann-Poisson equation concerning the distribution of stars above the galactic plane. The number density of stars is considered to follow a behaviour n(m,0) ∼H(m - m₀)m^−x, wherem is the mass of a star andx an arbitrary exponent greater than 2 and also the velocity dispersion of the stars is assumed to behave as < v²(m)> ∼ m^−θ the exponent θ being arbitrary and positive. It is shown that an analytic expression can be found for the gravitational field K_z, in terms of confluent hypergeometric functions, the limiting trends being K_z∼z for z →0, while K_z → constant for z → infinity. We also study the behaviour of < |z(m)|²>,i.e. the dispersion of the distance from the galactic disc for the stars of massm. It is seen that the quantity < |z(m)|²>∼ m^t-θ, for m→ t, while it departs significantly from this harmonic oscillator behaviour for stars of lighter masses. It is suggested that observation of < |z(m)|²> can be used as a probe to findx and hence obtain information about the mass spectrum.     

The X-ray properties of quasars determined from an iterative multiple regression analysis with censored data

We adopt the iterative least-squares method of Schmee and Hahn (1979) and extend it to the multiple regression case to investigate the dependence of the X-ray luminositíesL _x of quasars on their optical liminositiesL ₀ and redshiftsz. The method has several advantages, one of which is that we do not need the strong assumption that the values of the optical-X-ray index _0x of the detected and nondetected quasars should fall into the same range. We have found that correlations of _0x and log(1+z) or the look back time (z) are shown, but these are not firmly established due to the uncertainty present in the regression parameter. On the other hand, it is impossible for _0x to be independent ofL ₀. We have also shown thatL _x is less than proportional toL ₀.     

The Evolution of Brightest Cluster Galaxies

In this contribution we review the properties of Brightest Cluster Galaxies (BCGs) and discuss the impact that X-ray cluster selection is having on their use as cosmological probes. BCGs form a unique galaxy population. They are located near the gravitational centre of galaxy clusters and are the most massive galaxies in the universe, being some 10 times more luminous than L* systems. Historically, BCGs have been credited with small intrinsic dispersion in their absolute magnitudes (Δ≃0.2–0.3 mag) and used as standard candles to constrain the cosmological parameters. Although indirect signs of mass accretion out to z≃1 have been observed, uncovering their full evolutionary picture has remained an elusive goal. Studies of BCGs based on serendipitiously discovered X-ray cluster samples, particularly from ROSAT, provide large numbers of unbiased clusters at z≤1. Furthermore X-ray emission guarantees the presence of a large gravitationally bound potential well and the X-ray information can be used to locate the centroids of clusters, aiding the identification of the BCG. We show that this has important consequences for studies of distance determination and large-scale streaming flows based on the optical properties of BCGs. Recent results based on X-ray selected clusters show large differences in near-IR BCG properties with their cluster environment; such that those in clusters with L _x≥1.9×10⁴⁴erg s^-1 are brighter and more uniform than those in their low-L _x counterparts. The BCGs in highL _x systems show no evidence of having undergone mass growth, whereas those in low L _x systems show a widerrange of evolution, with evidence that some have grown by a factor of 4 ormore since z≃1. These results are a direct indication of howa single homogeneous population of galaxies evolves and are a challenge to simple semi-analytical hierarchical models. If future observations at high redshift are to seriously challenge theory then better predictions of the evolutionary process are required. This revised version was published online in July 2006 with corrections to the Cover Date.     

Parameters of the local warp of the stellar-gaseous galactic disk from the kinematics of Tycho-2 nearby red giant clump stars

We analyze the three-dimensional kinematics of about 82 000 Tycho-2 stars belonging to the red giant clump (RGC). First, based on all of the currently available data, we have determined new, most probable components of the residual rotation vector of the optical realization of the ICRS/HIPPARCOS system relative to an inertial frame of reference, (ω _x , ω _y , ω _z ) = (−0.11, 0.24, −0.52) ± (0.14, 0.10, 0.16) mas yr⁻¹. The stellar proper motions in the form μ_α cos δ have then be corrected by applying the correction ω _z = −0.52 mas yr⁻¹. We show that, apart from their involvement in the general Galactic rotation described by the Oort constants A = 15.82 ± 0.21 km s⁻¹ kpc⁻¹ and B = −10.87 ± 0.15 km s⁻¹ kpc⁻¹, the RGC stars have kinematic peculiarities in the Galactic yz plane related to the kinematics of the warped stellar-gaseous Galactic disk. We show that the parameters of the linear Ogorodnikov-Milne model that describe the kinematics of RGC stars in the zx plane do not differ significantly from zero. The situation in the yz plane is different. For example, the component of the solid-body rotation vector of the local solar neighborhood around the Galactic x axis is M ₃₂⁻ = −2.6 ± 0.2 km s⁻¹ kpc⁻¹. Two parameters of the deformation tensor in this plane, namely M ₂₃⁺ = 1.0 ± 0.2 km s⁻¹ kpc⁻¹ and M ₃₃ − M ₂₂ = −1.3 ± 0.4 km s⁻¹ kpc⁻¹, also differ significantly from zero. On the whole, the kinematics of the warped stellar-gaseous Galactic disk in the local solar neighborhood can be described as a rotation around the Galactic x axis (close to the line of nodes of this structure) with an angular velocity −3.1 ± 0.5 km s⁻¹ kpc⁻¹ ≤ Ω_W ≤ −4.4 ± 0.5 km s⁻¹ kpc⁻¹.