Generalized Chaplygin gas model with or without viscosity in the w–w′ plane

In this paper, we investigate the dynamics of generalized Chaplygin gas (GCG) model with or without viscosity in the w–w′ plane, which is defined by the equation of state parameter and its time derivative with respect to the logarithm of the scale factor. We show that GCG model without viscosity approaches to a late time de Sitter attractor (w _g =−1) and behaves like a “freezing” scalar field for the parameter α constrained by the latest observational data. However, introducing viscosity exerts an influence on the evolution of w and affects the location of the late time attractor (w _g >−1) in viscous GCG model. We also find numerically such a transition from w′>0 to w′<0 as the universe expands in viscous GCG model different from GCG model without viscosity (w′<0) in the w–w′ plane.     

Proper motions and CCD photometry of stars in the region of the open cluster NGC 6866

We present the results of our comprehensive study of the Galactic open star cluster NGC 6866. The positions of stars in the investigated region have been obtained with the “Fantasy” automatic measuring machine from 10 plates of the normal astrograph at the Pulkovo Astronomical Observatory. The size of the investigated field is 40′ × 40′, the limiting magnitude is B ∼ 16_· ^m 6, and the maximum epoch difference is 79 yr. For 1202 field stars, we have determined the relative proper motions with an rms error of 2.5 mas yr⁻¹. Out of them, 423 stars may be considered cluster members with a probability P > 70% according to the astrometric criterion. Photometric diagrams have been used as an additional criterion. We have performed two-color BV CCD photometry of stars with the Pulkovo ZA-320M mirror astrograph. The U magnitudes from the literature have also been used to construct the two-color diagrams. A total of 267 stars have turned out to be members of NGC 6866 according to the two criteria. We present refined physical parameters of the cluster and its age estimate (5.6 × 10⁸ yr). The cluster membership of red and blue giants, variable, double, and multiple stars is considered. We have found an almost complete coincidence of the positions of one of the stars in the region (a cluster nonmember) and a soft X-ray source in the ROSAT catalog. The “Fantasy” automatic measuring machine is described in the Appendix.     

Exploring morphological correlations among H2CO, 12CO, MSX and continuum mappings

There are relatively few H₂CO mappings of large-area giant molecular cloud (GMCs). H₂CO absorption lines are good tracers for low-temperature molecular clouds towards star formation regions. Thus, the aim of the study was to identify H₂CO distributions in ambient molecular clouds. We investigated morphologic relations among 6-cm continuum brightness temperature (CBT) data and H₂CO (1₁₁−1₁₀; Nanshan 25-m radio telescope), ¹²CO (1–0; 1.2-m CfA telescope) and midcourse space experiment (MSX) data, and considered the impact of background components on foreground clouds. We report simultaneous 6-cm H₂CO absorption lines and H110α radio recombination line observations and give several large-area mappings at 4.8 GHz toward W49 (50′×50′), W3 (70′×90′), DR21/W75 (60′×90′) and NGC2024/NGC2023 (50′×100′) GMCs. By superimposing H₂CO and ¹²CO contours onto the MSX color map, we can compare correlations. The resolution for H₂CO, ¹²CO and MSX data was ∼10′, ∼8′ and ∼18.3″, respectively. Comparison of H₂CO and ¹²CO contours, 8.28-μm MSX colorscale and CBT data revealed great morphological correlation in the large area, although there are some discrepancies between ¹²CO and H₂CO peaks in small areas. The NGC2024/NGC2023 GMC is a large area of HII regions with a high CBT, but a H₂CO cloud to the north is possible against the cosmic microwave background. A statistical diagram shows that 85.21% of H₂CO absorption lines are distributed in the intensity range from −1.0 to 0 Jy and the ΔV range from 1.206 to 5 km s⁻¹.     

Almost stable regions for an area-preserving mapping

The area preserving mapping x = x + a(y – y ³), y = y – a(x – x³), for 0.3 a 2.0 has been studied to locate approximately the x-axis points bounding almost stable regions. For each value of a, these are fixed points with variational trace just greater than 2.0. Transition to chaos can occur rapidly as a increases (with n/k fixed).     

Large-scale mapping of the IRAS 0042 + 5530 region in the 12CO (J = 1−0) and 13CO (J = 1−0) molecular lines

We present new radio observations of molecular lines in the region of high mass star formation, namely G122.0-7.1. A large-scale map of the emission observed in the ¹²CO (J = 1−0) and ¹³CO (J = 1−0) lines covers the area of 15′ × 9′, revealing two dense regions. The molecular bipolar outflows have been resolved in ASO1 region. It is associated with the known candidate YSO nearby IRAS 0042 + 5530. Also, a new dense region has been discovered in the North-Western part of the G122.0-7.1 at a distance of 5′ from IRAS 0042 + 5530. Its position is close to the peak of 4850 MHz emission. The text was submitted by the authors in English.     

Effect of perturbations on the non linear stability of triangular points in the restricted three-body problem with variable mass

The effect of small perturbations ε and ε ^′ in the Coriolis and the centrifugal forces, respectively on the nonlinear stability of the triangular points in the restricted three-body problem with variable mass has been studied. It is found that, in the nonlinear sense, the triangular points are stable for all mass ratios in the range of linear stability except for three mass ratios, which depend upon ε, ε ^′ and β, the constant due to the variation in mass governed by Jeans’ law.     

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.     

Effect of fluctuations in Doppler width on the center of strong absorption lines

Stochastic temperatures and turbulence are characterized by average velocities u _th and < u _turb  > ≡ u ₀ and fluctuations u￠_th {u'_{th}} and u′ (<u′ > = 0). Thus, the Doppler width of a line also has a fluctuating component Dl￠_D \Delta {\lambda '_D} . Observed spectra correspond to the radiative flux averaged over time and over a star’s surface, <H_λ>. Usually, only the average velocities u _th and u ₀ are taken into account in photospheric models and these yield the Doppler width Dl_D⁽⁰⁾ \Delta \lambda_D^{(0)} of a line in the customary way. The fluctuations Dl￠_D \Delta {\lambda '_D} mean that near a line center the average absorption coefficient < α_λ > is larger than the usual α_λ, which depends only on the average velocities u _th and u ₀. This enhances the absorption line near the center and is not explained by the photospheric models. This new statistical effect depends on the wavelength of the line. A comparison of observed lines with model profiles yields an estimate for the average level of fluctuations in the Doppler width, h = á | Dl￠_D | ñ

Accretion effects on compact members of binary stars

We explore the change in the period of axial rotation and in the radius of a magnetized compact star in a binary system, induced by the accretion on it of mass with angular momentum from the surface of its non-compact companion. No specific assumption is made concerning the accretion model, and the primary’s interior is described by the Fermi-Dirac statistics for degenerate matter. The rate of change with time of the period and radius is expressed in terms of the compact primary’s physical parameters and total absolute luminosity. The conditions are fully derived under which the above changes can be positive, negative or even vanish. In the case of the millisecond pulsars in binary X-ray sources the predicted values of the period time derivative, depending on the values of the accretion rate and. the absolute luminosity, can be positive or negative—if not vanishing—and they fall absolutely in the range 10⁻²¹ −10⁻¹⁷ ss⁻¹, in good agreement with current observational data. The corresponding rate of change of radius, either positive or negative, fall in the range of 10⁻³ −10⁻¹ cm y⁻¹. Finally, it is proved that the well-known bursters can be explained by thermonuclear flash due to gravitational instability in the accreted matter, but their explanation as a result of direct contraction could be possible only for quite high accretion rates (>10⁻⁷ M ⊙ y⁻¹). This last result indicates that, in contrast to the accretion-induced change in period, which can be of either sign irrespective of the primary’s age, the accretion-induced non-catastrophic contraction is impossible, while according to repent results the contraction in general is possible for young compact objects.     

Field-Dependent Adaptive Optics Correction Derived with the Spectral Ratio Technique

In this empirical study, we compare high-resolution observations obtained with the 65-cm vacuum reflector at Big Bear Solar Observatory (BBSO) in 2005 and with the Dunn Solar Telescope (DST) at the National Solar Observatory/Sacramento Peak (NSO/SP) in 2006. We measure the correction of the high-order adaptive optics (AO) systems across the field of view (FOV) using the spectral ratio technique, which is commonly employed in speckle masking imaging, and differential image motion measurements. The AO correction is typically much larger (10^′′ to 25^′′) than the isoplanatic angle and can be described by a radially symmetric function with a central core and extended wings. The full-width at half-maximum (FWHM) of the core represents a measure of the AO correction. The average FWHM values for BBSO and NSO/SP are 23.5^′′ and 18.2^′′, respectively. The extended wings of the function show that the AO systems still contribute to an improved speckle reconstruction at the periphery of the 80^′′×80^′′ FOV. The major differences in the level of AO correction between BBSO and NSO/SP can be explained by different contributions of ground-layer- and free-atmosphere-dominated seeing, as well as different FOVs of the wavefront sensors. In addition, we find an anisotropic spectral ratio in sunspot penumbrae caused by the quasi-one-dimensional nature of penumbral filaments, which introduces a significant error in the estimation of the Fourier amplitudes during the image restoration process.     

On accounting for temperature and pressure in determining the Rayleigh scattering in the earth’s atmosphere

We calculated the variations of Rayleigh optical depth with changes of pressure and temperature for three observation sites: Simferopol (φ = 44°57′N, λ = 34°8′E, h = 265 m above sea level), Nauchny (φ = 44°43′N, λ = 34°3′E, h = 583 m), and Ai-Petry meteorological station (φ = 44°24′N, λ = 34°6′E, h = 1180 m).     

HI fluctuations at large redshifts: I-visibility correlation

We investigate the possibility of probing the large scale structure in the universe at large redshifts by studying fluctuations in the redshifted 1420 MHz emission from the neutral hydrogen (HI) at early epochs. The neutral hydrogen content of the universe is known from absorption studies forz ≲ 4.5. TheHI distribution is expected to be inhomogeneous in the gravitational instability picture and this inhomogeneity leads to anisotropy in the redshifted HI emission. The best hope of detecting this anisotropy is by using a large low-frequency interferometric instrument like the Giant Meter-Wave Radio Telescope (GMRT). We calculate the visibility correlation function 〈V_v(U) V_v′(U)〉 at two frequenciesi andv′ of the redshiftedHI emission for an interferometric observation. In particular we give numerical results for the two GMRT channels centered aroundν = 325 MHz andν = 610 MHz from density inhomogeneity and peculiar velocity of the HI distribution. The visibility correlation is- 10^-10-10^-9 Jy². We calculate the signal-to-noise for detecting the correlation signal in the presence of system noise and show that the GMRT might detect the signal for integration times - 100 hrs. We argue that the measurement of visibility correlation allows optimal use of the uncorrelated nature of the system noise across baselines and frequency channels. On leave from Harish-Chandra Research Institute, Chhatnag Road, Jhusi, Allahabad 211 019, India.     

Structure of clusters with bimodal distribution of radial velocities of galaxies. IV: A1569

We report the results of study of the A1569 cluster (12 ^h 36^m.3, +16°35′) and the neighboring A1589 cluster (12 ^h 41^m.3, +18°34′), making up a pair (a supercluster) with a projected size of about 10Mpc. This study is done within the framework of our program for investigating the galaxy clusters with bimodal velocity distributions (i.e., clusters where the velocities of subsystems differ by more than Δcz ∼ 3000 km/s). In the A1569 cluster we have identified two subsystems: A1569A (cz = 20613 km/s) and A1569B (cz = 23783 km/s). These subsystems have the line-of-sight velocity dispersions of 484 km/s and 493 km/s, and dynamic masses within the R ₂₀₀ radius equal to 1.8 × 10¹⁴ and 2.0 × 10¹⁴ M _⊙, respectively. We directly estimate the distances to these subsystems using three methods applied to earlytype galaxies: the Kormendy relation, photometric plane, and fundamental plane. To this end, we use the results of our observations made with the 1-m telescope of the SAO RAS and the data adopted from the SDSS DR7 catalog. We found that A1569 consists of two independent clusters. The A1569B cluster is located at the Hubble distance corresponding to its radial velocity. The A1569A cluster has a peculiar velocity of −1290 ± 630 km/s, which can be explained by the effect of the more massive A1589 cluster (with a mass of 7.9 × 10¹⁴ M _⊙) and of the supercluster where it resides. In all the four bimodal clusters that we studied within the framework of our program, A1035, A1775, A1831, and A1569, the subsystems are independent clusters lying close to the Hubble relation between redshift and distance.     

Boltzmann Equilibrium of Endothermic Heavy Nuclear Synthesis in the Universe and a Quark Relation to the Magic Numbers

As laser–plasma interactions access ever-increasing ranges of plasma temperatures and densities, it is interesting to consider whether they will some day shed light on questions concerning nuclear synthesis. One such open question is the process of endothermic nuclear synthesis for elements with A > 60, thought to have taken place at a point in time during the big bang, or currently in supernovae. We present an explanation based on a Boltzmann equilibrium condition, in combination with the change of the Fermi-statistics from the relativistic branch for hadrons from higher than nuclear densities to the lower density subrelativistic branch. The Debye length confinement of nuclei breaks down at the relativistic change, thus leading to the impossibility of nucleation of the quark-gluon state at higher than nuclear densities. Taking the increment for the proton number Z as Z′ = 10 of the measured standard abundance distribution (SAD) of the elements for a Boltzmann probability for heavy element synthesis, a sequence 3 ⁿ was found with the exponent n for the sequence of the magic numbers. The jump between the magic numbers 20 and 28 does not need then the usual spin-orbit explanation.     

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.     

Astrophysically Useful Parameters for Some Vibronic Transitions of AlH and BH

For molecular identification in astrophysical sources, an astrophysicist needs some spectroscopic parameters such as dissociation energy, vibrational or rotational temperature of the source, band or line wavelengths, transition probability parameters, etc. The Franck-Condon(FC) factors are proportional to the transition probabilities. In this study, the FC factors and r-centroids for the vibronic (vibration-electronic) transitions C ¹ Σ ⁺ → X ¹ Σ ⁺ of aluminium hydride (AlH), b ³ Σ ^{( −)} → a ³ Π, C ¹ Σ ⁺ → A ¹ Π & C ^′1 Δ → Δ ¹ Π of boron hydride (BH) have been evaluated and the results are presented in tables which include band origin/head wavelengths. The physical & astrophysical significances of our evaluated FC factors & r-centroids have been discussed and the possible presence of AlH in sunspot umbral spectra is also predicted. PACS: 33 · 70 · Ca     

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.     

Limits of stability for an area-preserving polynomial mapping

The Henon-Heiles mappingx=x+a(y–y ³), y=y–a(x–x³) has been studied, with the aim of finding where the unstable regions of the (x, y) plane are. When this mapping is put into the normal form, it is found to be a typical twist mapping. The criteria of Moser (1971) are used to obtain an upper limit to the size of a stable region around the origin, and this limit decreases to zero as the value of the parameter a increases toward 2.0. However, direct calculation fora=1.99 shows that there is a fairly large region insidex=0.412,y=0, from which escape from near the outer boundary requires at least 160 mappings. The region of high stability thus appears to be much larger than any region of absolute stability predicted by the KAM theorem.A general survey has been made of instability regions for the parameter valuea=1.0, this survey having been carried out to the extent which is allowed by a computer with 18-decimal-place accuracy. First, for all thex-axis fixed points (of the above mapping) deemed to be representative and significant, both the locations and variational matrix traces have been calculated. (The latter show whether the fixed point is elliptic or hyperbolic.) Ifn is the number of mappings andk is the number of circuits around the origin, then the listing (Table IV) is for fractionsk/n between 1/6 and 1/22, inclusive. (This covers the range 0x<0.96, withx=0 the fixed point forn=6,k=1).Escape toward infinity can be rapid, with less than 200 mappings necessary to reach the vicinity of then=1 fixed points (atx=±1,y=0 andx=0,y=±1) from outer regions of the (x, y) plane, such as for |x|>0.93,y=0. In this case, the unstable regions may be tongues encircling the origin. However, as the distance from the origin is decreased, the tongues can be replaced by exceedingly fine threads rapidly becoming less than say 10^–16 in thickness. Such a thread issues fromx=0.905468199,y=0 and requires of the order of 40 000 mappings to escape. It does so by spiralling about the origin and penetrating through several series of loops associated with various fixed points at successively greater (absolute) values ofx(y=0). The region between this thread and the origin is therefore highly stable. Practical stability of a region may be regarded as attained when the region is interior to a series of loops for which the trace of the variational matrix is close to 2.0. This occurs forn=53,k=4, with fixed point atx=0.819786,y=0 and Trace=2.0000 0004.If an invariant curve does in fact exist, then one must be able to show that the outward spiralling from a given series of loops is brought to a halt at some stage. This does not occur in the region where direct computation is possible, as we show in this article, and it remains to be seen under what conditions it can take place.     

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.