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

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

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.     

Isovortical orbits in uniformly rotating coordinates

For the conservative, two degree-of-freedom system with autonomous potential functionV(x,y) in rotating coordinates; $$\dot u - 2n\upsilon = V_x , \dot \upsilon + 2nu = V_y $$ , vorticity (v _x -u _y ) is constant along the orbit when the relative velocity field is divergence-free such that: $$u(x,y,t) = \psi _y , \upsilon (x,y,t) = - \psi _x $$ . Unlike isoenergetic reduction using the Jacobi, integral and eliminating the time,non-singular reduction from fourth to second-order occurs when (u,v) are determined explicitly as functions of their arguments by solving for ψ (x, y, t). The orbit function ψ satisfies a second-order, non-linear partial differential equation of the Monge Ampere type: $$2(\psi _{xx} \psi _{yy} - \psi _{xy}^2 ) - 2(\psi _{xx} + \psi _{yy} ) + V_{xx} + V_{yy} = 0$$ . Isovortical orbits in the rotating frame arenot level curves of ψ because it contains time explicitly due to coriolis effects. Rather, (x, y) coordinates along the orbit are obtained, from (u, v) either by numerical integration of the kinematic equations, or by partial differentiation of the Legendre transform ? of ψ. In the latter case, ? is shown to satisfy a non-linear, second-order partial differential equation in three independent variables, derived from the Monge-Ampere Equation. Complete reduction to quadrature is possible when space-time symmetries exist, as in the case of central force motion.     

The restricted two-body problem in constant curvature spaces

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

The Dynamics of Low-Perihelion Meteoroid Streams

The Canadian Meteor Orbit Radar (CMOR) has collected information on a number of weak meteor showers that have not been well characterized in the literature. A subsample of these showers (1) do not show a strong orbital resemblance to any known comets or asteroids, (2) have highly inclined orbits, (3) are at low perihelion distances ( AU) and (4) are at small semimajor axes (<2 AU). Though one might conclude that the absence of a parent object could be the result of its disruption, it is unclear how this relatively inaccessible (dynamically speaking) region of phase space might have been populated by parents in the first place. It will be shown that the Kozai secular resonance and/or Poynting–Robertson drag can modify meteor stream orbits rapidly (on time scales comparable to a precession cycle) and may be responsible for placing some of these streams into their current locations. These same effects are also argued to act on these streams so as to contribute to the high-ecliptic latitude north and south toroidal sporadic meteor sources. There remain some differences between the simple model results presented here and observations, but there may be no need to invoke a substantial population of high-inclination parents for the observed high-inclination meteoroid streams with small perihelion distances.     

K emission-line widths and the solar chromosphere

Closely spaced microphotometer tracings parallel to the dispersion of one excellent frame of a K-line time sequence have been utilized for a study of the nature of the K_2v , K_2R intensities in the case of the solar chromosphere. The frequency of occurrence of the categories of intensity ratio are as follows: per cent; per cent; per cent; per cent; per cent. Two types of absorbing components are postulated to explain the pattern of observed K_2v , k_2R intensity ratios. One component with minor Doppler displacements acting on the normal K₂₃₂ profile, where K_2V >K_2R , produces the cases K_2v K_2R , K_2v = K_2R , K_2v <K_2R . The other component arises from dark condensations which are of size 3500 kms as seen in K_2R . They have principally large down flowing velocities in the range 5–8 km/sec and are seen on K₃ spectroheliograms with sizes of about 5000 kms, within the coarse network of emission. These dark condensations give rise to the situation K_2R = 0.K₂-line widths are measured for all tracings where K_2v , K_2R are measurable simultaneously. The distribution curve of these widths is extremely sharp. The K₂ emission source is identified with the bright fine mottles visible on the surface. Evidence for this interpretation comes from the study of auto-correlation functions of K₂ intensity variations and the spacing between the bright fine mottles from both spectrograms and spectroheliograms. The life time of the fine mottling is 200 sec.The supergranular boundaries which constitute the coarse network come in two intensity classes. A low intensity network has the fine mottles as its principal contributor to the K emission. When the network is bright, the enhancement is caused by increased K emission due to the accumulation of magnetic fields at the supergranule boundary. The K₂ widths of the low intensity supergranular boundary agree with the value found for the bright mottles. Those for the brighter network are lower than this value, similar to the K₂ widths as seen in the active regions.It is concluded that bright fine mottling is responsible for the relation, found by Wilson and Bappu, between K emission line widths and absolute magnitudes of the stars.The paper discusses the solar cycle equivalents that stellar chromospheres can demonstrate and indicates a possible line of approach for successful detection of cyclic activity in stellar chromospheres.     

The spectroscopic orbit of the K‐giant binary γ Canis Minoris

We have determined an improved orbit for the bright, evolved, double lined binary γ Canis Minoris. The system has an orbital period of 389.31 days and an eccentricity of 0.2586. We have revised the secondary to primary mass ratio to 0.987. The spectral types of the primary and secondary are K4 III and K1: III, respectively, and the components have a V magnitude difference of 2.2. Orbital fits to the Hipparcos astrometry are not definitive, but they suggest an orbital inclination of ∼ 66°, which produces masses of 1.88 and 1.85 M_⊙ for the components. A comparison with evolutionary tracks results in an age of 1.3 Gyr. STELLA very low amplitude radial velocity residuals of the secondary indicate a period of 278 days. We interpret this as the rotation period of the secondary, detectable because of star spots rotating in and out of view. This period is nearly identical to the pseudosynchronous rotation period of the star. The primary is rotating more slowly than its pseudosynchronous rate. (© 2013 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Bianchi type-III non-static magnetized cosmological model for perfect fluid distribution in general relativity

We have investigated Bianchi type III non-static magnetized cosmological model for perfect fluid distribution in general relativity. We assume that F ₁₂ is the only non-vanishing component of F _ij . Maxwell’s equation

Non-Spherical Dust Grains in the Envelopes of Late-Type Giants

Effects of the grain shape on circumstellar dust dynamics and polarization of stellar radiation are analyzed. The grains are modeled by rotating prolate and oblate spheroids. It is shown that an asymmetry of the geometry of light scattering by non-spherical particles results in a component of the radiation pressure force perpendicular to the wave-vector of incident light. For silicate spheroids, this component can exceed 20 % of . For small metallic grains, the radiation pressure force for a spheroid can be 5–10 times greater than that for a sphere of the same volume. A simple light scattering consideration demonstrates that the distinction in the scattering geometry of aligned non-spherical grains can explain the observed wavelength variations of the positional angle of polarization. This revised version was published online in September 2006 with corrections to the Cover Date.     

Cold gas accretion in galaxies

Evidence for the accretion of cold gas in galaxies has been rapidly accumulating in the past years. HI observations of galaxies and their environment have brought to light new facts and phenomena which are evidence of ongoing or recent accretion: (1) A large number of galaxies are accompanied by gas-rich dwarfs or are surrounded by HI cloud complexes, tails and filaments. This suggests ongoing minor mergers and recent arrival of external gas. It may be regarded, therefore, as direct evidence of cold gas accretion in the local universe. It is probably the same kind of phenomenon of material infall as the stellar streams observed in the halos of our galaxy and M 31. (2) Considerable amounts of extra-planar HI have been found in nearby spiral galaxies. While a large fraction of this gas is undoubtedly produced by galactic fountains, it is likely that a part of it is of extragalactic origin. Also the Milky Way has extra-planar gas complexes: the Intermediate- and High-Velocity Clouds (IVCs and HVCs). (3) Spirals are known to have extended and warped outer layers of HI. It is not clear how these have formed, and how and for how long the warps can be sustained. Gas infall has been proposed as the origin. (4) The majority of galactic disks are lopsided in their morphology as well as in their kinematics. Also here recent accretion has been advocated as a possible cause. In our view, accretion takes place both through the arrival and merging of gas-rich satellites and through gas infall from the intergalactic medium (IGM). The new gas could be added to the halo or be deposited in the outer parts of galaxies and form reservoirs for replenishing the inner parts and feeding star formation. The infall may have observable effects on the disk such as bursts of star formation and lopsidedness. We infer a mean “visible” accretion rate of cold gas in galaxies of at least . In order to reach the accretion rates needed to sustain the observed star formation (), additional infall of large amounts of gas from the IGM seems to be required.     

The First DIRECT Distance to a Detached Eclipsing Binary in M33

We present the first direct distance determination to a detached eclipsing binary in M33, which was found by the DIRECT Project. Located in the OB 66 association, it was one of the most suitable detached eclipsing binaries found by DIRECT for distance determination, given its 4.8938 day period. We obtained follow-up BV photometry and spectroscopy from which we determined the parameters of the system. It contains two O7 main sequence stars with masses of and and radii of and , respectively. We derive temperatures of K and K and determine the reddening . Using HST photometry for flux calibration in the V band, we obtain a preliminary distance modulus of mag ( kpc). The photometry and thus distance is subject to revision in the final paper.     

The Evolution of Dilatonic Universe with a Double Exponential Potential

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

Tidal effects in the earth–moon system and the earth's rotation

Analytical expressions for tidal torques induced by a tide‐arising planet which perturbs rotation of a nonrigid body are derived. Corresponding expressions both for secular and periodic perturbations of the Euler's angles are given for the case of the earth's rotation. Centennial secular rates of the nutation angle θ and of the earth's angular velocity ω, as well as the centennial logarithmic decrement ν of the Chandler wobble are evaluated:  mas, . In the Universal Time (UT) a large out‐of‐phase (sine) dissipative term with the period 18.6 years and the amplitude 2.3 ms is found. Corrections to nutation coefficients, which presumably have not been taken into account in IAU theory, are given. This revised version was published online in July 2006 with corrections to the Cover Date.     

Photometric Observation And Period Study Of Go Cygni

Photometric observations of GO Cyg were performed during July–October 2002, in B and V filters (Johnson system). Using the Wilson's computer codes, the light curve analysis were carried out to find the photometric elements of the system. The O-C diagram which is based on the observed times of minima as well as those found in the literature, suggests a negative rate of period variation (i.e. ) for the system.