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.     

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.     

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.     

Numerical theory of rotation of the deformable Earth with the two-layer fluid core. Part 2: Fitting to VLBI data

VLBI-based offsets of the Celestial Pole positions, as well as the variations of UT (series of Goddard Space Flight Center, 1984–2005) are processed applying the Earth’s rotation theory (ERA) 2005 constructed by the numerical integration of the differential equations of rotation of the deformable Earth. The equations were published earlier (Krasinsky 2006) as the first part of the work. The resulting weighted root mean square (WRMS) errors of the residuals , for the angles of nutation and precession are 0.136 and 0.129 mas, respectively. They are significantly less than the corresponding values 0.172 and 0.165 mas for the IAU 2000 model adopted as the international standard. In ERA 2005, the angles , are related to the inertial ecliptical frame J2000, the angle including the precessional secular motion. As the published observational data are theory-dependent being related to IAU 2000, a procedure to confront the numerical theory to the observed Celestial Pole offsets and UT variations is developed. Processing the VLBI data has shown that beside the well known 435-day FCN mode of the free core nutation, there exits a second mode, FICN, caused by the inner part of the fluid core, with the period of 420 day close to that of the FCN mode. Beatings between the two modes are responsible for the apparent damping and excitation of the free oscillations, and are implicitly modeled by ERA 2005. The nutational and precessional motions in ERA 2005 are proved to be mutually consistent but only in case the relativistic correction for the geodetic precession is applied. Otherwise, the overall WRMS error of the residuals would increase by 35%. Thus, the effect of the geodetic precession in the Earth rotation is confirmed experimentally. The other finding is the reliable estimation δ_c = 3.844 ± 0.028° of the phase lag δ_c of the tides in the fluid core. When processing the UT variations, a simple model of the elastic interaction between the mantle and fluid core at their common boundary made it possible to satisfactory describe the largest observed oscillations of UT with the period of 18.6 year, reducing the WRMS error of the UT residuals to the value 0.18 ms (after removing the secular, annual and semi-annual terms).     

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.     

The elimination of the critical terms of a first order Uranus-Neptune theory by Hori's method

In this part we determine the value ofS ₁, and in terms of the canonical variables of H. Poincaré. A complete solution of the auxiliary system of equations generated by the Hamiltonian is presented.     

Two Sets of Improved Approximate Expressions of the Gyrosynchrotron Radiation

In this paper two sets of improved approximate expressions of emissivity , absorptivity , effective temperature T_eff, and frequency of peak brightness _p of gyrosynchrotron radiation are presented respectively for the ranges from 5 to 10 and 10 to 100 of harmonic numbers s(= /_B). The expressions are designed for the range from 20° to 80° of viewing angle , and the range 2 to 7 of electron energy spectral index . They are expressed by a power-law function in which the indexes are fitted by polynomial expressions of . Their statistical errors are, respectively, 24% and 32% for and for and 28% for . Their accuracies are much better than those of linear fitting of the power-law index.     

Epstein weight functions for non-radial oscillations of polytropes

Weight functions for the determination of the periods of linear adiabatic non-radial oscillations have been calculated in the same manner as Epstein's classic treatment of purely radial oscillations. Quadrupole (l=2) oscillations for thef and lower orderp andg-modes were considered. One group of static models were polytropes in the range 1.0n4.0 with ; thus included were configurations that were convectively stable, unstable and neutrally stable throughout. Another group consisted ofn=3.0 polytropes with convective shells or convective cores; ₁ was set at different values in each region in order to produce stability ( ) or instability ( ). The weight function provides a pictorial means for assessing the relative importance of each region of a given static model with respect to generating a given non-radial mode.     

The Search for Solar Gravity-Mode Oscillations in the Solar Wind Using it Ulysses Plasma Data

A recent report that energetic particles measured in the solar wind may be influenced by solar gravity-mode ( -mode) oscillations motivated the search for -mode signatures in the Ulysses solar wind plasma data. Ulysses solar wind plasma data from 1 March 1992 through the 12 April 1996 were examined in this study for signs of possible solar oscillations. The multi-taper method for spectral analysis was used to look for significant spectral peaks in the entire four-year data set, as well as in the smaller, more heliographically homogenous data set over the solar poles. Several frequencies satisfying certain significance requirements were found in the -mode frequency range in both data sets that also agree with the previously published findings. However, these identifications are shown to be false detections, and hence the frequencies found cannot be identified as solar modes.     

3He enrichments by magnetosonic waves in current-driven instabilities

A theoretical model for³He enrichments in solar energetic particles is developed. First, current-driven, electrostatic instabilities that have frequencies ( is the cyclotron frequency of³He) are investigated for a plasma consisting of H,⁴He,³He, and electrons with the density of³He much lower than those of H and⁴He. It is found that in many cases the oblique ion-acoustic waves can have positive growth rates at frequencies and, at the same time, negative growth rates at and at _H. This can occur near the marginal state of the instability. The wave damping at these frequencies is caused by the cyclotron resonances of⁴He and H. The cyclotron damping at is negligible, however, because the abundance of³He is very small. The H cyclotron waves can be unstable at for a wide region of plasma parameters; the electron-to-ion temperature ratio must beT _e /T _H 1.5. To destabilize the₄He cyclotron waves with , high⁴He density and high electron temperature are both required. Then,³He enrichments are studied on the basis of the theory of nonlinear magnetosonic waves, which can promptly accelerate ions. The current-driven electrostatic waves with can enhance fluctuation velocities of³He. Thus, in the presence of these waves, magnetosonic waves can selectively accelerate³He particles to high energies. Finally, cyclotron resonances of heavy ions with the waves or are briefly discussed.     

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.     

Dynamical dark energy from extra dimensions

We consider multidimensional cosmological model with a higher-dimensional product manifold M = R × × /Γ, where is d _o-dimensional Ricci-flat external (our) space and /Γ is d ₁-dimensional compact hyperbolic internal space. M2-brane solution for this model has the stage of accelerating expansion of the external space. We apply this model to explain the late time acceleration of our Universe. Recent observational data (the Hubble parameter at the present time and the redshift when the deceleration parameter changes its sign) fix fully all free parameters of the model. As a result, we find that considered model has too big size of the internal space at the present time and variation of the effective four-dimensional fine structure constant strongly exceeds the observational limits. The article is published in the original.     

Tangential discontinuities in the solar wind

This paper considers six discontinuity surfaces which were observed by magnetometers on 3 spacecraft in the solar wind. It is shown that the actual surface orientations, determined from the measured time delays and solar wind speed, are consistent with the theoretical orientations which were computed from the relation , where is the normal to the surface of a hydromagnetic tangential discontinuity across which the magnetic field direction changes from to . The plasma and magnetic field data for these discontinuities are consistent with the pressure balance condition, and the magnetic field vectors in the associated current sheets are parallel to the discontinuity surface, as required theoretically. The 6 discontinuity surfaces extended without much distortion over ∼ 0.002 AU. A seventh surface is discussed which satisfies the condition but which extended without much distortion over 0.01 AU. This latter is not a typical surface, however, and its curvature is larger than average. Most of the surfaces tended to lie along the spiral direction, but one was nearly perpendicular to the spiral direction.     

Spectroscopic and photometric variability of HD 51585 as a manifestation of stellar wind

We present the results of our photoelectric observations of HD 51585 (OY Gem), a B[e] star with an infrared excess and a candidate for protoplanetary nebulae, obtained with a 60-cm telescope at the Crimean Station of the Sternberg Astronomical Institute in 1992–2005. The star exhibited rapid irregular brightness variations with amplitudes from We present the results of our photoelectric observations of HD 51585 (OY Gem), a B[e] star with an infrared excess and a candidate for protoplanetary nebulae, obtained with a 60-cm telescope at the Crimean Station of the Sternberg Astronomical Institute in 1992–2005. The star exhibited rapid irregular brightness variations with amplitudes from in the V band to in U band within the observing season as well as slow systematic variations with amplitudes from in the V band to in the U band and with a quasi-period of ∼2800 days. The B-V color index varied within and did not follow the slow systematic brightness variations, while U-B correlated with the U brightness and varied between at maximum light and at minimum light. Our low-resolution spectroscopy performed in 1994–2005 has revealed significant variability of the Balmer and Paschen hydrogen emission lines as well as the He I and O I lines. Equivalent widths are given for the H I, He I, O I, and Fe II lines; a correlation has been found between the star’s photometric variability and the hydrogen line intensities. Our joint analysis of the photometric and spectroscopic data suggests that variations in a strong stellar wind are responsible for the variability of the star. Original Russian Text ? V.P. Arkhipova, N.P. Ikonnikova, G. V. Komissarova, V. F. Esipo, 2006, published in Pis’ma v Astronomicheskiĭ Zhurnal, 2006, Vol. 32, No. 9, pp. 662–671.     

Short-term periodicities of the sun's ‘mean’ and differential rotation

We have looked for periodicities in solar differential rotation on time scales shorter than the 11-year solar cycle through the power- spectrum analysis of the differential rotation parameters determined from Mt. Wilson velocity data (1969–1994) and Greenwich sunspot group data (1879–1976). We represent the differential rotation by a set of Gegenbauer polynomials (()= + (5sin₂–1)+ (21sin₄–14sin₂+1)). For the Mt. Wilson data, we focus on observations obtained after 1981 due to the reduced instrumental noise and have binned the data into intervals of 19 days. We calculated annual averages for the sunspot data to reduce the uncertainty and corrected for outliers occuring during solar cycle minima. The power spectrum of the photospheric mean rotation , determined from the velocity data during 1982–1994, shows peaks at the periods of 6.7–4.4 yr, 2.2 ± 0.4 yr, 1.2 ± 0.2 yr, and 243 ± 10 day with 99.9% confidence level, which are similar to periods found in other indicators of solar activity suggesting that they are of solar origin. However, this result has to be confirmed with other techniques and longer data sets. The 11-yr periodicity is insignificant or absent in . The power spectra of the differential rotation parameters and , determined from the same subset, show only the solar cycle period with a 99.9% confidence level.The time series of determined from the yearly sunspot group data obtained during 1879–1976 is very similar to the corresponding time series of . After correcting for data with large error bars (occurring during cycle minima), we find periods, which are most likely harmonics of the solar cycle, such as 18.3 ± 3.0 yr and 7.5 ± 0.5 yr in and confirmed these and the 3.0 ± 0.1 yr period in . The original time series show in addition some shorter periods, absent in the corrected data, representing temporal variations during cycle minimum. Given their large error bars, it is uncertain whether they represent a solar variation or not. The results presented here show considerable differences in the periodicities of and determined from the velocity data and the spot group data. These differences may be explained by assuming that the rotation rates determined from velocity and sunspot data represent the rotation rates of the Sun's surface layers and of somewhat deeper layers.     

Models of galactic mass distribution

Three groups of galactic mass models, each consisting of nine inhomogeneous spheroids of two kinds are described, according to three adopted values of the total density near the Sun: 0.10, 0.15 and 0.20 M pc^–3. Approximately 20% of the total mass of each model is in the halo, constructed to adequately fit recent RR Lyrae star observations. It is shown that the maxima found in the RR Lyrae star densities towards the galactic axis (Plaut, 1970) should not be interpreted as being associated with the galactic nucleus, but as the result of the greater decrease in density with increasingz over the increase in density as the galactic axis is approached. Even at the low galactic latitude of 5° (l=0°), this effect causes a 0.5 kpc correction to the distance to the galactic centre. A basic model for kpc, km s^–1, M pc^–3 is first constructed, mainly to satisfy structural conditions near the sun and in the halo. An attempt to optimize the basic model is made by scaling it so as to retain constant density and angular velocity near the sun, and to best fit kinematic data, including the recent re-examination of the 21-cm data of Simonson and Mader (1972). No unknown matter is required in the models, in accordance with the results of Weistrop (1972b), and, as pointed out earlier (Innanen, 1966b) the faintM-stars must be in a highly flattened spheroid. The optimizing indicates that an adequate fit to kinematics can be achieved for km s^–1. More detailed results are tabulated for a representative model for which . Two new galactic density functions are discussed in the Appendix.     

Completely Integrable Systems Connected with Lie Algebras

In a recent paper Ballersteros and Ragnisco (1998) have proposed a new method of constructing integrable Hamiltonian systems. A new class of integrable systems may be devised using the following sequence: , where A is a Lie algebra is a Lie–Poisson structure on R ₃, C is a Casimir for is a reduced Poisson bracket and (A, ▵) is a bialgebra. We study the relation between a Lie-Poisson stucture Λ and a reduced Poisson bracket , which is a key element in using the Lie algebra A to constructing this sequence. New examples of Lie algebras and their related integrable Hamiltonian systems are given. This revised version was published online in July 2006 with corrections to the Cover Date.     

Secular frequencies of 3-D exoplanetary systems

Using a 12th order expansion of the perturbative potential in powers of the eccentricities and the inclinations, we study the secular effects of two non-coplanar planets which are not in mean–motion resonance. By means of Lie transformations (which introduce an action–angle formulation of the Hamiltonian), we find the four fundamental frequencies of the 3-D secular three-body problem and compute the long-term time evolutions of the Keplerian elements. To find the relations between these elements, the main combinations of the fundamental frequencies common to these evolutions are identified by frequency analysis. This study is performed for two different reference frames: a general one and the Laplace plane. We underline the known limitations of the linear Laplace–Lagrange theory and point out the great sensitivity of the 3-D secular three-body problem to its initial values. This analytical approach is applied to the exoplanetary system Andromedae in order to search whether the eccentricities evolutions and the apsidal configuration (libration of ) observed in the coplanar case are maintained for increasing initial values of the mutual inclination of the two orbital planes. Anne-Sophie Libert is FNRS Research Fellow.