Accurate Analytical Calculation of Effects of Rorations of the Central Planet on a Staellite's Orbit

Satellite orbital perturbations due to many rotations of the planet-fixed reference frame are calculated by a general analytical method. For the International Terrestrial Reference Frame (ITRF) the effects of the Earth irregular rotation, precession, nutation, and polar motion are considered. Gravity coefficients of the Earth potential expansion are expressed in an inertial Celestial Reference Frame (CRF) as functions of the set of standard constant coefficients derived in the ITRF and of the rotation angles between the CRF and ITRF. The analytical motion theory uses time dependent gravity coefficients, and the Lagrange motion equations are integrated in the CRF, as it is done by numerical methods. Comparison of the proposed analytical method with a numerical one is presented. Motion of the ETALON-1 geodetic satellite perturbed by the geopotential (36*36) and by the full effects of the Earth irregular rotation, precession, nutation and polar motion is predicted. The r.m.s. difference between the satellite's coordinates calculated by both methods over a year interval is 2 cm. This revised version was published online in July 2006 with corrections to the Cover Date.     

Harmonic development of tide-generating potential of terrestrial planets

The aim of this study is to obtain high-accurate harmonic developments of the tide-generating potential (TGP) of Mercury, Venus and Mars. The planets’ TGP values have been first calculated on the base of DE/LE-406 numerical planetary/lunar ephemerides over a long period of time and then processed by a new spectral analysis method. According to this method the development is directly made to Poisson series where both amplitudes and arguments of the series’ terms are high-degree polynomials of time. A new harmonic development of Mars TGP is made over the time period 1900 AD–2100 AD and includes 767 second-order Poisson series’ terms of minimum amplitude equal to 10⁻⁷ m² s⁻². Analogous series composing both Mercury and Venus TGP harmonic models are built over the time period 1000 AD–3000 AD and include 1,061 and 693 terms, respectively. A modification of the standard HW95 format for representation of the terrestrial planets’ TGP is proposed. The number of terms in the planets’ TGP models transformed to the modified HW95 format is 650 for Mercury, 422 for Venus, and 480 for Mars. The quality of the new developments of the terrestrial planets’ TGP is better than that of the similar developments obtained earlier.

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Electronic supplementary material  The online version of this article (doi:) contains supplementary material, which is available to authorized users.      

Lithium and the 6Li-7Li isotope ratio in the atmospheres of some sharp-lined roAp stars

The λ 6708 Å and 6103 Å lithium lines in the high-resolution spectra of some sharp-lined roAp stars are analyzed using three spectral-synthesis codes STARSP, ZEEMAN2, and SYNTHM. The lines from the VALD database were supplemented with lines of rare-earth elements from the DREAM database and new lines calculated using the NIST energy levels. Our synthetic-spectrum calculations take into account magnetic splitting and other line-broadening effects. Lithium overabundances were found in the atmospheres of the stars based on our analysis of both lithium lines, along with high values of the ⁶Li-⁷Li isotope ratio (0.2–0.5). This can be explained if lithium is produced in spallation reactions and the surface ⁶Li and ⁷Li is preserved by strong magnetic fields in the upper layers of the stellar atmospheres, around the poles of the dipole field. The asymmetry of lithium lines to the red may be due to the action of shocks in the optically thin upper atmosphere, with the shocked material subsequently falling onto the star.     

A study of rare earth elements in the atmospheres of chemically peculiar stars. Pr III and Nd III lines

We determine the abundances of Pr and Nd in the atmospheres of magnetic and non-magnetic chemically peculiar stars from the lines of rare earth elements in the first and second ionization states. The computations for the magnetic stars take into account the influence of the magnetic field on line formation. We studied the influence of errors in the stellar-atmosphere parameters and the atomic parameters of the spectral lines on the accuracy of abundance determinations. Within the derived accuracy, ionization equilibrium is satisfied in the atmospheres of non-pulsating magnetic and non-magnetic stars (so that abundances derived separately from lines of first and second ions agree). For all the pulsating magnetic (roAp) stars studied, the abundances derived from lines of second ions are 1.0 to 1.7 dex higher than those derived from first ions. The violation of ionization equilibrium in the atmospheres of pulsating stars is probably due to, first, considerable enrichment of Pr and Nd in the uppermost atmospheric layers, and second, a higher location for the layer of enhanced elemental abundance in roAp stars than in non-pulsating stars. Two objects from the list of non-pulsating magnetic stars, HD 62140 and HD 115708, exhibit anomalies of their Pr and Nd lines characteristic of roAp stars. The differences in the rare earth anomalies for the pulsating and non-pulsating peculiar stars can be used as a selection criterion for candidate roAp stars.     

Generation mechanisms for capillary-gravity wind wave spectrum

We investigate the role of different physical mechanisms in the generation of the capillary-gravity wind wave spectrum. This spectrum is calculated by integrating a nonstationary kinetic equation until the solution becomes stready. The mechanisms of spectrum generation under consideration include three-wave interactions, viscous dissipation, energy influx from wind, nonlinear dissipation, and the generation of a parasitic capillary ripple. The three-wave interactions are taken into account as an integral of collisions without additional simplifications. It is shown that the three-wave interactions lead to solution instability if the kinetic equation takes into account only linear sources. To stabilize the solution, the kinetic equation should incorporate a nonlinear dissipation term, which in the range of short gravity waves corresponds to energy losses during wave breaking and microscale wave breaking. In the range of capillary waves, the account of nonlinear dissipation is also needed to ensure a realistic level of the spectrum for large wind velocities. For the steady-state spectrum, the role of three-wave interactions remains essential merely in the range of the minimum of phase velocity, where a trough on the curvature spectrum is formed. At the remaining intervals of the spectrum, the main contribution into the spectral energy balance is provided by the mechanisms of wave injection, nonlinear dissipation, and the generation of parasitic capillaries.     

Spectral observations using a BTA telescope of chemically peculiar stars in the spectral region near the Li I (6708 Å) resonance doublet

New spectral observations of chemically peculiar (CP) magnetic stars were obtained using an NES echelle spectrometer with a BTA telescope in the Special Astrophysical Observatory (Russian Academy of Sciences). Several stars were shown to have anomalous Li abundances. Testing and monitoring the stars with Doppler shifts Vsini > 10 km/s indicated that the lithium 6708 Å line was variable in the spectra of some roaAP-CP stars. To distinguish variable features in the spectra, the dispersogram technique was used. The most peculiar among the stars studied is HD 12098. The strong and variable lithium 6708 Å line was detected in the spectrum of this star. The star has been shown to have greatly different lithium abundances in two rotation phases corresponding to opposite surface areas. As mentioned earlier, a similar behavior of the Li blend was found in the spectra of HD 83368 and HD 60435 which have lithium spots on their surface. Spectral observations of slowly rotating CP stars with the Doppler shifts Vsini < 10 km/s revealed the strong and nonvariable lithium 6708 Å line in the spectra of these stars. Quantitative spectral analysis using the Li I 6708 Å resonance doublet and the Li I 6103 Å line shows the lithium abundance, as determined by the 6103 Å line, to be somewhat greater than that determined by the 6708 Å line. A higher ratio of ⁶Li/⁷Li amounting to ～0.3–0.5 was found in these stars. ⁶Li production is assumed to be due to spallation reactions on the surface of magnetic CP stars; this isotope ratio remained in strong magnetic fields.     

Interaction between the surface and internal waves: The modulation and maser mechanisms

Two feedback mechanisms are considered which emerge from the interaction between the surface and internal waves. The energy exchange between the wave systems is coupled with the periodic variations of momentum and the losses of the wind wave momentum during their interaction with the internal wave (IW) current field. These mechanisms result in the IW attenuation which is the strongest when IW and wind propagate in the same direction. When attenuating, the IWs give rise to the inertial currents comparable to the Ekman background current.Translated by Mikhail M. Trufanov. UDK 551.466.3: 551.466.8.     

Calculation of a gigantic upward atmospheric discharge, accompanying optical phenomena, and penetrating radiations. II. Numerical simulation results

Gigantic upward atmospheric discharges have been numerically simulated. The space-time distributions of the self-consistent electric field strength and charged particle densities have been obtained. The brightness, color, and evolution in the space and time of fluorescence above a thundercloud, which agree with the data of field observations of such high-altitude optical phenomena as blue jets and red sprites, have been calculated. It has been indicated that large duration of blue jets results from the emission of a decaying ion plasma of the air. The yields of hard gamma rays and neutrons, generated by upward discharges, have been calculated.