Three-colour photometry of GH pegasi

The geometrical elements of the system GH Pegasi and a slightly improved period of 2 _. ^d 556136 have been given.     

A new period and period changes in VZ Hydrae

A new period (P=2 _. ^d 9042997) of the eclipsing binary system VZ Hydrae has been given, which is based on all the available times of minima. The period based on the photoelectric epochs has also been presented. The O?C diagram and detailed period study of VZ Hya have been presented for the first time, and the period changes have been estimated in different portions of the O?C diagram. Significant period changes do not appear to have occurred in VZ Hya, however, the O?C diagram suggests that the period of the system shows a slow tendency to increase. Period changes of 10^?5 d (?) to 10^?7 d have occurred around the years 1933, 1971, and 1975. All four period changes are noted in the time-interval 1918 to 1978. Upward treands appear stronger than the declining trends. Secondary minima show larger fluctuations than the primary minima. The fluctuations of the O?C values around the zero-line of VZ Hya demands notice for searching out the cause of period variations such as the presence of a third body.     

Period study of IT Persei

A new period (P=1 _. ^d 533731) of the eclipsing binary system IT Persei has been given, which is based on all available times of minima. O-C diagrams of IT Persei, based on the period given in PPEN (1980) and based on the new period, have been given.Long-term period changes are not present in the system, however, some period fluctuations of the order of 10^–5d are seen around the years 1907, 1921, and 1933.     

Three-colour photometry of the eclipsing binary EI Cephei

The photoelectric elements of the system EI Cephei have been determined inU, B, V colours. The absolute dimensions have been determined and some evolutionary aspects have been discussed. A modified period of 8^d.439334 has been obtained. The system is a detached one.     

A period study of V450 Herculis

A detailed period study of the eclipsing binary system V450 Her has been presented. A new period (P= _. ^d 12724) has been given. The period changes in different portions of the O-C diagram, based on new period, have been estimated. The total period change ranges from 3.28×10^–6 d to 7.06×10^–5 d, which is appreciable.     

Constancy of period in TX Ceti

A slightly improved period (P=0 _. ^d 7408401) of the eclipsing binary system TX Ceti has been given, which is based on all available times of minima. The O-C diagrams based on the period given in PPEN (1980) and based on the new period, have been given. The period of TX Ceti shows fair constancy between the time interval 1928 to 1988. The present O-C diagrams do not confirm, either the presence of a third body or the presence of mass transfer as suggested earlier.     

Photometric elements and apsidal motion of the eclipsing binary NSV 18773

The photometric elements of the eclipsing binary NSV 18773 (HD 99898) have been determined for the first time by analyzing its V-and I-band light curves from the ASAS-2 and ASAS-3 catalogs. Based on these elements and using other published spectroscopic and photometric data, we constructed a consistent system of geometrical and physical parameters for the system that consists of two stars (M ₁ = 20M _⊙, Sp₁=B0V, R ₁ = 5.0R _⊙ and M ₂ = 14M _⊙, Sp₂ = B1V, R ₂ = 6.5R _⊙) in elliptical orbits (P = 5 _. ^d 049, e = 0.365, a = 40.1R _⊙). The distance to the system is d = 3.3 kpc, the interstellar extinction is A _V = 2 _. ^m 0, and the age is t = 2.8 × 10⁶ yr. NSV 18773 is a visual binary with components V _A = 9 _. ^m 9 and V _B = 10 _. ^m 3 separated by 0 _. ^" 8. The third light (L ₃ = 0.61) that we found by analyzing the light curves shows that the eclipsing binary is the system’s fainter component B. We confirmed the rapid apsidal motion of the star detected by Otero and Wils (2006) and refined its observed period: U _obs = 150 ± 6 yr. Our photometric elements and physical parameters allowed the apsidal parameter $\bar k_2^{obs} = 0.0135(14)$ , which reflects the density distribution along the radii of the component stars, to be determined. Within the error limits, the derived parameter agrees with its theoretically expected value, $\bar k_2^{th} = 0.0119(8)$ , from current evolutionary models of stars of the corresponding masses and ages.     

Photoelectric photometry of the eclipsing binary EE Aqr

The system EE Aqr has been observed inUBV colours. A consistent set of orbital elements and a slightly improved period of 0 _. ^d 5089954 have been obtained. The eclipse is partial and variability is of Lyrae-type. The colour of the components has been determined.     

Results of a long-term monitoring of the multiple system SZ Cam

We present the results of the reduction of our photometric and spectroscopic observations for the eclipsing binary SZ Cam performed with the telescopes at the Astronomical Observatory of the Ural Federal University and the Special Astrophysical Observatory of the Russian Academy of Sciences in 1996–2014. Based on an 11-year-long photometric monitoring of SZ Cam, we have obtained new elements of its photometric orbit and parameters of its components. We have detected low-amplitude periodic light variations in SZ Cam that are possibly related to the ellipsoidal shape of the components of the spectroscopic binary third body. Based on published data and our new spectroscopy, we have found new values for the mass ratio, q = 0.72 ± 0.01, and parameters of the radial velocity curves of the components, V ₀ = ?3.6 ± 1.7 km s^?1, K ₁ = 190.2 ± 1.9 km s^?1, and K ₂ = 263.0 ± 2.4 km s^?1. The component masses have been estimated to be M ₁ = 16.1 M _⊙ and M ₂ = 11.6 M _⊙. We have obtained new light elements and parameters of the radial velocity curves for the third body, V ₀ ^3b = 4.2 ± 0.6 km s^?1 and K ₁ ^3b = 26.6 ± 0.8 km s^?1. We have improved the period of the relative orbit of SZ Cam and the third body, P _orb = 55.6 ± 1.5 yr.     

Eccentric Eclipsing Binary YY Sagittarii

Seven new precise times of minimum light have been gathered for the triple eccentric eclipsing binary YY Sgr (P = 2^d.63, e = 0.16). Its O--C diagram is presented and improved elements of the apsidal motion and the light-time effect are given. We found a new short period of the third body of about 18.5 years in an eccentric orbit (e ₃ ≃ 0.4).     

The impact of the oblateness of Regulus on the motion of its companion

The fast spinning B-star Regulus has recently been found to be orbited by a fainter companion in a close circular path with orbital period P _b=40.11(2) d. Being its equatorial radius R _e 32% larger than the polar one R _p, Regulus possesses a remarkable quadrupole mass moment Q. We investigate the effects of Q on the orbital period P _b of its companion in order to see if they are measurable, given the present-day level of accuracy in measuring P _b. Conversely, we will look for deviations from the third Kepler law, attributed to the quadrupole mass moment Q of Regulus, to constrain the ratio γ=m/M of the system’s masses. The impact of Q on the orbital period is analytically worked out with a straightforward perturbative approach. The resulting correction P ^Q is compared to other competing dynamical effects. P ^Q and the Keplerian period P ^Kep are expressed in terms of the phenomenologically determined system’s parameters; γ is treated as an unknown. P ^Q is compared to the observational accuracy in measuring the orbital period δ P _b=0.02 d and to the systematic uncertainty δ(P ^Kep) due to the errors in the system’s parameters entering it. The discrepancy ΔP=|P _b?P ^Kep| is examined in order to see for which values of γ it becomes statistically significant. The physical meaning of the obtained range of values for γ is discussed in terms of Q. P ^Q is larger than δ P _b but still smaller than the systematic uncertainty in P ^Kep by two orders of magnitude. The major sources of bias are the velocity semiamplitude K of the motion of the primary and its mass M. Assuming edge-on configuration, i.e. i=90 deg, if γ?0.096 Q would be positive, i.e. Regulus would be prolate, contrary to the observations. If γ?0.078 Q would be negative, but its magnitude would be one-two orders of magnitude larger than the approximate estimate Q≈M(R _p ² ?R _e ² )=?2.4±0.5×10⁴⁹ kg?m². Regulus is the first extrasolar binary system in which the orbital effects of the asphericity of the primary are larger than the observational sensitivity; moreover, no other competing aliasing orbital effects are present. Thus, it is desirable that it will become the object of future intensive observational campaigns in order to reduce the systematic uncertainty due to the system’s parameters below the measurability threshold.     

Two-colour photoelectric investigation of AR Lacertae

The RS CVn-type eclipsing binary AR Lac has been observed in two colours,B andV, in 1978 and 1979. Several times of minima have been obtained during the observations and the new light elements have been calculated. The orbital period of the system was found to be decreasing with an amount of 14.6 s century^–1.The light curves of the system obtained inB andV show a significant wave-like distortion outside eclipses. The amplitudes of the wave-like distortion inB andV are about 0 _. ^m 09 and 0 _. ^m 10 in 1978, and, 0 _. ^m 12 and 0 _. ^m 13 in 1979, respectively. The minima of the wave-like distortion have shifted with an amount of 0 _. ^p 40 in one year, thus indicating the migration period of the wave-like distortion is about 2.5 yr.A noticeable variation of light during the totality of primary minimum has also been observed. This variation can be attributed to the distortion wave which has been moving towards decreasing phases.     

New spectrophotometry for SZ cam (the problem of a third component)

We present the results of our spectroscopic observations of the eclipsing binary SZ Cam performed with the 1-m (Zeiss-1000) and 6-m (BTA) telescopes at the Special Astrophysical Observatory of the Russian Academy of Sciences in 2000 and 2003. Based on our results and published data, we have calculated new values for the component mass ratio, q = 0.72 ± 0.02, the radial velocity of SZ Cam relative to the Solar system barycenter, V ₀ =?10.6 ± 2.0 km s^?1, and the semi-amplitudes of the radial velocity curves for both components, K ₁ = 192.0 ± 2.6 and K ₂ = 266.4 ± 2.5 km s^?1. The orbital semimajor axes and masses of the components have been determined: α₁ = 10.4R _⊙, α₂ = 14.5R _⊙, M ₁ = 16.7M _⊙, M ₂ = 12.0M _⊙. New light elements and parameters of the radial velocity curve for the third body have been obtained. The mass of the secondary component of the third body M ₂ ^3b is discussed. Its lower limit is estimated to be M ₂ ^3b = 1.4M _⊙.     

Kinematics of stars in the northern and southern galactic hemispheres

We use vector spherical harmonics for a kinematic analysis of the proper motions of stars from the Hipparcos, Tycho-2, and UCAC3 catalogues in the northern and southern Galactic hemispheres. We have found that the statistically reliable values of the Ogorodnikov-Milne model parameters M ₃₂ ⁺ and M ₃₂ ^? have different signs in different hemispheres. This is a consequence of the Galaxy??s rotational retardation with distance from the principal Galactic plane. Based on various samples of stars from the above catalogues, we have obtained the following estimate for the magnitude of the vertical gradient of Galactic rotation velocity in the solar neighborhoods: (20.1 ± 2.9) < |?V_??/?z| < (49.2 ± 0.8) km s^?1 kpc^?1. Another result that is revealed by our analysis of the parameters M ₁₃ ^? and M ₁₃ ⁺ in different Galactic hemispheres is that the vertical gradient of expansion velocity for the stellar system ?V _R /? _z is positive in the northern hemisphere and negative in the southern one. This suggests that the expansion velocity V _R increases with distance fromthe Galactic plane. We show that both these gradients give rise to an apparent acceleration of the solar motion along the x and y axes of the rectangular Galactic coordinate system. Our analysis of the parameters M ₂₁ ^? and M ₁₂ ⁺ shows no significant differences in both hemispheres and has allowed us to determine the Oort parameters, to estimate the Galactic rotation velocity and period in the solar neighborhood, and to calculate the ratio of the epicyclic frequency to the angular velocity of Galactic rotation in the solar neighborhood. The derived diagonal elements of the velocity field deformation tensor suggest that the orientation of the rectangular Galactic coordinate system in space must be determined by taking into account not only the geometrical factors but also the dynamical ones. All these results agree well with these quantities estimated over the entire sphere by various authors.     

UBV photometry of ER Vulpeculae

UBV photometry of RS CVn-type eclipsing binary system ER Vulpeculae has been presented. The period comes out to be 0 _. ^d 698093. The average depths of primary and secondary minima are, respectively, 0 _. ^m 21 and 0 _. ^m 12. The colours at various phases have been given. A dip is seen around phase 0 _. ^p 73 as was seen in the observations of Arevaloet al. (1988). Large scatter is present in the observations as noticed earlier, and may be due to activity of the components.     

A galactic model with a pulsating active nucleus

The accumulation and distribution of rare-light elements in the Galaxy is investigated according to a model of the galaxy at which center there exists a pulsating active nucleus with decreasing activity with time. The abundances of rare-light elements rapidly decrease with approaching to the galactic center whereas the most abundant region of these elements is the annular region of the radial distance ofr=8～14 kpc from the galactic center. In the inner region ofr?8 kpc the abundances of these elements have varied by two to three orders of magnitude from the early days of the galactic history till now, but inr?8 kpc they have been almost constant within a factor of 2. It has become clear that if the nuclides D,³He,⁷Li,¹⁰B and¹¹B have been produced mainly by the shock process taking place in the outer envelope of type-II supernova, they must have been created by the mass fractions of the supernova of some 2.7×10^?3, 1.7×10^?4, 6.9×10^?8, 1.7×10^?7 and 7.9×10^?7, respectively, to account for the solar system abundances.     

Orbital elements and evolutionary nature of the long period RS CVn type eclipsing binary RZ eridani

Light curves of the long period RS CVn type eclipsing binary RZ Eri, obtained during the period 1976–1979 with the 1.2 m telescope of the Japal-Rangapur Observatory are analysed, using Wilson-Devinney method, by fixing the two parametersT _h (7400°K) andq(0.963), resulting in the following absolute elements:A = 72.5 ± 1.4R _⊙,R _h = 2.84 ± 0.12R _⊙,R _c = 6.94 ± 0.20R _⊙,M _bol,_h = 1.35 ± 0.28,M _bol ,_c= 1.41 ± 0.28,m _h = 1.69 ± 0.6m _⊙ andmc= 1.63 ± 0.13m _⊙. The presence of humps and dips of varying amplitudes at a few phases in the normal UBV light curves is explained as due to residual distortion wave. The derived (B-V) and (U-B) colours of both the components appear to have been reddened to an extent of 0 ^m .20 in (B-V) and 0 ^m .16 in (U-B) colours. This reddening is attributed to the presence of an envelope around the system, the material of which might have come from the loss of mass experienced by the evolving cooler component. Taking into consideration the dereddened colours and temperatures of the components, spectral types ofF0 IV for the primary and G 5–8 III–IV for the secondary component were derived. The fractional radii of 0.039 and 0.096 of the two components, when compared with the radii of their critical Roche lobes of 0.378 and 0.372 suggest that these components are well within their critical sizes. From the position of the components on the. isochrones and the evolutionary tracks of stars of Pop I composition computed by Maeder & Meynet, it is concluded that the evolution of the components of RZ Eri is abnormal. This system is found to be situated at a distance of 185 pc, with an age of about 2.5 × 10⁹ yrs.     

Photoelectric study of AW UMa

UBV photoelectric photometry of the eclipsing binary system AW UMa has been presented. A slightly improved period of 0 _. ^d 4387304 has been given. The colour of the system has been discussed. Eccentricity is present in the system. Light and colour curves show that intrinsic light variations may be present in the system. The presence of mass transfer is a possibility.     

Resonance in a geo-centric synchronous satellite under the gravitational forces of the Sun,the Moon and the Earth including it’s equatorial ellipticity

Resonances in a geo-centric synchronous satellite under the gravitational forces of the Sun, the Moon and the Earth including it’s equatorial ellipticity have been investigated. The resonance at two points resulting from the commensurability between the mean motion of the satellite and Γ (angle measured from the minor axis of the Earth’s equatorial ellipse to the projection of the satellite on the plane of the equator) is analyzed. The amplitude and the time period of the oscillation have been determined by using the procedure of Brown and Shook. We have observed that the amplitude and the time period of the oscillation decrease as Γ increases in the first quadrant. The radial deviation (Δr) and the tangential deviation (r _c Δθ) have been determined. Here r _c represents the synchronous altitude. The effects of the arithmetic sum of amplitudes λ _i involved in the perturbation equations on orbital inclination 0^°≤α ₀≤90^° are shown. It is observed that $\sum_{i = 1}^{46} \lambda_{i}$ increases as α ₀ increases. We have also determined the displacement ΔD (called drift) due to the oscillatory terms under the summation sign involved in the equations of motion of the satellite. We have observed that the value of ΔD is less than 0.5^°.     

Turbulent viscosity and lifetime of Saturn's rings

The viscosity (the angular momentum flux) in the disk of mutually gravitating particles of Saturn's rings is investigated. The hydrodynamic theory of the gravitational Jeans-type instability of small gravity perturbations (e.g., those produced by spontaneous disturbances) of the disk is developed. It is suggested that in such a system the hydrodynamic turbulence may arise as a result of the instability. The turbulence is related to stochastic motions of “fluid” elements. The objective of this paper is to show that in the Jeans-unstable Saturnian ring disk the turbulent viscosity may exceed the ordinary microscopic viscosity substantially. The main result of local N-body simulations of planetary rings by Daisaka et al. (2001. Viscosity in a dense planetary ring with self-gravitating particles. Icarus 154, 296-312) is explained: in the presence of the gravitationally unstable density waves, the effective turbulent viscosity ν_eff is given as ν_eff=CG²Σ²/Ω³, where G, Σ, and Ω are the gravitational constant, the surface mass density of a ring, and the angular velocity, respectively, and the nondimensional correction factor C≈10. We argue that both Saturn's main rings and their irregular of the order of 100 m or even less fine-scale structure (being recurrently created and destroyed on the time scale of an order of Keplerian period ) are not likely much younger than the solar system.