Effects of variations of parallel angular velocity and vorticity on the oscillations of compressible homogeneous rotating ellipsoids

Earlier work on the oscillations of an ellipsoid is extended to investigate the behaviour of a nonequilibrium compressible homogeneous rotating gaseous ellipsoid, with the components of the velocity field as linear functions of the coordinates, and with parallel angular velocity and uniform vorticity. The dynamical behaviour of the ellipsoid is obtained by numerically integrating the relevant differential equations for different values of the initial angular velocity and vorticity. This behaviour is displayed by the (a ₁,a ₂) and (a ₁,a ₃) phase plots, where thea _i's (i = 1, 2, 3) are the semi-diameters, and by the graphs ofa ₁,a ₂,a ₃, the volume, and the angular velocity as functions of time.The dynamical behaviour of the nonequilibrium ellipsoid depends on the deviation of the angular momentum from its equilibrium value; for larger deviations, the oscillations are more nonperiodic with larger amplitudes.An initially ellipsoidal configuration always remains ellipsoidal, but it cannot become spheroidal about its rotation axis, though it may become spheroidal instantaneously about either one of the other two principal axes.For an ellipsoid approaching axisymmetry about its axis of rotation, the angular velocity can suddenly increase by a large amount. Thus if an astrophysical object can be modelled by a nonequilibrium ellipsoid, it may occasionally undergo sudden large increases of angular velocity.     

Rotation of a two-component model neutron star in the GTR

Equations are obtained for the dynamics of the rotation of a two-component model neutron star within the framework of the generai theory of relativity. It is shown that for steady rotation of the star’s normal component, Ω_c = const, the angular velocity Ω_s of the superfluid component depends on the coordinates and is Ω_c + ω, where ω is the nondiagonal component of the metric tensor. Translated from Astrofizika, Vol. 40, No. 3, pp. 403–412, August, 1997.     

Galactic kinematics from OB3 stars with distances determined from interstellar Ca II lines

Based on data for 102 OB3 stars with known proper motions and radial velocities, we have tested the distances derived by Megier et al. from interstellar Ca II spectral lines. The internal reconciliation of the distance scales using the first derivative of the angular velocity of Galactic rotation Ω′₀ and the external reconciliation with Humphreys’s distance scale for OB associations refined by Mel’nik and Dambis show that the initial distances should be reduced by ≈20%. Given this correction, the heliocentric distances of these stars lie within the range 0.6–2.6 kpc. A kinematic analysis of these stars at a fixed Galactocentric distance of the Sun, R ₀ = 8 kpc, has allowed the following parameters to be determined: (1) the solar peculiar velocity components (u _⊙, v _⊙, ω _⊙) = (8.9, 10.3, 6.8) ± (0.6, 1.0, 0.4) km s⁻¹; (2) the Galactic rotation parameters Ω₀ = −31.5 ± 0.9 km s⁻¹ kpc⁻¹, Ω′₀ = +4.49 ± 0.12 km s⁻¹ kpc⁻², Ω″₀ = −1.05 ± 0.38 km s⁻¹ kpc⁻³ (the corresponding Oort constants are A = 17.9 ± 0.5 km s⁻¹ kpc⁻¹, B = −13.6 ± 1.0 km s⁻¹ kpc⁻¹ and the circular rotation velocity of the solar neighborhood is |V ₀| = 252 ± 14 km s⁻¹); (3) the spiral density wave parameters, namely: the perturbation amplitudes for the radial and azimuthal velocity components, respectively, f _R = −12.5±1.1 km s⁻¹ and f _ϑ = 2.0 ± 1.6 km s⁻¹; the pitch angle for the two-armed spiral pattern i = −5.3° ± 0.3°, with the wavelength of the spiral density wave at the solar distance being λ = 2.3 ± 0.2 kpc; the Sun’s phase in the spiral wave x _⊙ = −91° ± 4°.     

The Variation of Solar Wind Correlation Lengths Over Three Solar Cycles

We present the results of a study of solar wind velocity and magnetic field correlation lengths over the last 35 years. The correlation length of the magnetic field magnitude λ _|B| increases on average by a factor of two at solar maxima compared to solar minima. The correlation lengths of the components of the magnetic field l_BXYZ\lambda_{B_{XYZ}} and of the velocity l_VYZ\lambda_{V_{YZ}} do not show this change and have similar values, indicating a continual turbulent correlation length of around 1.4×10⁶ km. We conclude that a linear relation between λ _|B|, VB ², and Kp suggests that the former is related to the total magnetic energy in the solar wind and an estimate of the average size of geoeffective structures, which is, in turn, proportional to VB ². By looking at the distribution of daily correlation lengths we show that the solar minimum values of λ _|B| correspond to the turbulent outer scale. A tail of larger λ _|B| values is present at solar maximum causing the increase in mean value.     

Calculation of effective optical depth of absorption line formation in homogeneous semi-infinite planetary atmosphere during anisotropic scattering

The algorithm for determining effective optical thickness of absorption line formation in a plane-parallel homogeneous planetary atmosphere is presented. The case of anisotropic scattering is considered. The results of numerical calculations of τ _e (μ₀) at the scattering angle γ = π for some values of the single scattering albedo λ and the parameter of the Heyney-Greenstein scattering indicatrix g are given. The refined equation for the function T ^m (−μ, μ₀) is presented.     

Continuity and stability of families of figure eight orbits with finite angular momentum

Numerical solutions are presented for a family of three dimensional periodic orbits with three equal masses which connects the classical circular orbit of Lagrange with the figure eight orbit discovered by C. Moore [Moore, C.: Phys. Rev. Lett. 70, 3675–3679 (1993); Chenciner, A., Montgomery, R.: Ann. Math. 152, 881–901 (2000)]. Each member of this family is an orbit with finite angular momentum that is periodic in a frame which rotates with frequency Ω around the horizontal symmetry axis of the figure eight orbit. Numerical solutions for figure eight shaped orbits with finite angular momentum were first reported in [Nauenberg, M.: Phys. Lett. 292, 93–99 (2001)], and mathematical proofs for the existence of such orbits were given in [Marchal, C.: Celest. Mech. Dyn. Astron. 78, 279–298 (2001)], and more recently in [Chenciner, A. et al.: Nonlinearity 18, 1407–1424 (2005)] where also some numerical solutions have been presented. Numerical evidence is given here that the family of such orbits is a continuous function of the rotation frequency Ω which varies between Ω = 0, for the planar figure eight orbit with intrinsic frequency ω, and Ω = ω for the circular Lagrange orbit. Similar numerical solutions are also found for n > 3 equal masses, where n is an odd integer, and an illustration is given for n = 21. Finite angular momentum orbits were also obtained numerically for rotations along the two other symmetry axis of the figure eight orbit [Nauenberg, M.: Phys. Lett. 292, 93–99 (2001)], and some new results are given here. A preliminary non-linear stability analysis of these orbits is given numerically, and some examples are given of nearby stable orbits which bifurcate from these families.     

Evaluation of disturbances from solar radiation in orbital elements of geosynchronous satellites based on harmonics

Using specialized codes for the search of periodic and linear components we show that direct solar radiation leads to short-period variations of all the orbital elements of geosynchronous satellites. The variation period of the semimajor axis a, orbit inclination i and the longitude of the ascending node Ω is 1 day. Eccentricity e, the argument of perigee ω and the mean anomaly M vary with a period of 0.5 days. Direct solar radiation also leads to long-period variations in e, ω and M with a period of 1 year. The elements a, i and Ω undergo variations only in the amplitude of diurnal variations with a period of 1 or 0.5 years. Secular variability (linear components) are not detected. To obtain the initial value array of the orbital elements we used the Lagrange equations of perturbed motion in the form of a Gaussian with their subsequent integration via a special method of harmonics: the values of the derived orbital elements, obtained from the Lagrange equations, were presented through the periodic functions that are easy to integrate.     

Line profile analysis of a coronal formation observed near a quiescent prominence: Intensities,temperatures and velocity fields

A technique developed for analysing line profiles with both speed and high accuracy was used to study the physical conditions of a coronal formation near a quiescent prominence. Detailed analyses of five coronal lines (Fe xiv λ 5303, Fe x λ 6374, Ni xv λ 6702, Fe xv λ 7059, and Fe xi λ 7892) provided total intensities, Doppler width temperatures, ionization temperatures, and velocities. Dissimilar spatial fluctuations in intensity are obvious for ions grouped according to (low vs high) ionization potentials. The intensity of the green line shows a local minimum around the observed quiescent prominence; a corresponding but much more diffuse pattern is visible in the red line intensity. Large differences are observed in temperatures derived by different means. In particular, , while , and . The differences between and are taken as direct evidence of temperature inhomogeneity. One can thus put little significance in T _e (xi/x). T _D(λ5303) and T _e (xv/xiv) fluctuate nearly in parallel at each slit height, with a weak local minimum evident around the prominence. The discrepancy between these two can be removed if a non-thermal turbulent motion of 6–16 km s⁻¹ is assumed. Variations with height of both T _D(λ5303) and T _e (xv/xiv) suggest that the coronal temperature maximum is located no more than 15000 km above the top of spicules. A negative gradient of about 6 deg km⁻¹ is found in the height variation of T _D(λ5303). The height variation of the green line wavelength shows that the majority of coronal material in this region is flowing from west to east on the Sun, with the highest velocity of 12 km s⁻¹ found at the lowest heights. This motion is in the same sense as that of the nearby coronal rain, as determined both from the spectra and wavelength-shifted Hα filtergrams. Superposed on the above flow is a systematic velocity field of up to ±5 km s⁻¹. This field similarly reaches maximum amplitudes at lowest heights showing a local maximum around the prominence. On leave from Institute of Earth Science and Astrophysics, Shiga University, Ohtsu 520, Japan, as 1973–75 National Academy of Science/National Research Council Senior Post-Doctoral Research Associate at Sacramento Peak Observatory.     

Toroidal magnetic field in pulsars

The differential rotation of plasma in the core of pulsars (Ω_s ≠ Ω_e) generates convective currents increasing with time which in turn generates the toroidal magnetic field. To avoid difficulties of physical interpretation inherent to the theory of general relativity we have adopted the tetrad approach to discuss the generation of the magnetic field in the core of the neutron stars. The results which we have obtained are in agreement with those obtained earlier. Published in Astrofizika, Vol. 49, No. 4, pp. 613–620 (August 2006).     

Slowly Rotating Cosmological Universe Filled with Viscous Fluid

A study of the slowly rotating cosmological universe filled with viscous fluid has been made by assuming the matter angular velocity Ω is proportional to the metric angular velocity Ω and the Universe is expanding under the Hubble's law. The physical properties of the solutions obtained are also discussed. This revised version was published online in July 2006 with corrections to the Cover Date.     

Spectroscopic study of the variable planetary nebula IC 4997

Based on our spectroscopic observations of the variable planetary nebula IC 4997 in 2003–2009, we have obtained the relative fluxes in optical emission lines. The interstellar extinction c = 0.35 has been found from the Balmer decrement by taking into account the effect of self-absorption in hydrogen lines in dense nebular regions. The variations in the Balmer decrement point to variability of the self-absorption and circumstellar extinction. We have investigated the variations in the relative intensities of some spectral lines and their ratios with time. The drop in the ratios F(λ4363)/F(Hγ) and F(λ363)/F(λ4959) that began back in 1990–1995 has continued, suggesting a decrease in the electron density and temperature in the central nebular region. The ratio F(λ6731)/F(λ6717) has remained constant. It gives an estimate for the electron density in the outer regions of IC 4997, N _e ∼ 10⁴ cm⁻³.     

Charged particle motion on and off the equatorial plane of a magnetic star in Rosen's bimetric gravity

In this paper we have studied in detail (numerically) the trajectories of charged particles in a magnetic field (dipolar at infinity) associated with a static star in the framework of Rosen's bimetric theory of gravity. It was found that there do exist potential wells that allow possible trapping of particles in stable orbits both on and off the equatorial plane. A particularly interesting feature that has shown up is the fact that the characteristics of the effective potential wellV _eff depend on the ratio of the magnetic field strength parameter λ, and the angular momentumL of the charged particle. For values lower than a critical (λ/L) _c the potential well lies within the regionr≤2m.     

Carbon recombination lines from the Galactic plane at 34.5 & 328 MHz

We present the results of a search for carbon recombination lines in the Galaxy at 34.5 MHz (C575α) made using the dipole array at Gauribidanur near Bangalore. Observations made towards 32 directions resulted in detections of lines, in absorption at nine positions. Followup observations at 328 MHz (C272α) using the Ooty Radio Telescope detected these lines in emission. A VLA D-array observation of one of the positions at 330 MHz yielded no detection implying a lower limit of 10′ for the angular size of the line forming region. The longitude-velocity distribution of the observed carbon lines indicate that the line forming regions are located mainly between 4 kpc and 7 kpc from the Galactic centre. Combining our results with published carbon recombination line data near 76 MHz (Erickson, McConnell & Anantharamaiah 1995), we obtain constraintson the physical parameters of the line forming regions. We find thatif the angular size of the line forming regions is ≥ 4°, then the range of parameters that fit the data are:T _e =20–40 K,n _e ∼ 0.1–0.3 cm⁻³ and pathlengths ∼ 0.07–0.9 pc which may correspond to thin photodissociated regions around molecular clouds. On the other hand, if the line forming regions are ∼ 2° in extent, then warmer gas (T _e ∼ 60–300 K) with lower electron densities (n _e ∼ 0.03–0.05 cm⁻³) extending over several tens of parsecs along the line of sight and possibly associated with atomic HI gas can fit the data. Based on the range of derived parameters, we suggest that the carbon line regions are most likely associated with photo-dissociation regions.     

Estimation of cosmological parameters from peculiar velocities of flat EDGE-ON galaxies

We estimate the values of the cosmological parameters using the data about peculiar velocities of 1493 flat edge-on spirals from the RFGC catalogue. The obtained values Ω _m = 0.21_{− 0.09} ^{+ 0.22}, σ₈ = 1.07_{− 0.24} ^{+ 0.28} differ from the WMAP values by approximately 2–3σ, but well agree with modern constraints on these parameters. Due to a strong correlation between these quantities the shape of the 1σ, 2σ and 3σ-boundaries are rather narrow. This gives us the opportunity to use this estimation to verify the corresponding values, obtained by different methods.     

Optical imaging and spectroscopic observation of the galactic supernova remnant G85.9-0.6

Optical CCD imaging with Hα and [SII] filters and spectroscopic observations of the galactic supernova remnant G85.9-0.6 have been performed for the first time. The CCD image data are taken with the 1.5 m Russian-Turkish Telescope (RTT150) at TüBİTAK National Observatory (TUG) and spectral data are taken with the Bok 2.3 m telescope on Kitt Peak, AZ. The images are taken with narrow-band interference filters Hα, [SII] and their continuum. [SII]/Hα ratio image is performed. The ratio obtained from [SII]/Hα is found to be ∼0.42, indicating that the remnant interacts with HII regions. G85.9-0.6 shows diffuse-shell morphology. [SII]λ λ6716/6731 average flux ratio is calculated from the spectra, and the electron density N _e is obtained to be 395 cm⁻³. From [OIII]/Hβ ratio, shock velocity has been estimated, pre-shock density of n _c =14 cm⁻³, explosion energy of E=9.2×10⁵⁰ ergs, interstellar extinction of E(B−V)=0.28, and neutral hydrogen column density of N(HI)=1.53×10²¹ cm⁻² are reported.     

Motion Around The Triangular Equilibrium Points Of The Restricted Three-Body Problem Under Angular Velocity Variation

We study numerically the asymmetric periodic orbits which emanate from the triangular equilibrium points of the restricted three-body problem under the assumption that the angular velocity ω varies and for the Sun–Jupiter mass distribution. The symmetric periodic orbits emanating from the collinear Lagrangian point L ₃, which are related to them, are also examined. The analytic determination of the initial conditions of the long- and short-period Trojan families around the equilibrium points, is given. The corresponding families were examined, for a combination of the mass ratio and the angular velocity (case of equal eigenfrequencies), and also for the critical value ω = 2

Ammonia in the atmospheres of Jupiter and Saturn: Absorption coefficients

Spectral values (with 1 nm spectral resolution) of the product of γk _ν and γ′k _ν (where k _ν is the monochromatic coefficient of ammonia absorption and γ and γ′ are the relative (with respect to 0.85/0.15 hydrogen-helium mixture and methane, respectively)) concentrations of ammonia for the absorption bands at λλ = 552, 604, 645, 787, and 932 nm in thermal conditions of Jupiter’s and Saturn’s atmospheres are determined ().     

Radio synthesis imaging of anisotropic angular broadening in the solar wind

We present Very Large Array observations at wavelengths of 2, 3.5, 6, and 20 cm, of angular broadening of radio sources due to the solar wind in the region 2–16 solar radii. Angular broadening is anisotropic with axial ratios in the range 2–16. Larger axial ratios are observed preferentially at smaller solar distances. Assuming that anisotropy is due to scattering blobs elongated along magnetic field lines, the distribution of position angles of the elliptically broadened images indicates that the field lines are non-radial even at the largest heliocentric distances observed here. At 5R⊙, the major axis scattering angle is ∼ 0.7" atλ= 6 cm and it varies with heliocentric distance asR ^-1.6. The level of turbulence, characterized by the wave structure function at a scale of 10 km along the major axis, normalized toλ = 20 cm, has a value 20 ± 7 at 5R⊙and varies with heliocentric distance asR ^-3. Comparison with earlier resu lts suggest that the level of turbulence is higher during solar maximum. Assuming a power-law spectrum of electron density fluctuations, the fitted spectral exponents have values in the range 2.8–3.4 for scale sizes between 2–35 km. The data suggests temporal fluctuations (of up to 10%) in the spectral exponent on a time scale of a few tens of minutes. The observed structure functions at different solar distances do not show any evidence for an inner scale; the upper limits are l k m at 2R⊙ and 4 km at 13R⊙. These upper limits are in conflict with earlier determinations and may suggest a reduced inner scale during solar maximum.     

Optical depth effects on the formation of spectral lines in rotating and expanding spherical atmospheres

We have investigated the effects of increasing optical depths on spectral lines formed in a rotating and expanding spherical shell. We have assumed a shell whose outer radius is 3 times the inner radius, with the radial optical depths equal to 10, 50, 100, 500. We have employed a constant velocity with no velocity gradients in the shell. The shell is assumed to be rotating with velocities varying as 1/_ρ, where_ρ is the perpendicular distance from the axis of rotation, implying the conservation of angular momentum. Two expansion (radial) velocities are treated: (1)V = 0 (static case) and (2)V = 10 mean thermal units. The maximum rotational velocities areV _rot = 0, 5, 10 and 20. In the shell where there are no radial motions, we obtain symmetric lines with emission in the wings forV _rot = 0 and 5 while forV _rot ≥ 10 we obtain symmetric absorption lines. In the case of an expanding shell, we obtain lines with central emission.