Finite Larmor radius and Hall effects on thermosolutal instability of a plasma

The thermosolutal instability of a plasma with finite Larmor radius and Hall effects is studied. When the instability sets in as stationary convection, finite Larmor radius effects are always stabilizing forx(=k ² d ²/² greater than two and forx less than two, they have a stabilizing or destabilizing influence depending on the Larmor radius parameterN in the presence of Hall currents. On the other hand the Hall currents have both stabilizing and destabilizing effects on the thermosolutal instability forx less than two and forx greater than two depending on the Hall parameterM. The stable solute gradient is found to have a stabilizing effect on stationary convection. The case of overstability is also considered wherein the sufficient conditions for the non-existence of overstability are derived.     

Precise positions of selected minor planets from the observations of 1991–1993

We present two catalogues of positions of selected asteroids in the system of the Tycho Reference Catalogue from the photographic observations carried out on Mt. Maidanak with the AFR-1 wide-field astrograph (D = 230 mm, F = 2300 mm) and in Zvenigorod with the Zeiss wide-field astrograph (D = 400 mm, F = 2000 mm) in 1991–1993. The catalogue obtained on Maidanak contains 109 positions of selected asteroids; the one obtained in Zvenigorod contains 177 asteroid positions. The two catalogues are compared to show that they are uniform. The one-position mean square errors in the Maidanak and Zvenigorod catalogues are calculated: 0.306″, 0.153″ and 0.370″, 0.219″.     

Orbital Period Changes of Two Very Short-Period W UMa Stars CC Com and V523 Cas: A Possible Evidence for TRO Plus AML Model

Orbital period changes of the two very short-period contactbinaries, CC Com and V523 Cas, are presented. It is shownthat the period of CC Com varies in secular decrease withrate of dP/dt = –4.39 ×10^-8 days/year, while theperiod of V523 Cas is increasing at rate of dP/dt =+9.09 ×10^-8 days/year. The physical parameters of the twoW UMa stars are nearly equal which indicates that the physicalproperties of the two contact binaries are almost the same.The different types of period changes in the two systemsmay strongly suggest that, although they are undergoingsecular angular momentum loss (AML), the oscillatory characterpredicted by thermal relaxation oscilation (TRO) theory stillexist and they are on the different TRO stages, i.e., CC Comis on the shrinking TRO stage, but V523 Cas is on the expendingTRO stage. The present period changes of the two systems can beexplained by the combination of the TRO and the AML theories.     

Photospheric and chromospheric activity on EY Dra

Magnetic activity in the photosphere and chromosphere of the M dwarf EY Dra is studied and possible correlations between the two are investigated using photometric observations in the V and R bands and optical and near infrared spectroscopy. The longitudinal spot configuration in the photosphere is obtained from the V band photometry, and the chromospheric structures are investigated using variations in the Hα line profile and observations of the Paschen β line. The shape of the V band light‐curve indicates two active regions on the stellar surface, about 0.4 in phase apart. The spectroscopic observations show enhanced Hα emission observed close to the phases of the photometrically detected starspots. This could indicate chromospheric plages associated with the photospheric starspots. Some indications of prominence structures are also seen. The chromospheric pressure is limited to log m_TR < –4 based on the non‐detection of emission in the Paschen β wavelength region. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Damped Oscillations of Coronal Loops

A mechanism of damped oscillations of a coronal loop is investigated. The loop is treated as a thin toroidal flux rope with two stationary photospheric footpoints, carrying both toroidal and poloidal currents. The forces and the flux-rope dynamics are described within the framework of ideal magnetohydrodynamics (MHD). The main features of the theory are the following: i) Oscillatory motions are determined by the Lorentz force that acts on curved current-carrying plasma structures and ii) damping is caused by drag that provides the momentum coupling between the flux rope and the ambient coronal plasma. The oscillation is restricted to the vertical plane of the flux rope. The initial equilibrium flux rope is set into oscillation by a pulse of upflow of the ambient plasma. The theory is applied to two events of oscillating loops observed by the Transition Region and Coronal Explorer (TRACE). It is shown that the Lorentz force and drag with a reasonable value of the coupling coefficient (c _d ) and without anomalous dissipation are able to accurately account for the observed damped oscillations. The analysis shows that the variations in the observed intensity can be explained by the minor radial expansion and contraction. For the two events, the values of the drag coefficient consistent with the observed damping times are in the range c _d ≈2 – 5, with specific values being dependent on parameters such as the loop density, ambient magnetic field, and the loop geometry. This range is consistent with a previous MHD simulation study and with values used to reproduce the observed trajectories of coronal mass ejections (CMEs).     

Nature and distribution of dark matter: 2. binaries,groups and clusters

We study the mass-radius relationship for aggregates of galaxies, viz. binaries, small groups and clusters. The data are subjected to a simple best-fit analysis similar to the one carried out earlier for individual field galaxies. The analysis shows that: (i) The data on binary galaxies are consistent with the assumption that binaries are just two galaxies, each with an individual isothermal (M ∫R) dark matter halo, moving under the mutual gravitational attraction, (ii) The data on the groups of galaxies are too scattered to obey a single power-law relation of the formM = kR ⁿ with any degree of reliability, (iii) The data on groups and clusters fit better with a law of the formM = AR ³ +BR. This form suggests the existence of two components in dark matter—one which is clustered around the galaxies (M ∫R) and another which is distributed smoothly (M ∫R ³ ). The smooth distributions becomes significant only at scales ≥ 1 Mpc and hence does not affect binaries significantly. We briefly discuss the theoretical implications of this analysis     

Slow and Fast Rotating Coronal Holes from Geomagnetic Indices

The evolution of the 27-day recurrence in the series of two solar indices (Wolf number WN and 10.7 cm radio flux F) and two geomagnetic indices (Dst and ζ, variance of the geomagnetic field recorded at a magnetic observatory) have been studied over the 1957 – 2007 time span. Spectral energies contained in two period domains (25 – 27.3 and 27.3 – 31 days), designated as E ₁ and E ₂, have been computed. Whereas the evolution of E ₁ is the same for the four indices, that of E ₂ is essentially different for WN and F on the one hand, Dst and ζ on the other hand. Some general conclusions on the dynamics of the solar outer layers are inferred from these results. First the solar activity, as measured by WN, and when averaged over a few years, evolves in the same way whatever the latitude. Second, two families of coronal holes (CHs) are identified; the rapidly and the slowly rotating CHs evolve quite differently.     

Uranus and Neptune interior models

This paper is concerned with the interior structure of Uranus and Neptune. Our approach is three-fold. First, a set of three-layer models for both Uranus and Neptune are constructed using a method similar to that used in the study of the terrestrial planets. The variations of the mass density (s) and flattening e(s) with fractional mean radius s for two representative models of Uranus and Neptune are calculated. The results are tabulated. A comparison of these models shows that these two planets are probably very similar to each other in their basic dynamical features. Such similarity is very seldom seen in our solar system. Secondly, we check the conformance between the theoretical results and observational data for the two planets. And thirdly, the 6th degree Stokes zonal parameters for Uranus and for Neptune are predicted, based on the interior models put forward in this paper.     

On the observation of scattered radio emission from sources in the solar corona

The observations of a brief flaring region between two plages on the eastern limb of the Sun and the subsequent coronal transient are reported for June 16, 1972 by Koomen et al. (1974). Both of these events have unambiguous and closely timed associations with the solar noise bursts observed at 2800 and 2700 MHz and are also accompanied with good X-ray and SID effects but faint subflare (Solar-Geophysical Data). The two frequencies are those monitored at widely separated stations operated by the Astrophysics Branch of the National Research Council at Lake Traverse, Ontario and at Penticton, B.C.     

Gravity and effective temperature distribution on the surface of contact binary systems

The aim of this work is to study the gravity and the effective temperature distribution on the outer equipotential surface of a contact binary. In particular, the lines of constant g, (the iso‐g curves), are computed and plotted on the outer surface C_s of contact configurations. Since the gravity distribution would also specify the effective temperature distribution on the binary's common photosphere through the gravity darkening effect, these lines correspond to isothermals too. Applications have been made to two contact binaries; namely, to AW UMa and OO Aql, two systems with very different mass ratios. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Helical Eruptive Prominence Associated with a Pair of Overlapping CMEs on 21 April 2001

The eruption of limb prominence on 21 April 2001 associated with two coronal mass ejections (CMEs) is investigated. Hα images reveal two large-scale eruptions (a prominence body and a southern foot-point arch), both showing helical internal structure. These two eruptions are found to be spatially and temporally associated with the corresponding CMEs. The kinematics and the study of geometrical parameters of the prominence show that the eruption was quite impulsive (with peak acceleration ≈470 m s⁻²) and has taken place for relatively low pitch angle of helical threads, not exceeding tan θ≈1.2. The stability criteria of the prominence are revisited in the light of the model of Vršnak (1990, Solar Phys. 129, 295) and the analysis shows that the eruption violates the instability criteria of that model. Finally, the energy stored in the prominence circuit and the energies (kinetic, potential, and magnetic) of the associated CMEs are estimated and it is found that there was enough energy stored in the prominence to drive the two CMEs. S.S. Ali is on leave from Aligarh Muslim University, Aligarh, 202 002, India.     

An Improved Approach to Non-Force-Free Coronal Magnetic Field Extrapolation

We develop an approach to deriving the three-dimensional non-force-free coronal magnetic field from vector magnetograms. Based on the principle of minimum dissipation rate, a general non-force-free magnetic field is expressed as the superposition of one potential field and two constant-α (linear) force-free fields. Each is extrapolated from its bottom boundary data, providing the normal component only. The constant-α parameters are distinct and determined by minimizing the deviations between the numerically computed and measured transverse magnetic field at the bottom boundary. The boundary conditions required are at least two layers of vector magnetograms, one at the photospheric level and the other at the chromospheric level, presumably. We apply our approach to a few analytic test cases, especially to two nonlinear force-free cases examined by Schrijver et al. (Solar Phys. 235, 161, 2006). We find that for one case with small α parameters, the quantitative measures of the quality of our result are better than the median values of those from a set of nonlinear force-free methods. The reconstructed magnetic-field configuration is valid up to a vertical height of the transverse scale. For the other cases, the results remain valid to a lower vertical height owing to the limitations of the linear force-free-field solver. Because our method is based on the fast-Fourier-transform algorithm, it is much faster and easy to implement. We discuss the potential usefulness of our method and its limitations.     

Collisions of galaxies of different masses, forms and sizes

We study the tidal effects of close collisions between two spherical galaxies of various mass and mass distributions by numerical simulations. The galaxies are represented by polytropes of indices n=4 and n=0 which denote cases of highcentral concentration and uniform mass distribution respectively.The initial relative velocity of the galaxies is chosen to be 700 km s^-1.The results indicate that the tidal effects are quite sensitive to both mass and mass distribution of the galaxies. The dependence oftidal capture and tidal disruption on the choice of the model and mass ratio is investigated. The classification of collisionis given for each simulation. The results also indicate that in a collision between two identical galaxies relatively more spin is imparted to the galaxies ifthey are centrally concentrated than if they are homogeneous.     

Resonant Absorption of Fast Magnetoacoustic Waves due to Coupling into the Slow and Alfvén Continua in the Solar Atmosphere

Resonant absorption of fast magnetoacoustic (FMA) waves in an inhomogeneous, weakly dissipative, one-dimensional planar, strongly anisotropic and dispersive plasma is investigated. The magnetic configuration consists of an inhomogeneous magnetic slab sandwiched between two regions of semi-infinite homogeneous magnetic plasmas. Laterally driven FMA waves penetrate the inhomogeneous slab interacting with the localised slow or Alfvén waves present in the inhomogeneous layer and are partly reflected, dissipated and transmitted by this region. The presented research aims to find the coefficient of wave energy absorption under solar chromospheric and coronal conditions. Numerical results are analysed to find the coefficient of wave energy absorption at both the slow and Alfvén resonance positions. The mathematical derivations are based on the two simplifying assumptions that i) nonlinearity is weak, and ii) the thickness of the inhomogeneous layer is small in comparison to the wavelength of the wave, i.e. we employ the so-called long wavelength approximation. Slow resonance is found to be described by the nonlinear theory, while the dynamics at the Alvén resonance can be described within the linear framework. We introduce a new concept of coupled resonances, which occurs when two different resonances are in close proximity to each other, causing the incoming wave to act as though it has been influenced by the two resonances simultaneously. Our results show that the wave energy absorption is heavily dependent on the angle of the incident wave in combination with the inclination angle of the equilibrium magnetic field. In addition, it is found that FMA waves are very efficiently absorbed at the Alvén resonance under coronal conditions. Under chromospheric conditions the FMA waves are far less efficiently absorbed, despite an increase in efficiency due to the coupled resonances.     

Scattering of an Electromagnetic Wave on a Dielectric Layer Bounded on Two Sides by Two Different Homogeneous, Semi-Infinite Media

The problem of the passage of a plane electromagnetic wave through an arbitrary, inhomogeneous dielectric layer bounded on two sides by two different homogeneous, semi-infinite media is considered. Algebraic relations are obtained between the amplitudes of transmission and reflection (the scattering amplitudes) for the problem under consideration and the wave scattering amplitudes when the layer is bounded on both sides by a vacuum. It is shown that for s and p polarized fields the scattering problem (a boundary-value problem) can be formulated as a Cauchy problem directly for the s and p wave equations. It is also shown that the problem of finding the field inside the layer also reduces to a Cauchy problem in the general case.     

Bounds on the solution to Kepler's equation

For Kepler's equation two general linear methods of the bounds determination forE ₀ root are presented. The methods based on elementary properties of convex functions allow an approach toE ₀ root arbitrarily close.     

An analytical approach to small amplitude solutions of the extended nearly circular Sitnikov problem

The model of extended Sitnikov Problem contains two equally heavy bodies of mass m moving on two symmetrical orbits w.r.t the centre of gravity. A third body of equal mass m moves along a line z perpendicular to the primaries plane, intersecting it at the centre of gravity. For sufficiently small distance from the primaries plane the third body describes an oscillatory motion around it. The motion of the three bodies is described by a coupled system of second order differential equations for the radial distance of the primaries r and the third mass oscillation z. This problem which is dealt with for zero initial eccentricity of the primaries motion, is generally non integrable and therefore represents an interesting dynamical system for advanced perturbative methods. In the present paper we use an original method of rewriting the coupled system of equations as a function iteration in such a way as to decouple the two equations at any iteration step. The decoupled equations are then solved by classical perturbation methods. A prove of local convergence of the function iteration method is given and the iterations are carried out to order 1 in r and to order 2 in z. For small values of the initial oscillation amplitude of the third mass we obtain results in very good agreement to numerically obtained solutions.     

The light curve variations in AR Lacertae

The eclípsing binary AR Lac has been observed in two colours,B andV, in 1980 and 1981. The new times of minimal obtained during the observatons indicate that the period of the system is still continuing its decrease. The wave-like distortions outside eclipses have two maxima and are very similar in shape in successive two years.     

Restricted quantum-mechanical three-body problems

The Schrödinger equation is solved if an electron moves in the field of chargesZ ₁ andZ ₂ which are fixed in space. The wave function is expanded in power series, the eigenvalues are given graphically and partly in tabular form. The asymptotic behaviour of the eigenvalues is discussed when the distance of the two fixed charges is small and large. Some consequences are drawn on hydrogen line broadening, shift andgrenzkontinua. Further utilization of the calculations is indicated. The mathematical appendix helps to clarify some technical details of the calculations.     

Determination of the orbits of near-Earth asteroids from observations at the first opposition

Observations at the first opposition are used to determine the orbits of 16 near-Earth asteroids with two or more observed oppositions. The orbits are improved by the differential method. This paper considers two modifications of the improvement technique, which are compared to the classical method based on the principle of the least square method (LSM). The first modification uses the principle of least absolute deviations (LAD). In the second modification, the differences O - C (between the observed and calculated positions) are transformed to fit into a new coordinate system whereby the axes go parallel and perpendicular to the asteroid’s apparent path (the modified differential method (MDM)). The orbits determined from one opposition by the classical LSM, LAD, and MDM are compared to a more accurate orbit calculated by the LSM from all the available oppositions. The calculations show that in 13 cases out of 16, the asteroid orbits calculated by LAD are more accurate than those calculated by the classical LSM. The improvement by the modified differential method, which includes the O - C transformation, does not produce any perceptible increase in accuracy when compared to the orbits calculated by the classical method.