Effects of mass transfer on the hydromagnetic free convective flow in the Stokes' problem

The effects of the mass transfer on free convection flow of an electrically conducting viscous fluid (e.g., of a stellar atmosphere) past an impulsively started infinite vertical limiting surface (e.g., of a star) in presence of a transverse magnetic field is considered. Solutions for the velocity and skin-friction, in closed form are obtained with the help of the Laplace transform technique and the results obtained for various values of the parametersS _c (Schmidt number),P (Prandtl number) andM (Hartmann number) are given in graphical form. The paper is concluded with a discussion of the results obtained.     

Effects of mass transfer on the free convective flow in the Stokes' problem for an infinite vertical limiting surface

An exact analysis of the mass transfer effects on the free convection flow of an incompressible viscous fluid past an impulsively started infinite vertical (wall) limiting surface (Stokes's or Rayleigh's problem) has been carried out. Expressions for the velocity, temperature, species concentration and skin friction are obtained by using the Laplace transform technique. The velocity field and the skin friction are shown graphically for air (P=0.71) and mercury (P=0.025). The effects ofG (Grashof number),G _c (the modified Grashof number) andS _c (Schmidt number) are considered qualitatively during the course of discussion.     

Impact of a Rotational Discontinuity of the Solar Windon the Earth's Bow Shock

The interaction of a rotational (plane-polarized) discontinuity A of the solar wind with the Earth's bow shock S _b is studied in the parametric form. The velocity of displacement of the bow shock is estimated. An asymmetry of the impact on the flanks of S _b and an appreciable contribution of slow MHD waves to the process considered are revealed. This revised version was published online in July 2006 with corrections to the Cover Date.     

Symmetric Periodic Orbits in the Anisotropic Schwarzschild-Type Problem

Studying the two-body problem associated to an anisotropic Schwarzschild-type field, Mioc et al. (2003) did not succeed in proving the existence or non-existence of periodic orbits. Here we answer this question in the affirmative. To do this, we start from two basic facts: (1) the potential generates a strong force in Gordon’s sense; (2) the vector field of the problem exhibits the symmetries S _i , , which form, along with the identity, an Abelian group of order 8 with three generators of order 2. Resorting to S ₂ and S ₃, in connection with variational methods (particularly the classical lower-semicontinuity method), we prove the existence of infinitely many S ₂- or S ₃-symmetric periodic solutions. The symmetries S ₂ and S ₃ constitute an indicator of the robustness of the classical isotropic Schwarzschild-type system to perturbations (as the anisotropy may be considered).     

A New Method for Prediction of Peak Sunspot Number and Ascent Time of the Solar Cycle

The purpose of the present study is to develop an empirical model based on precursors in the preceding solar cycle that can be used to forecast the peak sunspot number and ascent time of the next solar cycle. Statistical parameters are derived for each solar cycle using “Monthly” and “Monthly smoothed” (SSN) data of international sunspot number (R _i). Primarily the variability in monthly sunspot number during different phases of the solar cycle is considered along with other statistical parameters that are computed using solar cycle characteristics, like ascent time, peak sunspot number and the length of the solar cycle. Using these statistical parameters, two mathematical formulae are developed to compute the quantities [Q _C] _n and [L] _n for each nth solar cycle. It is found that the peak sunspot number and ascent time of the n+1th solar cycle correlates well with the parameters [Q _C] _n and [L] _n /[S _Max] _n+1 and gives a correlation coefficient of 0.97 and 0.92, respectively. Empirical relations are obtained using least square fitting, which relates [S _Max] _n+1 with [Q _C] _n and [T _a] _n+1 with [L] _n /[S _Max] _n+1. These relations predict a peak of 74±10 in monthly smoothed sunspot number and an ascent time of 4.9±0.4 years for Solar Cycle 24, when November 2008 is considered as the start time for this cycle. Three different methods, which are commonly used to define solar cycle characteristics are used and mathematical relations developed for forecasting peak sunspot number and ascent time of the upcoming solar cycle, are examined separately.     

Integration theory for the restricted problem of three axisymmetric bodies

In this paper the circular planar restricted problem of three axisymmetric ellipsoids S _i (i = 1, 2, 3), such that their equatorial planes coincide with the orbital plane of the three centres of masses, be considered. The equations of motion of infinitesimal body S ₃ be obtained in the polar coordinates. Using iteration approach we have given an approximation for another integral, which independent of the Jacobian integral, in the case of P-type orbits (near circular orbits surrounding both primaries).     

Interplanetary magnetic field structure and solar wind parameters as inferred from solar magnetic field observations and by using a numerical 2-D MHD model

An attempt is made to infer parameters of the solar corona and the solar wind by means of a numerical, self-consistent MHD simulation. Boundary conditions for the magnetic field are given from the observations of the large-scale magnetic field at the Sun. A two-region, planar (the ecliptic plane is assumed) model for the solar wind flow is considered. Region I of transonic flow is assumed to cover the distances from the solar surface up to 10R _S (R _S is the radius of the Sun). Region II of supersonic, super-Alfvénic flow extends between 10R _S and the Earth's orbit. Treatment for region I is that for a mixed initial-boundary value problem. The solution procedure is similar to that discussed by Endler (1971) and Steinolfson, Suess, and Wu (1982): a steady-state solution is sought as a relaxation to the dynamic equilibrium of an initial state. To obtain a solution to the initial value problem in region II with the initial distribution of dependent variables at 10R _S (deduced from the solution for region I), a numerical scheme similar to that used by Pizzo (1978, 1982) is applied. Solar rotation is taken into account for region II; hence, the interaction between fast and slow solar wind streams is self-consistently treated. As a test example for the proposed formulation and numerical technique, a solution for the problem similar to that discussed by Steinolfson, Suess, and Wu (1982) is obtained. To demonstrate the applicability of our scheme to experimental data, solar magnetic field observations at Stanford University for Carrington rotation 1682 are used to prescribe boundary conditions for the magnetic field at the solar surface. The steady-state solution appropriate for the given boundary conditions was obtained for region I and then traced to the Earth's orbit through region II. We compare the calculated and spacecraft-observed solar wind velocity, radial magnetic field, and number density and find that general trends during the solar rotation are reproduced fairly well although the magnitudes of the density in comparison are vastly different.     

The action of the satellite 1981 S13, and the optical depth profile of the Encke-gap ringlet in the Saturn A ring

The radial optical depth profile of the Encke ringlet obtained by the occultation experiment of the Voyager photopolarimeter (PPS data) is explained to be caused by the gravitational action of the recently discovered stallite 1981 S13 and a second smaller moonlet orbiting near one of its either libration points — L₄ or L₅. To this aim the results of previous and new numerical particle simulations as well as an extension of the scattering theory concerning a single moonlet to a pair of satellites have been used leading to a triple-peaked ringlet near the orbits of the moonlets. The width and the shape of that ringlet and its separate peaks depend on the mass ratio of both moonlets and on their orbital eccentricites. The best resemblance between the PPS data and the theoretical profile is obtained if the mass ratio of the either moonlets takes M₂/M_1981S13 ≈ (0.8 … 3.0) × 10⁻² and the eccentricities hold: e_1981S13 < h_1981S13; e₂ ≈ h₂ (the values h are the Hill scales of either moonlets defined by h_1981S13/2 ≈ (M_1981S13/2/3M_h)^1/3, M_h = Saturn mass). Furthermore, our results yield a size of 1981 S13 of < 15 km in diameter.     

The equilibrium solutions of the restricted problem of three rigid bodies with variable mass

In this paper we consider the circular planar restricted problem of three rigid bodiesS _i(i=1, 2, 3), two of them are axisymmetric ellipsoids and a third bodyS ₃ is a spherical satellite with decreasing mass, under the gravitational forces. The effect of small perturbations in the Coriolis force and the centrifugal forces on the location of equilibrium points has been studied. It is found only in the case when the primaries have equal differences between their respective principal moments of inertial the pointsL ₄ andL ₅ form nearly equilateral tringles with the primaries. The equilibrium pointsL ₁,L ₂,L ₃ remain collinear an ies on the line joining the primaries.     

The Spectrum of Torsional Oscillations of the Moon

The diagnostic potentialities of the torsional oscillations for probing the structure of the interiors of the Moon are investigated. Models with no core, a liquid core, and a solid core are considered. The profiles of compressional and shear wave velocities V _P and V _S for the lunar interior estimated by Bills and Ferrari (1977), Goins et al. (1981), and Nakamura (1983) from the Apollo lunar seismic network are used. For all these models, the periods of torsional oscillations for n = 2–100 and four overtones have been calculated. The derivatives of the dimensionless eigenfrequency with respect to the dimensionless shear modulus and density are calculated and tabulated for use. These data can be used to determine corrections to the model density and shear modulus distributions due to their small change. The damping of torsional oscillations is studied. Several trial radial distributions of the dissipative function Q are considered.     

Effects of partial frequency redistribution functions RII,RIII and RV on source functions

The effects of partial frequency redistribution on the formation of spectral lines have been studied. We considered the angle-averaged R_II, R_III andR _v types of redistribution with isotropic phase function, Transfer equation with plane-parallel geometry is solved in isothermal atmospheres. For an atmosphere with constant thermal sources, the frequency-dependent source function S_L (R _v) lies below S_L (R_III) but above S_L(R _III) in the line wings.     

The statistics of the photometric accuracy based on MASS data and the evaluation of high-altitude wind

The effect of stellar scintillation on the accuracy of photometric measurements is analyzed. We obtain a convenient form of estimaton of this effect in the long exposure regime, when the turbulence shift produced by the wind is much larger than the aperture of the telescope. A simple method is proposed to determine index S ₃ introduced by Kenyon et al. (2006), directly from the measurements with the Multi Aperture Scintillation Sensor (MASS) without information on vertical profile of the wind. The statistics S ₃ resulting from our campaign of 2005–2007 at Maidanak observatory is presented. It is shown that these data can be used to estimate high-altitude winds at pressure level 70–100 mbar. Comparison with the wind speed retrieved from the NCEP/NCAR global models shows a good agreement. Some prospects for retrieval of the wind speed profile from the MASS measurements are outlined.     

GEOS-II and 13th order terms of the geopotential

The resonance of GEOS-II (1968-002A) with 13th-order terms of the geopotential is analyzed. The odd-degree geopotential coefficients (13, 13), (15, 13), and (17, 13) given by Yionoulis most accurately model the resonance effects on GEOS-II of any of the published sets of 13th-order coefficients. However, this set is not adequate for precision orbit determination; additional even-degree coefficients are required.Values ofC _14,13(=0.57×10^–21) andS _14,13(=6.5×10^–21) to be used with the odd-degree set of Yionoulis were obtained from an analysis of the observed along-track position variation of GEOS-II. These coefficients, when used with those of Yionoulis, yield greatly improved fits to the data and orbital prediction capability. However, further refinement is possible because the small effects of the remaining even-degree resonant terms were not modeled.The composite coefficientsC _13,13(=1.7×10^–20) andS _13,13(=+2.7×10^–20) were obtained under the assumption that the (13, 13) spherical harmonic of the geopotential is responsible for all of the observed along-track variation of GEOS-II due to resonance. The good agreement of these deliberately composite values with some published values ofC _13,13 andS _13,13 suggests that some of the published values may also be composite to some extent.These coefficients are hereinafter referred to as the APL coefficients.     

Preliminary results for RR Lyrae stars and Classical Cepheids from the Vista Magellanic Cloud (VMC) survey

The Vista Magellanic Cloud (VMC, PI M.R. Cioni) survey is collecting K _S -band time series photometry of the system formed by the two Magellanic Clouds (MC) and the “bridge” that connects them. These data are used to build K _S -band light curves of the MC RR Lyrae stars and Classical Cepheids and determine absolute distances and the 3D geometry of the whole system using the K-band period luminosity (PLK _S ), the period–luminosity–color (PLC) and the Wesenhiet relations applicable to these types of variables. As an example of the survey potential we present results from the VMC observations of two fields centered respectively on the South Ecliptic Pole and the 30 Doradus star forming region of the Large Magellanic Cloud. The VMC K _S -band light curves of the RR Lyrae stars in these two regions have very good photometric quality with typical errors for the individual data points in the range of ∼0.02 to 0.05 mag. The Cepheids have excellent light curves (typical errors of ∼0.01 mag). The average K _S magnitudes derived for both types of variables were used to derive PLK _S relations that are in general good agreement within the errors with the literature data, and show a smaller scatter than previous studies.     

Computedn=2 level populations in helium-like ions from Cv to Nixxvii

The population densities of all levels with principal quantum numbern=2 in a number of helium-like ions with nuclear charge numberZ, in the range 6 to 28 have been evaluated as a function of various parameters, i.e., electron temperature,T _e, electron density,N _e, radiation temperature,T _r, dilution factor,W, and of the state of ionization. The spectral line fluxes from all possible radiative transitions from these levels have been calculated for an optically thin plasma. The effects of cascades following collisional excitation of higher levels or radiative and dielectronic recombination have been computed in detail. Innershell ionization of the lithium-like ion to form the helium-like ion in a 2³ S or 2¹ S state has been considered. It can have a strong influence on the forbidden line intensity in a non-equilibrium plasma. Collisional and radiative coupling of levels of the same multiplicity (e.g. 2³ S ₁ and 2³ P _2,1,0) have been considered as a function ofT _e, N_e orT _r, W, respectively. The computations were performed both for stationary and time-varying plasmas. In the latter case strong departures from a stationary ionization equilibrium can significantly alter the line fluxes. A few examples of the results are shown and discussed.     

The curious case of the greenwich faculae

We analyze the record of facular areas compiled by the Royal Greenwich Observatory (RGO) from daily white-light observations between 1874 and 1976. Curiously, the relative amplitudes of the three largest sunspot cycles 17, 18, and 19 in this record are reversed when they are ranked by facular area. We show that this negative correlation arises from a general decrease of the ratioA _F/A _S, of facular to sunspot area, with increasingA _S. Within a given cycle,A _F/A _Sdecreases in active regions of largeA _S, butA _F/A _Sis also lower at allA _S, in cycles of higher peak amplitude inA _S. This decrease ofA _F/A _Sin large spot groups is consistent with its decrease in younger, more active solar-mass stars, and it may explain why stars only slightly more magnetically active than the Sun tend to exhibit much greater variability in broad-band photometry. We suggest that the physical explanation is an increased spatial filling factor of magnetic flux, favoring formation of sunspots over faculae. We also explain why the decrease inA _F/A_Sis not seen in the disc-integrated Ca K plage areas, nor in theF10.7 microwave index, both of which exhibit remarkable linearity when plotted against smoothed sunspot area. This explanation suggests how complementary data on faculae and plages from RGO and Mt. Wilson could be used to improve empirical models of total irradiance variation, extending back to 1874.     

Forbidden sulphur I lines in the solar spectrum

The [SI] lines are due to transitions within the 3s²3p⁴ ground configuration of neutral sulphur. The results are presented from a search for the [Si] lines in the Fraunhofer spectrum. Two identifications are proposed with faint features in the Fraunhofer spectrum: ¹D₂-¹S₀ at = 7725.02 Å and ³P₂-¹D₂ at = 10821.23 Å. Their measured equivalent widths are shown to confirm the value for the solar abundance of sulphur, logN _S = 7.21 (in the scale logN _H = 12.00), which is derived from the permitted high-excitation lines. These lines give the first convincing identification of [Si] lines in an astrophysical source.     

On a relation between the indices of solar activity in the photosphere and the corona

In the first part a new index of solar activity in the photosphere is introduced i.e. the areas index I _a defined with the help of the relation, where A and f are the total areas of the sunspots and faculae respectively corrected for foreshortening.In the second part a relation of the form: is proposed, where S represents the intensity of solar radio-emission in the frequency range 1000 f < 10000 MHz, i _f is the index of solar flares, S ₀o is the corresponding value of s for I _a = 0 and K is a constant.In the third part a relation of the form: is proposed, where I 5303 is the mean intensity of the coronal line 5303 Å for each quarter of the years 1954–1964, n _pf is the corresponding number of proton flares, I ₀ is the value of I ₅₃₀₃ corresponding to I = 0 and K is a constant.     

Free molecular flow of rarefied gas over an oscillating plate under a periodic external force

The free molecular flow over an infinite oscillating plane wall under external periodic force is considered. The Boltzmann equation is solved by using moments method with two-stream distribution functions. The boundary condition is obtained by assuming that the reflection of the particles from the solid surface takes place with complete energy accommodation. An analytical form for the velocity (X) and shear stress (Y) at any point is obtained. The results show that the amplitude of both the velocity change (X ₁) and the shear stress change (Y ₁) due to the periodic external force at the boundary (y=0) is an increasing function of time (t).     

UVbYβ electrophotometry of the RR Lyrae stars

The behaviour of the spectral metallicity parameters S of the RR Lyrae stars in the course of light change is considered. Electrophotometry results of 9 stars of the given class inUVbY are presented. Analysis of the data obtained shows that the variables for which variation of S with the light phase was established do not show any real variations of metallicity indexm ₁.