The Energy Equation in the Lower Solar Convection Zone

As a consequence of the Taylor–Proudman balance, a balance between the pressure, Coriolis and buoyancy forces in the radial and latitudinal momentum equations (that is expected to be amply satisfied in the lower solar convection zone), the superadiabatic gradient is determined by the rotation law and by an unspecified function of r, say, S(r), where r is the radial coordinate. If the rotation law and S(r) are known, then the solution of the energy equation, performed in this paper in the framework of the ML formalism, leads to a knowledge of the Reynolds stresses, convective fluxes, and meridional motions. The ML-formalism is an extension of the mixing length theory to rotating convection zones, and the calculations also involve the azimuthal momentum equation, from which an expression for the meridional motions in terms of the Reynolds stresses can be derived. The meridional motions are expanded as U _r(r,)=P ₂(cos)₂(r)/r ²+P ₄(cos)₄(r)/r ² +..., and a corresponding equation for U (r,). Here is the polar angle, is the density, and P ₂(cos), P ₄(cos) are Legendre polynomials. A good approximation to the meridional motion is obtained by setting ₄(r)=–H₂(r) with H–1.6, a constant. The value of ₂(r) is negative, i.e., the P ₂ flow rises at the equator and sinks at the poles. For the value of H obtained in the numerical calculations, the meridional motions have a narrow countercell at the poles, and the convective flux has a relative maximum at the poles, a minimum at mid latitudes and a larger maximum at the equator. Both results are in agreement with the observations.     

The implications of intrinsic luminosity evolution on the value of the density parameter (Ω) and the evolution of radio sizes of radio galaxies and quasars

The implications of the intrinsic luminosity evolution with cosmological epoch on the value of the density parameter () and evolution of radio sizes of extragalactic radio sources have been considered. It is shown that a power law evolution model of the sortP (1 +z) can be used to contrain the value of . In the presence of a strong luminosity evolution, the model yields an upper limit of 0.5.It is also shown that the angular diameter redshift ( – z) relation for quasars can be interpreted in terms of the assumed luminosity evolution combined with a luminosity-linear size correlation with little or no linear size evolution required. On the other hand, strong linear size evolution is needed to explain the – z data for radio galaxies independent of luminosity.     

Geometrical dynamics: A new approach to periodic orbits aroundL 4

Geometrical dynamics is the study of the geometry of the orbits in configuration space of a dynamical system without reference to the system's motion in time.Generalized coordinates for the circular restricted problem of three bodies are taken as polar coordinatesr, centered at the triangular libration pointL ₄. A time-independent nonlinear second order ordinary differential equation forr as a function of is derived. Approximations to periodic solutions are obtained by perturbations and Fourier series.     

Non-linear analysis of the stability of the Screw Pinch

Non-linear effects on the stability of the Screw Pinch in cylindrical system surrounded by a uniform pitch magnetic field in an incompressible pressureless plasma have been studied. A linear dispersion relation governing the stability of interface has been obtained with the help of normal mode analysis. Perturbation technique has been used to obtain the non-linear Schrödinger equation for the time variation of amplitudeA(t) which evolves according to . This can lead to non-linear stabilization, explosive instability or eventual decay, depending on the sign of . The whole calculations have been made form=1, kink modes in a sharp boundary plasma pinch. Non-linear analysis for -pinch (0) andz-pinch () have also been discussed in detail. It has been found that non-linear theory have a destabilizing influence on both - andz-pinches.     

Hα line emission and infrared excess in Be stars

The H observations of a selected sample of bright Be stars are presented. The available infrared observations at K band (2.2 m) of these stars have been used to find the infrared excess emission. The analysis of the combined data show thatL _H, the luminosity of the H emission line, is proportional toL _IR, the luminosity of the infrared excess emission. The linear correlation betweenL _IR andL _H shows that both the infrared excess and the H line originate in a common region. It is also detected that the infrared excess emission is produced throughout the whole envelope whereas the H is emitted in some defined region of the circumstellar (CS) envelope.     

The determination of coronal potential magnetic fields using line-of-sight boundary conditions

Previous efforts to construct solar coronal fields using surface magnetograph data have generally employed a least squares minimization technique in order to determine the spherical harmonic expansion coefficients of the magnetic scalar potential. Provided there is no source surface high up in the corona, we show that knowledge of the line-of-sight component of the surface magnetic field, B _i = B _r sin + B cos , is sufficient to uniquely determine the potential coronal magnetic field by an explicit construction of the magnetic scalar potential for an arbitrary B _l (, ).The National Center for Atmospheric Research is sponsored by the National Science Foundation.     

The proper motion VS redshift relation for superluminal radio sources

Two models for superluminal radio sources predict sharp lower bounds for the apparent velocities of separation. The light echo model predicts a minimum velocityv _min=2c, and the dipole field model predictsv _min=4.446c. Yahil (1979) has suggested that, if either of these models is correct, thenv _min provides a standard velocity which can be used to determine the cosmological parametersH andq ₀. This is accomplished by estimating a lower envelope for the proper motion vs redshift relation. Yahil also argued that the procedure could easily be generalized to include a nonzero cosmical constant . We derive the formulas relating the proper motion to the redshiftz in a Friedmann universe with a nonzero . We show that the determination of a lower envelope for a given sample of measured points yields an estimate of the angle of inclination _i for each source in the sample. We formulate the estimation of the lower envelope as a constrained maximum likelihood problem with the constraints specified by the expected value of the largest order statistic for the estimated _i . We solve this problem numerically using an off-the-shelf nonlinearly constrained nonlinear optimization program from the NAg library. Assuming =0, we apply the estimation procedure to a sample of 27 sources with measured values , using both the light echo and the dipole field models. The fits giveH=103 km s^–1 Mpc^–1 for the light echo model andH=46 km s^–1 Mpc^–1 for the dipole field model. In both cases the fits giveq ₀=0.4, but the uncertainty in this result is too large to rule out the possibility thatq ₀>0.5. When is allowed to be a free parameter, we obtainH=105 km s^–1 Mpc^–1 for the light echo model andH=47 km s^–1 Mpc^–1 for the dipole field model. In both cases the fits giveq ₀=–1 and /H ₀ ² =6.7, but no significance can be attached to these results because of the paucity of measured data at hight redshifts. For all of the fits, we compute the corresponding estimates of the _i and compare the cumulative distribution of these values with that expected from a sample of randomly oriented sources. In all cases we find a large excess of sources at low-inclination angles (high apparent velocities). The expected selection effect would produce such an excess, but the excess is large enough to suggest a strong contamination of the sample by relativistic beam sources which would only be seen at low inclination angles.Applied Research Corporation     

Linear current instability in loop prominences

By use of the dispersion equation given by Song, Wu, and Dryer (1987) for a cylinder plasma with mass motion and gravity included, we investigate the linear current instabilities developed in loop prominences. The results indicate that the mode of linear instability depends mainly on whetherv _s ² > or not, wherev _s is the sonic velocity at heightz, =GM/(R +z) is the gravity potential,G the gravitational constant,M andR the mass and the radius of the Sun respectively. Ifv _s ² > , then the sausage instability will be dominant. Otherwise, the kink instability will be more important. A possible explanation of knot structure, which appears sometimes in solar loop prominences has been given.     

Implications of a strongly peaked polar magnetic field

Using the flux-transport equation in the absence of sources, we study the relation between a highly peaked polar magnetic field and the poleward meridional flow that concentrates it. If the maximum flow speed _m greatly exceeds the effective diffusion speed /R, then the field has a quasi-equilibrium configuration in which the poleward convection of flux via meridional flow approximately balances the equatorward spreading via supergranular diffusion. In this case, the flow speed () and the magnetic field B() are related by the steady-state approximation () (/R)B()/B() over a wide range of colatitudes from the poles to midlatitudes. In particular, a general flow profile of the form sin ^p cos ^q which peaks near the equator (q p) will correspond to a cos ⁿ magnetic field at high latitudes only if p = 1 and _m = n /R. Recent measurements of n 8 and 600 km² s^–1 would then give _m 7 m s^–1.     

Effects of hall current on the hydromagnetic free convection with mass transfer in a rotating fluid

An exact analysis of Hall current on hydromagnetic free convection with mass transfer in a conducting liquid past an infinite vertical porous plate in a rotating fluid has been presented. Exact solution for the velocity field has been obtained and the effects ofm (Hall parameter),E (Ekman number), andS _c (Schmidt number) on the velocity field have been discussed.Nomenclature C species concentration - C _w concentration at the porous plate - C species concentration at infinity - C _p specific heat at constant pressure - D chemical molecular diffusivity - g acceleration due to gravity - E Ekman number - G Grashof number - H ₀ applied magnetic field - j _x, j_y, j_z components of the current densityJ - k thermal conductivity - M Hartman number - m Hall parameter - P Prandtl number - Q heat flux per unit area - S _c Sehmidt number - T temperature of the fluid near the plate - T _w temperature of the plate - T temperature of the fluid in the free-stream - u, v, w components of the velocity fieldq, - U uniform free stream velocity - w ₀ suction velocity - x, y, z Cartesian coordinates - Z dimensionless coordinate normal to the plate. Greek symbols coefficient of volume expansion - ^* coefficient of expansion with concentration - _e cyclotron frequency - dimensionless temperature - ^* dimensionless concentration - v kinematic viscosity - density of the fluid in the boundary layer - coefficient of viscosity - _e magnetic permeability - angular velocity - electrical conductivity of the fluid - _e electron collision time - _u skin-friction in the direction ofu - _v skin-friction in the direction ofv     

Satellite attitude acquisition by momentum transfer-the controlled wheel speed method

An implementation of the momentum transfer method for spacecraft attitude acquisition of momentum wheel stabilized geostationary satellites is presented, in which the wheel speed is varied in a predeterminable manner to reduce the nutation usually associated with the method. The implementation is found to be capable of achieving the transfer to the desired zero nutation end point with 5° to 20° of residual nutation in practical situations without additional nutation damping. The transfer time is typically 10–30 min. The implementation is described in terms of the momentum sphere and energy ellipsoid. The detailed functional dynamics and parametric relationships are given in terms of phase planes and elliptic integral solutions. Feasibility of the implementation is shown to be dependent on the moment of inertia configuration and the degree to which tolerances on moments of inertia, satellite spin rate, and wheel speed are predeterminable.Nomenclature A, B, C Principal moments of inertia of the total spacecraft - b ₁,b ₂,b ₃ Unit vectors parallel to principal axes - E, E(t) Energy of the spacecraft body (excludes the spin energy of momentum wheel) - E ₀ Initial energy of the spacecraft (wheel not spinning) - E _c A constant arbitrary value ofE(t) - E _i Energy after an impulse which causes to equal zero, Equation (13) - E ₂ The constant value ofE during Stage 2 - E ₃ Energy at the end of Stage 3 - E _s The separatrix value ofE, i.e.E when =0 - H ₀,H ₀ Angular momentum vector of the total spacecraft - H _x ,H _y ,H _z Variable components ofH ₀ resolved with respect tob ₁,b ₂, andb ₃ - J Moment of inertia of the momentum wheel - L The slope of the wheel speed profile, Equation (31) - L _y Momentum wheel torque - m Direction cosine of the angle, , betweenH ₀ andb ₂ - m ₁,m ₂ Constant values ofm - O The centre of the momentum sphere - Oxyz Spacecraft coordinate axes - P Represents a state on the momentum sphere and energy ellipsoid - s Momentum wheel speed - s ₂ Constant value ofs during Stage 2 - s _i Wheel speed after an impulse which causes to be zero - t Time - t ₁, t ₂, t ₃ Elapsed time for Stages 1, 2, and 3 respectively - ₁ to ₄ Roots of Equation (19) (poles on the phase plane) - Parameter defined in Equation (9) - cos^–1 m - ₂ The value of at the termination of Stage 2 - _min The minimum of the periodic function (t) (during Stage 2) - _x , _y , _z Angular rates of spacecraft body - ₀ Initial value of _z - K _m Curvature of the momentum sphere - K _xy ,K _yz Curvatures of the principal lines of the energy ellipsoid at (O,H ₀,O), in theOH _x H _y ) and (OH _y H _z ) planes respectively     

Redshift difference between emission and absorption lines of QSOs

Distribution of the redshift difference (z) between emission and absorption lines of QSOs is half-gaussian. Also, the quantity z increases with increase in emission line redshift (z _em). The correlation between the two quantities (z andz _em) is statistically significant. The interpretation of the results indicate that the co-moving density of absorbing clouds decreases with redshift and that the absorbing clouds are associated with the QSOs rather than completely unrelated intervening material.     

A new type of a photoelectric magnetograph

The electro-optic deflector as an analyzer of circular polarization in the photoelectric magnetograph is described. The electro-optic deflector consists of an electro-optic crystal and a polarizing beamsplitter. The plane bifurcation of this beamsplitter coincides with the spectrograph dispersion direction. The beamsplitter bifurcates a spectral line in two components. The distance between them is ₀. The photometer slit is situated between these components. Both components of Zeeman splitting fall on the photometer slit but the distance between them varies from ₀ + 2 _H to ₀ – 2 _H (where _H is the Zeeman splitting) with the electric voltage frequency applied to the electro-optic crystal. The intensity variations at the photometer slit are proportional to 4 _H .     

Modelling of the effect of current-carrying jets on the temperature of an astrophysical surrounding

Numerical solution of the effect of current-carrying jets on the temperature of an astrophysical surrounding is carried out using classical magnetohydrodynamic equations. Under the assumption of small hydrodynamic and magnetic Reynolds numbers and invoking a jet magnetic field intensityB , which confines high pressure jets along thez-axis, a non-linear equation is generated and solved by asymptotic approximation. It is found that when the field intensity is large, the temperature of the surrounding is small and vice-versa. The problem is of interest in the astrophysical studies of current-carrying jets or magnetised radio jets.     

Study of the nonradial directional property of the rays of the streamer belt and chains in the solar corona

Based on analyzing corona images taken by the LASCO C1, C2, and C3 instruments, a study is made of the behavior of the streamer belt spanning one half of the 1996–2001 cycle of solar activity, from minimum to maximum activity, in the absence of coronal mass ejections. It is shown that: (1) The position of the streamer belt relative to the solar equator is generally characterized by two angles: _o and _E, where _o is the latitudinal position (near the solar surface) of the middle of the base of the helmet, the top of which gradually transforms to a ray of the streamer belt with a further distance from the Sun, and _E is the latitude of this ray for R>5–6 R from the Sun's center where the ray becomes radial. (2) Only rays lying at some of the selected latitudes _o retain their radial orientation (_oE) throughout their extent. Namely: _o0° (equator), _o±90° (north and south poles), and the angle _o lying in the range ±(65°–75°) in the N- and S-hemispheres. (3) A deviation of rays from their radial orientation in the direction normal to the surface of the streamer belt occurs: for latitudes _o<|65°–75°| toward the equator (>0°) reaching a maximum in the N and S hemispheres, respectively, when _OM40°, and _OM–42° for latitudes _o>|65°–75°| toward the pole (<0°). The regularities obtained here are a numerical test which can be used to assess of the validity of the theory for describing the behavior of the Sun's quasi-stationary corona over a cycle of solar activity.     

On symmetrical planetary corotations

Exact corotations are equilibrium points in the phase space of the asteroidal elliptic restricted problem of three bodies averaged over the synodic period, at a mean-motions resonance. If the resonant critical angle is =(p+q) _jup –p–q, exact corotations are double resonant motions defined by the conditionsd/dt=0 andd(– _jup )/dt=0. The first condition is characteristic of the periods resonance(p + q) : p and the second one is a secular resonance equivalent to that usually known as thev ₅-resonance. This paper presents the symmetric solutions =0 (mod ), = _jup (mod ). Corotations have a coherence property which is unique in non-collisional Celestial Mechanics: An elementary calculation shows that, in the neighbourhood of these solutions, the motions cluster aroundp independent longitude values and are, in each cluster, as close together as and are close to the equilibrium values.     

Macro-and micro-turbulent filter functions for weak lines in stellar atmospheres

Following a similar discussion given earlier for the solar case (De Jager, 1972) we compute in this paper spectral line profiles for the spatial wavelengths in which a stellar motion field can be decomposed, and thereafter the macro-and micro-turbulent filter functionsf _M(k) andf (k), where is the optical scale height andf ²(k) dk the fraction of the energy of the turbulent motions between wavenumbersk andk+dk of the spectrum of turbulence that contributes to either kind of turbulence. If micro-and macro-turbulent velocity components are known for a certain star, and if the spectrum of turbulence is sharp enough, the ratiof _M/f would enable one to derive the average size of the turbulent elements in the star's atmosphere. The computations apply to weak lines in idealized stellar atmospheres, and refer to two cases: isotropic turbulence, and radial pulsations. These filters can be suitably used in a diagnostic method for the analysis of the motion field in the solar and stellar atmospheres. Some examples of applications to stars of very different kinds are given.     

Expanding and shearing magneto-viscous fluid cosmological model in general relativity

The object of this paper is to investigate the behavior of a magnetic field in a viscous fluid cosmological model. It has been assumed that the expansion () is proportional to the eigenvalue ₁ of the shear tensor _i ^j and the coefficient of shearing viscosity is proportional to the scalar of expansion. The paper also discusses the behavior of the model when the magnetic field tends to zero and comments on some other physical properties.     

Evolution and nature of north-south asymmetry in the heliospheric current sheet

The nature and evolution of north-south asymmetry in the heliospheric current sheet (HCS) has been investigated using solar and interplanetary magnetic field (IMF) observations for the past few solar cycles. The mean heliographic latitude of the HCS (averaged over the solar longitude) a ₀ is found to be non-zero during many solar rotations indicating that the large-scale solar magnetic field is more ordered in a system where the origin is shifted away from the centre of the Sun. We have shown that the asymmetry in HCS manifests in different forms depending on the transition heliographic latitude of the reversal of dominant polarity of the IMF ( _T) and the difference in the maximum latitudinal extension of the HCS in the two solar hemispheres (). The classification of the observed asymmetry during 1971–1985 and its effect on IMF observations near Earth has been studied. We have also inferred the sign of _T during 1947–1971 using inferred IMF polarity data. The observed sign reversals of _T suggest the importance of periodicities less than the solar cycle period to be associated with the evolution of asymmetry in HCS. Asymmetry in sunspot activity about the solar equator does not seem to relate consistently well with the asymmetry in HCS about the heliographic equator.     

Quantitative analysis and spectral variation of the Ap star HD 151 199

The radial velocity, intensity variations of the Caii line and chemical composition of the suspected magnetic star HD 151 199 have been studied using three 9.6 A/mm and twenty-one 40 A/mm dispersion spectrograms which were taken at St. Michel and Asiago Observatories respectively. The radial velocity and the intensity of the Caii K line suggest a variation with a 6.143 day period. The range is about 40 km/sec for the radial velocity and the K line changes in intensity by 50%. Preliminary results of the photometric data in the Geneva system show a similar trend of variation in (B ₂–B ₁) with the same period. H and H contours and the Balmer discontinuity give _eff=0.50 and logg=4. The most probable microturbulence is found to be 6.4 km/sec. The excitation temperature, _exc=0.50, is derived from the Fe lines and adopted for the other elements as well. A quantitative analysis by curve of growth and weighting function method, using Mihalas and Conti's atmospherical models was made. HD 151 199 shows an overabundance of Ca, Sr, Ba, by factors of 2, 40, and 5 with respect to 30 L Mi. Euii is probably overabundant also but it is not possible to give this element a numerical value. The other elements seem to be normal.