Spatial correlation of Hα filaments and photospheric velocity

The location of H filaments is compared with maps of the photospheric line of sight velocity V and the magnetic field H . It is found that (1) H filaments are associated with regions of ¦V ¦ 300m s^–1, (2) always both positive as well as negative velocities are present under H structures, (3) stable (long lasting) portion of filaments frequently occur at the position of H = 0 as well as V = 0 lines, (4) this association remains valid for the longitudes less than 50° from central meridian.     

Magnetic and thermal pressures in the solar wind

Explorer 34 solar wind data for the period June to December, 1967 show that(a) The magnetic pressure, P _BB ²/8, and thermal pressure,P _kn _p kTp+n kT+n _e kTe,are variable and positively correlated on a scale of 2 days, but (b) changes in P _b and P _k are anticorrelated on a scale 1 hr (0.01 AU). Thus, dynamical hydromagnetic processes (dv/dto) must occur on the mesoscale, but the solar wind tends to be in equilibrium(P _B+P _Kconstant) on a smaller scale, the microscale. The 3-hr averages show that the most probable value of P _{k/P B} is =1.0±0.1, which implies that the most probable state of the solar wind at 1 AU is not one of equipartition between the thermal energy and magnetic energy. The average total pressure for a given bulk speed(P(V)=P ^k+P _k+P _B) is essentially independent of V, implying that P is not determined by the heating or acceleration mechanisms of the solar wind; the average pressure is P=(2.9±1.5)×10^-10dyne/cm².     

Effects of mass transfer on the unsteady free convection flow past an accelerated vertical porous plate with variable suction

An exact analysis of the effects of mass transfer on the flow of a viscous incompressible fluid past an uniformly accelerated vertical porous and non-porous plate has been presented on taking into account the free convection currents. The results are discussed with the effects of the Grashof number Gr, the modified Grashof number Sc, the Schmidt number Sc, and the suction parametera for Pr (the Prandtl number)=0.71 representating air at 20°C.Nomenclature a suction parameter - C species concentration - C species concentration at the free stream - g acceleration due gravity - Gc modified Grashof number (vg^*(C –C )/U ₀ ³ ) - Pr Prandtl number (C _p/K) - T temperature of the fluid near the plate - T dimensionless temperature near the plate ((T-T )/(T -T )) - U(t) dimensionless velocity of the plate (U/U ₀) - v normal velocity component - v ₀ suction/injection velocity - x, y coordinate along and normal to the plate - v kinematic viscosity (/gr) - C _p specific heat at constant pressure - C _w species concentration at the plate - C non-dimensional species concentration ((C-C )/(C _w -C )) - Gr Grashof number (g(T _w -T )/U ₀ ³ ) - D chemical molecular diffusivity - K thermal conductivity - Sc Schmidt number (/D) - T _w temperature of the plate - T free stream temperature - t time variable - t dimensionless time (tU ₀ ² /) - U ₀ reference velocity - u velocity of the fluid near the plate - u non-dimensional velocity (u/U ₀) - v dimensionless velocity (v/U ₀) - v ₀ non-dimensionalv ₀ (v ₀ /U₀)=–at^–1/2 - y dimensionless ordinate (yU ₀/) - density of the fluid - coefficient of viscosity     

Observed oddities in the lines H,K, b and Hβ

We compare microphotometer intensity traces perpendicular to dispersion in simultaneous spectrograms of good spatial resolution traced at various 's in each of the lines. Cross correlations between the different traces show the following: (a) For each _K there is a corresponding _{b 1}at which the coefficient of correlation, r, is a maximum, usually > 0.8. (b) No such high correlations are found between H and H. (c) Comparison of traces in the continuum and at all observed 's in K, H, b₁, b₂ show a range of 's in each line over which r is very significantly negative, while H shows no such peculiarity.     

The relationship between r.m.s. doppler velocities and temperature in the solar transition region

An attempt is made in this paper to determine the coefficient a in a power-law relationship of the form V ~T between the r.m.s. velocity fluctuation, V for raster images with 3 resolution and the temperature, T of line formation using SMM solar data. For T between 8000 and 10⁵ K, the data suggest a best fit with 3/4 < 1. It is argued, however, that unresolved fine structure tends to reduce the observed value of V and that higher resolution data may yield different values for . Skylab data have shown that the non-thermal line broadening velocity, , is proportional to T ^1/2. Also, for all temperatures less than 10⁵ K, V . This latter result, however, is again dependent on spatial resolution and may not be true in observations made with sufficient spatial resolution. The magnitudes of both V and indicate that bulk motions play important roles in the structure of the solar atmosphere as well as in its energy and momentum balance. It is important, therefore, to identify the true nature of such motions with better accuracy than is possible with currently available data.The National Center for Atmospheric Research is sponsored by the National Science Foundation.     

Doubly averaged effect of the Moon and Sun on a high altitude Earth satellite orbit

Infinite series expansions are obtained for the doubly averaged effects of the Moon and Sun on a high altitude Earth satellite, and the results used to interpret numerically integrated examples. New in this paper are: (1) both sublunar and translunar satellites are considered; (2) analytic expansions include all powers in the satellite and perturbing body semi-major axes; (3) the fact that retrograde orbits have more benign eccentricity behavior than direct orbits should be exploited for high altitude satellite systems; and (4) near circular orbits can be maintained with small expenditures of fuel in the face of an exponential driving force one forI _ab, whereI _b=180°–I _a andI _a is somewhat less than 39.2° for sublunar orbits and somewhat greater than 39.2° for translunar orbits.Nomenclature a semi-major axis - A _lk coefficient defined in Equation (11) - B _lk coefficient defined in Equation (24) - C _km coefficient defined in Equation (25) - D, E, F coefficients in Equations (38), (39) - e eccentricity - H _k expression defined in Equation (34) - expression defined in Equation (35) - I inclination of satellite orbit on lunar (or solar) ring plane - J ₂ coefficient of second harmonic of Earth's gravitational potential (1082.637×10^–6 R _E ² ) - K _k, L_k, M_k expressions in Section 4 - expressions in Section 4 - p=a(1–e ²) semi-latus rectum - P _l Legendre polynomial of degreel - q argument of Legendre polynomial - radial distance of satellite - R _E Earth equatorial radius (6378.16 km) - R, S, W perturbing accelerations in the radial, tangential and orbit normal directions - syn synchronous orbit radius (42 164.2 km=6.6107R _E) - t time - T satellite orbital period - T orbital period of perturbing body (Moon) - T _e period of long periodic oscillations ine for |I|<I _a - T _s synodic period - U gravitational potential of lunar (or solar) ring - x, y, z Cartesian coordinates of a satellite with (x, y) being the ring plane - coefficient defined in Equation (20) - average change in orbital element over one orbit (=a, e, I, , ) - ₁,₂₃ unit vectors in thex, y, z coordinate directions - _r , _s , _w unit vectors in the radial, tangential and orbit normal directions - =+ angle along the orbital plane from the ascending node on the ring plane to the true position of the satellite - angle around the ring - gravitational constant times mass of Earth (3.986 013×10⁵ km s^–2) - gravitational constant times mass of Moon (or Sun) - _m gravitational constant times mass of Moon (/81.301) - _s gravitational constant time mass of Sun (332 946 ) - ratio of the circumference of a circle to its diameter - radius of lunar (or solar) ring - _m radius of lunar ring (60.2665R _E) - _s radius of solar ring (23455R _E) - true anomaly - argument of perigee - ₀ initial value of - _i critical value of in quadranti(i=1, 2, 3, 4) - longitude of ascending node on ring plane This work was sponsored by the Department of the Air Force.     

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 .     

A Study of the Rotation of the Solar Corona

Synoptic photoelectric observations of the coronal Fexiv and Fex emission lines at 530.3 nm and 637.4 nm, respectively, are analyzed to study the rotational behavior of the solar corona as a function of latitude, height, time and temperature between 1976 (1983 for Fex) and 2001. An earlier similar analysis of the Fexiv data at 1.15 R over only one 11-year solar activity cycle (Sime, Fisher, and Altrock, 1989, Astrophys. J. 336, 454) found suggestions of solar-cycle variations in the differential (latitude-dependent) rotation. These results are tested over the longer epoch now available. In addition, the new Fexiv 1.15 R results are compared with those at 1.25 R and with results from the Fex line. I find that for long-term averages, both ions show a weakly-differential rotation period that may peak near 80° latitude and then decrease to the poles. However, this high-latitude peak may be due to sensing low-latitude streamers at higher latitudes. There is an indication that the Fexiv rotation period may increase with height between 40° and 70° latitude. There is also some indication that Fex may be rotating slower than Fexiv in the mid-latitude range. This could indicate that structures with lower temperatures rotate at a slower rate. As found in the earlier study, there is very good evidence for solar-cycle-related variation in the rotation of Fexiv. At latitudes up to about 60°, the rotation varies from essentially rigid (latitude-independent) near solar minimum to differential in the rising phase of the cycle at both 1.15 R and 1.25 R . At latitudes above 60°, the rotation at 1.15 R appears to be nearly rigid in the rising phase and strongly differential near solar minimum, almost exactly out of phase with the low-latitude variation.     

(Super) cosmological solution for the Kasner model

In the theory of supergravity (N=1), the supersymmetric version of general relativity, and for the Kasner cosmological model (Bianchi type I) we find a non-trivial solution (for the metric and spinor-vector) under the most simple assumption =₁₁ + ₂₂; ₁₂+₂₁=0 and for a special choosed gaugeN=1,N ^j=0, ₀=0. This method could be also applied to other cosmological metrics and extended to enlarged Grassmann basis.O. Obregón was partially supported by the Alexander von Humboldt Stiftung.     

О влиянии флукаций электронной концентрации на меру дисперсии и мету вращения

, (DM) (RM). , DM RM N _e = n _e ds. M _e = n _e H cos ds ; . Lerche (1970a, b) , DM RM N _e M _e . .     

О колебаниях хвоста магнитосферы в приБлижении квазигидро динамики

-- () ., , , , , . , , . , .     

Kelvin-Helmholtz instability of composite plasma in an oblique magnetic field with resistivity

Analytic structure of high-density steady isothermal spheres is discussed using the TOV equation of hydrostatic equilibrium which satisfies an equation of state of the kind:P = K _g , = _g c ².Approximate analytical solutions to the Tolman-Oppenheimer-Volkoff (TOV) equations of hydrostatic equilibrium in (, ), (,U) and (u, v) phase planes in concise and simple form useful for short computer programmes or on small calculator, have been given. In Figures 1, 2, and 3, respectively, we display the qualitative behaviours of the ratio of gas density _g to the central density _gc , _g / _gc ; pressureP to the _gc ,P/ _gc ; and the metric componente ^–, for three representative general relativistic (GR) isothermal configurations =0.1, 0.2, and 0.3. Figure 4 shows the solution curve (, ) for =0.1, 0.2, and 0.3 (=0 represents the classical (Newtonian) curve). Numerical values of physical quantitiesv (=4r ² P ^*(r)), in steps ofu (=M(r)/r)=0.03, and the mass functionU, in steps of =0.2 (dimensionless radial distance), are given, respectively, in Tables I and II. Other interesting features of the configurations, such as ratio of gravitational radius 2GM/c ² to the coordinate radiusR, mass distributionM(r)/M, pressure (or density) distributionP/P _c , binding energy (B.E.), etc., have also been incorporated in the text. It has further been shown that velocity of sound inside the configurations is always less than the velocity of light.Part of the work done at Azerbaijan State University, Baku, U.S.S.R., and Mosul University, Mosul, Iraq, 1985-1986     

Stability of the libration points of a rotating triaxial ellipsoid

The problem of stability of the equilibrium points (the libration points) in the problem of motion of a mass point in the neighbourhood of a rotating triaxial ellipsoid is investigated in the strict sense.In the plane of parameters, depending on the form and dynamical characteristics of the ellipsoids, the regions of stability and instability of the libration points are obtained.It is shown that the libration points of the ellipsoids, the form and dynamical characteristics of which are close to the planets of the solar system, are stable.

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( ) . , , . , , , .

     

Absolute and relative amplitudes of variations in radius of classical cepheids

On the basis of observational data for the absolute R and relative R/R amplitudes of variations in radius of galactic classical cepheids (55 stars from Balona and Stobie (1979) and 30 stars from Sollazzoet al. (1981)), four kinds of empirical linear relations are obtained: log(P V)–logR, logP–logR, log(P V)–log(R/R), and logP–log(R/R);P, R, and V are the pulsation periods, the mean stellar radii, and the amplitudes of light variations, respectively. Three groups of stars are considered: short-period cepheids (SPC)-with logP1.1; long-period cepheids (LPC)-with logP>1.1; and s-cepheids (sC). Both the R values and the R/R values increase withP andP V, for a given group of variables. A comparison is performed with our results obtained from data in other sources (Kurochkin, 1966; Gieren, 1982; etc.). The investigated relations can be applied for determining R and R/R of galactic classical cepheids, by using their observedP and V. All studied galactic classical cepheids have R/R<0.35, R<10R for SPC and 10R <R60R for LPC. The sC have smaller R and R/R values than other classical cepheids, at the same periods (the difference is about 2 times for R and 1.4–2.8 times for R/R); the studied sC have R/R in the range 0.025–0.075 and R in the range 1–3R (only Y Oph has R8R ).     

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.     

A note on the correspondence between Mathieu's transformations and redundant variables in lagrangian mechanics

It is shown that, to any change of variables:q _i=q_i(r, t) (i=1,..., n; =1,...,n+m; mn) increasing the number of variables, it is possible to associate a Mathieu's transformation and conversely. The results are applied to the theory of the osculating plane of motion.

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Resumé On montre qu'à toute transformation:q _i=q_i(r, t)(i=1,..., n; =1,...,n+m; mn) augmentant le nombre de variables, on peut associer une transformation de Mathieu et réciproquement. Les résultats sont appliqués à la théorie du plan osculateur du mouvement.

     

Predicting the maximum amplitude for the sunspot cycle from the rate of rise in sunspot number

Examined are associational aspects as they relate the maximum amplitude R _M for the sunspot cycle to the rate of rise R _t during the ascending phase, where R _M is the smoothed sunspot number at cycle maximum and R _t is the sum of the monthly mean sunspot numbers for selected 6-month intervals (t) measured from cycle onset. One finds that, prior to about 2 yr into the cycle, the rate of rise is not a reliable predictor for maximum amplitude. Only during the latter half of the ascent do the fits display strong linearity, having a coefficient of correlation r 0.9 and a standard error S _yx 20. During the first four intervals, the expected R _M and the observed R _M were found to differ by no more than 20 units of smoothed sunspot number only 25, 42, 50, and 58 % of the time; during the latter four intervals, they differed by no more than 20 units 67, 83, 92, and 100% of the time.     

Индуцированное комптоновское рассеяние изотропного излучения релятивистскими электронами

, kT _b mc ² . . , , . E ^–5, - E ², mc ²(kT /mc ²)^1/7. , (>2.10⁵ cm ^–3) . , -, , .     

The interpretation of absorption-line shifts in the solar spectrum

The shifts of Fraunhofer lines of different chemical elements in a homogeneous medium with a plane monochromatic progressive adiabatic sound waves are derived. The calculations indicate that lines of neutral elements (6 ₀ 14) with lower excitation potentials ₀ i= 0–2 eV are red shifted, those with excitation potential ₀ i= 4–12 eV are blue shifted, and with ₀ i= 3 eV are both blue and red shifted. The lines of ions are shifted toward the blue. The shifts of Fraunhofer lines are found to decrease from the centre of the solar disk to the limb. These results agree qualitatively and quantitatively with observations.     

Об устойчивости лагранжевых решений пространственной эллиптической задачи трех тел

. . ,e, , . . e, . , .

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Stability of the librational triangular points of the three-dimensional elliptic restricted three-body problem is studied. The problem is solved in the non-linear statement at the small values of eccentricity.For all values ofe, , besides ones which correspond to the resonances of the third and the fourth order the librational points are stable taking into account the terms up to the fourth order in the normal form of the Hamiltonian function of the perturbed motion.At sufficiently smalle and the non-stability in sense of Liapunov has been proved. The approximate equations of the boundary of the stability area in the planee, has been obtained. The cause of the non-stability is an equality of the rotational period of the principal attracting masses in the elliptic orbit and the period of oscillation of indefinitely small mass along the direction perpendicular to the plane of their motion.