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.     

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     

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     

Effects of metal abundances on the evolutionary period changes of classical Cepheids

Some peculiarities in the behaviour of a model self-gravitating system described by hydrodynamical equations and isothermal equation of state connected with the presence of thermodynamical fluctuations in real systems were investigated in numerical experiment. The values of density and velocity , , respectively, were computed by numerical code perturbed on each time-step and in each computational cell by random values , for modeling such fluctuations. Perturbed values _i = _i + _i ,v _i = _i + v _i were used to initiate the next step of computations. This procedure is equivalent to an introduction into original hydrodynamical equations of Langevin sources which are random functions. It is shown that these small fluctuations (= v =0,² =v ² = 10^–8) grow many times in marginally-stable state.     

The peculiarities of diffusion of the galactic cosmic rays at low energies

I give an interpretation of a result of Simpsonet al. (1988) on the variation with kinetic energyT _i of the mean pathlengthX _m (T _i ) of the galactic cosmic rays (CGRs) in the range 0.1T _i 10.0 GeV nucl^–1. I argue that the data onX _m (T _i ) may be interpreted in terms of a model of GCR diffusion on the one-dimensional Alfvén-wave turbulence, having a cutoff in the spectrum at frequencies _h , where _h is the proton gyrofrequency. The cutoff results in changing of the character of variation of the GCR diffusion coefficientD(T _i )T ^a in the rangeT _i 1 GeV nucl^–1 towards some more complicated variation at 0.1T _i 1.0 GeV nucl^–1 due to the peculiarities of the pitch-angle scattering at 90⁰.     

О колебаниях хвоста магнитосферы в приБлижении квазигидро динамики

-- () ., , , , , . , , . , .     

Pulsar dispersion measures and the mean and mean-squared interstellar electron density

Theoretical distributions of pulsar dispersion measures (times sinb ^II) are computed for various assumed pulsar spatial distributions above (and below) the galactic plane, assuming a distribution for the ionized gas. The statistics on the twelve high-latitude pulsars lead to the conclusion that the pulsar distribution inz is at least as broad as the distribution of the ionized gas. The value derived for the local mean interstellar electron density in the galactic plane is 0.12 cm^–3 and is interpreted to be due to a uniform ionized intercloud medium.Interstellar absorption of radio waves at low frequencies and cosmic X-rays at low energies are considered with regard to irregularities in the distribution of ionized gas. It is shown that if the obervations are made with a wide angle receiver the effective absorption optical deph is –²/2 where is the mean value and is the dispersion in . This relation assumes is much larger than . Analysis of recent low-frequency radio measurements from a satellite-borne receiver, however, leads to the conclusion that effects of irregulatirities are large.     

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.     

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.     

The configuration of a thin,rotating self-similar disk in general relativity

Einstein's equations for a rotating pressure-free space-time are reduced to a system of four first-order non-linear ordinary differential equations in one self-similar dimensionless variable. Numerical results are given for the vacuum solution. A compatible thin disk can be specified by a surface density and an angular velocity . Self-similarity as a statement of the absence of scales implies that and can be written as=c ²/4Gr, =c/r, and demands that and be pure numbers.     

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.

     

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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( ) . , , . , , , .

     

Electromagnetic velocity gradient instabilities in the magnetosphere

The velocity gradients of the contrastreaming electron beams observed in the Earth's magnetosphere can excite three types of ordinary mode instabilities, namely (i) B-resonance electron instability, (ii) ion cyclotron instability, and (iii) unmagnetized ion instability. The B-resonance electron instability occurs at small values of the shear parameter 10^–4<S<10^–3, whereS = [(1/e){dU _o(x)}/(dx)] (U ₀(x) and _e being the streaming velocity of the electron beams and the electron cyclotron frequency, respectively). Near the equatorial plane of the bouncing electron beams region, this instability can generate electromagnetic waves having frequenciesf(0.045–0.2) Hz and wavelentghs (0.5–10)km, and the wave magnetic field is polarised in a radial direction. This instability can also occur in the plasma sheet region during the earthwards and tailwards plasma flows events and can generate waves, with wave magnetic field polarised along north-south direction, in the frequency rangef(0.007–0.02) Hz with (10–100)km nearR=–35R _E . For 10^–3<S<10^–2, the ion cyclotron instability is excited and it can generate waves up to 5th harmonic or so of ion cyclotron frequency. ForS>10^–2, the unmagnetized ion instability is excited which can generate electromagnetic waves having frequences from 5 to 50 Hz and typical wavelengths (0.5–6)km. The growth rates of all the three velocity shear driven instabilities are reduced in the presence of cold background plasma. The turbulence generated by these instabilities may give rise to enhanced effective electron-electron and electron-ion collisions and broaden the bouncing electron beams.     

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.     

(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.     

Effect of various cross-section energy dependences in calculations of cosmological viscosity

The Einstein Field Equations for homogeneous cosmologies are considered within the viscosity approximation. It is shown that some power laws T ^m (whereT is the temperature) for the cross-section lead to collisionless behavior near the initial singularity in a big bang model. Under some circumstances one may have two viscous phases, as the cosmic fluid passes from collisionless to collisional to collisionless again, while the universe expands.Research was sponsored in part by the Aerospace Research Laboratories, Office of Aerospace Research, United States Air Force, Contract F33615-68-C-1675.     

A new microwave/X-ray diagnostic for the thermal phase of solar flares

We have observed 10 solar bursts during the thermal phase using the Haystack radio telescope at 22 GHz. We show that these high frequency flux observations, when compared with soft X-ray band fluxes, give useful information about the temperature profile in the flare loops. The microwave and X-ray band fluxes provide determinations of the maximum loop temperature, the total emission measure, and the index of the differential emission measure (q(T)/T = cT^–1). The special case of an isothermal loop ( = ) has been considered previously by Thomas et al. (1985), and we confirm their diagnostic calculations for the GOES X-ray bands, but find that the flare loops we observed departed significantly from the isothermal regime. Our results ( = 1–3.5) imply that, during the late phases of flares, condensation cooling ( 3.5) competes with radiative cooling ( 1.5). Further, our results appear to be in good agreement with previous deductions from XUV rocket spectra ( 2–3).     

Distribution of polarization and intensity of radiation across the stellar disk and numberical values of atmospheric characteristics governing this distribution

Computations of polarization and intensity of radiation from a unit stellar surface area are presented, as well as a study of the numerical characteristics of atmospheres — single-scattering albedo and the initial source function(), which define the polarization behaviour of atmospheres. The radiatively stable models of stellar atmospheres presented by Kuruczet al. (1974) and Kurucz (1979) have been used for calculations. Since the versus optical depth dependence is rather weak, it has been assumed that (=cost. With a fixed effective temperatureT _eff maximum values of are characteristic of stars featuring the lowest surface gravity accelerationg. Among stars with radiatively stable atmospheres, maximum values of (=5000 Å) 0.4–0.6 are exhibited by supergiants withT _eff=8000–20 000 K. The plot of () is characterized by discontinuities at the boundaries of spectral series for hydrogen and, sometimes, for helium. Maximum are attained in the Lyman region of =912–1200 Å, where can reach the value 0.7–0.9 for supergiants, this value being 0.3 for Main-Sequence stars. For stars withT _eff 35 000 K, high values of also are attained for <912 Å. Within the infrared region, is always small because of bremsstrahlung absorption.A rapid growth of the source functionB with < typical for ultraviolet range (within the Wien part of spectrum), together with high values of results in the strong polarization of emission from a unit stellar surface element, sometimes exceeding the values for the case of a pure electron scattering. For longer wavelengths, where the limb-darkening coefficient is smaller, the plane of polarization abruptly turns 90° in the central parts of the visible stellar disk.     

Effects of Hall current on hydromagnetic free-convective flow through a porous medium

An analysis of the effects of Hall current on hydromagnetic free-convective flow through a porous medium bounded by a vertical plate is theoretically investigated when a strong magnetic field is imposed in a direction which is perpendicular to the free stream and makes an angle to the vertical direction. The influence of Hall currents on the flow is studied for various values of .Nomenclature c _p specific heat at constant pressure - e electrical charge - E Eckert number - E electrical field intensity - g acceleration due to gravity - G Grashof number - H ₀ applied magnetic field - H magnetic field intensity - (j _x , j _y , j _z ) components of current densityJ - J current density - K permeability of porous medium - M magnetic parameter - m Hall parameter - n _e electron number density - P Prandtl number - q velocity vector - (T, T _w , T ) temperature - t time - (u, v, w) components of the velocity vectorq - U ₀ uniform velocity - v ₀ suction velocity - (x, y, z) Cartesian coordinates Greek Symbols angle - coefficient of volume expansion - _e cyclotron frequency - frequency - dimensionless temperature - thermal conductivity - coefficient of viscosity - magnetic permeability - kinematic viscosity - mass density of fluid - _e charge density - electrical conductivity - _e electron collision time     

A study of massive classical polytropes in general relativity

A detailed study of classical polytropes in general relativity has been presented for _O ((dP/dE)_O) 1.0 and _O((P/E _O)_O. The behaviour of various structural parameters with _O/_O, _O and _O are the values ofP/E and dP/dE at the centre) has been studied. The most important result of this study is the fact the qualitative behaviour of all the structural parameters depends only on the value of µ_O for the various assigned _O values. The maximum value of surface red shift occurs when µ_O=0.6 and for _O=1.0 it equals 0.618. These structures are gravitationally bound for µ_O0.8 and most so for µ_O=0.4. The maximum value of binding coefficient comes out to be 0.181 when _O=1.0. These structures have been used to model neutron stars. The maximum mass of neutron star based upon such a model comes out to be 2.55M (for µ_O=0.4 and _O=1.0) and maximum size comes out to be 15.0 km (for µ_O=0.2 and _O=1.0). It is also seen that the structures are pulsationally stable for µ0.6.