A statistical analysis of large-scale brightness and velocity fluctuations in the solar atmosphere

Simultaneous photoelectric recordings of the intensities and the Doppler shifts in 5 Fraunhofer lines (H, Na D₁, Mg b₂, Fe5123, Fe5223) were used to study the structure of local large-scale fluctuations of the intensity and velocity in different layers of the solar atmosphere. We derived the autocorrelation and cross-correlation functions and the powerspectra of the fluctuations. Fluctuation patterns with a characteristic size of 3–4 × 10⁴ km were found in all observed lines. The intensity of the fluctuations decreases sharply from the chromospheric H-core to the weak iron lines. The results are discussed in terms of the solar supergranulation pattern.     

Effects of the Sector Structure of the Interplanetary Magnetic Field on Galactic Cosmic Ray Anisotropy

We study the effects of the sector structure of the interplanetary magnetic field (IMF) on the Galactic cosmic ray (GCR) anisotropy at solar minimum by using Global Network neutron monitor data. The hourly neutron monitor data for 1976 were averaged for the positive (+) and negative (–) IMF sectors (+ and – correspond to the antisolar and solar directions of magnetic field lines, respectively) and then processed by the global survey method. We found that the magnitude of the GCR anisotropy vector is larger in the positive IMF sector and that the phase shifts toward early hours. The derived GCR components A _r, A , and A for the different + and – sectors are then used to calculate the angle ( 46°) between the IMF lines and the Sun–Earth line, the solar wind velocity U ( 420 km/s), the ratio of the perpendicular (K ) and parallel (K _||) diffusion coefficients K /K _|| = ( 0.33), and other parameters that characterize the GCR modulation in interplanetary space.     

Chromospheric ‘active region loops’

Archshaped structures above or around sunspot groups are considered as tracers of the magnetic lines of force. A study of the chromospheric contribution to the 3D general pattern is necessary to quantify this relationship. The emissive features detected in nine different active regions (AR) and observed on the disk at different levels in the chromosphere have been analysed (6 maps/AR). A good spatial correspondence is found between the maxima of Ca II K₃ and H emissions. Eleven archshaped structures may be easily interpreted as loops. The footpoints are located on both sides of an inversion region in the magnetic field. They always avoid the local maxima and minima of the photospheric line-of-sight magnetic fields (H ) pattern independent of the heliographic longitude. This suggests that the magnetic lines of force may have an oblique direction relative to the solar surface.Underneath the footprints, H is about 400–500 G and V the line-of-sight component of velocity in the photosphere) is less than 100 m s^-1 (frequently involving an inversion of velocity sign, i.e., V = 0 line). The mean distance between the feet of the arches is about 30000 km. Height is variable: the arches are lower in the young AR, higher when it evolves, scarcely or not detectable when the AR is dying. The maximum peaks in K ₁ v(the blue wing of K line) are observed at the periphery of the highest values of H and K ₃ intensities, or at the periphery of the AR.There are no great morphological differences between the slowly-varying arches and the flaring ones. However, a new relation is found between these two kinds of chromospheric features: at the maximum of flares, the flaring arch has one of its footpoints in common with a closer stable, pre-existing arch.On leave from Nanjing University, China.     

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.     

A prominence model based on spectral observations

Intensities and profiles of the H, H, H, K, and D₃ lines are measured in a solar prominence. From the profiles of these lines we estimate T = 6400 K and _t = 5.7 km s^–1. We construct a simple isothermal model which explains the H intensity and profile for an assumed total particle density n _T = 3 × 10¹¹ cm^–3, and a filling factor, = 1/6.From this model we find that the source function in the H line is nearly constant through the prominence. We estimate from the model that the radiative energy loss at the center of the prominence is of the order of 10⁷ erg s^–1 g^–1.     

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 solar abundance of thorium and lead

Two new Th ii lines have been identified in the spectrum of the solar photosphere. The abundance derived from these lines together with the previously known Th ii line at 4019 Å, is log _Th = 0.85 ± 0.20 in the log _H = 12.00 scale. Analysis of three Pb i lines in the photospheric spectrum resulted in an abundance of log _pb = 1.90 ± 0.10. The solar Th/Pb ratio is: _Th/ _Pb = 0.09 _-0.005 ^0.09 .     

Activity in the quiet Sun

Macrospicules have been observed in H and He i D₃, on the disk and above the limb. In 1975, a rate of 1400 (A day)^–1 is inferred, and the ratio of equatorial to polar rates 2. D₃ intensities are a few × 10^–3 of the disk center, and do not decrease in coronal holes. The ratio of H to D₃ intensities is 10. The integral number of macrospicules with D₃ intensity I ₀ is proportional to I ₀ ^–1.     

On the elimination of the critical terms of a first order theory of Jupiter perturbed by Saturn carried out through Hori's method and Poincaré canonical variables

The elimination of the critical terms inside the Hamiltonian of a first order theory of Jupiter perturbed by Saturn is carried out through the Poincaré canonical variables and the Hori's procedure. Powers of the eccentricities and the sines of inclinations which are>3 are neglected. The Poincaré variablesL ₁,H ₁,P ₁, ₁,K ₁,Q ₁ of Jupiter which result from a previous elimination of the short period terms are expressed in terms of the Poincaré canonical variablesL _u ,H _u ,P _u , _u ,Q _u ;u=1, 2; index 1 Jupiter, index 2 Saturn resulting from the elimination of the short period and critical terms. The differential equations inH _u ,P _u ,K _u ,Q _u are solved through the method of Lagrange and the analytical expressions ofL ₁,H ₁,P ₁, ₁,K ₁,Q ₁ as functions of timet are finally obtained.     

Rapidly rotating polytropes in the post-Newtonian approximation to general relativity

The study of uniformly polytropes with axial symmetry is extended to include all rotational terms of order ⁴, where is the angular velocity, consistently within the first post-Newtonian approximation to general relativity. The equilibrium structure is determined by treating the effects of rotation and post-Newtonian gravitation as independent perturbations on the classical polytropic structure. The perturbation effects are characterized by a rotation parameter = ²/2G _c and a relativity parameter, =p _c / _c C ² , wherep _c and _c are the central pressure and density respectively. The solution to the structural problem is obtained by following Chandrasekhar's series expansion technique and is complete to the post-Newtonian rotation terms of order ². The critical rotation parameterv _c , which characterizes the configuration with maximum uniform rotation, is accurately evaluated as a function of . Numerical values for all the structural parameters needed to determine the equilibrium configurations are presented for polytropes with indicesn=1, 1.5, 2, 2 5, 3, and 3.5.     

On the rotation of rigid Venus

According to A.A. Khentov Venus' rotation is in the quasi-stationary state as a result of the balance interaction of the solar tidal torque with the aerodynamical torque of the rotating Venus' atmosphere. In case of the nonconservative forces are negligible and the solar attraction is the stabilizing factor, the rotation of the rigid Venus may be assumed as the first approximation. The theory of the rotation of the rigid Venus in the coordinates,, had been constructed. It have been found that Venus rotates almost uniformly and the libration harmonics are negligible.     

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.     

Mean free paths of energetic particles at very large heliodistances (Pioneer 11 at 20 AU)

Pioneer 11 magnetic field data at 20 AU are analysed by the computational method of Moussas, Quenby, and Webb (1975), Moussas and Quenby (1978), and Moussas, Quenby, and Valdes-Galicia (1982a, b) to obtain the parallel mean free path , and the diffusion coefficient parallel to the magnetic field line K . This method is the most appropriate for the mean free path calculation at large heliodistances since the alternative method which is based on fitting of energetic particle intensities cannot be easily and accurately be used because the association of energetic particles with their parent flares is not precise. The results show that the mean free path has values between 0.85 and 0.98 AU, linearly increasing with energy according to (T_kinetic) = + MT, where = 0.846 AU and M = 4.44 × 10 ^–5 AU MeV^–1 for energies between 10 MeV and 3 GeV for protons. These values of the parallel mean free path are much larger than the values estimated by previous studies up to 6 AU. The diffusion coefficient dependence upon energy follows a relation which simply reflects an almost constant mean free path and a linear dependence on the velocity of the particle, so that at 20 AU heliodistance K (T _kin) = K _{, 1 MeV}(T _kin)T _kinetic , with = 1/2. The distance dependence of the parallel diffusion mean free path follows a power law, (R) = _{, 1 AU} R , where is 1 ± 0.1. While the parallel diffusion coefficient obeys a power-law relation with heliodistance R, K (R, T _kin) = K _{, 1 AU}(T _kin)R , with = 1 ± 0.1. The radial diffusion coefficient of cosmic rays is not expected to strongly depend upon the parallel diffusion coefficient because the nominal magnetic field at these large heliodistances (20 AU) is almost perpendicular to the radial direction and the contribution of the diffusion coefficient perpendicular to the magnetic field is expected to play a dominant role. However, the actual garden hose angle varies drastically and for long time periods and hence the contribution of the diffusion parallel to the field may continue to be important for the small scale structure of intensity gradients.     

CCD-Doppler measurements of solar differential rotation

Using the AT1 CCD camera at the Echelle spectrograph of the GCT at Tenerife, solar Doppler rotation measurements in the photospheric lines Fe I 6301.5 Å and 6302.5 Å and in the chromospheric line Na-D₂ 5890.0 Å have been made. The line shifts measured at different heliographic latitudes around the limb were corrected for observer motion and converted into sidereal rotation rates. At the equator the observed chromospheric rotation rate is about 8 % larger than the photospheric rate, and the average observed Doppler rotation rate is not very much different from the mean rotation rates deduced from all published tracer works and all published Doppler works. Near the poles (where tracer methods rely on extrapolation) both the chromospheric and the photospheric rotation rate are slightly smaller than the all Doppler rate and are considerably smaller than the extrapolated all tracer rate. If all previous measurements of solar rotation are taken into account, a surface rotation law with lower error bounds than previously possible can be derived.     

Unsteady free-convective flow and mass transfer in a rotating porous medium with Hall current,I

The Hall effect on the unsteady hydromagnetic free-convection resulting from the combined effects of thermal and mass diffusion of an electrical-conducting liquid through a porous medium past an infinite vertical porous plate in a rotating system have been analysed. The expressions for the mean velocity, mean skin friction, and mean rate of heat transfer on the plate are derived. The effects of magnetic parameterM, Hall parameterm, Ekman numberE, and permeability parameterK ^* on the flow field are discussed with the help of graphs and tables.Nomenclature C _p specific heat at constant pressure - C the species concentration inside the boundary layer - C _w the species concentration at porous plate - C the species concentration of the fluid at infinite - C dimensionless species concentration - D chemical molecular diffusivity - E Ekman number - Ec Eckert number - g acceleration due to gravity - Gr Grashof number - Gm modified Grashof number - H ₀ applied magnetic field - (J _x, J_y, J_z) components of current density - M magnetic parameter - m Hall parameter - P Prandtl number - q _m mean rate of heat transfer - Sc Schmidt number - t time - t dimensionless time - T temperature of fluid - T _w temperature of the plate - T temperature of fluid at infinite - T dimensionless temperature - (u, v, w) components of the velocityq - w ₀ suction velocity - (x, y, z) Cartesian coordinates - z dimensionless coordinate normal to the plate Greek symbols coefficient of volume expansion - * coefficient of thermal expansion with concentration - frequency - dimensionless frequency - k thermal conductivity - K ^* permeability parameter - dinematic viscosity - density of the fluid in the boundary layer - coefficient of viscosity - _e magnetic permeability - angular velocity - electrical conductivity of the fluid - _m mean skin friction - _mn mean skin friction in the direction ofx - _mv mean skin friction in the direction ofy     

Isothermal neutron star cores

By considering the relativistic expression for isothermal NS cores,T·e ^/2 = constant, we have shown that some of the standard equations of state, when applied to NS cores, correspond to constancy of some adiabatic exponents. It has been shown that the equation of state,P=KE, corresponds to ₁ = to ₂ = ₃ 1 +K and the equation of state, dP/dE=K, corresponds to ₃ 1 +K. The conditions under which different equations of state represent isothermal cores have been obtained: For isothermal NS, the local temperatureT, can be expressed in terms of pressureP, energy densityE, and rest mass density . For example: (a)P =KE :T = constant × (E/); (b)P=KE :T = constant × (P/); (c) dP/dE =K :T ^K ; (d) = ₂ :T = constant × (P/E); and (e) = ₃ :T = constant × (P/)^1/2. Equation of state corresponding to = ₂ is obtained as:P=E/ln(K/E) and the equation corresponding to = ₃ comes out as:E=P ln(K/P). Core-envelope models can be developed for these two cases. When core equation corresponding to = ₂ or = ₃ is used in the core, we can ensure the continuity of dP/dE at the core-envelope boundary, along with the continuity ofP, E, , and . The parameters of isothermal NS cores corresponding to the cases = ₂ and = ₃, have been obtained. The maximum mass of these NS cores comes out to be 2.7 .     

Emission cores in H and K lines

Calculations are made for the center-limb variations of the K₂ and K₃ components of the solar Ca ii K line using an optically thick model of the chromosphere. The center-limb variations are shown to require an increase of Doppler width with height in the chromosphere and to depend critically upon the location of the point where _D has increased by a factor e. Good agreement with observations is found when, and only when, the increase in _D occurs nearly simultaneously with the increase in chromospheric temperature.     

On Geovenelli's approximate form of j(τ)

The accuracy of the approximate replacement of the frequency meanj() of the total intensityJ () byJ _c+a{J ₀()–J _c} by Geovenelli, whereJ _c is the total intensity at the continuum,J ₀() is that at the line center anda is independent of depth, is studied. Numerical calculations for strong solar lines show very high values of the residual intensities. A slight change in the approximation is then suggested to get a result quite consistent with observational and existing calculated data.     

Emission cores in H and K lines

Profiles of the H and K lines of Mgii and the K line of Ca ii are computed using a two-level atom for five model atmospheres distinguished from each other mainly by the location of the temperature minimum. In the five models the temperature minimum and the chromospheric temperature are adjusted to give best agreement between computed and observed profiles. The parameters and r ₀ are prescribed as functions of from a density model of the atmosphere. By comparing computed and observed profiles of the K₃, K₂ and inner K₁ components of the lines we determine both the approximate depth variation of _D and the best of the temperature models. We find that the Doppler width increases rapidly with height in the chromosphere beginning from a value of 1.6 km/sec at ₀ 10^–2. This latter value corresponds closely to the thermal velocity of Mg atoms in the upper photosphere. The preferred temperature model is one for which the temperature minimum occurs near ₀( 2800) 10^–4–10^–5 with a value T _min 4200 ° and which has a temperatu near 7000 ° at ₀ = 10^–6 where K₂ is formed. The intensity in K₃ is determined largely by d _D/d in the K₂ and K₃ regions.     

Effect of perturbations in Coriolis and centrifugal forces on the stability of libration points in the restricted problem

The location and the stability of the libration points in the restricted problem have been studied when small perturbation and are given to the Coriolis and the centrifugal forces respectively. It is seen that the pointsL ₄ andL ₅ form nearly equilateral triangles with the primaries and the pointsL ₁,L ₂,L ₃ remain collinear. It is further observed that for the pointsL ₄ andL ₅, the range of stability increases or decreases depending upon whether the point (, ) lies in one or the other of the two parts in which the (, ) plane is divided by the line 36-19=0 and the stability of the collinear points is not influenced by the perturbations and they remain unstable.