The magnetic fields of active regions

The Mount Wilson coarse array magnetograph data set is analyzed to determine characteristics of magnetic regions as a function of distance from the average latitude, ₀, of regions in each hemisphere, a quantity which varies during the activity cycle. Regions with normal polarity axis orientations are distributed asymmetrically about ₀ with the median latitude about 1 deg equatorward of ₀. Reversed polarity orientation regions show a somewhat broader and more symmetric distribution. Average sizes for regions at = 0 ( ₀) are nearly twice as large as those located at 10 deg latitude in either direction. Regions poleward of ₀ tend to show a net magnetic field biased toward the following polarity, and regions equatorward of ₀ are biased toward the leading polarity, both by around 10%. Neither region growth rates nor decay rates are related to . The average polarity axis tilt angles of regions are lower for regions near the equator than for those nearer the poles. It is most likely that this is basically an effect of latitude rather than . Meridional motions of young regions are shown to be toward ₀. Older regions do not show this behavior. This may be a magnetic effect rather than being due to large-scale circulatory motion, as has been suggested in the past. East-west inclination angles of active region magnetic fields show a slight tendency to trail the rotation direction (eastward inclination) by a few deg for regions with ₀> 0 and lead the rotation (westward inclination) by a few deg for regions with ₀ > 0. This effect may be related to the torsional oscillations. These various results are discussed in terms of a hypothetical subsurface magnetic flux tube which gives rise to the surface activity.Operated by the Association of Universities for Research in Astronomy, Inc., under Cooperative Agreement with the National Science Foundation.     

Hollow beam distribution of energetic electrons and higher harmonics of electron cyclotron maser

The variations of the growth rates of ECM at first four harmonics in X-, Z-, and O-modes excited by a hollow beam distribution of weakly relativistic electrons with a parameter _p / _e are presented in this paper. The results show that the second harmonic of ECM in X-mode dominates the instability if < 1, and if 1.2 , 2 or 2.2 3 the third or fourth harmonic will dominate. The second and third harmonics of Z-mode waves grow faster only if 2 2.2 and 3 3.2, respectively, so it would not be a competition in most cases. It is suggested that the ECM emission at these harmonics in X-mode is a possible mechanism to produce solar spike emissions with high brightness temperature at shorter and longer decimetric wavelengths.Proceedings of the Workshop on Radio Continua during Solar Flares, held at Duino (Trieste), Italy, 27–31 May, 1985.On leave from the Department of Astronomy, Nanjing University, Nanjing, The People's Republic of China.     

On the integrability of the Roche coordinates

The aim of the present paper is to prove that the system of partial differential equations, which define a set of curvilinear coordinates , , that are orthogonal to the Roche equipotentials (r, , ) incorporating the effects of both rotationaland tidal distortion, does not admit of any formal integrals; and can be solved only numerically in an asymptotic manner. This fact is related with analytic properties of the problem of three bodies, in which represents the potential.     

Dissipative MHD solutions for resonant AlfvÉn waves in 1-dimensional magnetic flux tubes

The present paper extends the analysis by Sakurai, Goossens, and Hollweg (1991) on resonant Alfvén waves in nonuniform magnetic flux tubes. It proves that the fundamental conservation law for resonant Alfvén waves found in ideal MHD by Sakurai, Goossens, and Hollweg remains valid in dissipative MHD. This guarantees that the jump conditions of Sakurai, Goossens, and Hollweg, that connect the ideal MHD solutions for _r , andP across the dissipative layer, are correct. In addition, the present paper replaces the complicated dissipative MHD solutions obtained by Sakurai, Goossens, and Hollweg for _r , andP in terms of double integrals of Hankel functions of complex argument of order with compact analytical solutions that allow a straightforward mathematical and physical interpretation. Finally, it presents an analytical dissipative MHD solution for the component of the Lagrangian displacement in the magnetic surfaces perpendicular to the magnetic field lines which enables us to determine the dominant dynamics of resonant Alfvén waves in dissipative MHD.     

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     

Entropy per baryon in a ‘many-worlds’ cosmology

We imagine the universe split into infinitely many branches, or worlds, only one of which we can observe. Our world has an entropy per baryon 10⁹: other worlds can have all possible values of entropy per baryon. High-entropy worlds with >5×10¹¹ do not form galaxies, but only giant black holes. Low entropy worlds with <3×10⁵ do form galaxies, but only metal-poor dwarf galaxies with no planets. Life can evolve only in worlds with entropy per baryon in the range 3×10⁵<<5×10¹¹, and life is abundant only in a much narrower range.     

Cycle latitude effects for sunspot groups

Digitized Mount Wilson sunspot data from 1917 to 1985 are analyzed to examine meridional motion and rotation properties as a function of latitude and distance () from the average latitude of activity (₀) in each hemisphere. Latitude dependence similar to previous results is found, but only for spot groups whose areas are decreasing from one day to the next. A previous study of active region magnetic fields, using this technique of motions as a function of the average latitude of activity, had shown meridional motions on average toward ₀. In this analysis of spot data some evidence is seen for motion away from ₀, with some slight evidence for faster rotation equatorward of ₀ and slower motion poleward of ₀, similar to the torsional oscillation phenomenon. For reasons that are not clear, both of these effects are significantly more pronounced for sunspot groups whose areas are decreasing.Operated by the Association of Universities for Research in Astronomy, Inc., under Cooperative Agreement with the National Science Foundation.     

Quelques résultats d'observation des spicules chromosphériques en K et D3

Résumé On étudie les spectres des spicules observés simultanément dans les raies K et D3 en fonction du temps et de l'altitude (2000<h<5000 km). Les mesures de la variation de l'intensité centrale I ₀ avec l'altitude, sont données dans le Tableau I. On donne des résultats comparatifs concernant l'énergie émise E _k et E _D3.La Figure 1 représente les variations de la largeur à mi-intensité des profils d'émission, (L) en fonction du temps et la Figure 2 en fonction de la hauteur.La classification des spicules en deux groupes: profil large (LW) et profil étroit (LN) a été confirmée. Il y a 2 fois plus de spicules LW que LN, la durée de vie des LN étant <2,5 min. Le Tableau II donne les valeurs moyennes de la largeur réduite L/.A l'aide des valeurs L, on détermine la microturbulence () dans les spicules en fonction de la hauteur (Figure 3, pour la raie K). La turbulence de la raie D3 est donnée dans un tableau dans le texte. Les résultats sont en bon accord. L'interprétation de ces résultats suggère que la microturbulence a deux composantes ₀ et _e. Pour les LN on a ₀ seul pour les LW on a ₀ + ₀, où ₀ est la turbulence au centre des spicules à l'endroit du champ magnétique fort (Figure 4a) et ₀ est la turbulence vers l'extérieur des spicules LW, là où le champ est faible (Figure 4b).

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We study in this paper the spectra of spicules on the solar limb observed simultaneously in the K and D3 lines in terms of time and altitude (2000<h<5000 km). The measures of the variation of the central intensity I ₀ with the altitude are given in Table I. We are also giving comparative results concerning the energy emitted E_K and E_D3 (Section 4).For different spicules, Figure 1 represents the variations of the total width at half intensity (L) of the emission profiles in terms of time and Figure 2 in terms of height.The classification of spicules in two groups: wide profile (LW) and narrow profile (LN) has been confirmed. There are approximately twice as many LW spicules as LN, the lifetime of LN spicules seems to be <2.5 min. Table II gives the average values of L/.With the help of L values, we can determine the microturbulence () in the spicules in function of the height (Figure 3, for the K line). The turbulence of the D3 line is given in a table in the text (Section 5.3). The results of both lines are concordant and the interpretation which we suggest (Section 5.4) is that the microturbulence has, generally speaking, two components ₀ and ₀. For the LN we have ₀ alone, and for the LW we have ₀ + _e, ₀ being the turbulence at the center of spicules where the magnetic field is strong (Figure 4a), whereas the _e is the turbulence towards the exterior of the LW spicules, where the magnetic field is weak (Figure 4b).

     

The geometry of the Roche coordinates

The exact geometry of the Roche curvilinear coordinates (, , ) in which corresponds to the zero-velocity surfaces is investigated numerically in the plane, as well as in the spatial, case for various values of the mass-ratio between the two point-masses (m ₁,m ₂) constituting a binary system.The geometry of zero-velocity surfaces specified by -values at the Lagrangian points are first discussed by taking their intersections with various planes parallel to thexy-, xz- andyz-planes. The intersection of the zero-velocity surface specified by the -value at the Lagrangian equilateral-triangle pointsL _4,5 with the planex=1/2 discloses two invariable curves passing through the pointsL _4,5 and situated symmetrically with respect to thexy-plane whose form is independent of the mass-ratio.The geometry of the remaining two coordinates (, ) orthogonal to the zero-velocity surfaces is investigated in thexy- andxz-planes from extensive numerical integrations of differential equations generated from the orthogonality relations among the coordinates. The curves (x, y)=constant in thexy-plane are found to be separated into three families by definite envelopes acting as boundaries whose forms depend upon the mass-ratio only: the inner -constant curves associated with the masspointm ₁, the inner -constant curves associated with the mass-pointm ₂ and the outer -constant curves. All the -constant curves in thexy-plane coalesce at either of the Lagrangian equilateraltriangle pointsL _4,5, except for a limiting case coincident with thex-axis. The curves (x, z)=constant in thexz-plane are also separated by definite envelopes depending upon the mass-ratio into different families: the inner -constant curves associated with the mass-pointm ₁, the inner -constant curves associated with the mass-pointm ₂ and the outer -constant curves on both sides out of the envelopes. For larger values ofz, the curves =constant tend asymptotically to the line perpendicular to thex-axis and passing through the centre of mass of the system, except for a limiting case coincident with thex-axis. The geometrical aspects of the envelopes for the curves (x, y)=constant in thexy-plane and the curves (x, z)=constant in thexz-plane are also discussed independently.In the three-dimensional space, the Roche coordinates can be conveniently defined in such a way as to correspond to the polar coordinates in the immediate neighbourhood of the origin, and to the cylindrical coordinates at great distances. From numerical integrations of simultaneous differential equations generating spatial curves orthogonal to the zero-velocity surfaces, the surfaces (x, y, z)=constant and the surfaces (x, y, z)=constant are constructed as groups of such spatial curves with common values of some parameters specifying the respective surfaces.On leave of absence from the University of Tokyo as an Honorary Fellow of the Victoria University of Manchester.     

Temperature variations in the solar photosphere

From the variations in equivalent width of a selected set of Fraunhofer lines, we derived the variation of effective temperature and microturbulence velocity between the equator and the regions at heliographic latitude of - 72°. The reliability of the results (T/T = 0 ± 0.6%, / = 6% ± 13%) needs further investigations, but from the analysis of our data we can state that temperature variations, if any, are very small. Some suggestions for more fruitful measurements are also given.     

Temperature et microturbulence dans les regions externes des protuberances

A spectroscopic investigation of a quiescent prominence has been performed: the line profiles of the H and K lines have been carefully determined in all regions of the prominence where these emissions are likely to originate in optically thin layers. Therefore we have been able to study the electron temperature T _e and the microturbulent velocity in the outer parts of the prominence. We find that on the average, T _e = 5700 K (Figure 1) and = 6.7 km s^-1 (Figure 2) which are in very good agreement with classical data. Figure 3 represents the radial velocity measurements and Figure 4 the ratio of the total intensity of H to K lines. Thus the prominence we have observed does not show for T _e and the regular increase outward which has been described by Hirayama (1971). On the other hand increases towards the Equator, in the dynamically active part of the prominence, which could indicate that represents the effect of macroturbulence rather than microturbulence (Kawaguchi, 1966). In this part of the prominence only the K line is in emission and the average value of the microturbulence is 9.4 km s^-1, the radial velocity is also generally increasing. At last, according to the absolute intensities of the H and K lines, the electron density in the outer layers of the prominence is no more than 1 × 10¹⁰ cm^-3.     

Observation of far ultraviolet radiation from early-type stars

Rocket-borne photon counters sensitive to bands 1060–1180, 1230–1350, and 1350–1480 were used to measure the celestial ultraviolet radiation above the terrestrial atmosphere. The energy spectra of six objects, Leo, CMa, Ori, , , Ori (combined), Ori, and Tau were obtained. The comparison of them with those calculated with the stellar model atmospheres indicates the deficiency of about 1 mag. in the ultraviolet region, when corrected for interstellar extinction, for all stars except Tau. The observed spectrum of Tau agreed with the theoretical one for normal interstellar extinction. The effects of line blanketing were examined for B1 and B2 stars, and found to account for a part of the difference between the observed and the theoretical values.     

The influence of satellite flexibility on orbital motion

The orbital perturbations induced by the librational motion and flexural oscillations are studied for satellites having large flexible appendages. Using a Lagrangian procedure, the equations for coupled motion are derived for a satellite having an arbitrary number of appendages in the nominal orbital plane and two flexible members normal to it. The formulation enables one to study the influence of flexibility on both the orbital and attitude motions. The orbital coordinates are expanded as perturbation series in =(l/a ₀)²,l anda ₀ being a characteristic length of the satellite and unperturbed semi-major axis of the orbit, respectively. The first order perturbation equations are solved in terms of elastic deformations and librational angles using the WKBJ method in conjunction with the variation of parameter technique. Existence of secular perturbations is noted for certain librational flexural motions. Three specific examples, Alouette II, Radio Astronomy Explorer and Tethered Orbiting Interferometer, are considered subsequently and their possible secular drifts estimated.List of Symbols A _ij, B_ij coefficients in the eigenfunction expansion ofv _i andw _i respectively, Equation (10) - C _k, D_k constants, Equation (21) - EI _i flexural rigidity of theith appendage - E(u₀) ²(1+e ₀ cosu ₀)² h ₀ ³ - F(u₀) perturbation function, Equation (17b) - F ,F ,F functions of librational angles and flexural displacements, Equation (11i) - F ,F ,F F ,F ,F with change of independent variable fromt tou ₀ - I _xx, I_yy, I_zz principal moments of inertia of the undeformed satellite - [J ⁱ] inertia dyadic of the deformedith appendage - [J _d] inertia dyadic of the deformed satellite - M mass of the satellite - P _R, P_u functions of librational angles and flexural displacements, Equation (15d) and (15e), respectively - R _c magnitude ofR _c - R _c0, R₁ unperturbed value and first order perturbation ofR _c, respectively - R _c ,R ₀ position vectors of the c.m. of the deformed and undeformed satellite, respectively - T kinetic energy of the satellite - U potential energy of the satellite - U _e, U_g elastic and gravitational potential energy, respectively - X, Y, Z orbital co-ordinate axes, located at the c.m. of the deformed satellite - Y ₁(u₀), Y₂(u₀) functions ofu ₀, Equation (18b) and (18c), respectively - a semi-major axis - a ₀ unperturbed value ofa - e eccentricity - e ₀ unperturbed value ofe - h ₀ unperturbed angular momentum per unit mass of the satellite - i inclination of the orbital plane to the ecliptic - i, j, k unit vectors alongx (or ),y (or ) andz (or ) axes, respectively - l characteristic length of the satellite - l _i length of theith appendage - [l ⁱ] matrix of direction cosines ofx _i, v_i andw _i - l ,l ,l direction cosines ofR _c - m ₀, m_i mass of the main body andith appendage, respectively - p _i ² - q _m, Q_m generalized co-ordinate and force, respectively - r ₁ R ₁/R_c0 - r position vector of an element of the body referred toxyz axes - r _u position vector of an element after deformation, referred to axes - r _c x _c i+y _c j+z _c k, position vector of the c.m. of the deformed body referred toxyz axes - s x _i/l_i - t time - u true anomaly - u ₀, u₁ unperturbed value and the first order perturbation ofu, respectively - u elastic displacement vector - u _c u–r _c - velocity of an element relative to axes - v _i, w_i flexural deformations - x, y, z body co-ordinate axes with origin at the c.m. of the undeformed satellite - x _i distance of an element of theith appendage from the root - _j jth eigenfunction (normalized) of a cantilever - angle between the line of nodes and vernal equinox - , , components of nondimensionalized angular velocity of the satellite - , , pitch (spin), yaw and roll, respectively - _i nominal inclination of theith appendage in the orbital plane - - small parameter, (l/a ₀)² - _j jth eigenvalue of a cantilever - gravitational constant - _jk constant, Equation (11j) - , , body co-ordinate axes with origin at the c.m. of the deformed satellite - ( i + j + k), angular velocity of the satellite     

Spectral analysis of cyclotron radiation in anisotropic plasmas

Following up our previous analysis of cyclotron radiation in anisotropic plasmas, we derived expression for the power received at a far field point per unit frequency range along the group velocity direction dP(, )/d. We then carry out a series of numerical analysis presenting the spectral features rather than directional features of cyclotron radiation. In particular, we analyse the power received per unit solid angle per unit frequency range d² P(, )/(d d). It is expected the analysis result presented here can be compared directly with observation for parameters pertaining to astrophysical plasmas in stellar and terrestrial atmospheres.     

Radio-emitting electrons and cosmic ray confinement

The propagation of cosmic ray electrons in the framework of the Disk-Halo diffusion model in which the diffusion coefficientD z E (wherez is the distance from the galactic plane andE is the energy), and the magnetic fieldHz ^– has been examined by making use of the recently available radio data up to 8 GHz toward the Anticenter (A) and Halo Minimum (M). The following inferences are then made. From the difference in the frequency at which steepening occurs in the radio spectra towardA andH, it is found that the observations are consistent with the magnetic field decreasing withz such that =0.24–0.37. An electron injection spectrum with a single power law down to energies well below 1 GeV cannot explain satisfactorily the observed radio spectra. All observations, however, can be understood in a self consistent way if the observed steepening of the radio spectra, and hence the interstellar electron spectrum, is due partly to the deviation in the power law electron injection spectrum below a few GeV and partly to the first break arising from electron energy losses occurring in the same energy region. In this case, using the value of obtained above and a value of =0.3–0.6, it is found that the spectral index ₀ of the injected electrons above a few GeV has a value between 1.9 and 2.3 and the index a value between 0.5 and 1. Further, if the electrons and protons have the same spectral shape at injection, then ₀=2.1–2.3.NASA-NRC, Senior Research Associate on leave from Tata Institute of Fundamental Research, Bombay, India.     

The spherically-symmetrical trajectories of spin particles in the Schwarzschild field

The motion of spin particles in the Schwarzschild field is examined in this paper. It is shown that Mathisson-Papapetrou equations under additional conditions , where is the Lie derivative of the Killing vector _j , permit only radial motion, motion in the equatorial plane and in the equilibrium points. All these types of motion are considered more in detail.     

Bidimensional spectroscopy of network bright points

We develop an automatic, computer controlled procedure to select and to analyze the Network Bright Points (NBPs) on solar images. These have been obtained at the Sac Peak Vacuum Tower Telescope by means of the Universal Birefringent Filter and Zeiss H filters, tuned, respectively, along the profiles of the H, Mg-b1, Na-D2, and H lines.A structure is identified as an NBP if at the wavelength H- 1.5 A its maximum intensity is greater than I + 3 and its area is greater than 1.5 arc sec² at I + 1.5, where I is the mean value and the standard deviation of the intensity distribution on the image. Each detected NBP is then searched and confirmed in all the remaining 31 images at different wavelengths.For each NBP several parameters are measured (position, area, mean and maximum contrast, Dopplergram velocity, compactness, and so on) and some identification constraints are applied.The statistical analysis of the various parameter distributions, for NBPs present within an active region and its surroundings, shows that two types of NBPs can be identified according to the value of their mean contrast C _min the H- 1.5 Å image (C _m 0.1 type I, C _m> 0.1 type II). The type I NBPs (all occurring on the boundaries of the supergranular network) appear to be much more frequent (180/26) than the type II ones.The size A of type I NBPs is less than 1.0 arc sec for H/H wings but of the order of 1.2 arc sec for Na-D2 and Mg-bl. The mean contrast C _m is around the value of 10% along the Na-D2 and Mg-bl profiles and of 20% along the H/H wings.The C _m - A scatter diagrams show, for the photospheric radiation (h < 100 km), a narrow range of variability for C _min correspondence with a wide range for A. For radiation orginated at higher levels (h > 200 km), the C _m- A scatter diagrams seem to indicate, even if with a large variance, that the highest C _m's tend to correspond to the highest A values.The mean Doppler shift is close to zero for Na-D2 and Mg-bl lines but negative (downward motion) for H and H lines.The type II NBPs tends to be preferentially located in the neighbourhood of small, compact sunspots and their detectability is almost constant through all the 4 studied line profiles. No conclusions can be derived on the mean size, contrast and Doppler shift values because their distributions are too dispersed. The only positive information is that its C _m- A scatter diagram, in H and H wings, indicates a wide range of variability for C _m in correspondence with very narrow range of variability for A.     

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.     

Equipotential surfaces in close binary systems: Remarks on the time-dependent potential function

By use of the mass-point model, the equations of the equipotential surfaces are reviewed. A difference between the time-dependent potential function and zero relative velocity surfaces is put in evidence. A drawback in the time-dependent transformation between (, , ) and (x, y, z) coordinate systems is underlined.     

Околозвездные оБлака по данным 2800 Mgii

2800 Mgii (. 1). (N ⁺/N ₁1000) , , (N ⁺/N ₁10). , . —, , . — . : ; 0.002 1 , 0.1 ; () 100 ^–3; ; ; , 10 ; 10^–4 1 . 2800 Mgii .