On determining the electron density distribution of the solar corona from K-coronameter data

The electron density distribution of the inner solar corona (r 2 R ) as a function of latitude, longitude, and radial distance is determined from K-coronameter polarization-brightness (pB) data. A Legendre polynomial is assumed for the electron density distribution, and the coefficients of the polynomial are determined by a least-mean-square regression analysis of several days of pB-data. The calculated electron density distribution is then mapped as a function of latitude and longitude. The method is particularly useful in determining the longitudinal extent of coronal streamers and enhancements and in resolving coronal features whose projections on the plane of the sky overlap.The National Center for Atmospheric Research is sponsored by the National Science Foundation.     

On a cold emission in the solar corona

The faint emission of hydrogen, helium and metals in the corona which appeared near an active prominence is studied. The calculations showed that the temperature of the emission region is in the limits from 10 000 K to 30 000 K and the electron density is between 10⁹-10¹⁰ cm^-3, respectively.     

On the abundance of calcium in the solar corona

Measured values for the total intensity of the continuum and the ratio of integrated intensities I( 5694)/I/(5446) are used to estimate the fraction of electrons along the line of sight contributing to the excitation of Caxv. This estimate of electron density along with an estimate of the dimension of the emitting region are used to find a value of the abundance of Ca in the solar corona. The estimated abundance is logN _Ca/N _H = -4.35.     

On green-to-red line intensity ratio in the solar corona

An improved formula for the green-to-red line intensity ratio in the solar corona is proposed. The results are compared with those given by the previous expression.     

Brightness temperature distribution in solar corona based on RATAN-600 observations of the maximum phase of the March 29, 2006 solar eclipse

We describe the technique and results of modelling the solar radio emission during the maximum phase of the solar eclipse of March 29, 2006 on the RATAN-600. The aim of modelling is to refine the brightness temperature of the solar corona at the distances up to two solar radii from the center of the optical disk of the Sun. We obtained the distribution of brightness temperature in the vicinity of the coronal hole above the solar North Pole at the wavelength of 13 cm. The results of modelling showed that brightness temperatures of the coronal hole at the distances greater than 1.02 R_C (here R_C is the radius of the optical disk of the Sun) is substantially lower than the expected average brightness temperature of a typical coronal hole, and that of the quiescent Sun (below 30000 K) at the wavelength of 13 cm. The classical Baumbach-Allen formula for electron density in a spherically symmetric corona agrees with the results of observations starting at distances of (1.4–1.5) R_C.     

Electrons in the solar corona

We discuss a model for the formation of the chromospheric Ca ii K line which does not make the usual assumption of complete redistribution. Using a physically reasonable scattering model, we find significant departures due to the frequency dependence of the line source function, particularly in the relative intensity and centre-to-limb behaviour of the K₁ parts of the line and in the asymmetry produced by differential velocity fields. We conclude that the frequency dependence of the K line source function must be considered in quantitative models for the formation of the K line.     

Electrons in the solar corona

During a balloon flight in France on September 13, 1971, at altitude 32 000 m, the solar corona was cinematographed from 2 to 5R during 5 hr, with an externally occulted coronagraph.Motions in coronal features, when they occur, exhibit deformations of structures with velocities not exceeding a few 10 km s^–1; several streamers were often involved simultaneously; these variations are compatible with magnetic changes or sudden reorganizations of lines of forces.Intensity and polarization measurements give the electron density with height in the quiet corona above the equator. Electron density gradient for one of the streamers gives a temperature of 1.6 × 10⁶ K and comparisons with the on-board Apollo 16 coronal observation of 31 July, 1971 are compatible with the extension of this temperature up to 25 R _bd.Three-dimensional structures and localizations of the streamers are deduced from combined photometry, polarimetry and ground-based K coronametry. Three of the four coronal streamers analysed have their axis bent with height towards the direction of the solar rotation, as if the upper corona has a rotation slightly faster than the chromosphere.     

On the geometric flattening index of the solar corona

Values of the Nikol??skii geometric flattening index of the solar corona, H, have been collected for 77 total solar eclipses from 1860 to 2010. The dependence of the H index on the Wolf number and the phase of solar activity is studied. The H index is found to take values in the range 0.9 to 2.5 and to anticorrelate with solar activity: the maximum values of the index are observed at solar minima and the minimum values are observed at solar maxima. In addition, the correlations between the H index and the Ludendorff photometric flattening index a + b and between the H index and extent of polar ray systems along the limb are investigated.     

Electrons in the solar corona

The polarimetric survey of electrons in the K-corona initiated at Pic-du-Midi and Meudon Observatories in 1964 now covers a full solar cycle of activity. The measurements are photometrically calibrated in an absolute scale.In June 1967 a persistent coronal feature was fan-shaped as a lame coronale above quiescent prominences. We deduce an electron density of N ₀ = 1.5 × 10⁸ at 60 000 km above the photosphere, a total number of 14 × 10³⁹ electrons, a hydrostatic temperature of 1.7 × 10⁶ K, and a total thermal energy 3N _eKT = 1.0 × 10³¹ ergs. When a center of activity appeared, a major localized condensation developed to replace the old elongated feature, with N ₀ = 4.5 × 10⁸, a total of 4.5 × 10³⁹ electrons and the same temperature of 1.7 × 10⁶ K.Also, a fan-shaped feature of exceptional intensity was analysed on 8 September 1966, with N ₀ = 6 × 10⁸ and a total of 24 × 10³⁹ electrons.Fan-shaped features are frequent above quiescent prominences. They degenerate above a height of 2R into thinner isolated columns or blades with temperatures also around 1.7 × 10⁶ K.     

A method for the evaluation of the brightness distribution in the solar corona

With photography of the solar corona at eclipses as an example, a method is given to calculate the relative brightnesses along a solar radius from a set of photographs. This set must be taken with different exposures, the ratio of two successive exposures, however, being constant. From the photometry of the density the relative brightnesses can be derived by a procedure consisting of three steps:

1. Reconstruction of a differential characteristic curve,
2. Compensation of the whole set of photographs. This leads to a discrete number of density-values to be associated with the relative brightnesses of the corona. For an arbitrary density-value
3. an improved method of interpolation based on the least square method is required. The procedure can more easily be carried out by computer-analysis.

     

On the reality of potential magnetic fields in the solar corona

Global magnetic field calculations, using potential field theory, are performed for Carrington rotations 1601–1610 during the Skylab period. The purpose of these computations is to quantitatively test the spatial correspondence between calculated open and closed field distributions in the solar corona with observed brightness structures. The two types of observed structures chosen for this study are coronal holes representing open geometries and theK-coronal brightness distribution which presumably outlines the closed field regions in the corona. The magnetic field calculations were made using the Adams-Pneuman fixed-mesh potential field code based upon line-of-sight photospheric field data from the KPNO 40-channel magnetograph. Coronal hole data is obtained from AS&E's soft X-ray experiment and NRL's Heii observations and theK-coronal brightness distributions are from HAO'sK-coronameter experiment at Mauna Loa, Hawaii.The comparison between computed open field line locations and coronal holes shows a generally good correspondence in spatial location on the Sun. However, the areas occupied by the open field seem to be somewhat smaller than the corresponding areas of X-ray holes. Possible explanations for this discrepancy are discussed. It is noted that the locations of open field lines and coronal holes coincide with the locations ofmaximum field strength in the higher corona with the closed regions consisting of relatively weaker fields.The general correspondence between bright regions in theK-corona and computed closed field regions is also good with the computed neutral lines lying at the top of the closed loops following the same general warped path around the Sun as the maxima in the brightness. One curious feature emerging from this comparison is that the neutral lines at a given longitude tend systematically to lie somewhat closer to the poles than the brightness maxima for all rotations considered. This discrepancy in latitude increases as the poles are approached. Three possible explanations for this tendency are given: perspective effects in theK -coronal observations, MHD effects due electric currents not accounted for in the analysis, and reported photospheric field strengths near the poles which are too low. To test this latter hypothesis, we artificially increased the line-of-sight photospheric field strengths above 70° latitude as an input to the magnetic field calculations. We found that, as the polar fields were increased, the discrepancy correspondingly decreased. The best agreement between neutral line locations and brightness maxima is obtained for a polar field of about 30 G.The National Center for Atmospheric Research is sponsored by the National Science Foundation.     

Improved three-dimensional mapping of the electron density distribution of the solar corona

Three-dimensional maps of the distribution of coronal electron density can now be computed with two radial functions in the series expansion for the density (rather than with only one radial function as shown in our previous paper). With the improved maps we can determine the topological variation of the electron density with radial distance, and thus can (1) distinguish coronal condensations from coronal streamers, (2) trace the structure of a streamer as a function of height, and (3) determine the non-radial orientation of a streamer. We summarize the previous work in concise mathematical notation, show examples of the improved maps derived from two radial functions, and discuss in detail the expectations and limitations of the method. Of great utility are computer-simulated pictures showing the solar corona as it would appear if veiwed from above the north (or south) pole.The National Center for Atmospheric Research is sponsored by the National Science Foundation.     

Siphon flows in the solar corona

The flows in a coronal magnetic arch associated with a pressure difference between the footpoints are investigated. Steady flows are of different types: always subsonic; subsonic in one branch of the arch, supersonic in the second; subsonic-supersonic with stationary shocks which adjust the flow to the boundary conditions in the second footpoint. The large velocity increase along the loop in subsonic-supersonic flows is associated with a large density decrease. A velocity drop and a density jump occur across the shock. The emission of such arches in coronal lines (625 of Mg x and 499 of Si xii) is calculated. It is suggested that the intensity drop along the axis observed in some UV loops is due to the density drop associated with subsonic-supersonic flows.     

Plasma drift in the solar corona

Model calculations of plasma drifts in the solar corona were performed. We established that only drifts in crossed fields could result in velocities V of several hundred kilometers per second. Such velocities are typical of coronal mass ejections (CMEs). We derived an analytic expression for V where n, the expansion harmonic of the magnetic-field strength, varies with time. As follows from this expression, V is a power function of the distance with index (2?n) and the radial component changes sign (n?1) times in the latitude range from ?π/2 to +π/2. We found that if the magnetic dipole moment varies with time, the similarity between the spiral structures of coronal plasma is preserved when they displace within several solar radii and the density gradient at the conical boundaries increases (the apparent contrast is enhanced). There is a correspondence between the inferred model effects and the actually observed phenomena that accompany CMEs.     

Heating of the solar corona

The suggestion is advanced that heating of the solar corona results from Landau damping of ion-acoustic waves generated in the motion of photospheric granules. Laboratory experiments relevant to the question of corona heating are discussed, together with the available observational information on the extent of energy deposition in the corona.Of the European Space Research Organization (ESRO).     

Geometrical considerations in imaging the solar corona

X-ray observations of the solar corona show that it is comprised of three-dimensional magnetic structures which appear to be primarily in the form of fluxtubes or loops. Imaging the X-ray corona has led to a greater understanding of the dynamical behaviour of and the energy distribution in these magnetic structures. However, imaging observations, by their very nature, integrate along the line of sight resulting in a two-dimensional representation of the actual three-dimensional distribution. The optically thin nature of the solar corona to X-ray radiation makes the integrated images particularly difficult to interpret. The analysis of the two-dimensional observations must, therefore, inlcude the effect of the orientation of the coronal structure to the line-of-sight direction; a fact which is almost always ignored. In this paper we discuss the effect of loop orientation on the two-dimensional representation and argue that these effects may lead to a misinterpretation of the physics occurring in the structures observed. In particular, we discuss observations taken by the Soft X-ray Telescope (SXT) on board the Yohkoh satellite, taking account of the instrumental thermal response, spatial resolution, and point-spread-function.We test the effect of geometry on the determination of the loop pressure by considering equatorial loops at various longitudes and discuss the implications of this for studies of coronal soft X-ray loops.     

A piston-driven shock in the solar corona

A solar flare that occurred on the west limb at 1981, March 25, 2038 UT generated a massive, rapidly-expanding optical coronal transient, which moved outward with an approximately constant velocity of 800 km s^–1. An associated magnetohydrodynamic shock travelled out ahead of the transient with a velocity estimated to be approximately 1000 km s^–1. The optical and radio data on the transient and shock fit well with general theories concerning piston-driven shocks and with current MHD models for propagation of such shocks through the solar corona.     

Gas-magnetic field interactions in the solar corona

It is evident from eclipse photographs that gas-magnetic field interactions are important in determining the structure and dynamical properties of the solar corona and interplanetary medium. Close to the Sun in regions of strong field, the coronal gas can be contained within closed loop structures. However, since the field in these regions decreases outward rapidly, the pressure and inertial forces of the solar wind eventually dominate and distend the field outward into interplanetary space. The complete geometrical and dynamical state is determined by a complex interplay of inertial, pressure, gravitational, and magnetic forces. The present paper is oriented toward the understanding of this interaction. The helmet streamer type configuration with its associated neutral point and sheet currents is of central importance in this problem and is, therefore, considered in some detail.Integration of the relevant partial differential equations is made tractable by an iterative technique consisting of three basic stages, which are described at length. A sample solution obtained by this method is presented and its physical properties discussed.The National Center for Atmospheric Research is sponsored by the National Science Foundation.