Flattening Index of the Solar Corona and the Solar Cycle

The photometrical flattening index of the solar corona a+b is defined according to Ludendorff. In this paper we have investigated how the flattening index varies with respect to the phase of solar activity and the sunspot number. We have compiled 170 values of the flattening index using the data on 60 total solar eclipses from 1851 to 2010. We have found that the flattening index takes values from 0 to 0.4, and is anticorrelated with solar activity. The value of the flattening index at the beginning of solar cycle 24 was used as a precursor to forecast the amplitude of the cycle. It was found that the amplitude of solar cycle 24 will be about 95 in terms of the smoothed monthly sunspot numbers.     

Solar corona during the total solar eclipse on August 1, 2008

Shape and structure of the solar corona during the August 1, 2008, total solar eclipse is reported. The August 1, 2008, corona is classified as of near-minimum type with well developed northern and southern polar ray systems over polar coronal holes and several streamers of different brightness at the middle and low heliographic latitude. The flattening index was found to be 0.21.     

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.     

Structure and shape of the solar corona during the total solar eclipse on March 29, 2006

The structure and the shape of the solar corona during the total solar eclipse on March 29, 2006 were studied. The corona was of the intermediate pre-minimal type, it had northern and southern polar ray systems above the polar coronal holes and six streamers of different brightness in the middle and low heliographic latitudes. All the coronal structural features were found to have counterparts at the photosphere-chromosphere level on the limb and near it. The corona’s photometric flattening index was equal to 0.17.     

The Flattening Index of the Eclipse White-Light Corona and Magnetic Fields

From observations of the solar white-light corona at 65 eclipses from 1851 to 2015 we confirm earlier findings that the flattening index of the white-light corona depends on the phase, rather than the magnitude of solar cycles, which is in contrast with behavior of other major solar activity indices like the sunspot number, the 2800 MHz radio flux, etc. This indicates that mechanisms responsible for creation and distribution of helmet streamers, the most essential coronal structures influencing the flattening index, could be of different magnetic nature from those of other manifestations of solar surface activity.     

Radial variation of differential rotation in the solar electron corona

Long-lived brightness structures in the solar electron corona persist over many solar rotation periods and permit an observational determination of coronal magnetic tracer rotation as a function of latitude and height in the solar atmosphere. For observations over 1964–1976 spanning solar cycle 20, we compare the latitude dependence of rotation at two heights in the corona. Comparison of rotation rates from East and West limbs and from independent computational procedures is used to estimate uncertainty. Time-averaged rotation rates based on three methods of analysis demonstrate that, on average, coronal differential rotation decreases with height from 1.125 to 1.5 R _S. The observed radial variation of differential rotation implies a scale height of approximately 0.7 R _S for coronal differential rotation.Model calculations for a simple MHD loop show that magnetic connections between high and low latitudes may produce the observed radial variations of magnetic tracer rotation. If the observed tracer rotation represents the rotation of open magnetic field lines as well as that of closed loops, the small scale height for differential rotation suggests that the rotation of solar magnetic fields at the base of the solar wind may be only weakly latitude dependent. If, instead, closed loops account completely for the radial gradients of rotation, outward extrapolation of electron coronal rotation may not describe magnetic field rotation at the solar wind source. Inward extrapolations of observed rotation rates suggest that magnetic field and plasma are coupled a few hundredths of a solar radius beneath the photosphere.     

Connections Between the White-Light Eclipse Corona and Magnetic Fields over the Solar Cycle

Observations of ten solar eclipses (1973–1999) enabled us to reveal and describe mutual relations between the white-light corona structures (e.g., global coronal forms and most conspicuous coronal features, such as helmet streamers and coronal holes) and the coronal magnetic field strength and topology. The magnetic field strength and topology were extrapolated from the photospheric data under the current-free assumption. In spite of this simplification the found correspondence between the white-light corona structure and magnetic field organization strongly suggests a governing role of the field in the appearance and evolution of local and global structures. Our analysis shows that the study of white-light corona structures over a long period of time can provide valuable information on the magnetic field cyclic variations. This is particularly important for the epoch when the corresponding measurements of the photospheric magnetic field are absent.     

Coronal general magnetic field evolution as a new parameter of the solar cycle

The magnetic field lines of the corona associated with the solar-cycle surface general magnetic field are calculated by a potential-field approximation to study the solar-cycle evolution of the geometry of the coronal field. The surface field evolution used here is the radial field evolution, predicted by a model of the solar cycle driven by the dynamo action of the global convection, and justified observationally using Mount Wilson magnetic synoptic chart data. The evolution of the calculated coronal general field is now good for comparison with observations and shows the following. (i) The field of the polar and high-altitude corona has dipolar structure in almost all phases of the solar cycle except in a short time interval around maximum phase despite the quadrupolar structure of the general magnetic field at the surface; quadrupolar field forms loop-like structure in the lower corona. The almost-dipolar structure of the polar and high-latitude corona and the loop formation of the equatorial lower corona explain the appearance of the undisturbed minimum corona observed at eclipses. (ii) The polar field lines are directed almost radially at the minimum phase, which should be responsible for polar plumes. The field lines slowly open up to participate in the loop-like structure of the equatorial lower corona, and rapidly change their structure and polarity at the maximum phase, to resume the almost radial configuration slowly, (iii) During the rapidly changing maximum phase, the field lines do not penetrate deep into the interplanetary space resulting in the absence of polar plumes and the appearance of the circular corona- the maximum corona. In this phase, the coronal field should not be approximated by a dipole field. The surface field evolution which can explain such behaviors of the corona is characteristic of the solar-cycle process dominated by the latitudinal gradient of the differential rotation. If the radial gradient dominated in the subsurface process, the coronal evolution would look quite different and would show latitudinal propagation of enhancement of activity. Although nonaxisymmetric features should be superposed on the axisymmetric general field to express the real corona, the general field can be a basic coronal field in studying long-term interaction between the convection zone and the interstellar space especially in studying the magnetic braking of the solar rotation.     

Comparison of computed fluxes for Fex and Fexiv lines with observed values at 1980 eclipse

Fluxes have been computed for Fex (6374 Å) and Fe xiv (5303 Å) lines as a function of solar radii and at various coronal tempratures. The electron density derived from the white light corona during the total solar eclipse of 1980 were used in the computations. Fluxes in adjacent continua have also been computed. The computed ratios of line flux to the square of continuum flux at a coronal temperature of 1.6 × 10⁶ K show a good fit with the observed values for Fex line. Further, radiative excitation seems to dominate over collisional excitation beyond 1.3 solar radius.     

Long-term modulation of the coronal index of solar activity

Monthly mean values of the coronal index of solar activity and other solar indices are analyzed for the period 1965–1997 covering three solar cycles. The coronal index is based upon the total irradiance of the coronal 530.3 nm green line from observations at five stations. The significant correlation of this index with the sunspot number and the number of the grouped solar flares have led to an analytical expression which can reproduce the coronal index of solar activity as a function of these parameters. This expression well explains the existence of the two maxima during the solar cycles taking into account the evolution of the magnetic field that can be expressed by a sinusoidal term with a 6-year period. The agreement between observed and calculated values of the coronal index on a monthly basis is high enough and reaches the value of 92%. It is concluded that the coronal index can be used as a representative index of solar activity in order to be correlated with different periodic solar–terrestrial phenomena useful for space weather studies.     

On the Magnetic Correspondence between the Photosphere and the Heliosphere

The solar magnetic field maps every point in the corona to a corresponding place on the solar surface. Identifying the magnetic connection map is difficult at low latitudes near the heliospheric current sheet, but remarkably simple in coronal hole interiors. We present a simple analytic magnetic model (‘pseudocurrent extrapolation’) that reproduces the global structure of the corona, with significant physical advantages over other nearly analytic models such as source-surface potential field extrapolation. We use the model to demonstrate that local horizontal structure is preserved across altitude in the central portions of solar coronal holes, up to at least 30 R_s, in agreement with observations. We argue that the preserved horizontal structure may be used to track the magnetic footpoint associated with the location of a hypothetical spacecraft traveling through the solar corona, to relate in situ measurements of the young solar wind at ∼10–30 R_s to particular source regions at the solar surface. Further, we discuss the relationship between readily observable geometrical distortions and physical parameters of interest such as the field-aligned current density.     

An empirical model of the daily evolution of the coronal index

Global changes of the solar activity can be expressed by the coronal index that is based upon the total irradiance of the coronal 530.3 nm green line from observations at five stations. Daily mean values of the coronal index of solar activity and other well-correlated solar indices are analyzed for the period 1966–1998 covering over three solar cycles. The significant correlation of this index with the sunspot number and the solar flare index have led to an analytical expression which can reproduce the coronal index of solar activity as a function of these parameters. This expression explains well the existence of the two maxima during the solar cycles taking into account the evolution of the magnetic field that can be expressed by some sinusoidal terms during solar maxima and minima. The accuracy between observed and calculated values of the coronal index on a daily basis reaches the value of 71%. It is concluded that the representative character of the coronal index is preserved even when using daily data and can therefore allow us to study long-term, intermediate and short-term variations for the Sun as a star, in association with different periodical solar–terrestrial phenomena useful for space weather studies.     

The solar X-ray corona

The solar corona, and the coronae of solar-type stars, consist of a low-density magnetized plasma at temperatures exceeding 10⁶ K. The primary coronal emission is therefore in the UV and soft x-ray range. The observed close connection between solar magnetic fields and the physical parameters of the corona implies a fundamental role for the magnetic field in coronal structuring and dynamics. Variability of the corona occurs on all temporal and spatial scales—at one extreme, as the result of plasma instabilities, and at the other extreme driven by the global magnetic flux emergence patterns of the solar cycle.     

Coronal index of solar activity VIII, years 1992–1994

The coronal index of solar activity over the period 1992–1994 is given. The data are a good tool to study solar activity, for the Sun as a star, in the solar corona over a solar cycle and its influence in the heliosphere.     

The Depiction of Coronal Structure in White-Light Images

The very steep decrease in density with heliocentric distance makes imaging of coronal density structures out to a few solar radii challenging. The radial gradient in brightness can be reduced using numerous image processing techniques, thus quantitative data are manipulated to provide qualitative images. We introduce a new normalizing-radial-graded filter (NRGF): a simple filter for removing the radial gradient to reveal coronal structure. Applied to polarized brightness observations of the corona, the NRGF produces images which are striking in their detail. Total-brightness, white-light images include contributions from the F corona, stray light, and other instrumental contributions which need to be removed as effectively as possible to properly reveal the electron corona structure. A new procedure for subtracting this background from LASCO C2 white-light, total-brightness images is introduced. The background is created from the unpolarized component of total-brightness images and is found to be remarkably time-invariant, remaining virtually unchanged over the solar cycle. By direct comparison with polarized-brightness data, we show that the new background-subtracting procedure is superior in depicting coronal structure accurately, particularly when used in conjunction with the NRGF. The effectiveness of the procedures is demonstrated on a series of LASCO C2 observations of a coronal mass ejection (CME).     

The Varying Multipolar Structure of the Sun's Magnetic Field and the Evolution of the Solar Magnetosphere Through the Solar Cycle

The Sun's magnetic field extends far from the photosphere, into the corona, defining a magnetically dominated region before being drawn out radially by the solar wind flow. This region, where the internal sources of the solar field dominate the plasma structures and the energetic particle movement, can be properly considered the solar magnetosphere. The magnetic field in this region can be approximately described by models that extrapolate photospheric magnetic field observations under some simplifying assumptions. In this paper we use a potential field model which describes the solar field up to a source surface at 3.25 R_s, where the field is constrained to become radial. We present the variation of the magnitude and inclination of the various multipolar components throughout the solar magnetic cycle that characterise the changes in the structure of the solar magnetosphere over a period of 22 years. We also present some 3-D images of the coronal magnetic structure to show the global evolution of the solar magnetosphere throughout the solar cycle and discuss the importance of taking this structure into account in order to relate interplanetary and solar features.     

Filamentary Structures of Coronal White-Light Images

In the absence of magnetic field measurements of the solar corona, the density structure of white-light images has provided important insight into the coronal magnetic field. Recent work sparked by highly sensitive radio occultation measurements of path-integrated density has elucidated the density structure of unprocessed solar eclipse pictures. This paper does the same for processed images that reveal low-contrast small-scale structures, specifically Koutchmy’s edge-enhanced white-light image of the 11 August 1999 solar eclipse. This processed image provides visual evidence for two important results deduced from radio occultation measurements of small-scale density variations. First, in addition to the closed loops readily seen at the base of the corona in high-resolution EUV and soft X-ray images, open filamentary structures permeate the corona including active regions generally thought to be magnetically closed. Observed at the image resolution, the filamentary structures are 1° wide in latitude and an order of magnitude smaller than polar plumes. Second, although inhomogeneities that are convected along with the solar wind are also present, filamentary structures dominate the image because of their steeper density gradients. The quantitative profile of polarized brightness (pB) at the base of the corona shows that the filamentary structures have transverse density gradients that are proportional to their density. This explains why edge-enhanced images, limited in sensitivity to density gradients, tend to detect filamentary structures more readily in high-density regions (e.g., active regions, streamer stalks, and prominences) than in low-density polar coronal holes, and why filamentary structures seem more prevalent in solar eclipse pictures during solar maximum. The pB profile at the base of the corona also fills the gap in Doppler measurements there, reinforcing that open ultra-fine-scale filamentary structures observed by the radio measurements are predominantly radial and that they are an integral part of the radial expansion of the solar wind.     

Dynamic Three-Dimensional Tomography of the Solar Corona

Empirical, three-dimensional electron-density maps of the solar corona can be tomographically reconstructed using polarized-brightness images measured from ground- and space-based observatories. Current methods for computing these reconstructions require the assumption that the structure of the corona is unchanging with time. We present the first global reconstructions that do away with this static assumption and, as a result, allow for a more accurate empirical determination of the dynamic solar corona. We compare the new dynamic reconstructions of the coronal density during February 2008 to a sequence of static reconstructions. We find that the new dynamic reconstructions are less prone to certain computational artifacts that may plague the static reconstructions. In addition, these benefits come without a significant increase in computational cost.     

Solar Cycle Variation of Magnetic Flux Ropes in a Quasi-Static Coronal Evolution Model

The structure of electric current and magnetic helicity in the solar corona is closely linked to solar activity over the 11-year cycle, yet is poorly understood. As an alternative to traditional current-free “potential-field” extrapolations, we investigate a model for the global coronal magnetic field which is non-potential and time-dependent, following the build-up and transport of magnetic helicity due to flux emergence and large-scale photospheric motions. This helicity concentrates into twisted magnetic flux ropes, which may lose equilibrium and be ejected. Here, we consider how the magnetic structure predicted by this model – in particular the flux ropes – varies over the solar activity cycle, based on photospheric input data from six periods of cycle 23. The number of flux ropes doubles from minimum to maximum, following the total length of photospheric polarity inversion lines. However, the number of flux rope ejections increases by a factor of eight, following the emergence rate of active regions. This is broadly consistent with the observed cycle modulation of coronal mass ejections, although the actual rate of ejections in the simulation is about a fifth of the rate of observed events. The model predicts that, even at minimum, differential rotation will produce sheared, non-potential, magnetic structure at all latitudes.     

LASCO observations of the coronal rotation and morphology of tracers seen at solar maximum and comparison with solar minimum

We present data obtained from the Large Angle Spectrometric Coronagraph (LASCO) aboard the Solar and Heliospheric Observatory spacecraft (SOHO). We compare the rotation of the white-light corona as seen during a period approaching the maximum of the solar 11-year activity cycle with that observed in a previous study made at solar minimum (Lewis et al., 1999). We find no fundamental difference in the rotation characteristics and again find the white-light corona to be radially rigid. The rotation has been observed at altitudes from 2.5 R _⊙ to beyond 15 R _⊙ and as predicted in the previous study, the greater level of complexity in the coronal structures and their relatively rapid evolution has not allowed periods to be determined as accurately as at solar minimum. Our best estimate of the mean synodic rotation period during the period of study (7 March 1999 to 6 March 2000) is 27.5±0.3 days. This is consistent with the relatively small scale structures associated with the surface activity imposing their rotation signature on an otherwise axisymmetric background corona. The short-lived nature of the small scale coronal morphologies at this epoch has made a thorough analysis of the latitudinal variation difficult, although we again find some evidence for the white light corona's increased latitudinal rigidity when compared to the underlying photosphere. However, we again note how projection effects create difficulties in confirming the exact degree of rigidity in the corona at these altitudes and a very simple coronal model is used to highlight how the appearance of lower latitude features in projection can contaminate the coronal signal observed at other latitudes. We also note evidence for a sudden and apparently fundamental change to the global coronal morphology on the approach to solar maximum and suggest this may represent the time beyond which the classical solar dipole ceases to dominate the coronal field.