The Green Corona and Magnetic Fields

We present results of a study of the green corona (530.3 nm, Fexiv) and photospheric magnetic fields over the period 1976–1999 when both quantities were observed by ground-based observatories. By comparing both the limb green-line intensities and photospheric magnetograms we have found a relation between the strength of magnetic field and coronal intensities. This relation enables us to extend solar surface magnetic fields since 1976 back to 1939. From 1947 to 1992 the magnetic field strength grew at the cycle maxima by a factor of 1.5–2. On the other hand, both the green corona intensity and magnetic field strength in the present cycle are smaller compared to cycle 22, by a factor of 2. No relationship was found between the green corona intensities and magnetic field polarity as was previously supposed. Behavior for the green corona intensities is different between high-latitude and mid-latitude regions, and this break occurs at the heliographic latitude of ± 45°. Homogeneous coronal data set cannot be directly used to derive `the tilt angle', even though some similarities between the green coronal holes, poleward branches in the green corona and prominences and the tilt angle can be found.     

Magnetic diffusion and flare energy buildup

Photospheric motion shears or twists solar magnetic fields to increase magnetic energy in the corona, because this process may change a current-free state of a coronal field to force-free states which carry electric current. This paper analyzes both linear and nonlinear two-dimensional force-free magnetic field models and derives relations of magnetic energy buildup with photospheric velocity field. When realistic data of solar magnetic field (B ₀ 10³ G) and photospheric velocity field (v _max 1 km s^–1) are used, it is found that 3–4 hours are needed to create an amount of free magnetic energy which is of the order of the current-free field energy. Furthermore, the paper studies situations in which finite magnetic diffusivities in photospheric plasma are introduced. The shearing motion increases coronal magnetic energy, while the photospheric diffusion reduces the energy. The variation of magnetic energy in the coronal region, then, depends on which process dominates.     

Constructing the Coronal Magnetic Field By Correlating Parameterized Magnetic Field Lines With Observed Coronal Plasma Structures

A method is presented for constructing the coronal magnetic field from photospheric magnetograms and observed coronal loops. A set of magnetic field lines generated from magnetogram data is parameterized and then deformed by varying the parameterized values. The coronal flux tubes associated with this field are adjusted until the correlation between the field lines and the observed coronal loops is maximized. A mathematical formulation is described which ensures that (i) the normal component of the photospheric field remains unchanged, (ii) the field is given in the entire corona over an active region, (iii) the field remains divergence-free, and (iv) electric currents are introduced into the field. It is demonstrated that a parameterization of a potential field, comprising a radial stretching of the field, can provide a match for a simple bipolar active region, AR 7999, which crossed the central meridian on 1996 November 26. The result is a non-force-free magnetic field with the Lorentz force being of the order of 10^–5.5 g cm s^–2 resulting from an electric current density of 0.079 A m^–2. Calculations show that the plasma beta becomes larger than unity at a relatively low height of 0.25 r supporting the non-force-free conclusion. The presence of such strong non-radial currents requires large transverse pressure gradients to maintain a magnetostatic atmosphere, required by the relatively persistent nature of the coronal structures observed in AR 7999. This scheme is an important tool in generating a magnetic field solution consistent with the coronal flux tube observations and the observed photospheric magnetic field.     

Photospheric electric current and transition region brightness within an active region

Distributions of vertical electric current density (J _z) calculated from vector measurements of the photospheric magnetic field are compared with ultraviolet spectroheliograms to investigate whether resistive heating is an important source of enhanced emission in the transition region. The photospheric magnetic fields in Active Region 2372 were measured on 6 and 7 April, 1980 with the MSFC vector magnetograph; ultraviolet wavelength spectroheliograms (L and Nv 1239 Å) were obtained with the UVSP experiment aboard the Solar Maximum Mission satellite. Spatial registration of the J _z (5 arc sec resolution) and UV (3 arc sec resolution) maps indicates that the maximum current density is cospatial with a minor but persistent UV enhancement, but there is little detected current associated with other nearby bright areas. We conclude that although resistive heating may be important in the transition region, the currents responsible for the heating are largely unresolved in our measurements and have no simple correlation with the residual current measured on 5 arc sec scales.National Research Council Resident Research Associate.National Oceanic and Atmospheric Administration Space Environment Laboratory; currently at MSFC/SSL.     

The coronal and interplanetary magnetic fields at the time of the solar eclipse of 7 March, 1970

The magnetic field in the outer corona and in interplanetary space has been calculated from the photospheric magnetic fields measured around the time of the 7 March, 1970 eclipse. The field-line maps are compared with eclipse photographs showing coronal structures out to about 12 r . The projected field lines as well as the observed streamers appear straight. This is caused by the rapid expansion of the outer corona and is not an indication of corotation. The calculations show that the angular velocity of the coronal plasma decreases rapidly with distance.The relation between magnetic fields and density enhancements is discussed. The field strength in the photosphere seems to determine the amount of mechanical heating of the lower corona. The density structure higher up in the corona will, however, depend decisively on the topology of the field, particularly on whether we are on open or closed field lines, and not simply on field strength.The calculations show a sector structure of the interplanetary field, which agrees well with spacecraft observations. Also the magnitudes of the observed and calculated interplanetary field agree after the Mt. Wilson magnetograph data have been corrected to account for the temperature and saturation effects in the spectral line Fei 5250 Å.On leave from the Astronomical Observatory, Lund, Sweden.The National Center for Atmospheric Research is sponsored by the National Science Foundation.     

Including stereoscopic information in the reconstruction of coronal magnetic fields

We present a method to include stereoscopic information about the three-dimensional structure of flux tubes into the reconstruction of the coronal magnetic field. Due to the low plasma beta in the corona we can assume a force-free magnetic field, with the current density parallel to the magnetic field lines. Here we use linear force-free fields for simplicity. The method uses the line-of-sight magnetic field on the photosphere as observational input. The value of is determined iteratively by comparing the reconstructed magnetic field with the observed structures. The final configuration is the optimal linear force-free solution constrained by both the photospheric magnetogram and the observed plasma structures. As an example we apply our method to SOHO MDI/EIT data of an active region. In the future it is planned to apply the method to analyse data from the SECCHI instrument aboard the STEREO mission.     

The structure of the white-light corona and the large-scale solar magnetic field

The large-scale density structure of the white-light solar corona has been compared to the organization of the solar magnetic field as identified by the appearance of neutral lines in the photosphere in order to examine whether any consistent relationship exists between the two. Data from the High Altitude Observatory's Mk-III K-coronameter have been used to describe the coronal density structure, and observations from several sources, beginning with observations from the University of Hawaii Stokes Polarimeter have been used to establish the magnetic field distribution. Stanford magnetograms as well as the neutral line inferred from potential field models have also been examined. During the period covering Carrington rotations 1717 to 1736 brightness enhancements in the low corona tend to lie over the global neutral sheet identified in the photospheric magnetic field. The brightest of these enhancements, however, are associated with neutral lines through active regions. These associations are not 1-1, but do hold both in stable and evolving conditions of the corona. We find a significant number of long-lived neutral lines, including filaments seen in H, for which there are not coronal enhancements.The National Center for Atmospheric Research is sponsored by the National Science Foundation.     

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.     

The derivation of temperature gradient and electron density maps from EUV spectroheliograms

We discuss spatial variations in electron density at the base of the corona and in the temperature gradient in the chromospheric-coronal transition layer as determined from analysis of maps constructed from Mgx and OVI spectroheliograms. Both the mapping techniques and results of analyzing EUV spectra from OSO 6 observations are presented. Comparisons of these maps with photospheric magnetograms and spectroheliograms made in chromospheric EUV lines and continua indicate that the electron density and temperature gradient in the transition layer tend to be enhanced in areas where the photospheric magnetic field and chromospheric EUV emission are enhanced. Relationships among the coronal electron density, transition-layer temperature gradient, chromospheric emission, and photospheric magnetic field strength are derived.     

Culgoora radio and skylab euv observations of emerging magnetic flux in the lower corona

Detailed comparisons of Culgoora 160 MHz radioheliograms of solar noise storms and Skylab EUV spectroheliograms of coronal loop structures are presented. It is concluded that: (1) there is a close association between changes in large-scale magnetic fields in the corona and the onset or cessation of noise storms; (2) these coronal changes result from the emergence of new magnetic flux at the photospheric level; (3) although new magnetic flux at the photospheric level is often accompanied by an increase in flare activity the latter is not directly responsible for noise storm activity; rather the new magnetic flux diffuses slowly outwards through the corona at rates 1–2 km s^–1 and produces noise storms at 160 MHz 1–2 days later; (4) the coronal density above or in large-scale EUV loop systems is sufficiently dense to account for noise storm emission at the fundamental plasma frequency; (5) the scatter in noise storm positions can be accounted for by the appearance and disappearance of individual loops in a system.     

The evolution of a coronal streamer and the photospheric magnetic field

A large equatorial coronal streamer observed in the outer corona (3R ) grew in brightness and size during successive limb passages between October 6, 1973 and January 10, 1974 (solar rotations 1606–1611). Unlike previous studies of streamers and their photospheric associations, no definite surface feature could be identified in the present case. This suggests that the streamer is associated with the large scale photospheric magnetic field. Comparison of the streamer growth with observed underlying photospheric magnetic flux changes indicated that as the streamer increased in brightness, areal extent, and density, the photospheric magnetic flux decreased. Three possible explanations for the streamer's growth are presented; the conceptually simplest being that the decrease in photospheric field results in an opening of the flux tubes under the streamer which permits an increased mass flux through the streamer.The National Center for Atmospheric Research is sponsored by the National Science Foundation.     

Solar Wind Speed and Expansion Rate of the Coronal Magnetic Field during Carrington Rotation 1909

The synoptic map of the solar wind speed (SWS) estimated by the computer-assisted tomography (CAT) method with interplanetary scintillation observations is constructed for the 1909 Carrington rotation. A similar synoptic map of expansion rate (RBR) of the coronal magnetic field calculated by the so-called 'potential model' with the photospheric magnetic field is also constructed under the radial field assumption (RF model). These maps consist of 64800 (180×360) data points of equal area. We examine for the first time relations between the SWS estimated by the CAT technique and the RBR calculated by the RF model. A highly significant correlation is found between the SWS and the RBR. A simple correlation coefficient is about –0.72; that is, high-velocity winds emanate from photospheric areas corresponding to a low expansion rate of the coronal magnetic field, and low-velocity winds emanate from photospheric areas of high expansion rate. This result suggests that there is some acceleration mechanism relating to the coronal field expansion.     

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.     

Differential Rotation of the Solar Corona from Magnetic Field Data

A method for investigating the differential rotation of the solar corona using the coronal magnetic field as a tracer is proposed. The magnetic field is calculated in the potential approximation from observational data at the photospheric level. The time interval from June 24, 1976, to December 31, 2004, is considered. The magnetic field has been calculated for all latitudes from the equator to ±75? with a 5? step at distances from the base of the corona 1.0 R_⊙ to 2.45 R_⊙ near the source surface. The coronal rotation periods at 14 distances from the solar center have been determined by the method of periodogram analysis. The coronal rotation is shown to become progressively less differential with increasing heliocentric distance; it does not become rigid even near the source surface. The change in the coronal rotation periods with time is considered. At the cycleminimumthe rotation has been found to bemost differential, especially at small distances from the solar center. The change in coronal rotation with time is consistent with the tilt of the solar magnetic equator. The results from the magnetic field are compared with those obtained from the brightness of the green coronal Fe XIV 530.3 nm line. The consistency between these results confirms the reliability of the proposed method for studying the coronal rotation. Studying the rotation of the coronal magnetic field gives hope for the possibility of using this method to diagnose the differential rotation in subphotospheric layers.     

Analysis of EUV limb brightening observations from ATM

Magnetic fields in the low corona are the only plausible source of energy for solar flares. Other energy sources appear inadequate or uncorrelated with flares. Low coronal magnetic fields cannot be measured accurately, so most attention has been directed toward measurements of the photospheric magnetic fields from which coronal developments may be inferred. Observations of these magnetic fields are reviewed. It is concluded that, except possibly for the largest flares, changes in the photospheric magnetic fields in flaring centers are confined to evolutionary changes associated with emergence of new magnetic flux. Flare observations with the 10830 Å line of helium, in particular, are discussed. It is concluded that the brightest flare knots appear near points of emergent magnetic flux. Pre-flare activation and eruptions of H filaments are discussed. It is concluded that the rapid motions in filaments indicate unambiguously that the magnetic fields in the low corona are severely disrupted prior to most flares. The coronal signature of H filament eruptions is illustrated with soft X-ray photographs from the S-054 experiment of the NASA Skylab mission. An attempt is made, by studying X-ray flare morphology, to determine whether flares grow by reconnections between adjacent or intertwined magnetic elements or by triggering, in which each flaring loop drives adjacent loops to unstable states. It is concluded that successive loop brightenings are most easily interpreted as the result of magnetic field reconnections, although better time resolution is required to settle the question. A model of magnetic field reconnections for flares associated with filament activation and emerging magnetic flux is presented.     

Background-Induced Measurement Errors of the Coronal Intensity, Density, Velocity, and Magnetic Field

The effect of a background signal on the signal-to-noise ratio is discussed, with particular application to ground-based observations of emission lines in the solar corona with the proposed Advanced Technology Solar Telescope. The concepts of effective coronal aperture and effective coronal integration time are introduced. Specific expressions are developed for the 1 measurement errors for coronal intensity, coronal electron density, coronal velocity, and coronal magnetic field measurements using emission lines and including a background.     

The Importance of Photospheric Intense Flux Tubes for Coronal Heating

Dissipation of magnetic energy in the corona requires the creation of very fine scale-lengths because of the high magnetic Reynolds number of the plasma. The formation of current sheets is a natural possible solution to this problem and it is now known that a magnetic field that is stressed by continous photospheric motions through a series of equilibria can easily form such sheets. Furthermore, in a large class of 3D magnetic fields without null points there are locations, called quasi-separatrix layers (QSLs), where the field-line linkage changes drastically. They are the relevant generalisation of normal separatrices to configurations without nulls: along them concentrated electric currents are formed by smooth boundary motions and 3D magnetic reconnection takes place when the layers are thin enough. With a homogenous normal magnetic field component at the boundaries, the existence of thin enough QSL to dissipate magnetic energy rapidly requires that the field is formed by flux tubes that are twisted by a few turns. However, the photospheric field is not homogeneous but is fragmented into a large number of thin flux tubes. We show that such thin tubes imply the presence of a large number of very thin QSLs in the corona. The main parameter on which their presence depends is the ratio between the magnetic flux located outside the flux tubes to the flux inside. The thickness of the QSLs is approximately given by the distance between neighbouring flux tubes multiplied by the ratio of fluxes to a power between two and three (depending on the density of flux tubes). Because most of the photospheric magnetic flux is confined in thin flux tubes, very thin QSLs are present in the corona with a thickness much smaller than the flux tube size. We suggest that a turbulent resistivity is triggered in a QSL, which then rapidly evolves into a dynamic current sheet that releases energy by fast reconnection at a rate that we estimate to be sufficient to heat the corona. We conclude that the fragmentation of the photospheric magnetic field stimulates the dissipation of magnetic energy in the corona.     

LASCO observations of the coronal rotation

The near-rigid rotation of the corona above the differential rotation of the photosphere has important implications for the form of the global coronal magnetic field. The magnetic reconfiguring associated with the shear region where the rigidly-rotating coronal field lines interface with the differentially-rotating photospheric field lines could provide an important energy source for coronal heating. We present data on coronal rotation as a function of altitude provided by the Large Angle Spectrometric Coronagraph (LASCO) instrument aboard the Solar and Heliospheric Observatory (SOHO) spacecraft. LASCO comprises of three coronagraphs (C1, C2, and C3) with nested fields-of-view spanning 1.1 R to 30 R. An asymmetry in brightness, both of the Fexiv emission line corona and of the broad-band electron scattered corona, has been observed to be stable over at least a one-year period spanning May 1996 to May 1997. This feature has presented a tracer for the coronal rotation and allowed period estimates to be made to beyond 15R, up to 5 times further than previously recorded for the white-light corona. The difficulty in determining the extent of differential motion in the outer corona is demonstrated and latitudinally averaged rates formed and determined as a function of distance from the Sun. The altitude extent of the low latitude closed coronal field region is inferred from the determined rotation periods which is important to the ability of the solar atmosphere to retain energetic particles. For the inner green line corona (<2 R) we determine a synodic rotation period of (27.4±0.1) days, whereas, for the outer white- light corona, (>2.5 R) we determine a rotation period of (27.7±0.1) days.     

The topology of a mixed-polarity potential field,and inferences for the heating of the quiet solar corona

We study the statistical properties of the connectivity of the corona over the quiet Sun by analyzing the potential magnetic field above the central area of source planes sprinkled randomly with some 300 magnetic monopoles each. We find that the field is generally more complex than one might infer from a study of the field within the source plane alone, or from a study of the 3D field around a small number of sources. Whereas a given source most commonly connects to only its nearest neighbors, it may connect to up to several dozen sources; only a weak trend relates the source strength and the number of connections. The connections between pairs of sources define volumes, or domains, of connectivity. Domains that have a finite cross section with the source plane are enclosed by surfaces that contain a pair of null points. In contrast, most of the bounding surfaces of domains that lie above the source plane appear not to contain null points. We argue that the above findings imply (i) that we should expect at best a weak correlation between coronal brightness and the flux in an underlying flux concentration, and (ii) that the low-lying chromospheric field lines (such as are observable in H) provide information on source connections that are largely complementary to those traced by the higher-reaching coronal field lines (observable in the extreme ultraviolet). We compare sample TRACE and SOHO/MDI observations of the quiet corona and photosphere with our finding that the number density of null points within the source plane closely matches that of the sources; because we find essentially no foci of coronal brightening away from significant photospheric magnetic flux concentrations, we conclude that coronal heating at such null points does not contribute significantly to the overall heating. We argue that the divergence of field lines towards multiple sources restricts the propagation of braids and twists, so that any coronal heating that is associated with the dissipation of braids induced by footpoint shuffling in mixed-polarity network is likely (a) to occur predominantly low in the corona, and (b) to be relatively more efficient in quiet Sun than in active regions for a given field strength and loop length.     

Flare-produced coronal MHD-fast-mode wavefronts and Moreton's wave phenomenon

The propagation characteristics of MHD fast-mode disturbances, which can emanate from flare regions, are computed for realistic conditions of the solar corona at the times of particular flares. The path of a fast-mode disturbance is determined by the large-scale (global) coronal distributions of magnetic field and density, and can be computed by a general raytracing procedure (eikonal equation) adapted to MHD. We use the coronal (electron) density distribution calculated from daily K-coronameter data, and the coronal magnetic field calculated under the current-free approximation from magnetograph measurements of the photospheric magnetic field. We compare the path and time-development of an MHD fast-mode wavefront emitted from the flare region (as calculated from a realistic model corona for the day of the observed Moreton wave event) with actual observations of the Moreton wave event, and find that the Moreton wave can be identified with the rapidly moving intersection of the coronal fast-mode wavefront and the chromosphere (as hypothesized in our previous paper); the directivity (anisotropic propagation), as well as other characteristics of the propagation of the Moreton wave can be successfully explained.sponsored by the National Science Foundation.