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.     

Relation between circular polarization of moving type IV bursts and polarity of photospheric magnetic fields

Two-dimensional, high-resolution observations of about 30 moving type IV bursts allow us to compare the polarization structure of the radio sources high in the corona with the distribution of magnetic fields measured at the photospheric level. Left- and right-handed circularly polarized moving type IV bursts are associated with active regions dominated by magnetic fields of plus and minus polarity respectively. The result suggests that the polarity of magnetic fields within the type IV source which moves high in the corona ( 1R above the photosphere) is closely related to the polarity of local magnetic fields at the photosphere. The above relation between the sense of polarization and the polarity of magnetic field is contrary to what would be expected from the generally accepted synchroton hypothesis. One way of resolving this conflict is to postulate that the magnetic field within the radio source has the opposite polarity to that of the ambient magnetic fields.     

Coronal force-free magnetic field: Source-surface model

Models of the magnetic field in the solar chromosphere and corona are still mainly based on theoretical extrapolations of photospheric measurements. For the practical calculation of the global field, the so-called source-surface model has been introduced, in which the influence of the solar wind is described by the requirement that the field be radial at some exterior (source) surface. Then the assumption that the field is current-free in the volume between the photosphere and this surface allows for its determination from the photospheric measurement. In the present paper a generalization of the source-surface model to force-free fields is proposed. In the generalized model the parameter( = ×B·B/B ²)must be non-constant (or vanish identically) and currents are restricted to regions with closed field lines. A mathematical algorithm for computing the field from boundary data is devised.     

PROBLEMS AND PROGRESS IN COMPUTING THREE-DIMENSIONAL CORONAL ACTIVE REGION MAGNETIC FIELDS FROM BOUNDARY DATA

An overview of the whole process of reconstructing the coronal magnetic field from boundary data measured at the photosphere is presented. We discuss the errors and uncertainties in the data and in the data reduction process. The problems include noise in the magnetograph measurements, uncertainties in the interpretation of polarization signals, the 180° ambiguity in the transverse field, and the fact that the photosphere is not force-free. Methods for computing the three-dimensional structure of coronal active region magnetic fields, under the force-free assumption, from these boundary data, are then discussed. The methods fall into three classes: the extrapolation technique, which seeks to integrate upwards from the photosphere using only local values at the boundary; the current-field iteration technique, which propagates currents measured at the boundary along field lines, then iteratively recomputes the magnetic field due to this current distribution; and the evolutionary technique, which simulates the evolution of the coronal field, under quasi-physical resistive magnetohydrodynamic equations, as currents injected at the boundary are driven towards the observed values. The extrapolation method is mathematically ill-posed, and must be heavily smoothed to avoid exponential divergence. It may be useful for tracing low-lying field lines, but appears incapable of reconstructing the magnetic field higher in the corona. The original formulation of the current-field iteration method had problems achieving convergence, but a recent reformulation appears promising. Evolutionary methods have been applied to several real datasets, with apparent success.     

Evolution of the Fine Structure of Magnetic Fields in the Quiet Sun: Observations from Sunrise/IMaX and Extrapolations

Observations with the balloon-borne Sunrise/Imaging Magnetograph eXperiment (IMaX) provide high spatial resolution (roughly 100 km at disk center) measurements of the magnetic field in the photosphere of the quiet Sun. To investigate the magnetic structure of the chromosphere and corona, we extrapolate these photospheric measurements into the upper solar atmosphere and analyze a 22-minute long time series with a cadence of 33 seconds. Using the extrapolated magnetic-field lines as tracer, we investigate temporal evolution of the magnetic connectivity in the quiet Sun’s atmosphere. The majority of magnetic loops are asymmetric in the sense that the photospheric field strength at the loop foot points is very different. We find that the magnetic connectivity of the loops changes rapidly with a typical connection recycling time of about 3±1 minutes in the upper solar atmosphere and 12±4 minutes in the photosphere. This is considerably shorter than previously found. Nonetheless, our estimate of the energy released by the associated magnetic-reconnection processes is not likely to be the sole source for heating the chromosphere and corona in the quiet Sun.     

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.     

Numerical simulation of the current sheet above solar spots

Current sheet (CS) creation in a region with anX-type zero magnetic field line in plasma was simulated by numerically solving the 3D MHD equations for conditions which were close to the solar corona: the disturbance propagated from the photosphere boundary under which the magnetic field sources were situated. Some of values (B,,V) were set on the photosphere boundary, while others were determined from the conditions inside the region. Several Alfvén times after its creation, the CS motion practically ceased, and the plasma velocity changed its direction above the sheet, so that the plasma flow was directed into the CS from both sides.     

The Generating Region of Bidirectional Electron Beams in the Corona

Metric and decimetric type III bursts and microwave spike emissions with negative and positive frequency drift rates which were observed with radio spectrometers at Yunnan and Beijing Observatories are presented. The frequencies and heights at which the bidirectional electron beams originated are estimated. Three events reveal a separatrix frequency (at 250, 1300, and 2900 MHz) between normal- and reverse-drifting radio bursts, indicating a compact acceleration source where electron beams are injected in both upward and downward directions. These cases may indicate that the changeover frequencies of bidirectional electron beams are within a large band from 250 to 2900 MHz and the frequency bands of separatrices are in very small (4 to 100 MHz) and different bands. These type III bursts appear to be a plasma emission phenomenon from a beam of electrons which seem to have widely separated acceleration regions from the high to the low corona. These cases suggest that current sheets that separate open and closed magnetic fluxes in the low corona, and oppositely directed open field lines in the high corona are possible sites for bidirectional electron acceleration. The regions of magnetic topology from closed to open magnetic field structures should be very large (from about 20000 to 107000 km above the photosphere).     

The Role of the Kink Instability of a Long-Lived Active Region AR 9604

We have traced the long-term evolution of a non-Hale active region composed of NOAA 9604–9632–9672–9704–9738, which displayed strong transient activity with associated geomagnetic effects from September to December, 2001. By studying the development of spot-group and line-of-sight magnetic field together with the evolution of H_α filaments, the EUV and X-ray corona (TRACE 171 Å, Yohkoh/SXT), we have found that the magnetic structure of the active region exhibited a continuous clockwise rotation throughout its entire life. Vector magnetic data obtained from Huairou Solar Observing Station (HSOS) and full-disk line-of-sight magnetograms from SOHO/MDI allowed the determination of the best-fit force-free parameter (proxy of twist), α_best, and the systematic tilt angle (proxy of writhe) which were both found to take positive values. Soft X-ray coronal loops from Yohkoh/SXT displayed a pronounced forward-sigmoid structure in period of NOAA 9704. These observations imply that the magnetic flux tube (loops) with the same handedness (right) of the writhe and the twist rotated clockwise in the solar atmosphere for a long time. We argue that the continuous clockwise rotation of the long-lived active region may be a manifestation that a highly right-hand twisted and kinked flux tube was emerging through the photosphere and chromosphere into the corona.     

Relating White-Light Coronal Images to Magnetic Fields and Plasma Flow

The solar magnetic field is key to a detailed understanding of the Sun's atmosphere and its transition to the solar wind. However, the lack of detailed magnetic field measurements everywhere except at the photosphere has made it challenging to determine its topology and to understand how it produces the observed plasma properties of the corona and solar wind. Recent progress based on the synthesis of diversified observations has shown that the corona is highly filamentary, that the coronal magnetic field is predominantly radial, and that the ability of closed fields to trap plasma at the base of the corona is a manifestation of how the solar field controls the solar wind. In this paper, we explain how these results are consistent with the relationship between density structure of white-light images and fields and flow. We point out that the ‘shape’ of the corona observed in white-light images is a consequence of the steep fall-off in density with radial distance, coupled with the inherent limitation in the sensitivity of the observing instrument. We discuss how the significant variation in radial density fall-off with latitude leads to a coronal shape that is more precisely revealed when a radial gradient filter is used, but which also gives a false impression of the tracing of highly non-radial fields. Instead, the coronal field is predominantly radial, and the two magnetic features that influence the shape of the corona are the closed fields at the base of the corona, and the polarity reversal forming the heliospheric current sheet in the outer corona. An erratum to this article is available at .     

On the magnetic structure of the quiet transition region

Existing models of the quiet chromosphere-corona transition region predict a distribution of emission measure over temperature that agrees with observation for T 10⁵ K. These network models assume that all magnetic field lines that emerge from the photosphere extend into and are in thermal contact with the corona. We show that the observed fine-scale structure of the photospheric magnetic network instead suggests a two-component picture in which magnetic funnels that open into the corona emerge from only a fraction of the network. The gas that makes up the hotter transition region is mostly contained within these funnels, as in standard models, but, because the funnels are more constricted in our picture, the heat flowing into the cooler transition region from the corona is reduced by up to an order of magnitude. The remainder of the network is occupied by a population of low-lying loops with lengths 10⁴ km. We propose that the cooler transition region is mainly located within such loops, which are magnetically insulated from the corona and must, therefore, be heated internally. The fine-scale structure of ultraviolet spectroheliograms is consistent with this proposal, and theoretical models of internally heated loops can explain the behavior of the emission measure below T 10⁵ K.Operated by the Association of Universities for Research in Astronomy, Inc., under contract with the National Science Foundation.     

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.     

The ideal magnetohydrodynamic stability of a line-tied coronal magnetohydrostatic equilibrium

An energy method is used to determine a condition for local instability of field lines in magnetohydrostatic equilibrium which are rooted in the photosphere. The particular equilibrium studied is isothermal and two-dimensional and may model a coronal arcade of loops where variations along the axis of the arcade are weak enough to be ignorable. If line tying conditions are modelled by perturbations that vanish on the photosphere, then, when the field is unsheared, the condition for stability is necessary and sufficient. However, when the axial field component is non-zero, so that the field is sheared, the stability condition is only sufficient.It is found that when < 0.34 the equilibrium is stable. When = 0.34 a magnetic neutral line appears at the photosphere and it is marginally stable. When > 0.34 a magnetic island is present and all the field lines inside the island are unstable as well as some beyond it. As increases, the size of the island and the extent of unstable field lines increase. The effect of the instability is likely to be to create small-scale filamentation in the solar corona and to enhance the global transport coefficients.     

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.     

Coronal Magnetic Topologies in a Spherical Geometry II. Four Balanced Flux Sources

The Sun’s magnetic field is the primary factor determining the structure and evolution of the solar corona. Here, magnetic topology is used in combination with a Green’s function method to model the global coronal magnetic field with a spherical photosphere. We focus on the case of three negative flux sources and one positive source, completing our previous categorisation of the topological states and bifurcations that are present in quadrupolar configurations in a spherical geometry. Three fundamental varieties of topological state are found, with three types of bifurcation taking one to the other. A comparison to the equivalent results for a planar photosphere is then carried out, and the differences between the two cases are explained.     

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.     

Spatial Structure of Solar Coronal Magnetic Loops Revealed by Transient Microwave Brightenings

We present the measurement of magnetic field gradient in magnetic loops in the solar corona, based on the multi-wavelength Very Large Array observations of two transient microwave brightenings (TMBs) in the solar active region 7135. The events were observed at 2 cm (spatial resolution 2=) and 3.6 cm (spatial resolution 3=) with a temporal resolution of 3.3 s in a time-sharing mode. Soft X-ray data (spatial resolution 2.5=) were available from the Soft X-ray Telescope on board the Yohkoh satellite. The three-dimensional structure of simple magnetic loops, where the transient brightenings occurred, were traced out by these observations. The 2-cm and 3.6-cm sources were very compact, located near the footpoint of the magnetic loops seen in the X-ray images. For the two events reported in this paper, the projected angular separation between the centroids of 2 and 3.6-cm sources is about 2.3= and 3.1=, respectively. We interpret that the 2 and 3.6-cm sources come from thermal gyro-resonance emission. The 2-cm emission is at the 3rd harmonic originating from the gyro-resonance layer where the magnetic field is 1800 G. The 3.6-cm emission is at the 2nd harmonic, originating from the gyro-resonance layer with a magnetic field of 1500 G. The estimated magnetic field gradient near the footpoint of the magnetic loop is about 0.09 G km=¹ and 0.12 G km=¹ for the two events. These values are smaller than those observed in the photosphere and chromosphere by at least a factor of 2.     

A model of the solar atmosphere and wind

Using a combination of solar and interplanetary measurements, a topological model is developed of the overall magnetic and plasma structures.

Microwave Mode Coupling Above Active Regions as a Coronal Density Diagnostic

It is well recognized that the phenomenon of depolarization (the conversion of polarized radio emission into unpolarized emission) of microwaves over solar active regions can be used to infer the coronal electron density once the coronal magnetic field is known. In this paper we explore this technique using an active region for which we have excellent radio data showing depolarization at two frequencies, and for which we have an excellent magnetic field model which has been tested against observations. We show that this technique for obtaining coronal densities is very sensitive to a number of factors. When Cohen's (1960) theory where depolarization is due to magnetic field rotation alone is used, the result is particularly sensitive to the location of the surface on which the magnetic field is orthogonal to the line of sight. Depending on whether we take into account the presence of electric currents in the photosphere or not, their extrapolation into the corona can result in very different heights being deduced for the location of the depolarization strip, and this changes the density which is then deduced from the depolarization condition. Such extreme sensitivity to the magnetic field model requires that field extrapolations be able to accurately predict the polarity of magnetic fields up to coronal heights as high as 10⁵ km in order to exploit depolarization as a density diagnostic.