Solar-cycle evolution of the coronal general magnetic field of 1959–1974 and the synchronous variation of high-speed solar wind streams and galactic cosmic rays

The simultaneous enhancement or subsidence of both the high-speed solar wind streams and the galactic cosmic rays in the minimum or the maximum phase of the solar cycle are interpreted in a unified manner by the concept of geometrical evolution of the general magnetic field of the corona-heliomagnetosphere system. The coronal general magnetic field evolves from an open dipole-like configuration in the minimum phase to a closed configuration with many loop-like formations in the maximum phase of the solar cycle. This concept, developed in a theoretical solar-cycle model driven by the dynamo action of the global convection, is examined and found to be valid by studying the evolution of the coronal general magnetic field calculated from the observed surface general magnetic field of 1959–1974. It is also found that the energy density of the poloidal component of the general surface field, from which the coronal field originates, attained a maximum in the maximum phase and showed a evolution with virtually no phase delay with respect to that of the toroidal component of the field, to which the sunspot activity is related. The subsidence of the high-speed solar wind in the maximum phase is understood as a braking of the solar wind streams by the tightly closed and strong coronal field lines in the lower corona in the maximum phase. The field lines of the heliomagnetosphere, which originate from the coronal field lines drawn by the solar wind, are inferred to be also more tightly closed at the heliopause in the maximum phase than in the minimum phase. The decrease of the galactic cosmic rays in the maximum phase (known as the Forbush's negative correlation between the galactic cosmic ray intensity and the solar activity or the Forbush solar-cycle modulation of the galactic cosmic rays) is interpreted as a braking of the cosmic rays by the closed magnetic field lines at the heliopause. The observed phase lag (approximately one year) of the galactic cosmic ray modulation with respect to the evolution of the solar cycle, and the observed absence of the gradient of the total cosmic ray intensity between 1 AU and 8 AU, are discussed to support this view of the cosmic ray modulation at the remote heliopause, and reject other hypotheses to explain the phenomenon in terms of the magnetic irregularities of various kinds carried by the solar wind: The short-term Forbush decrease at a time of a flare shows that the magnetic irregularities can react on the cosmic rays relatively near the Sun if they even played a dominant role in the long-term modulation. The concept of the general magnetic field of the corona and the surface is also used to understand the basic nature of the surface field itself, by comparing the geometry of the calculated coronal field lines with the eclipse photographs of the corona, and by discussing, in the context of the coronal general magnetic field associated with the solar cycle, the process of the emergence of the coronal field lines from the interior and the formation of the transequatorial arches and loops connecting the two hemispheres in the corona.     

Different Types of Coronal Mass Ejections At Minimum and Maximum of Solar Activity and Their Relation to Magnetic Field Evolution

Coronal mass ejections (CMEs) are considered to be associated with large-scale, closed magnetic field structures in the corona. These structures change throughout the solar activity cycle following the evolution of the general solar magnetic field. To study the variation of CME characteristics with the evolution of coronal magnetic structures, we compute the 3-D coronal magnetic field at minimum and maximum of activity with a source-surface potential field model. In particular, we study the central latitude distribution of CMEs and the frequency of occurrence of the different CME types in these two periods. We find that most CMEs are indeed associated with large-scale, magnetically closed structures, and their latitudinal distribution follows the solar cycle latitudinal changes of the location of these structures. We also find that different CME types, which constitute different fractions of the total during the maximum and the minimum, are associated with different shapes and orientations of the closed structures at different times of the solar cycle.     

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.     

Polar Coronal Structures and the Global Magnetic Field Evolution Through the Cycle

We compare the shape and position of some plasma formations visible in the polar corona with the cyclic evolution of the global magnetic field. The first type of object is polar crown prominences. A two-fold decrease of the height of polar crown prominences was found during their poleward migration from the middle latitudes to the poles before a polar magnetic field reversal. The effect could be assigned to a decrease of the magnetic field scale. The second type of object is the polar plumes, ray like structures that follow magnetic field lines. Tangents to polar ray structures are usually crossed near some point, “a magnetic focus,” below the surface. The distance q between the focus and the center of the solar disk changes from the maximum value about 0.65 R _⊙ at solar minimum activity to the minimum value about 0.45 R _⊙ at solar maximum. At first glance this behaviour seems to be contrary to the dynamics of spherical harmonics of the global magnetic field throughout a cycle. We believe that the problem could be resolved if one takes into account not only scale changes in the global magnetic field but also the phase difference in the cyclic variations of large-scale and small-scale components of the global field.     

A coronal magnetic field model with horizontal volume and sheet currents

When globally mapping the observed photospheric magnetic field into the corona, the interaction of the solar wind and magnetic field has been treated either by imposing source surface boundary conditions that tacitly require volume currents outside the source surface (Schatten, Wilcox, and Ness, 1969) or by limiting the interaction to thin current sheets between oppositely directed field regions (Wolfson, 1985). Yet observations and numerical MHD calculations suggest the presence of non-force-free volume currents throughout the corona as well as thin current sheets in the neighborhoods of the interfaces between closed and open field lines or between oppositely directed open field lines surrounding coronal helmet-streamer structures. This work presents a model including both horizontal volume currents and streamer sheet currents. The present model builds on the magnetostatic equilibria developed by Bogdan and Low (1986) and the current-sheet modeling technique developed by Schatten (1971). The calculation uses synoptic charts of the line-of-sight component of the photospheric magnetic field measured at the Wilcox Solar Observatory. Comparison of an MHD model with the calculated model results for the case of a dipole field and comparison of eclipse observations with calculations for CR 1647 (near solar minimum) show that this horizontal current-current-sheet model reproduces polar plumes and axes of corona streamers better than the source-surface model and reproduces coronal helmet structures better than the current-sheet model.     

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 .     

First order latitude effects in the solar wind

The Weber-Davis model of the solar wind is generalized to include the effects of latitude. The principal assumptions of perfect electrical conductivity, rotational symmetry, a polytropic relation between pressure and density, and a flow aligned magnetic field in a system rotating with the Sun, are retained. A flow aligned magnetic field in the rotating system may be expressed in terms of the flow velocity and density. Rotational symmetry fixes the longitudinal flow velocity V_φ in terms of the flow in the r?θ plane. Thus, the original three dimensional magnetohydrodynamic flow problem is reduced to a two dimensional hydrodynamic flow problem in the r?θ plane.There are three critical surfaces associated with the equations which supply conditions to determine three of six required boundary conditions. The specified boundary conditions at the base of the corona are the temperature, density, and magnitude of the magnetic field. The equations are then expanded about the radial, nonrotating Parker solution and an analytic solution is obtained for the resulting first order equations. The results show that for constant coronal boundary conditions there is a latitudinal flow toward the solar poles, as a result of magnetic stresses, which persists out to large distances for the Sun. Associated with this flow is a latitudinal component of the magnetic field. The radial flow parameters are, to within small first order differences, in agreement with those of the Parker and the Weber-Davis models of the solar wind.The equations are further generalized to permit first order latitudinal variations in the specified coronal boundary conditions. Results at 1 a.u. are presented for 5 per cent latitudinal differences between the equatorial and polar values. These results show that the solution at 1 a.u. is most sensitive to a latitudinal dependence in the boundary temperature and least sensitive to a latitudinal dependence in the magnetic field magnitude.A solution is then obtained for an approximate dipolar variation in the coronal magnetic field magnitude. This solution predicts that the latitudinal flow is initially toward the Equator due to magnetic channeling; however, this effect is rapidly overcome and the latitudinal flow at 1 a.u. is toward the pole and not significantly different from the solution for constant boundary conditions.     

Impulses of activity and the Solar cycle

Extreme-ultraviolet data from EIT/SOHO (1996–2002), soft X-ray data from Yohkoh (1991–2001), and magnetic field data from MDI/SOHO (1996–2002) and Kitt Peak Observatory, NSO/NOAO (1991–2002) are analyzed together in the form of synoptic maps for the investigation of solar cycle variations of the corona and their relation to the magnetic field. These results show new interesting relations between the evolution of the topological structure of the corona, coronal heating and the large-scale magnetic field. The long-lived coronal structures are related to complexes of solar activity and display quasi-periodic behavior (in the form of impulses of coronal activity) with periods of 1.0–1.5 year, in the axisymmetric distribution of EUV and X-ray fluxes during the current solar cycle 23. In particular, during the second maximum of this cycle the solar corona became somewhat hotter than it was in the period of the first maximum.     

THE CORRELATION BETWEEN SUNSPOT AND CORONAL HOLE CYCLES AND A FORECAST OF THE MAXIMUM OF SUNSPOT CYCLE 23

We have shown in previous papers that a close relationship exists between the evolution of polar coronal hole area, estimated from K-coronameter observations, and the Wolf sunspot number, with a time lag of about half a solar cycle. In this paper we study the same relationship, but with the total coronal hole area at the base of the corona as obtained from a potential field model of the coronal magnetic field, which provides a more complete series of about three solar cycles. We confirm the relationship for the two last cycles and find that the forward time shift in the coronal hole area for the best correlation with sunspot number is almost the same for cycles 21 and 22, and this shift is also the time between peaks in both series. We use this result to make an early prediction of the time and size of the sunspot maximum for solar cycle 23, and find that this should occur early in 2001 and have a magnitude of about 190, similar to that of the two previous sunspot cycles.     

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.     

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.     

EUV analysis of polar plumes

Three polar plumes were studied using Skylab Mg x and O vi data. The plumes lie within the boundaries of a polar coronal hole. We find that the mean temperature of the plumes is about 1.1 × 10⁶ K and that they have a small vertical temperature gradient. Densities are determined and found consistent with white light analyses. The variation of density with height in the plumes is compared with that expected for hydrostatic equilibrium. As is the case for other coronal features, polar plumes will be a source of solar wind if the magnetic field lines are open. On the basis of the derived plume model and estimates of the numbers of plumes in polar coronal holes, it appears that polar plumes contain about 15% of the mass in a typical polar hole and occupy about 10% of the volume.Skylab Solar Workshop post-doc appointee 1975–1976. The Skylab Solar Workshops are sponsored by NASA and NSF and managed by the High Altitude Observatory, National Center for Atmospheric Research.     

The magnetic field in the solar atmosphere

This publication provides an overview of magnetic fields in the solar atmosphere with the focus lying on the corona. The solar magnetic field couples the solar interior with the visible surface of the Sun and with its atmosphere. It is also responsible for all solar activity in its numerous manifestations. Thus, dynamic phenomena such as coronal mass ejections and flares are magnetically driven. In addition, the field also plays a crucial role in heating the solar chromosphere and corona as well as in accelerating the solar wind. Our main emphasis is the magnetic field in the upper solar atmosphere so that photospheric and chromospheric magnetic structures are mainly discussed where relevant for higher solar layers. Also, the discussion of the solar atmosphere and activity is limited to those topics of direct relevance to the magnetic field. After giving a brief overview about the solar magnetic field in general and its global structure, we discuss in more detail the magnetic field in active regions, the quiet Sun and coronal holes.     

How To Use Magnetic Field Information For Coronal Loop Identification

The structure of the solar corona is dominated by the magnetic field because the magnetic pressure is about four orders of magnitude higher than the plasma pressure. Due to the high conductivity the emitting coronal plasma (visible, e.g., in SOHO/EIT) outlines the magnetic field lines. The gradient of the emitting plasma structures is significantly lower parallel to the magnetic field lines than in the perpendicular direction. Consequently information regarding the coronal magnetic field can be used for the interpretation of coronal plasma structures. We extrapolate the coronal magnetic field from photospheric magnetic field measurements into the corona. The extrapolation method depends on assumptions regarding coronal currents, e.g., potential fields (current-free) or force-free fields (current parallel to magnetic field). As a next step we project the reconstructed 3D magnetic field lines on an EIT-image and compare with the emitting plasma structures. Coronal loops are identified as closed magnetic field lines with a high emissivity in EIT and a small gradient of the emissivity along the magnetic field.     

Solar-interplanetary modeling: 3-D solar wind solutions in prescribed non-radial magnetic field geometries

A model is presented which describes the 3-dimensional non-radial solar wind expansion between the Sun and the Earth in a specified magnetic field configuration subject to synoptically observed plasma properties at the coronal base. In this paper, the field is taken to be potential in the inner corona based upon the Mt. Wilson magnetograph observations and radial beyond a certain chosen surface. For plasma boundary conditions at the Sun, we use deconvoluted density profiles obtained from synopticK-coronameter brightness observations. The temperature is taken to be 2 × 10⁶ K at the base of closed field lines and 1.6 x 10⁶K at the base of open field lines. For a sample calculation, we employ data taken during the period of the 12 November 1966 eclipse. Although qualitative agreement with observations at 1 AU is obtained, important discrepancies emerge which are not apparent from spherically symmetric models or those models which do not incorporate actual observations in the lower corona. These discrepancies appear to be due to two primary difficulties - the rapid geometric divergence of the open field lines in the inner corona as well as the breakdown in the validity of the Spitzer heat conduction formula even closer to the Sun than predicted by radial flow models. These two effects combine to produce conductively dominated solutions and lower velocities, densities, and field strengths at the Earth than those observed. The traditional difficulty in solar wind theory in that unrealistically small densities must be assumed at the coronal base in order to obtain observed densities at 1 AU is more than compensated for here by the rapid divergence of field lines in the inner corona. For these base conditions, the value ofβ(ratio of gas pressure to magnetic pressure) is shown to be significantly greater than one over most of the lower corona - suggesting that, for the coronal boundary conditions used here, the use of a potential or force-free magnetic field configuration may not be justified. The calculations of this paper point to the directions where future research on solar-interplanetary modelling should receive priority:

1. better models for the coronal magnetic field structure
2. improved understanding of the thermal conductivity relevant for the solar wind plasma.

     

Magnetic field configurations associated with fast solar wind

In this paper, we consider the implications of the observed inverse correlation between solar wind speed at Earth and the expansion rate of the Sun-Earth flux tube as it passes through the corona. We find that the coronal expansion rate depends critically on the large-scale photospheric field distribution around the footpoint of the flux tube, with the smallest expansions occurring in tubes that are rooted near a local minimum in the field. This suggests that the fastest wind streams originate from regions where large coronal holes are about to break apart and from the facing edges of adjacent like-polarity holes, whose field lines converge as they transit the corona. These ideas lead to the following predictions:

1. Weak holes and fragmentary holes can be sources of very fast wind.
2. Fast wind with steep latitudinal gradients may be generated where the field lines from the polar hole and a lower-latitude hole of like polarity converge to form a mid-latitude ‘apex’.
3. The fastest polar wind should occur shortly after sunspot maximum, when trailing-polarity flux converges onto the poles and begins to establish the new polar fields.

     

To the problem of solar coronal heating

We consider the adequacy of various solar coronal heating models. We show that the correlation between the intensity of the coronal Fe XIV 530.5 nm green line and the calculated magnetic field strength in the solar corona can be a useful tool for this purpose. We have established this correlation for coronal structures and magnetic fields of large spatial and temporal scales. The correlation found exhibits a strong dependence on both solar cycle phase and heliolatitude. The efficiency of a particular coronal heating mechanism is probably determined by the relative area occupied by low and high loops (including open structures). The direct current models based on slow field dissipation (DC) and the wave models based on Alfvén and magnetosonic wave dissipation (AC) are more efficient in the equatorial and polar zones, respectively.