The Solar Magnetic Field as a Coronal Hole Extension Forms: Effects of Magnetic Helicity and Boundary Conditions

An analytical solution is presented for linear force fields within a spherical shell, representing the solar corona. Allowing for a global magnetic helicity, we find magnetic fields over the entire corona with realistic inner boundary conditions obtained from transformation and extrapolation of photospheric magnetograms and considering alternative outer boundary conditions. Such fields are found for the well known coronal hole extension event of August 1996. This revised version was published online in June 2006 with corrections to the Cover Date.     

Electrodynamics of the outer solar atmosphere

The structure of the outer solar atmosphere and its magnetic coupling to the photospheric motions indicate the existence of large-scale current systems. The heating and the dynamics of coronal structures is therefore governed by electrodynamic coupling of these structures to the underlying photosphere. In a structured corona, the heating is enhanced because of several processes such as resonance absorption of Alfvénic surface waves, anomalous Joule heating, reconnection and the related topological dissipation. The global thermal and dynamic behaviour of coronal structures can be fruitfully described in terms of equivalent electrodynamic circuits, taking into account the paramount role of the photospheric boundaries. Coronal current systems may be stable, as in the case of coronal loops, but occassionally they show catastrophic behaviour if the current intensity surpasses a critical threshold.     

Magnetic fine structures in coronal loops

The formation of magnetic fine structures and associated electric currents is considered in the context of the coronal heating problem. The penetration of field-aligned electric currents into the lower atmosphere is discussed. It is argued that currents strong enough to heat the corona can persist only for short periods of time. The formation of thin current sheets is discussed. It is argued that photospheric magnetic structures (flux tubes) play an important role in the generation of coronal currents.     

Modeling coronal streamers and their eruption

Numerical solutions of the time-dependent MHD equations are used to generate ambient coronal streamer structures in a corona characteristic of that near solar minimum. The streamers are then disrupted by slow photospheric shear motion at the base of magnetic field lines within the closed field region, which is currently believed to be responsible for producing at least some CMEs. In contrast to several other simulations of this phenomena, the polytropic index is maintained at a value of 5/3 through the addition of coronal heating. Observations are used as a guide in determining the thermodynamic structure and plasma beta in the ambient corona. For a shear speed of 2.5 km/sec, the streamer configuration evolves slowly for about 65 hours before erupting outward with the formation of a CME. The bright CME leading edge travels outward at a speed of about 240 km/sec, and the sheared field lines follow at a somewhat slower speed. A closed magnetic field region is ejected as the magnetic field lines that were opened by the CME reconnect and reform the streamer.     

Coronal heating by dissipation of magnetic structure

Coronal loops are heated by the release of stored magnetic energy and by the dissipation of MHD waves. Both of these processes rely on the presence of internal structure in the loop. Tangled or sheared fields dissipate wave energy more efficiently than smooth fields. Also, a highly structured field contains a large reservoir of free magnetic energy which can be released in small reconnection events (microflares and nanoflares). The typical amount of internal structure in a loop depends on the balance between input at the photosphere and dissipation. This paper describes measures of magnetic structure, how these measures relate to the magnetic energy, and how photospheric motions affect the structure of a loop.The magnetic energy released during a reconnection event. can be estimated if one knows the equilibrium energy before and after the event. For a loop with highly tangled field lines, a direct solution of the equilibrium equations may be difficult. However, lower bounds can be placed on the energy of the equilibrium field, given a measure of the tangling known as the crossing number. These bounds lead to an estimate of the buildup of energy in a coronal loop caused by random photospheric motions. Parker's topological dissipation model can plausibly supply the 10⁷ erg cm^–2 s^–1 needed to heat the active region corona. The heating rate can be greatly enhanced by fragmentation of flux tubes, for example by the breakup of photospheric footpoints and the formation of new footpoints.     

The high latitude heliospheric magnetic field

As the Ulysses spacecraft approaches its first pass under the south pole of the sun, it is an appropriate time to review our current knowledge and predictions regarding the three dimensional behaviour of the heliospheric magnetic field, in particular at high heliographic latitudes. Optical techniques for measuring the photospheric magnetic field and observations of coronal brightness structures provide indications of the behaviour of the source of the heliospheric field in the corona. As the coronal fields are carried out into the heliosphere by the solar wind, from Parker's model we would expect that the spiral field observed in the equatorial plane should gradually unwind with latitude leading to open, approximately radial, field lines over the polar regions. Predictions of departures from, and models extending this simple picture are discussed. Both the Pioneer and Voyager spacecraft have spent brief periods in the regions above the maximum latitude of the heliospheric current sheet-relevant results from these missions are reviewed as well as results from the early stages of the out-of-ecliptic phase of the Ulysses mission. The configuration of the coronal magnetic field exhibits a strong dependence on the phase of the solar activity cycle. While the forthcoming Ulysses polar passes take place near to solar minimum, the different conditions which might be encountered on a second orbit of the sun at solar maximum are described.     

An Introduction to the Pre-CME Corona

Coronal mass ejections provide a gateway to understanding the physics of energy release and conversion in the solar corona. While it is generally accepted that the energy required to power a CME is contained in the pre-eruption coronal magnetic field, the pre-CME state of that field and the conditions leading up to the release of the magnetic energy are still not entirely clear. Recent studies point to various phenomena which are common to many, if not all, CME events, suggesting that there may be identifiable characteristics of the pre-CME corona which signal the impending eruption. However, determining whether these phenomena are necessary or even sufficient has yet to be achieved. In this paper we attempt to summarize the state of the solar corona and its evolution in the build up to a CME.     

Reconnective release of magnetic energy in astrophysical plasmas

Two particular examples are considered of astrophysical objects containing a highly conducting tenuous plasma with an excess magnetic energy supplied by an external source. The first example is the solar corona, whose magnetic field is continuously distorted by footpoint shuffling due to photospheric motions. The second case it an extragalactic jet extending from a galactic nucleus with an immersed magnetic field, and which is perturbed by variations in the pressure of the external medium. In both cases it is assumed that the system tends towards its lowest magnetic energy equilibrium via magnetic reconnection, thus providing a fast release of injected magnetic energy. Explicit relations between the characteristics of the external driver and the magnetic energy dissipation rate in these objects have been obtained. The relevance of this mechanism for heating the solar corona and maintaining radio emission from extragalactic jets is then. discussed by comparing these results with observational data.     

Global Non-Potential Magnetic Models of the Solar Corona During the March 2015 Eclipse

Seven different models are applied to the same problem of simulating the Sun’s coronal magnetic field during the solar eclipse on 2015 March 20. All of the models are non-potential, allowing for free magnetic energy, but the associated electric currents are developed in significantly different ways. This is not a direct comparison of the coronal modelling techniques, in that the different models also use different photospheric boundary conditions, reflecting the range of approaches currently used in the community. Despite the significant differences, the results show broad agreement in the overall magnetic topology. Among those models with significant volume currents in much of the corona, there is general agreement that the ratio of total to potential magnetic energy should be approximately 1.4. However, there are significant differences in the electric current distributions; while static extrapolations are best able to reproduce active regions, they are unable to recover sheared magnetic fields in filament channels using currently available vector magnetogram data. By contrast, time-evolving simulations can recover the filament channel fields at the expense of not matching the observed vector magnetic fields within active regions. We suggest that, at present, the best approach may be a hybrid model using static extrapolations but with additional energization informed by simplified evolution models. This is demonstrated by one of the models.     

Coronal holes and solar magnetic fields

Since 1972, nearly continuous observations of coronal holes and their associated photospheric magnetic fields have been made using a variety of satellite and ground-based equipment. The results of comparisons of these observations are reviewed and it is demonstrated that the structure and evolution of coronal holes is basically governed by the large-scale distribution of photospheric magnetic flux. Non-polar holes form in the decaying remnants of bipolar magnetic regions in areas with a large-scale flux imbalance. There is strong indirect evidence that the magnetic field in coronal holes is always open to interplanetary space but not all open-field regions have associated coronal holes. The well-observed declining phase of the last solar cycle was characterized by stable magnetic field and coronal hole patterns which were associated with recurrent, high-speed wind streams and interplanetary magnetic field patterns at the Earth. The ascending phase of the current cycle has been characterized by transient magnetic field and coronal hole patterns which tend to occur at high solar latitudes. This shift in magnetic field and coronal hole patterns has resulted in a less obvious and more complicated association with high-speed wind streams at the Earth.Proceedings of the Symposium on Solar Terrestrial Physics held in Innsbruck, May–June 1978.Operated by the Association of Universities for Research in Astronomy, Inc., under contract with the National Science Foundation.Visiting Scientist, Kitt Peak National Observatory.     

On the Role of Interchange Reconnection in the Generation of the Slow Solar Wind

The heating of the solar corona and therefore the generation of the solar wind, remain an active area of solar and heliophysics research. Several decades of in situ solar wind plasma observations have revealed a rich bimodal solar wind structure, well correlated with coronal magnetic field activity. Therefore, the reconnection processes associated with the large-scale dynamics of the corona likely play a major role in the generation of the slow solar wind flow regime. In order to elucidate the relationship between reconnection-driven coronal magnetic field structure and dynamics and the generation of the slow solar wind, this paper reviews the observations and phenomenology of the solar wind and coronal magnetic field structure. The geometry and topology of nested flux systems, and the (interchange) reconnection process, in the context of coronal physics is then explained. Once these foundations are laid out, the paper summarizes several fully dynamic, 3D MHD calculations of the global coronal system. Finally, the results of these calculations justify a number of important implications and conclusions on the role of reconnection in the structural dynamics of the coronal magnetic field and the generation of the solar wind.     

MHD waves in coronal flux tubes

The basic MHD waves of a coronal flux loop are investigated for the rectangular box model of a plasma with oblique magnetic field and line-tied at the ends. The waves found are completely different from those in a periodic box, representative for tokamaks. They consist of a mixture of Alfvén components with a ballooning factor, favouring minimal field line bending, and fast components without such a factor. Pure Alfvén modes are only found as singular limiting cases of cluster spectra of Alfvén-fast waves, where the fast components are localised in a photospheric boundary layer which is dictated by the requirements of line-tying. This justifies the assumption of continuous spectra in coronal loops, required for the mechanism of resonant Alfvén wave heating. The waves consist of large amplitude Alfvén components in the corona and fast components with a small but rapidly varying amplitude in the boundary layer, so that they appear to have the right signature for effective transfer of energy from the photosphere to the corona.     

Coronal index of solar activity – Solar-terrestrial research

The purpose of this paper is to introduce a coronal index of solar activity (CI) as computed from ground-based observations of the green coronal line intensities (Fe?xiv; 530.3 nm). This index, expressed in W s^?1, is derived for the period 1939–1998 and belongs to the class of ground-based indices used to study solar activity and its influence on the heliosphere. The smoothed peak solar cycle intensity of the CI increased monotonically during the period of research. On the other hand, comparative studies have shown relatively good agreement with similar solar indices. CI can be used to study, among other things, the rotation of the Sun as a star, and long-term, intermediate- and short-term periodicities. The CI is inferred from a homogeneous coronal data set that can be used to study such topics as the 2D distribution of the green corona and photospheric/chromospheric activity, the differential rotation of the emission green corona, and the relationship between the green corona and cosmic rays.     

Coronal Hole Boundaries and their Interactions with Adjacent Regions

Coronal hole boundaries are the interfaces between regions where the coronal magnetic field contains a significant component which is open into the heliosphere and regions where the field is primarily closed. It is pointed out that there are constraints on the magnetic field which opens into the heliosphere that must be satisfied in the corona: it must come into pressure equilibrium in the high corona, and the component of the field which connects to the polar regions of the Sun must differentially rotate. A model is presented in which satisfying these constraints determines which field lines are open and which are closed, and thus where the polar coronal hole boundaries occur. Some of the consequences of this model are discussed. This revised version was published online in June 2006 with corrections to the Cover Date.     

Plasma-physical aspects of the solar cycle

Mass motions below the photosphere drive the solar cycle which is associated with variations in the magnetic field structure and accompanying phenomena. In addition to semi-empirical models, dynamo theories have been used to explain the solar cycle. The emergence of magnetic field generated by these mechanisms and its expansion into the corona involves many plasma physical processes. Magnetic buoyancy aids the expulsion of magnetic flux. The corona may respond dynamically or by continually adjusting to a quasi-static force-free or pressure-balanced equilibrium. The formation and disruption of current sheets is significant for the overall structure of the coronal magnetic field and the physics of quiescent prominences. The corona has a fine structure consisting of magnetic loops. The structure and stability of these are important as they are one of the underlying elements which make up the corona.     

Modeling the out-of-ecliptic interplanetary magnetic field in the declining phase of sunspot Cycle 22

We have developed a new model of the coronal and interplanetary magnetic field. The model includes the effects of large-scale horizontal electric currents flowing in the inner corona, of the warped heliospheric current sheet, and of heliospheric volume currents in the super-Alfvenic solar wind. The model determines the interplanetary magnetic field (IMF) strength as well as its polarity from measurements of the photospheric magnetic field. A detailed comparison between the observed and calculated in-ecliptic IMF Bx in Cycles 22, confirms the fitness of the optimal set of free parameters inferred using data in Cycle 21. We can predict the latitudinal gradient of Bx in the declining phase of Cycle 22 and the temporal variation of the amplitude of the radial component of the IMF at various latitudes. The calculated IMF polarity and Bx strength agree best with the in-ecliptic observations when the photospheric field (measured with a 5250Å magnetograph) is scaled up by a factor of two. Ulysses may provide the critical data to improve the model and check these inferences.     

Reconstructed 3-d magnetic field structure and hard X-ray two ribbons for 2000 Bastille-day event

The Bastille-day event in 2000 produced energetic 3B/X5.6 flare with a halo CME, which had great geo-effects consequently. This event has been studied extensively and it is considered that it follows the two-ribbon flare model. The flare/CME event was triggered by an erupting filament and TRACE observations showed formation of giant arcade structures during the flare process. Hard X-ray (HXR) two ribbons revealed for the first time in this flare event (Masuda et al., 2001). The reconstruction of 3-D coronal magnetic fields revealed a magnetic flux rope structure, for the first time, from extrapolation of observed photospheric vector magnetogram data and the flux rope structure was co-spatial with portion of the filament and a UV bright lane (Yan et al., 2001a, 2001b). Here we review some recent work related to the flux rope structure and the HXR two ribbons by comparing their locations and the flux temporal profiles during the flare process so as to understand the energy release and particle accelerations. It is proposed that the rope instability may have triggered the flare event, and reconnection may occur during this process. The drifting pulsation structure in the decimetric frequency range is considered to manifest the rope ejection, or the initial phase of the coronal mass ejection. The HXR two ribbons were distributed along the flux rope and the rope foot points coincide with HXR sources. The energy dissipation from IPS observations occurred within about 100 R _⋅ is consistent with the estimate for the flux rope system. This revised version was published online in August 2006 with corrections to the Cover Date.     

Varieties of Coronal Mass Ejections and Their Relation to Flares

Most coronal mass ejections (CMEs) start as coronal storms which are caused by an opening of channels of closed field lines along the zero line of the longitudinal magnetic field. This can happen along any zero line on the Sun where the configuration is destabilized. If the opening includes a zero line inside an active region, one observes a chromospheric flare. If this does not happen, no flare is associated with the CME in the chromosphere, but the process, as well as the response in the corona (a Long Decay Event in X-rays) remains the same. The only difference between flare-associated and non-flare-associated CMEs is the strength of the magnetic field in the region of the field line opening. This can explain essentially all differences which have been observed between these two kinds of CMEs. However, there are obviously also other sources of CMEs, different from coronal storms: sprays (giving rise to narrow, pointed ejections), erupting interconnecting loops (often destabilized by flares), and growing coronal holes. This paper tries to summarize and interpret observations which support this general picture, and demonstrates that both CMEs and flares must be properly discussed in any study of solar-terrestrial relations.     

Solar Energetic Particles: Sampling Coronal Abundances

In the large solar energetic particle (SEP) events, coronal mass ejections (CMEs) drive shock waves out through the corona that accelerate elements of the ambient material to MeV energies in a fairly democratic, temperature-independent manner. These events provide the most complete source of information on element abundances in the corona. Relative abundances of 22 elements from H through Zn display the well-known dependence on the first ionization potential (FIP) that distinguishes coronal and photospheric material. For most elements, the main abundance variations depend upon the gyrofrequency, and hence on the charge-to-mass ratio, Q/A, of the ion. Abundance variations in the dominant species, H and He, are not Q/A dependent, presumably because of non-linear wave-particle interactions of H and He during acceleration. Impulsive flares provide a different sample of material that confirms the Ne:Mg:Si and He/C abundances in the corona. This revised version was published online in June 2006 with corrections to the Cover Date.     

UVCS Observations of Temperature and Velocity Profiles in Coronal Holes

The spectroscopic observations of the Ultraviolet Coronagraph Spectrometer (UVCS), on board the SOHO observatory, allow the study and the full characterization of the expansion of the solar atmosphere by means of measurements of the outflow speeds and the physical properties of the wind, directly in the region where the solar plasma is heated and accelerated: the extended corona. During solar minimum, when the magnetic configuration of the corona is rather simple, the open magnetic fields emerging from the wide polar coronal holes channel toward the heliosphere both the fast and the slow wind. The fast wind flows along flux tubes with lower areal divergence than the slow wind which is guided by flux tubes characterized by non-monotonic areal expansion functions. Differences in the physical properties, such as kinetic temperature, electron density, composition and density fluctuations, of the fast and slow wind in the corona are discussed.