Progress, Challenges, and Perspectives of the 3D MHD Numerical Modeling of Oscillations in the Solar Corona

Recent high temporal and spatial resolution satellite observations of the solar corona provide ample evidence of oscillations in coronal structures. The observed waves and oscillations can be used as a diagnostic tool of the poorly known coronal parameters, such as magnetic field, density, and temperature. The emerging field of coronal seismology relies on the interpretation of the various coronal oscillations in terms of theoretically known wave modes, and the comparison of observed and theoretical wave mode properties for the determination of the coronal parameters. However, due to complexity of coronal structures the various modes are coupled, and the application of linear theory of idealized structures to coronal loops and active regions limits the usefulness of such methods. Improved coronal seismology can be achieved by the development of full 3D MHD dynamical model of relevant coronal structures and the oscillation phenomena. In addition to improved accuracy compared to linear analysis, 3D MHD models allow the diagnostic method to include nonlinearity, compressibility, and dissipation. The current progress made with 3D MHD models of waves in the corona is reviewed, and the challenges facing further development of this method are discussed in the perspective of future improvement that will be driven by new high resolution and high cadence satellite data, such as received from Hinode and STEREO, and expected from SDO.     

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.     

Modeling the coronal magnetic field in a polar hole

The coronal magnetic field in the northern polar coronal hole in 1986 is predicted on the basis of the photospheric magnetic field observations and the horizontal current-current sheet coronal model (Zhao and Hoeksema, 1993). The predicted magnetic field intensity is stronger near the center of the hole than near the edge. The calculated expansion factor for the entire hole does not match the expansion factor of any flux tube in the hole, suggesting that it would not be appropriate to use the expansion factor for entire hole to represent the divergence of the flux tube in analyzing the acceleration and heating of the plasma in coronal holes.     

Signature of coronal holes and streamers in the interplanetary space

The properties of different solar wind streams depend on the large scale structure of the coronal magnetic field. We present average values and distributions of bulk parameters (density, velocity, temperature, mass flux, momentum, and kinetic and thermal energy, ratio of thermal and magnetic pressure, as well as the helium abundance) as observed on board the Prognoz 7 satellite in different types of the solar wind streams. Maximum mass flux is recorded in the streams emanating from the coronal streamers while maximum thermal and kinetic energy fluxes are observed in the streams from the coronal holes. The momentum fluxes are equal in both types of streams. The maximum ratio of thermal and magnetic pressure is observed in heliospheric current sheet. The helium abundance in streams from coronal holes is higher than in streams from streamers, and its dependences on density and mass flux are different in different types of the streams. Also, the dynamics of -particle velocity and temperature relative to protons in streams from coronal holes and streamers is discussed.     

Large scale structure of the solar corona in the declining phase of the solar cycle

Maps of the corona, obtained at meter wavelengths with the Nançay Radioheliograph (France), are used to study, on the disk, the radio counterpart of the coronal plasma sheet observed in K-corona on the limb. We study here the evolution of the coronal plasma sheet from the maximum of the activity cycle in 1980 to the minimum in 1986 and identify some of its large scale structures.     

A CDS Observation of the Relationship Between a Coronal Hole and Chromospheric Structure

This paper studies the relationship between chromospheric structure and the location of the coronal hole boundary, using a SOHO-CDS observation made on 13 June 1996. The cell structure visible in the oxygen and helium data is smoothed and a basin algorithm is used to find the individual cells. As the smoothing scale increases, cells merge to form larger ones. A trade off between merging and smoothing was made, a scale of 5,000 km being used. There is good agreement between the edges of cells and the coronal hole boundary, as determined in Mg IX 368 Å, although it is not perfect. This preliminary analysis shows that the coronal hole boundary is located along chromospheric network cell edges in most places, as would be expected if the chromosphere is the source of the coronal structure and solar wind.     

The coronal context of transition region explosive events

Transition region explosive events are observed throughout the quiet Sun and represent an interesting local heating phenomenon. The coronal counterparts of these events, if they exist, were not observed in a sounding rocket campaign dedicated to this objective. The coronal instrument complement on the SOHO spacecraft provides an opportunity to extend this search for the coronal counterparts of the transition region explosive events, as well as to explore the correspondence of explosive events with large scale coronal structures, such as with coronal dark lanes.     

Solar Wind Sources and Their Variations Over the Solar Cycle

In this paper I will briefly summarize the present status of our knowledge on the four different sorts of solar wind, their sources and their short- and long-term variations. First: the fast solar wind in high-speed streams that emerges from coronal hole regions. Second: the slow solar wind emerging from the non-active Sun near the global heliospheric current sheet above helmet streamers and underlying active regions. Third: the slow solar wind filling most of the heliosphere during high solar activity, emerging above active regions in a highly turbulent state, and fourth: the plasma expelled from the Sun during coronal mass ejections. The coronal sources of these different flows vary dramatically with the solar activity cycle.     

Coupling of the coronal he abundance to the solar wind

Models of the transition region — corona — solar wind system are investigated in order to find the coronal helium abundance and to study the role played by coronal helium in controlling the the solar wind proton flux. The thermal force on -particles in the transition region sets the flow of helium into the corona. The frictional coupling between -particles and protons and/or the electric polarization field determines the proton flux in the solar wind as well as the fate of the coronal helium content.     

Signatures of Coronal Hole Spectra Between 660 Å and 1460 Å Measured with Sumer on Soho

Spectra of the northern polar coronal hole measured with the SUMER spectrometer on SOHO on 25 October 1996 are analyzed. We present spectra taken at locations on the solar disk where part of the spectrometer slit intersects a polar coronal hole region and an area of brighter emission from outside of the coronal hole area. By comparing the line intensities between the parts of the spectrum taken inside the "dark" area of the coronal holes and the brighter regions, we work out the signatures of the specific coronal hole in the chromosphere, transition region and lower corona. We find that emissions of neutral atom lines, of which there are many in the spectrum of SUMER, show no difference between the coronal hole and the bright boundary areas, whereas all ionized species show strong intensity enhancements, including the continuum emissions of carbon and hydrogen. These enhancements are larger than in normal quiet Sun areas. This revised version was published online in June 2006 with corrections to the Cover Date.     

Broadening of Fe X (6374 Å) profiles above the limb in a coronal hole

Profiles of the visible Fe X (6374 Å) coronal emission line as a function of height above the limb were obtained out to 1.16 solar radii in a coronal hole using the NSO/Sacramento Peak Observatory Coronagraph, Universal Spectrograph and a CCD camera. These are the first coronal line profiles obtained as a function of height in a coronal hole from the ground. Analysis of the line widths suggests a large component of nonthermal broadening which increases with height ranging from 40 to 60 km/s, depending upon the assumed temperature or thermal component of the profile.     

On the application of the boundary element method in coronal magnetic field reconstruction

Solar magnetic field is believed to play a central role in solar activities and flares, filament eruptions as well as CMEs are due to the magnetic field re-organization and the interaction between the plasma and the field. At present the reliable magnetic field measurements are still confined to a few lower levels like in photosphere and chromosphere. Although IR technique may be applied to observe the coronal field but the technique is not well-established yet. Radio techniques may be applied to diagnose the coronal field but assumptions on radiation mechanisms and propagations are needed. Therefore extrapolation from photospheric data upwards is still the primary method to reconstruction coronal field. Potential field has minimum energy content and a force-free field can provide the required excess energy for energy release like flares, etc. Linear models have undesirable properties and it is expected to consider non-constant-alpha force-free field model. As the recent result indicates that the plasma beta is sandwich-ed distributed above the solar surface (Gary, 2001), care must be taken in modeling the coronal field correctly. As the reconstruction of solar coronal magnetic fields is an open boundary problem, it is desired to apply some technique that can incorporate this property. The boundary element method is a well-established numerical techniques that has been applied to many fields including open-space problems. It has also been applied to solar magnetic field problems for potential, linear force-free field and non-constant-alpha force-free field problems. It may also be extended to consider the non-force-free field problem. Here we introduce the procedure of the boundary element method and show its applications in reconstruction of solar magnetic field problems. This revised version was published online in August 2006 with corrections to the Cover Date.     

Equivalent Electric Circuit Models of Coronal Magnetic Loops and Related Oscillatory Phenomena on the Sun

Coronal loops, which trace closed magnetic field lines, are the primary structural elements of the solar atmosphere. Complex dynamics of solar coronal magnetic loops, together with action of possible subphotospheric dynamo mechanisms, turn the majority of the coronal loops into current-carrying structures. In that connection none of the loops can be considered as isolated from the surroundings. The current-carrying loops moving relative to each other interact via the magnetic field and currents. One of the ways to take into account this interaction consists in application of the equivalent electric circuit models of coronal loops. According to these models, each loop is considered as an equivalent electric LCR-circuit with variable inductive coefficients L, capacitance C, and resistance R, which depend on shape, scale, position of the loop with respect to neighbouring loops, as well as on the plasma parameters in the magnetic tube. Such an approach enables to describe the process of electric current dynamics in the groups of coronal loops, as well as the related dynamical, energy release and radiation processes. In the present paper we describe the major principles of LCR-circuit models of coronal magnetic loops, and show their application for interpretation of the observed oscillatory phenomena in the loops and in the related radiation.     

FIP Effect in the Solar Upper Atmosphere: Spectroscopic Results

Recent spectroscopic measurements from instruments on the Solar and Heliospheric Observatory (SOHO) find that the coronal composition above a polar coronal hole is nearly photospheric. However, similar SOHO observations show that in coronal plasmas above quiet equatorial regions low-FIP elements are enhanced by a factor of ≈ 4. In addition, the process of elemental settling in coronal plasmas high above the solar surface was shown to exist. Measurements by the Ulysses spacecraft, which are based on non-spectroscopic particle counting techniques, show that, with the exception of He, the elemental composition of the fast speed solar wind is similar to within a factor of 1.5 to the composition of the photosphere. In contrast, similar measurements in the slow speed wind show that elements with low first ionization potential (FIP < 10 eV) are enhanced, relative to the photosphere, by a factor of 4-5. By combining the SOHO and Ulysses results, ideas related to the origin of the slow speed solar wind are presented. Using spectroscopic measurements by the Solar Ultraviolet Measurement of Emitted Radiation (SUMER) instrument on SOHO the photospheric abundance of He was determined as 8.5 ± 1.3% (Y = 0.248). This revised version was published online in June 2006 with corrections to the Cover Date.     

Coronal Hole Properties Observed with Sumer

We analyze SUMER spectra of 14 lines belonging to 12 ions, obtained on both sides of the boundary of polar coronal holes as well as at other locations along the limb. We compare line intensities, shifts and widths in coronal holes with values obtained in the quiet Sun. We find that with increasing formation temperature, spectral lines show an increasingly stronger blueshift in coronal holes relative to the quiet Sun at an equal heliospheric angle. The width of the lines is generally larger (by a few km/s) inside the coronal hole. Intensity measurements show the presence of the coronal hole in Ne VIII lines as well as in Fe XII, with evidence for a slightly enhanced emission in polar coronal holes for lines formed below 10⁵ K. This revised version was published online in June 2006 with corrections to the Cover Date.     

UV spectral lines from coronal transients

We investigated the UV emission expected from solar coronal transients, selecting some spectral lines which will be observed with the UVCS spectrocoronagraph onboard the SOHO spacecraft. The line intensities were calculated starting from a representative, simplified model of coronal transient. We discuss how the considered intensities depend on the physical parameters of the examined structures. This work is aimed to give a contribution in defining and preparing the future observations of coronal transients and coronal mass ejections by the UVCS/SOHO.     

Observations of the solar wind from coronal holes

The solar wind emanating from coronal holes (CH) constitutes a quasi-stationary flow whose properties change only slowly with the evolution of the hole itself. Some of the properties of the wind from coronal holes depend on whether the source is a large polar coronal hole or a small near-equatorial hole. The speed of polar CH flows is usually between 700 and 800 km/s, whereas the speed from the small equatorial CH flows is generally lower and can be <400 km/s. At 1 AU, the average particle and energy fluxes from polar CH are 2.5×10⁸ cm^–2 sec^–1 and 2.0 erg cm^–2 s^–1. This particle flux is significantly less than the 4×10⁸ cm^–2 sec^–1 observed in the slow, interstream wind, but the energy fluxes are approximately the same. Both the particle and energy fluxes from small equatorial holes are somewhat smaller than the fluxes from the large polar coronal holes.Many of the properties of the wind from coronal holes can be explained, at least qualitatively, as being the result of the effect of the large flux of outward-propagating Alfvén waves observed in CH flows. The different ion species have roughly equal thermal speeds which are also close to the Alfvén speed. The velocity of heavy ions exceeds the proton velocity by the Alfvén speed, as if the heavy ions were surfing on the waves carried by the proton fluid.The elemental composition of the CH wind is less fractionated, having a smaller enhancement of elements with low first-ionization potentials than the interstream wind, the wind from coronal mass ejections, or solar energetic particles. There is also evidence of fine-structure in the ratio of the gas and magnetic pressures which maps back to a scale size of roughly 1° at the Sun, similar to some of the fine structures in coronal holes such as plumes, macrospicules, and the supergranulation.     

Transverse Oscillations of Coronal Loops

On 14 July 1998 TRACE observed transverse oscillations of a coronal loop generated by an external disturbance most probably caused by a solar flare. These oscillations were interpreted as standing fast kink waves in a magnetic flux tube. Firstly, in this review we embark on the discussion of the theory of waves and oscillations in a homogeneous straight magnetic cylinder with the particular emphasis on fast kink waves. Next, we consider the effects of stratification, loop expansion, loop curvature, non-circular cross-section, loop shape and magnetic twist. An important property of observed transverse coronal loop oscillations is their fast damping. We briefly review the different mechanisms suggested for explaining the rapid damping phenomenon. After that we concentrate on damping due to resonant absorption. We describe the latest analytical results obtained with the use of thin transition layer approximation, and then compare these results with numerical findings obtained for arbitrary density variation inside the flux tube. Very often collective oscillations of an array of coronal magnetic loops are observed. It is natural to start studying this phenomenon from the system of two coronal loops. We describe very recent analytical and numerical results of studying collective oscillations of two parallel homogeneous coronal loops. The implication of the theoretical results for coronal seismology is briefly discussed. We describe the estimates of magnetic field magnitude obtained from the observed fundamental frequency of oscillations, and the estimates of the coronal scale height obtained using the simultaneous observations of the fundamental frequency and the frequency of the first overtone of kink oscillations. In the last part of the review we summarise the most outstanding and acute problems in the theory of the coronal loop transverse oscillations.     

Coronal plumes and fine scale structure in high speed solar wind streams

We present a solar wind model which takes into account the possible origin of fast solar wind streams in coronal plumes. We treat coronal holes as being made up of essentially 2 plasma species, denser, warmer coronal plumes embedded in a surrounding less dense and cooler medium. Pressure balance at the coronal base implies a smaller magnetic field within coronal plumes than without. Considering the total coronal hole areal expansion as given, we calculate the relative expansion of plumes and the ambient medium subject to transverse pressure balance as the wind accelerates. The magnetic flux is assumed to be conserved independently both within plumes and the surrounding coronal hole. Magnetic field curvature terms are neglected so the model is essentially one dimensional along the coronal plumes, which are treated as thin flux-tubes. We compare the results from this model with white-light photographs of the solar corona and in-situ measurements of the spaghetti-like fine-structure of high-speed winds.