Our New View of the Solar Corona from Yohkoh and Soho

The Yohkoh satellite has now been orbiting the Earth for about 6 years and during this time it has revealed a number of new features in the solar corona. These include the discovery of X-ray jets and active region transient brightenings, as well as observations of hard X-ray sources above and at the feet of soft X-ray flare loops. SOHO, the newest solar space mission, is not orbiting the Earth, but is in fact orbiting the Sun and has been at the Earth's L1 point for about 2 years. During this time it too has identified some new and interesting characteristics of both the solar corona, the photosphere and the solar interior. For example, studies of high resolution MDI/SOHO magnetograms indicate that the magnetic carpet may play an important role in the heating of the coronal. Also polar plume studies from EIT/SOHO data suggest that they may be a possible source for the fast solar wind. Together these two missions have dominated solar research throughout the 90s and are expected to continue to do so during the rise from solar minimum to the next solar maximum. This revised version was published online in July 2006 with corrections to the Cover Date.     

Viscous Damping of Non-Adiabatic MHD Waves in an Unbounded Solar Coronal Plasma

The damping of MHD waves in solar coronal magnetic field is studied taking into account thermal conduction and compressive viscosity as dissipative mechanisms. We consider viscous homogeneous unbounded solar coronal plasma permeated by a uniform magnetic field. A general fifth-order dispersion relation for MHD waves has been derived and solved numerically for different solar coronal regimes. The dispersion relation results three wave modes: slow, fast, and thermal modes. Damping time and damping per periods for slow- and fast-mode waves determined from dispersion relation show that the slow-mode waves are heavily damped in comparison with fast-mode waves in prominences, prominence–corona transition regions (PCTR), and corona. In PCTRs and coronal active regions, wave instabilities appear for considered heating mechanisms. For same heating mechanisms in different prominences the behavior of damping time and damping per period changes significantly from small to large wavenumbers. In all PCTRs and corona, damping time always decreases linearly with increase in wavenumber indicate sharp damping of slow- and fast-mode waves.     

Real and virtual unipolar regions

Difficulties in relating magnetograph measurements to the actual solar magnetic field are discussed. After a brief review both of problems inherent in the nature of the measurements and of sources of instrumental error, we show that field measurements taken within the photosphere can map out large-scale regions of a single magnetic polarity even though these regions contain no footpoints of large-scale magnetic structures, but instead only aggregates of small, unresolved bipoles. This may occur wherever the density of unresolved bipoles has a preferred orientation and a spatial variation along the direction of that orientation. We call these regionsvirtual unipolar regions, as they are not connected to regions of opposite polarity by field loops or lines passing through the corona. Investigation of these regions shows that they can arise at widely separated locations, and that they may evolve into real unipolar magnetic regions which are connected to the chromospheric and coronal fields. These results can explain a number of puzzling aspects of magnetograph observations of the solar background magnetic field.     

On Solving the Coronal Heating Problem

The question of what heats the solar corona remains one of the most important problems in astrophysics. Finding a definitive solution involves a number of challenging steps, beginning with an identification of the energy source and ending with a prediction of observable quantities that can be compared directly with actual observations. Critical intermediate steps include realistic modeling of both the energy release process (the conversion of magnetic stress energy or wave energy into heat) and the response of the plasma to the heating. A variety of difficult issues must be addressed: highly disparate spatial scales, physical connections between the corona and lower atmosphere, complex microphysics, and variability and dynamics. Nearly all of the coronal heating mechanisms that have been proposed produce heating that is impulsive from the perspective of elemental magnetic flux strands. It is this perspective that must be adopted to understand how the plasma responds and radiates. In our opinion, the most promising explanation offered so far is Parker's idea of nanoflares occurring in magnetic fields that become tangled by turbulent convection. Exciting new developments include the identification of the “secondary instability” as the likely mechanism of energy release and the demonstration that impulsive heating in sub-resolution strands can explain certain observed properties of coronal loops that are otherwise very difficult to understand. Whatever the detailed mechanism of energy release, it is clear that some form of magnetic reconnection must be occurring at significant altitudes in the corona (above the magnetic carpet), so that the tangling does not increase indefinitely. This article outlines the key elements of a comprehensive strategy for solving the coronal heating problem and warns of obstacles that must be overcome along the way.     

A Comparison Between Nonlinear Force-Free Field and Potential Field Models Using Full-Disk SDO/HMI Magnetogram

Measurements of magnetic fields and electric currents in the pre-eruptive corona are crucial to the study of solar eruptive phenomena, like flares and coronal mass ejections (CMEs). However, spectro-polarimetric measurements of certain photospheric lines permit a determination of the vector magnetic field only at the photosphere. Therefore, there is considerable interest in accurate modeling of the solar coronal magnetic field using photospheric vector magnetograms as boundary data. In this work, we model the coronal magnetic field above multiple active regions with the help of a potential field and a nonlinear force-free field (NLFFF) extrapolation code over the full solar disk using Helioseismic and Magnetic Imager (SDO/HMI) data as boundary conditions. We compare projections of the resulting magnetic field lines with full-disk coronal images from the Atmospheric Imaging Assembly (SDO/AIA) for both models. This study has found that the NLFFF model reconstructs the magnetic configuration closer to observation than the potential field model for full-disk magnetic field extrapolation. We conclude that many of the trans-equatorial loops connecting the two solar hemispheres are current-free.     

Mechanisms of coronal heating

The Sun is a mysterious star. The high temperature of the chromosphere and corona present one of the most puzzling problems of solar physics. Observations show that the solar coronal heating problem is highly complex with many different facts. It is likely that different heating mechanisms are at work in solar corona. Recent observations show that Magnetic Carpet is a potential candidate for solar coronal heating.     

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 .     

Development of a complex of activity in the solar corona

Skylab observations of the Sun in soft X-rays gave us the first possibility to study the development of a complex of activity in the solar corona during its whole lifetime of seven solar rotations. The basic components of the activity complex were permanently interconnected (including across the equator) through sets of magnetic field lines, which suggests similar connections also below the photosphere. However, the visibility of individual loops in these connections was greatly variable and typically shorter than one day. Each brightening of a coronal loop in X-rays seems to be related to a variation in the photospheric magnetic field near its footpoint. Only loops (rarely visible) connecting active regions with remnants of old fields can be seen in about the same shape for many days. The interconnecting X-ray loops do not connect sunspots.We point out several examples of possible reconnections of magnetic field lines, giving rise to the onset of the visibility or, more likely, to sudden enhancements of the loop emission. In one case a new system of loops brightened in X-rays, while the field lines definitely could not have reconnected. Some striking brightenings show association with flares, but the flare occurrence and the loop brightening seem to be two independent consequences of a common triggering action: emergence of new magnetic flux. In old active regions, growing and/or brightened X-ray loops can be seen quite often without any associated flare; thus, the absence of any flaring in the chromosphere does not necessarily mean that the overlying coronal active region is quiet and inactive.We further discuss the birth of the interconnecting loops, their lifetime, altitude, variability in shape in relation to the photospheric magnetic field, the similarity of interconnecting and internal loops in the late stages of active regions, phases of development of an active region as manifested in the corona, the remarkably linear boundary of the X-ray emission after the major flare of 29 July 1973, and a striking sudden change in the large-scale pattern of unipolar fields to the north of the activity complex.The final decay of the complex of activity was accompanied by the penetration of a coronal hole into the region where the complex existed before.     

Energy source of the solar wind

A direct transfer of energy from photospheric activity to the solar wind by means of electric currents is discussed. Currents are assumed to flow in quiescent prominences which occasionally erupt and give rise to expanding loop-like structures in the corona, as observed from Skylab. Due to expansion, the legs of the loops are transformed into coronal rays which carry currents from the photosphere to the outer parts of the corona or interplanetary medium and then back again to the photosphere. It is proposed that energy is transferred from photospheric activity to the solar wind in the following ways: (1) as kinetic energy of the ejected loop matter; (2) as electric power directly fed into the extended loops; and (3) as torsional waves produced by fluctuations in the loop currents.     

An explanation of the observed differences between coronal holes and quiet coronal regions

The main differences between a coronal hole and quiet coronal regions are explained by a reduction of the thermal conduction coefficient by transverse components of the magnetic field in the transition region of quiet coronal regions.Calculations of minimum flux coronae show that if the flux of energy heating the corona is maintained constant while the thermal conductivity in the transition region is reduced, the coronal temperature, the pressure in the transition region and the corona, and the temperature gradient in the transition region all increase. At the same time the intensities of lines emitted from the transition region are almost unchanged. Thus all the main spectroscopically observed differences between coronal holes and quiet coronal regions are explained.The flux of energy heating the corona in both coronal holes and quiet coronal regions is 3.0 × 10⁵ erg cm^-2 s^-1.The energy lost from coronal holes by the high speed streams in the solar wind is not sufficient to explain the difference in the coronal temperature in coronal holes and quiet coronal regions. The most likely explanation of the high velocity streams in the solar wind associated with coronal holes is that of Durney and Hundhausen.     

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.     

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.     

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.     

Very Large Array and SOHO Observations of Type I Noise Storms,Large-Scale Loops and Magnetic Restructuring in the Corona

Very Large Array (VLA) observations at 91-cm wavelength are combined with data from the SOHO EIT, MDI and LASCO and used to study the evolving coronal magnetic environment in which Type I noise storms and large-scale coronal loops occur. On one day, we have shown the early evolution of a coronal mass ejection (CME) in projection in the disk by tracing its decimetric continuum emission. The passage of the CME and an associated EUV ejection event coincided with an increase in the 91-cm brightness temperature of an extended coronal loop located a significant distance away and with the displacement of the 91-cm source during the early stage of the CME. We suggest that the energy deposited into the corona by the CME may have caused a local increase in the thermal or nonthermal electron density or in the electron temperature in the middle corona resulting in a transient increase in the brightness of the 91-cm loop. On a second observing day, we have consolidated the known association between magnetic changes in the photosphere and low corona with noise storm enhancements in an overlying radio source well in advance of a flare event in the same region. We find anti-correlated changes in the brightness of a bipolar 91-cm Type I noise storm that appear to be associated with the cancellation and emergence of magnetic flux in the underlying photosphere. In this case, the evolving fields may have led to magnetic instabilities and reconnection in the corona and the acceleration of nonthermal particles that initiated and sustained the Type I noise storm.     

The Topological Behaviour of Stable Magnetic Separators

It is important to understand the complex topology of the magnetic field in the solar corona in order to be able to comprehend the mechanisms which give rise to phenomena such as coronal loop structures and x-ray bright points. A key feature of the magnetic topology is a separator. A magnetic separator is a field line which connects two magnetic null points, places where the magnetic field becomes zero. A stable magnetic separator is important as it is the intersection of two separatrix surfaces. These surfaces divide the magnetic field lines into regions of different connectivity, so a separator usually borders four regions of field-line connectivity. This work examines the topological behaviour of separators that appear in a magnetic field produced by a system of magnetic sources lying in a plane (the photosphere). The questions of how separators arise and are destroyed, the topological conditions for which they exist, how they interact and their relevance to the coronal magnetic field are addressed.     

Three-Dimensional Geometry of Planar Magnetic Structure in the Corona

The coronal magnetic field (CMF) during Carrington rotation 1870 is inferred by using the so-called 'potential model' with the photospheric magnetic field observed at Kitt Peak. Magnetic field lines starting at areas restricted (90deg; ± 30deg; in longitude and 0deg; ± 20deg; in latitude) in both the photosphere and the source surface of 2.5 solar radii are traced to examine fine geometrical structures of the CMF. We found a well-ordered planar magnetic structure (PMS) near 90° Carrington longitude in the corona. The PMS consists of magnetic flux of negative polarity emanating from several small areas in the photosphere. The magnetic flux expands into a wide longitudinal angle in the source surface making a planar magnetic structure.     

Solar activity and the corona

This review puts together what we have learned about coronal structures and phenomenology to synthesize a physical picture of the corona as a voluminous, thermally and electrically highly-conducting atmosphere responding dynamically to the injection of magnetic flux from below. The synthesis describes complementary roles played by the magnetic heating of the corona, the different types of flares, and the coronal mass ejections as physical processes by which magnetic flux and helicity make their way from below the photosphere into the corona, and, ultimately, into interplanetary space. In these processes, a physically meaningful interplay among dissipative magnetohydrodynamic turbulence, ideal ordered flows, and magnetic helicity determines how and when the rich variety of relatively long-lived coronal structures, spawned by the emerged magnetic flux, will evolve quasi-steadily or erupt with the impressive energies characteristic of flares and coronal mass ejections. Central to this picture is the suggestion, based on recent theoretical and observational works, that the the emerged flux may take the form of a twisted flux rope residing principally in the corona. Such a flux rope is identified with the low-density cavity at the base of a coronal helmet, often but not always encasing a quiescent prominence. The flux rope may either be bodily transported into the corona from below the photosphere, or reform out of a state of flaring turbulence under some suitable constraint of magnetic-helicity conservation. The appeal of this synthesis is its physical simplicity and the manner it relates a large set of diverse phenomena into a self-consistent whole. The implications of this view point are discussed.The topics covered are: the large-scale corona; helmet streamers; quiescent prominences; coronal mass ejections; flares and heating; magnetic reconnection and magnetic helicity; and, the hydromagnetics of magnetic flux emergence.The National Center for Atmospheric Research is sponsored by the National Science Foundation.     

A Relationship Between Transition Region Brightenings,Abundances, and Magnetic Topology

We present multi-instrument observations of active region (AR) 8048, made between 3 June and 5 June 1997, as part of the SOHO Joint Observing Program 33. This AR has a sigmoid-like global shape and undergoes transient brightenings in both soft X-rays and transition region (TR) lines. We compute a magneto-hydrostatic model of the AR magnetic field, using as boundary condition the photospheric observations of SOHO/MDI. The computed large-scale magnetic field lines show that the large-scale sigmoid is formed by two sets of coronal loops. Shorter loops, associated with the core of the SXT emission, coincide with the loops observed in the hotter CDS lines. These loops reveal a gradient of temperature, from 2 MK at the top to 1 MK at the ends. The field lines most closely matching these hot loops extend along the quasi-separatrix layers (QSLs) of the computed coronal field. The TR brightenings observed with SOHO/CDS can also be associated with the magnetic field topology, both QSL intersections with the photosphere, and places where separatrices issuing from bald patches (sites where field lines coming from the corona are tangent to the photosphere) intersect the photosphere. There are, furthermore, suggestions that the element abundances measured in the TR may depend on the type of topological structure present. Typically, the TR brightenings associated with QSLs have coronal abundances, while those associated with BP separatrices have abundances closer to photospheric values. We suggest that this difference is due to the location and manner in which magnetic reconnection occurs in two different topological structures. Supplementary material to this paper is available in electronic form at http://dx.doi.org/10.1023/A:1013302317042     

Waves and Oscillations in the Corona – (Invited Review)

It has long been suggested on theoretical grounds that MHD waves must occur in the solar corona, and have important implications for coronal physics. An unequivocal identification of such waves has however proved elusive, though a number of events were consistent with an interpretation in terms of MHD waves. Recent detailed observations of waves in events observed by SOHO and TRACE removes that uncertainty, and raises the importance of MHD waves in the corona to a higher level. Here we review theoretical aspects of how MHD waves and oscillations may occur in a coronal medium. Detailed observations of waves and oscillations in coronal loops, plumes and prominences make feasible the development of coronal seismology, whereby parameters of the coronal plasma (notably the Alfvén speed and through this the magnetic field strength) may be determined from properties of the oscillations. MHD fast waves are refracted by regions of low Alfvén speed and slow waves are closely field-guided, making regions of dense coronal plasma (such as coronal loops and plumes) natural wave guides for MHD waves. There are analogies with sound waves in ocean layers and with elastic waves in the Earth's crust. Recent observations also indicate that coronal oscillations are damped. We consider the various ways this may be brought about, and its implications for coronal heating.