Corona and Heliosphere (C&H)

Coronal Structure and Dynamics

Coronal Mass Ejection (CME) Studies

-Relative Magnetic Helicity in Equilibrium Magnetic Fields- Mei Zhang (NCAR Afficilate Scientist, National Astronomical Observatory, China) and Boon Chye Low (HAO) investigated the nature of relative magnetic helicity in equilibrium magnetic fields in unbounded domains. As is well known, the total magnetic energy of a force-free magnetic field in an unbounded space anchored to an inner boundary is bounded above by a value defined entirely by the boundary flux distribution. Zhang and Low are using a simple formula (discovered by Zhang) for the relative total helicity of an external, axisymmetric, force-free field anchored to a unit sphere, to theoretically determine similar upper bounds for the total relative helicity of force-free magnetic fields.

-Numerical Investigations of 2D Magnetic Equilibria- Gordon Petrie (HAO/SCD Visiting Scientist, University of Athens, Greece) is developing a finite-element code to treat two-dimensional, equilibrium magnetic fields, in order to conduct studies of such equilibria in parameter regimes not previously investigated. The theory of Low and Zhang (2002) describing the two kinds of CMEs and their possible relationship to inverse and normal prominences motivates this study. The prominence observations of Lin, Penn and Kuhn (1998) showing a reversal of sign of the axial magnetic field of the prominence suggests that the magnetic configurations in prominences may be richer than previously thought. A two-dimensional hydromagnetic study is a first step toward exploring new possibilities for prominence magnetic structures.

-Collaborative Studies of 2D and 3D Magnetic Equilibria- The collaboration between HAO (Low, Zhang), SCD (Natasha Flyer, Steve Thomas), and the University of Colorado (Bengt Fornberg) continues to study axisymmetric equilibrium fields external to a unit sphere. In a previous publication (Flyer et al, 2004), it was shown that an equatorial magnetic flux rope in a force-free magnetic field may store energy above the Aly open field limit. But the excess energy above this limit is small, of the order of less than 8 percent, confirming other similar results. A systematic parameter search of the solutions by Zhang and Flyer shows that the 8 percent limit is common, and may be related to a bound on the total relative helicity of the force-free fields in unbounded domain. A new study introducing plasma pressure and gravitational stratification of a static atmosphere in equilibrium with the field shows that flux ropes embedded in the atmosphere may break the 8 percent limit on the energy in excess of the Aly limit, provided mass is loaded in strategic parts of the magnetic structure. A high-precision numerical solver, capable of treating the governing, nonlinear, elliptic partial differential equation, was developed for this project.

This collaboration has expanded to treat force-free magnetic fields and fields in static equilibrium in the presence of pressure and gravitational forces in realistic three-dimensional geometry. A complete generalization is not possible because three-dimensional magnetostatic problems are intractable in general. Low reduced the governing equations to a more tractable form describing a large sub-set of the general solutions which retains three-dimensionality and holds the potential of modeling the rich field topologies of observed coronal structures (Low, 1991). Included in the sub-set are the force-free magnetic fields. The reduced governing equations require the proper formulation of boundary conditions which hitherto have been elusive and poorly understood. This obstacle has been removed, and the door is open for generating fully three-dimensional equilibrium magnetic field for modeling solar coronal magnetic structures (Low 2005, in prepartation). The powerful numerical solver developed by Flyer and Fornberg for treating axisymmetric force-free magnetic fields can be extended to treat this class of three-dimensional problems. Ellen Zweibel (University of Wisconsin) has joined the HAO/SCD/Colorado collaboration.

-Flux Emergence and the Evolution of the Coronal Magnetic Field- Yuhong Fan and Sarah Gibson (both of HAO) have extended the numerical simulations of coronal flux ropes to 3D spherical geometry, so as to address the question of magnetic energy storage and release in coronal mass ejections. In an earlier study, Sturrock et al. (2001) have considered a 3D coronal magnetic field that consists of a twisted magnetic flux rope anchored at both ends, confined within an external potential arcade, as a possible configuration for CME precursors. Through an order of magnitude estimate, they found that with a moderate amount of total twist (less than 2 full field line winds), the free magnetic energy associated with the twisted magnetic flux rope is sufficient for the flux rope to rupture through the arcade and extend to infinity as a CME, without opening up all the arcade field. Fan modeled this dynamic scenario by performing isothermal, low-beta MHD simulations of the evolution of the coronal magnetic field as a twisted, line-tied magnetic flux rope is transported slowly into the corona previously occupied by a potential arcade field. The simulations show two distinct phases for the evolution of the coronal magnetic field (see the accompnaying Figure and Movie). In the earlier phase, the coronal flux rope evolves quasi-statically with both the magnetic energy and twist being built up as a result of flux emergence. In this stage the rise velocity is nearly constant, being about 0.01 times the characteristic Alfven speed (top panel of the Figure), and the magnetic energy evolution accurately tracks the energy build-up due to the Poynting flux through the lower boundary (bottom panel of the Figure). When sufficient twist and magnetic energy are transported into the corona, the flux rope undergoes a significant acceleration (top panel of the Figure) and is able to rupture through the overlying arcade, producing a CME-like eruption (see the Movie). The flux rope continues to accelerate after the flux emergence is stopped at t=97 (as marked by the vertical dotted lines in the Figure), and the rise velocity reaches about 550 km/sec when the flux rope begins to exit the outer boundary of the domain at r = 6 R⊙. In this latter dynamic phase of the evolution, the flux rope becomes kinked, which facilitates the loss of confinement of the flux rope by changing its orientation at the apex such that it becomes easier for the flux rope to part and erupt through the arcade field. A sigmoid shaped current layer develops as a result of the onset of the kink instability (Fan and Gibson, 2004), and there is significant magnetic energy release in the eruption phase as can be seen in the bottom panel of the Figure.

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CME-related solar atmospheric phenomena

-CME-related Coronal and Chromospheric Waves- Although Moreton waves have historically been observed in Hα data, more recently waves have also been observed in chromospheric He I (λ=1083nm) images obtained at the Mauna Loa Solar Observatory. In an effort to better understand the nature of chromospheric waves and their relationship to coronal waves observed in EIT data, Holly Gilbert (HAO), Barbara Thompson (Goddard Space Flight Center), Tom Holzer (HAO), and Joan Burkepile (HAO) focused on two events in which waves are observed simultaneously in He I and Fe XII (λ=195Å), lines formed in the chromosphere and corona, respectively (Gilbert et al, 2004). Comparing the waves observed in these two lines allows the determination of the spatial relationship between coronal and chromospheric waves, and thus aids in the understanding of the underlying physics of waves in the solar atmosphere. The main goal of this work was to begin an investigation into whether coronal and chromospheric waves are both mechanical (e.g., MHD waves) by looking at their spatial relationship. Gilbert and colaborators found the chromospheric waves in these two events to be roughly co-spatial with their coronal counterparts, indicating they are not mechanical in nature but are chromospheric imprints of mechanical waves propagating through the corona. This conclusion is based upon the nature of the formation of the He I absorption line.

Another study involving chromospheric waves was completed by Gilbert and Holzer (2004) where the focus is on the same two wave events observed in He I from their previous work. Two interesting phenomena occur in these wave events: the waves are visible in the He I velocity data and multiple waves are observed for each event. The velocity signal provides evidence for the downward propagation from the corona to the chromosphere of a slow-mode hydromagnetic wave generated at the front of the fast coronal hydromagnetic wave. In this work, it is also suggested that the observed multiple waves indicate more than one driving mechanism may be involved.

-A New Technique for Estimating Prominence Masses- Prominences are cool condensations of partially ionized plasma in the million-degree corona. They often appear in absorption when the sun is viewed in EUV emission lines formed at coronal temperatures. The coronal EUV radiation at wavelengths less than 504Å undergoes Lyman continuum absorption by both hydrogen and helium (i.e., the coronal radiation ionizes hydrogen and helium atoms from their ground states). It is presently unclear what role prominences play in the initiation and dynamics of CMEs, although erupting prominences are strongly correlated with CMEs. The masses of prominences involved in CMEs are not generally measured, but the accurate determination of such masses may help in assessing the dynamical importance of prominences in CME events. Gilbert, Holzer, and Robert MacQueen (HAO) have developed a new technique for deriving prominence mass, one that uses observations of coronal radiation in the Fe XII (19.5 nm) spectral line, which is absorbed by prominence material. This new method makes it possible to consider the effects of both foreground and background radiation in the analysis, and it can be applied to both quiescent and erupting prominences by using two versions of the method, labelled as the "spatial-interpolative" version and the "temporal-interpolative" version. Gilbert, Holzer and MacQueen find that when both versions can be applied to the same event, the temporal-interpolative approach yields the more accurate results. They have applied both versions to an erupting prominence observed on 1999 July 12 (this prominence had an associated CME), and find that the two approaches result in similar mass determinations:(6.0 ± 2.5) X ¹⁴g for the temporal-interpolative approach and (7.4 ± 4.6) X ¹⁴g for the spatial-interpolative approach (Gilbert, Holzer and MacQueen, 2004).

-Observational Studies of Prominence Acceleration- Giuliana de Toma (HAO), Holzer, Burkepile, and Gilbert are carrying on an observational study of prominence acceleration, aimed at investigating the relationship between the acceleration of eruptive prominences and the speed of their associated CMEs, in order to better understand the acceleration phase of prominences in the low corona. This study considers events near or at the solar limb when eruptive prominences observed in Mauna Loa Solar Observatory (MLSO) ground observations show a clear association with CMEs. To determine the prominence acceleration, Hα observations from the MLSO/Polarimeter for Inner Coronal Studies (PICS) instrument are used. This instrument obtains observations off limb with a broadband filter of about 1.0 nm, and on disk with a narrower filter of about 0.05 nm. The broad filter of the MLSO/PICS instrument used with the occulting disk avoids a common problem with narrow band filters where the prominence material can disappear because it is Doppler-shifted out of the instrument band pass. The MLSO/PICS instrument also has the advantage of a wide field-of-view, extending from 1.01 solar radii to ~2.3 solar radii in the east and west directions, and a high temporal cadence of 3-minute which is crucial for measuring trajectories accurately. Previous coronagraph observations have shown that the prominence material of a CME moves slower than the leading front, but that the two appear to travel outward as a unit. It is thus expected that the prominence acceleration in the low corona will be related to the acceleration of the CME itself and can be a good indicator of the CME final velocity. To test this hypothesis, the plane-of-sky projection of the maximum radial accelerations of the eruptive prominences are compared with the projected asymptotic velocities of the corresponding CMEs. Preliminary results from this study show that, while there is a broad range of observed accelerations for prominences, there appears to be a correlation between the prominence maximum acceleration and the CME asymptotic velocity. In particular, all CMEs with v > 600 km/s have accelerations of the order of 20 m/s² or larger and all fast CMEs with v > 900 km/s have accelerations greater than 100 m/s².

-Composite Kippenhan-Schluter Prominence Models- Low and Petrie have generalized the classical Kippenhahn-Schluter prominence-sheet model. They showed that one-dimensional Kippenhahn-Schluter solutions, each representing a thin vertical layer of magnetized plasma, can be stacked against one another in a collection of such layers to form a prominence rich in small-scale structure, without losing the equilibrium among the Lorentz, plasma and gravitational forces. Moreover, for each such composite solution, each layer may be given a uniform motion of an arbitrary magnitude in its plane, in which case, this hydromagnetic state is described by the steady state equations. These solutions present an opportunity to perform forward modeling of the polarimetric signals one might expect to encounter in the observation of prominence magnetic fields. A collaboration has been set up with Roberto Casini (HAO) and Haosheng Lin (NCAR Affiliate Scientist, University of Hawaii) to exploit this opportunity in support of observational efforts at HAO and Hawaii to observe prominence magnetic fields with new techniques and instrumentation. Low and Petrie are also investigating the theoretical freedom to prescribe arbitrary sliding motions between the vertical prominence plasma sheets, both as a basic hydromagnetic problem and as representations of the motions observed in real prominences.

-Formation and Dissipation of Magnetic Tangential Discontinutities- Low, Petrie and Zhang investigated the formation of magnetic tangential discontinuities between vertical magnetic flux surfaces in a stratified atmosphere. This is generally a three-dimensional effect with variations in the two dimensions of each flux surface and variations in the third direction perpendicular to the surfaces. They have found analytical solutions describing such discontinuities in force equilibrium. These explicit solutions provide an opportunity to analyze the dynamical consequences of magnetic reconnection dissipating the tangential discontinuity. Spontaneous magnetic dissipation of tangential discontinuities within prominences is being investigated as a mechanism whereby fully ionized plasma can drain from prominences and magnetic flux escape into the atmosphere.

-Transient Coronal Holes Observed in the He I 1083 nm Line- Observations from Yohkoh/SXT and SOHO/EIT have shown that dimming regions often appear on the solar disk near the location of a CME. Brightenings in He I 1083 nm are also visible in observations made at MLSO that form at the same time and are co-spatial with the EUV intensity dimmings observed from space. The He I 1083 nm brightenings are induced by a decrease of the overlying coronal radiation. The EUV and X-ray dimmings and He I 1083 nm brightenings can thus be interpreted as different manifestations of the decreased coronal density caused by the ejection of coronal material, that is, as transient coronal holes. de Toma, Holzer, Burkepile and Gilbert have studied six cases when transient coronal holes developed in association with a CME onset and were seen in He I 1083 nm and in the EIT Fe XII 19.5 nm line. They find the transient coronal holes at the EUV wavelengths observed by EIT and in the IR He I 1083 nm line form at the same time, within the 12-minute cadence of the EIT observations and there is good agreement in both shape and size of the holes at these wavelengths. The high, 3-minute temporal cadence of the He I 1083 nm observations taken at MLSO allows them to determine the appearance and evolution of transient coronal holes accurately and to study the relationship with other manifestations of activity at the CME onset. They find the transient coronal holes typically form during the impulsive phase of the flare, and follow the CME onset by several minutes to up to an hour. Transient coronal holes tend to form within regions of weak magnetic flux (5-20 Mx/cm²) and their formation time varies from between 20 minutes to about an hour.

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Coronal Structure and its Evolution

-Multi-Wavelength Determination of Coronal Holes- In collaboration with the Center for Integrated Space Weather Modeling (CISM), de Toma, Nick Arge (NOAA) and Gibson have worked on the validation of coronal models. As part of this effort, models and observations of coronal holes have been compared. Coronal holes have been historically observed as regions of reduced emission on the solar disk in X-Ray and EUV wavelengths, or as regions of reduced brightness in coronagraph images at the limb. They can also be seen as relatively bright regions in He I 1083 nm. They are usually identified with the footpoints of magnetic field lines that open into the heliosphere, as derived from potential field model extrapolations. Since the appearance of coronal holes is different at different wavelengths, and since we do not have observational data to determine which regions on the Sun have open or closed magnetic field lines, the identification of coronal holes has always been difficult. de Toma, Arge, and Gibson have used relative intensity images in EUV wavelengths from SOHO/EIT, ground-based observations in the He I 1083 nm line, Hα line, and magnetograms in an attempt to identify coronal hole regions in a more objective way. Data are assembled in the form of synoptic maps, and a set of criteria based of the intensity contrast and the magnetic property of coronal holes are used to identify them using an automatic procedure. Hα and magnetograms are used to identify filament channels and to resolve the ambiguity with coronal holes. The observed coronal holes are then compared with the modeled ones and used to evaluate the model accuracy and the model sensitivity to the initial conditions.

-Observable Properties of Coronal Magnetic Flux Ropes- Gibson, Fan, and collaborators George Fisher (University of California, Berkeley), Cristina Mandrini (Instituto de Astronomía y Física del Espacio, IAFE, Argentina), and Pascal Demoulin (University of Paris, France) (Gibson et al., 2004) have considered the observable properties of a magnetic flux rope in the corona, as modeled in Fan and Gibson (2003, 2004). In particular, the structure, evolution, and relative location and orientation of S-shaped, or sigmoid active regions and filaments were compared to topological features of the magnetic flux rope, testing the theories that: 1) X-ray sigmoids appear at the regions of the flux rope known as bald patch-associated separatrix surfaces (BPSS), where, under dynamic forcing, current sheets can form leading to reconnection and localized heating; and that 2) filaments are regions of enhanced density contained within dips in the magnetic flux rope. Analysis demonstrates that the shapes and relative orientations and locations of the BPSS and dipped field in the emerging flux rope are consistent with observations of X-ray sigmoids and their associated filaments. Moreover, current layers indeed form along the sigmoid BPSS as the flux rope is driven by the kink instability, which is evidence in support of the theory that X-ray sigmoids appear when this critical topological surface is dynamically forced.

Figure: Comparison of t=56 BPSS (red field lines) to current sheets (yellowish-green isosurfaces). (right) Same, with t=39 BPSS also shown (purple field lines). Color contours at bottom boundary represent magnitude of current at photosphere (same color scaling as coronal isosurfaces).

Figure: Two views of t=39 BPSS (purple field lines) and dipped field representing filament (brown) (note, dipped field has been filled from the dip bottom up a distance .1 L or to where the field direction becomes horizontal, whichever comes first. L is the shorter of the horizontal lengths of the simulation domain). Color contours at lower boundary represent normal component of the magnetic field at the photosphere.

-Coronal Cavities, Flux Ropes, and CMEs- Gibson, David Foster (HAO), Burkepile, and Andrew Stanger (HAO) are investigating the currently debated question of whether or not magnetic flux ropes are present in the corona prior to a CME, or whether they are formed during eruptions. This is important to establish because a flux rope precursor is a reservoir of magnetic energy, so observations that can be clearly associated with a flux rope are strong indicators for eruption. Good candidates for flux rope precursors are observed quiescent white light coronal cavities. It has long been established that CMEs often possess three parts, a front, a cavity, and a bright core. Even in cases where no core (identified with the erupting prominence) can be found, a cavity is often present. Observations of the low solar corona, such as those taken by HAO's MLSO, demonstrate that this three-part structure can be present well before the eruption, as a helmet streamer, embedded white light cavity, and prominence core. As in the case of CMEs, sometimes the prominence itself is not visible, but the helmet and cavity are. Magnetic flux rope models provide a physical explanation for the cavity, forming a region of depleted density surrounding the prominence core (Low and Hundhausen, 1995). The quiescent cavities observed in white light are thus consistent with a precursor magnetic flux rope in the corona. Gibson, Foster, Burkepile and Stanger are currently studying quiescent cavities using MLSO Mark IV coronagraph data and tabulatng their sizes, shapes, locations, orientations, intensity contrasts, and relation to CMEs. They are also conducting an analytic study of how cavity appearance changes using a modified three-dimensional density model (Gibson et al. 2003) to quantitatively model cavity density.

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Physics of the Solar Wind

Quasi-steady processes

-New Transport Equation for Fully Ionized Gases- Mari Anne Killie, Åse Marit Janse, Øystein Lie-Svendsen (all of the University of Oslo, Norway), and Egil Leer (NCAR Affiliate Scientist, University of Oslo, Norway) have worked on the development of new transport equations for fully ionized gases, which improve the description of Coulomb collisions compared to fluid transport equations that are in common use today (Killie at al. 2004). The main motivation for this work has been to improve the description of energy transport and collisional forces in the solar corona and transition region, which in turn are important for understanding, for example, the origin of the solar wind mass flux, as well as coronal abundances of helium and minor ions.

-Solar Wind Minor Ion Energy Budget- Lie-Svendsen and Ruth Esser (University of Tromsø, Norway) have also studied the energy budget of minor ions in the corona and solar wind, using a solar wind model extending from the chromosphere to 1 AU (Lie-Svendsen and Esser 2005). The model results show that coronal heavy ions become very hot, with temperatures that may easily exceed 10⁸ K. This occurs even without strong heating of the ions, because the minor ion energy loss is small unless they become hot. However, without preferential heating of the minor ions (that is, a coronal heating rate per particle larger than for protons), the collisional coupling to protons causes extremely large minor ion abundances in the corona, which are ruled out by observations.

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Transient processes

-Transient Outflows from Closed Coronal Loops- The solar wind model mentioned in the preceding paragraph has been used by Eirik Endeve, Lie-Svendsen, Leer, and Viggo Hansteen (all of the University of Oslo, Norway) to study the outflow of solar wind plasma from closed coronal loops that periodically open into the solar wind. The main finding is that such loops do not seem to be a source of helium-rich material that can explain the high helium abundances that have occasionally been observed in situ in the solar wind (mainly in association with coronal mass ejections). The reason is that in closed regions, the high density leads to collisional coupling between α-particles and protons, causing a low α- particle temperature in the corona. The α-particles therefore do not have sufficient (thermal) energy to escape from the gravitational potential when the flux tube is opened. Only many hours, or even days, after opening will an enhanced α-particle flux emerge.

-MHD Simulations of the Inner Corona and Solar Wind- Endeve, Holzer, and Leer (Endeve et al. 2004) have used an MHD simulation to study heating of electrons and protons in an axially symmetric model of the solar corona, extending from the coronal base to 15 solar radii. To consider heating of electrons and protons separately, as well as the collisional coupling between the particle species, a two-fluid description of the electron- proton plasma is used. A steady coronal heat input, uniform base pressure, and dipole field boundary conditions produce a magnetic field configuration similar to that seen with white-light coronagraphs during quiet-Sun conditions: a helmet streamer is formed in the inner corona around the equator, surrounded by coronal holes at higher latitudes. The plasma inside the helmet streamer is in hydrostatic equilibrium, while in the coronal holes a transonic solar wind is accelerated along the field. The collisional coupling between electrons and protons becomes weak close to the coronal base. In the case of proton heating, the thermal structure along open and closed field lines is very different, and there is a large pressure jump across the streamer- coronal hole boundary. When the simulation is run on a long time scale, the helmet streamer becomes unstable, and massive plasmoids are periodically released into the solar wind. These plasmoids contribute significantly to the total mass and energy flux in the solar wind. The mass of the plasmoids is reduced when electrons are heated. In a model that is not axisymmetric, it is possible that this streamer instability can give rise to the slow solar wind.