A. A. van Ballegooijen

Formation and eruption of solar prominences

A model for the magnetic field associated with solar prominences is considered. It is shown that flux cancellation at the neutral line of a sheared magnetic arcade leads to the formation of helical field lines which are capable, in principle, of supporting prominence plasma. A numerical method for the computation of force-free, canceling magnetic structures is presented. Starting from an initial potential field we prescribe the motions of magnetic footpoints at the photosphere, with reconnection occurring only at the neutral line. As more and more flux cancels, magnetic flux is transferred from the arcade field to the helical field. Results for a particular model of the photospheric motions are presented. The magnetic structure is found to be stable: the arcade field keeps the helical field tied down at the photosphere. The axis of the helical field moves to larger and larger height, suggestive of prominence eruption. These results suggest that prominence eruptions may be trigered by flux cancellation. 73 refs.

Evidence for Alfvén Waves in Solar X-ray Jets

Coronal magnetic fields are dynamic, and field lines may misalign, reassemble, and release energy by means of magnetic reconnection. Giant releases may generate solar flares and coronal mass ejections and, on a smaller scale, produce x-ray jets. Hinode observations of polar coronal holes reveal that x-ray jets have two distinct velocities: one near the Alfvén speed (∼800 kilometers per second) and another near the sound speed (200 kilometers per second). Many more jets were seen than have been reported previously; we detected an average of 10 events per hour up to these speeds, whereas previous observations documented only a handful per day with lower average speeds of 200 kilometers per second. The x-ray jets are about 2 × 103 to 2 × 104 kilometers wide and 1 × 105 kilometers long and last from 100 to 2500 seconds. The large number of events, coupled with the high velocities of the apparent outflows, indicates that the jets may contribute to the high-speed solar wind.

ON THE GENERATION, PROPAGATION, AND REFLECTION OF ALFVEN WAVES FROM THE SOLAR PHOTOSPHERE TO THE DISTANT HELIOSPHERE

We present a comprehensive model of the global properties of Alfven waves in the solar atmosphere and the fast solar wind. Linear non-WKB wave transport equations are solved from the photosphere to a distance past the orbit of the Earth, and for wave periods ranging from 3 s to 3 days. We derive a radially varying power spectrum of kinetic and magnetic energy fluctuations for waves propagating in both directions along a superradially expanding magnetic flux tube. This work differs from previous models in three major ways. (1) In the chromosphere and low corona, the successive merging of flux tubes on granular and supergranular scales is described using a two-dimensional magnetostatic model of a network element. Below a critical flux-tube merging height the waves are modeled as thin-tube kink modes, and we assume that all of the kink-mode wave energy is transformed into volume-filling Alfven waves above the merging height. (2) The frequency power spectrum of horizontal motions is specified only at the photosphere, based on prior analyses of G-band bright point kinematics. Everywhere else in the model the amplitudes of outward and inward propagating waves are computed with no free parameters. We find that the wave amplitudes in the corona agree well with off-limb nonthermal line-width constraints. (3) Nonlinear turbulent damping is applied to the results of the linear model using a phenomenological energy loss term. A single choice for the normalization of the turbulent outer-scale length produces both the right amount of damping at large distances (to agree with in situ measurements) and the right amount of heating in the extended corona (to agree with empirically constrained solar wind acceleration models). In the corona, the modeled heating rate differs by more than an order of magnitude from a rate based on isotropic Kolmogorov turbulence.

The Ultraviolet Coronagraph Spectrometer for the Solar and Heliospheric Observatory

The SOHO Ultraviolet Coronagraph Spectrometer (UVCS/SOHO) is composed of three reflecting telescopes with external and internal occultation and a spectrometer assembly consisting of two toric grating spectrometers and a visible light polarimeter. The purpose of the UVCS instrument is to provide a body of data that can be used to address a broad range of scientific questions regarding the nature of the solar corona and the generation of the solar wind. The primary scientific goals are the following: to locate and characterize the coronal source regions of the solar wind, to identify and understand the dominant physical processes that accelerate the solar wind, to understand how the coronal plasma is heated in solar wind acceleration regions, and to increase the knowledge of coronal phenomena that control the physical properties of the solar wind as determined by in situ measurements. To progress toward these goals, the UVCS will perform ultraviolet spectroscopy and visible polarimetry to be combined with plasma diagnostic analysis techniques to provide detailed empirical descriptions of the extended solar corona from the coronal base to a heliocentric height of 12 solar radii.

HEATING OF THE SOLAR CHROMOSPHERE AND CORONA BY ALFVÉN WAVE TURBULENCE

A three-dimensional magnetohydrodynamic (MHD) model for the propagation and dissipation of Alfv?n waves in a coronal loop is developed. The model includes the lower atmospheres at the two ends of the loop. The waves originate on small spatial scales (less than 100?km) inside the kilogauss flux elements in the photosphere. The model describes the nonlinear interactions between Alfv?n waves using the reduced MHD approximation. The increase of Alfv?n speed with height in the chromosphere and transition region (TR) causes strong wave reflection, which leads to counter-propagating waves and turbulence in the photospheric and chromospheric parts of the flux tube. Part of the wave energy is transmitted through the TR and produces turbulence in the corona. We find that the hot coronal loops typically found in active regions can be explained in terms of Alfv?n wave turbulence, provided that the small-scale footpoint motions have velocities of 1-2?km?s?1 and timescales of 60-200?s. The heating rate per unit volume in the chromosphere is two to three orders of magnitude larger than that in the corona. We construct a series of models with different values of the model parameters, and find that the coronal heating rate increases with coronal field strength and decreases with loop length. We conclude that coronal loops and the underlying chromosphere may both be heated by Alfv?nic turbulence.

Observations and Modeling of a Filament on the Sun

Hα observations of a filament were obtained at the Swedish Vacuum Solar Telescope in 1998 June. The U-shaped filament has a prominent barb that exhibits interesting fine structure and internal motions. A three-dimensional magnetic model of the filament is presented. The model is based on a National Solar Observatory (Kitt Peak) magnetogram and is constructed by inserting a twisted flux rope into a potential field representing the overlying coronal arcade; the flux rope has an axial flux of 3.4 × 1019 Mx and poloidal flux of 3.7 × 109 Mx cm-1. Magnetofrictional relaxation is used to drive the configuration to a nonlinear force-free field. The shape of the resulting flux rope is distorted by neighboring network elements. The dips in the helical field lines reproduce the observed filament barb, which is caused by a local distortion of the flux rope resulting from a weak-field extension (~4 G) of a neighboring network element. The pitch of the helical field lines is larger than expected on the basis of a model of flux rope formation. I suggest that this is due to magnetic diffusion within the flux rope. A simple model of magnetic diffusion in a cylindrical flux rope is presented.

Models of the Large-Scale Corona. I. Formation, Evolution, and Liftoff of Magnetic Flux Ropes

The response of the large-scale coronal magnetic field to transport of magnetic flux in the photosphere is investigated. In order to follow the evolution on long timescales, the coronal plasma velocity is assumed to be proportional to the Lorentz force (magnetofriction), causing the coronal field to evolve through a series of nonlinear force-free states. Magnetofrictional simulations are used to study the formation and evolution of coronal flux ropes, highly sheared and/or twisted fields located above polarity inversion lines on the photosphere. As in our earlier studies, the three-dimensional numerical model includes the effects of the solar differential rotation and small-scale convective flows; the latter are described in terms of surface diffusion. The model is extended to include the effects of coronal magnetic diffusion, which limits the degree of twist of coronal flux ropes, and the solar wind, which opens up the field at large height. The interaction of two bipolar magnetic regions is considered. A key element in the formation of flux ropes is the reconnection of magnetic fields associated with photospheric flux cancellation at the polarity inversion lines. Flux ropes are shown to form both above the external inversion line between bipoles (representing type B filaments) and above the internal inversion line of each bipole in a sigmoid shape. It is found that once a flux rope has formed, the coronal field may diverge from equilibrium with the ejection of the flux rope. After the flux rope is ejected, the coronal field once again relaxes down to an equilibrium. This ability to follow the evolution of the coronal fields through eruptions is essential for future full-Sun simulations in which multiple bipoles are evolved for many months or years.

Alfvénic Turbulence in the Extended Solar Corona: Kinetic Effects and Proton Heating

We present a model of magnetohydrodynamic (MHD) turbulence in the extended solar corona that contains the effects of collisionless dissipation and anisotropic particle heating. Recent observations have shown that preferential heating and acceleration of positive ions occur in the first few solar radii of the high-speed solar wind. Measurements made by the Ultraviolet Coronagraph Spectrometer aboard SOHO have revived interest in the idea that ions are energized by the dissipation of ion cyclotron resonant waves, but such high-frequency (i.e., small-wavelength) fluctuations have not been observed. A turbulent cascade is one possible way of generating small-scale fluctuations from a preexisting population of low-frequency MHD waves. We model this cascade as a combination of advection and diffusion in wavenumber space. The dominant spectral transfer occurs in the direction perpendicular to the background magnetic field. As expected from earlier models, this leads to a highly anisotropic fluctuation spectrum with a rapidly decaying tail in the parallel wavenumber direction. The wave power that decays to high enough frequencies to become ion cyclotron resonant depends on the relative strengths of advection and diffusion in the cascade. For the most realistic values of these parameters, however, there is insufficient power to heat protons and heavy ions. The dominant oblique fluctuations (with dispersion properties of kinetic Alfven waves) undergo Landau damping, which implies strong parallel electron heating. We discuss the probable nonlinear evolution of the electron velocity distributions into parallel beams and discrete phase-space holes (similar to those seen in the terrestrial magnetosphere), which can possibly heat protons via stochastic interactions.

Cascade of magnetic energy as a mechanism of coronal heating

A statistical model is defined for the quasi-static evolution of the motion of photospheric structures through a cascade process. Since the magnetic footprints move slowly, the coronal field can adapt to changing boundary conditions as free magnetic energy is transported over timescales significantly smaller than those of the movements of the footprints. The energy is transported as coronal loops are shredded into increasingly finer segments by randomly changing velocity gradients in the photosphere, a process which is stochastic. Numerical computations are provided which show that the magnetic energy is transferred to larger wavenumbers by a cascade process. Application of the model to coronal heating is discussed. 34 references.

Electric currents in the solar corona and the existence of magnetostatic equilibrium

The random motions of magnetic field lines induced by convective flows below the solar surface cause braiding and twisting of the coronal magnetic field, and may be responsible for heating the solar corona. The suggestion by Parker (1972) that the field does in general not attain equilibrium, and must develop current sheets in which the braiding patterns are dissipated (topological dissipation), is considered. Using an analogy with two-dimensional flows, it is shown that invariance of the winding pattern in the general direction of the field is not a necessary requirement for equilibrium, as Parker suggested. Discontinuities in the magnetic field (current sheets) arise only if the velocity field at the photospheric boundary is itself a discontinuous function of position. This suggests that the corona field can simply adjust to the slowly changing boundary conditions in the photosphere, and that topological dissipation of the winding patterns does not take place. Some implications for coronal heating are discussed. 35 references.