Phase I Final Report: May 1996
Scientific Achievements
In this section we summarize our studies which are particularly relevant
to our HPCC Grand Challenge: exploring and understanding the manifestations of
solar activity.
Chromospheric Eruptions
One of the most intriguing facets of the so-called "quiet" chromosphere and
transition region is the ubiquitous presence of highly dynamic behavior.
Examples of chromospheric eruptions are spicules, surges, sprays, and the HRTS
explosive events all of which appear to be associated with flux emergence,
cancellation, or reconnection at the network and other sites characterized by
strong, mixed-polarity magnetic fields. The jets detected by Yohkoh's Soft
X-ray Telescope (SXT) also may be part of this continuum of chromospheric
activity. Based on these observations and our previous numerical studies
of the effects of photospheric motions on simple arcades we set out to
investigate the hypothesis that chromospheric eruptions all result from
magnetic reconnection and so occur in more complex configurations than we
had modeled thus far.
Our ensuing 2.5D simulations of shear-driven chromospheric
reconnection in symmetric and asymmetric arcades
provided the first numerical evidence that reconnection is a viable
explanation for the transient dynamical signatures of chromospheric
eruptions. Our model reproduced such fundamental observed features
as intermittency and large velocities, as well as the approximately
concurrent appearance of oppositely directed flows. The calculations
were performed on nonuniform Cartesian grids as large as 420x500 cells.
This relatively high resolution was essential to observing the intricate
process of current sheet formation and instability underlying the prominent
dynamic signatures. The work is continuing with a parallel version of the
2.5D code which is expected to illuminate the roles of field geometry and
shear magnitude in determining the likelihood and the detailed development
of these eruptive events.
Coronal Loop Dynamics
The heating of the solar corona in quiet and active regions remains one of
the biggest puzzles in solar physics, and as such is a prime target for the
Yohkoh SXT and TRACE. Yohkoh and green-line observations exhibit numerous
instances of apparent loop-loop interactions and other dynamic restructuring
from the smallest to the largest scales. Theories of coronal heating, whether
favoring Ohmic dissipation of currents or resonant absorption of wave energy,
all require the formation of fine-scale dissipative regions as well as a
mechanism for transporting the energy thus released into the observed loops.
In this context, our chromospheric reconnection studies yielded
an important discovery: if the interacting flux systems are of unequal
strength, as will generally be the case, the reconnection process can cause
adjacent field lines to exhibit very different shears after undergoing
reconnection. A wide band of highly filamentary, intense currents is formed
throughout the volume occupied by reconnected field lines. These structures
occur only through shear-driven (2.5D or 3D) reconnection in an asymmetric
topology, and not in the commonly studied symmetric or compression-driven (2D)
systems. This phenomenon has clear implications for direct-current models of
coronal heating, which have postulated the existence of such fine structure in
coronal loops without explaining its origin.
These results encouraged us to explore current sheet formation
and reconnection in models of increasing complexity, including systems
with null points and separatrices and laminar 3D systems with current sheets
Most recently we investigated the simplest possible examples of reconnection
in a fully 3D system -- two interacting flux tubes -- in order to understand
the details of the reconnection process uncluttered by geometric complexity
and to establish a baseline for further studies. Even the simplest initial
conditions lead to complex behavior, such as the eventual shredding of
antiparallel fluxtubes. An astounding new phenomenon results
when a pair of orthogonal, twisted fluxtubes collide magnetic
tunneling, in which the tubes apparently pass through each other so
long as the resistivity is sufficiently low. Careful inspection of the
magnetic connectivity reveals that the field lines actually become quite
tangled while undergoing multiple reconnections, as illustrated in Fig. 1.
These calculations were performed on the NRL CM-5 with 128x128x138 Fourier
modes, the minimum required to resolve a complex process that we expect to be
prevalent in the much less dissipative solar corona.
Figure 1. Magnetic tunneling of two orthogonal, interacting
fluxtubes. Shown are several indvidual magnetic field lines of the two
tubes (in black and green, respectively). The tubes have exchanged their
central sections through multiple reconnections, resulting in the red
field line having been intermittently shared between the two fluxtubes.
The spectral MHD calculations were performed on the 256-node NRL CM-5.
For wave heating models of coronal loops, resonance layers are the analogue
of the filamentary current sheets discussed above. Here the major issues
are whether resonance layers will form and remain stable under typical
photospheric driving conditions, and whether the resultant velocities
and heating in the layers are consistent with observations. Our initial
research focused on
the development and saturation of resonant layers in a 3D coronal loop
responding to periodic driving forces. We then investigated
the parametric dependence of the heating rate and velocity amplitudes on
the resistivity and driver amplitude for both traveling and standing
Alfven waves. For typical values of the coronal resistivity,
theory predicts that the layers must become exceedingly thin
and sustain unphysically high flows in order to produce the required heating
rate. It has been suggested, however, that small-scale turbulence developing
within the highly sheared layers could dramatically increase the effective
dissipation scale. Our calculations have confirmed this hypothesis.
Scaling the results to realistic values of the coronal magnetic
Reynolds number yields velocity amplitudes in the resonance layer
that agree reasonably well with observations of nonthermal coronal velocities
The underlying shear instability can develop only in adequately resolved
calculations; 128x128x128 grid points were required to reach magnetic Reynolds
numbers of 10^5.
Prominences and CMEs
Prominences are large, dramatic manifestations of solar activity, long noted
for spectacular eruptions and well studied observationally. Yet, until
recently very little was understood about their origin, support, and dynamical
behavior. Understanding these issues, as well as the genesis of the coronal
mass ejections (CMEs) which accompany erupting prominences, is among the
primary goals of both SOHO and TRACE. We have made substantial progress
in all of these areas by combining nonlinear MHD simulations, numerical
modeling of force-free fields, and theory to study stressed 2.5D and 3D
magnetic configurations. Our first success was the identification of a
plausible mechanism by which chromospheric material is transported into
the corona and condenses to form a prominence. More recently, we discovered
a mechanism for prominence support. Photospheric shear, localized around
the neutral line as observed, readily yields coronal field lines with the
requisite geometry and produces regions of inverse polarity - observed
features which have long been a theoretical puzzle. An example of such
a configuration is shown in Fig. 2. We are continuing
to investigate the role of shears and twists of finite-length arcades,
not only in forming the magnetic superstructure of prominences but also
in initiating their eruption. As we investigate larger stresses and more
complex magnetic topologies, and compare the results with observations, the
need for computational grids larger than our present limits will become
critical.
Figure 2. Model for the magnetic field of prominences. The
distribution of sheared photospheric flux is given by the color contours
on the bottom grid. Contours (red) of the magnitude of positive (upward)
field line curvature are shown overlying the neutral line. Two representative
field lines (black) are shown as well.
Coronal Holes and Solar Wind
Coronal holes occupy much of the solar corona at certain times and are thought
to be the main sources of the high-speed solar wind. Thus, they are of
considerable interest to both solar and heliospheric physics. Coronal holes
pose a particular challenge to heating models, because the magnetic field is
predominantly unipolar: mechanisms which rely on interactions between
oppositely directed fields are inapplicable. The most likely energy source
for heating and solar-wind acceleration in coronal holes is MHD waves, but in
classical analyses these waves either damp in the transition region or pass
through the corona with negligible losses. Our numerical studies of the
propagation and dissipation of MHD waves suggest a possible solution to this
dilemma: resonant absorption of coupled fast and shear Alfven waves can occur
in an open field configuration with cross-field density gradients, and phase
mixing in dense plumes within the holes can heat a larger volume of plasma
than resonant absorption alone. These calculations were performed on a CM-5
with 2D grids of 300x500 points, at magnetic Reynolds numbers of about
10^5. Still, only a coarse representation of the density variations due to
plumes was allowed. To provide detailed comparisons between this model and
the latest coronagraph data (e.g., from SPARTAN and LASCO), we must increase
the resolution substantially, as well as pursue 3D modeling of the coronal
hole and its surroundings.
Report Overview
Highlights
Computational Achievements
Progress Toward Metrics
Bibliography