Peter MacNeice

A Numerical Study of the Breakout Model for Coronal Mass Ejection Initiation

A leading theory for the initiation of coronal mass ejections (CMEs) is the breakout model, in which magnetic reconnection above a filament channel is responsible for disrupting the coronal magnetic field. We present the first simulations of the complete breakout process including the initiation, the plasmoid formation and ejection, and the eventual relaxation of the coronal field to a more potential state. These simulations were performed using a new numerical code that solves the numerical cavitation problems that prevented previous simulations from calculating a complete ejection. Furthermore, the position of the outer boundary in the new simulations is increased out to 30 R☉, which enables determination of the full structure and dynamics of the ejected plasmoid. Our results show that the ejection occurs at a speed on the order of the coronal Alfven speed and hence that the breakout model can produce fast CMEs. Another key result is that the ejection speed is not sensitive to the refinement level of the grid used in the calculations, which implies that, at least for the numerical resistivity of these simulations, the speed is not sensitive to the Lundquist number. We also calculate, in detail, the helicity of the system and show that the helicity is well conserved during the breakout process. Most of the helicity is ejected from the Sun with the escaping plasmoid, but a significant fraction (of order 10%) remains in the corona. The implications of these results for observation and prediction of CMEs and eruptive flares is discussed.

Observable Properties of the Breakout Model for Coronal Mass Ejections

We compare the magnetic breakout model for coronal mass ejections (CMEs) with observed general properties of CMEs by analyzing in detail recent high-resolution MHD simulations of a complete breakout CME. The model produces an eruption with a three-part plasma density structure that shows a bright circular rim outlining a dark central cavity in synthetic coronagraphic images of total brightness. The model also yields height-time profiles similar to most three-part CMEs, but the eruption speed by 2.5 R☉ is of order the Alfven speed, indicative of a fast CME. We show that the evolution of the posteruptive flare loop and chromospheric ribbons determined from the model are in agreement with observations of long-duration flares, and we propose an explanation for the long-standing observation that flares have an impulsive and gradual phase. A helical magnetic flux rope is generated during eruption and is consistent with a large class of interplanetary CME observations. The magnetic fields in this flux rope are well approximated by the Lundquist solution when the ejecta are at 15 R☉ and beyond. Furthermore, the interior density structure of the magnetic flux rope appears to have some of the basic features of an average magnetic cloud profile at 1 AU. Future simulation improvements and more stringent observational tests are discussed.

Constraints on the Magnetic Field Geometry in Prominences

This paper discusses constraints on the magnetic field geometry of solar prominences derived from one-dimensional modeling and analytic theory of the formation and support of cool coronal condensations. In earlier numerical studies we identified a mechanism—thermal nonequilibrium—by which cool condensations can form on field lines heated at their footpoints. We also identified a broad range of field line shapes that can support condensations with the observed sizes and lifetimes: shallowly dipped to moderately arched field lines longer than several times the heating scale. Here we demonstrate that condensations formed on deeply dipped field lines, as would occur in all but the near-axial regions of twisted flux ropes, behave significantly differently than those on shallowly dipped field lines. Our modeling results yield a crucial observational test capable of discriminating between two competing scenarios for prominence magnetic field structure: the flux rope and sheared-arcade models.

The Thermal Nonequilibrium of Prominences

We present numerical simulations and analytic theory for the thermal nonequilibrium of solar coronal flux tubes that have a stretched-out, dipped geometry, appropriate for a prominence/filament. Our simulations indicate that if the heating in such a flux tube is localized near the chromosphere, then condensations appear which undergo a continuous cycle of formation, motion, and destruction, even though the heating and all other imposed conditions on the loop are purely time independent. We show how this nonsteady evolution can be understood in terms of simple scaling-law theory. The implications of thermal nonequilibrium for observations of the solar corona are discussed. We argue that the model can explain both the formation of prominence condensations and recent observations of their dynamics.

The Role of Magnetic Helicity in Coronal Mass Ejections

We investigate the factors responsible for initiating coronal mass ejections (CMEs), specifically, the role of magnetic helicity. Using numerical simulations of the breakout model for CMEs, we show that eruption occurs at a fixed magnitude of free energy in the corona, independent of the value of helicity. Almost identical eruptions are obtained for both large and zero-helicity cases. Furthermore, the eruption can actually lead to an increase in the helicity remaining in the corona. These results argue strongly against recent models that postulate a critical helicity buildup and shedding as the determining factors for CME initiation.

Interface conditions for wave propagation through mesh refinement boundaries

We study the propagation of waves across fixed mesh refinement boundaries in linear and nonlinear model equations in 1-D and 2-D, and in the 3-D Einstein equations of general relativity. We demonstrate that using linear interpolation to set the data in guard cells leads to the production of reflected waves at the refinement boundaries. Implementing quadratic interpolation to fill the guard cells suppresses these spurious signals.

Numerical Simulation of Interacting Magnetic Flux Ropes

A 212‐D MHD numerical model is used to investigate the dynamic interaction between two flux ropes (clouds) in a homogeneous magnetized plasma. One cloud is set into motion while the other is initially at rest. The moving cloud generates a shock which interacts with the second cloud. Two cases with different characteristic speeds within the second cloud are presented. The shock front is significantly distorted when it propagates faster (slower) in the cloud with larger (smaller) characteristic speed. Correspondingly, the density behind the shock front becomes smaller (larger). Later, the clouds approach each other and by a momentum exchange they come to a common speed. The oppositely directed magnetic fields are pushed together, a driven magnetic reconnection takes a place, and the two flux ropes gradually coalescence into a single flux rope.

An Overview of the PARAMESH AMR Software Package and Some of Its Applications

The latest release of the PARAMESH parallel, adaptive mesh refinement software package is discussed. Its features and some of the applications it is being used with are highlighted. Further, we discuss the philosophy of the design of the package as well as some the problems and solutions we have found when importing into various applications.

Three-dimensional adaptive evolution of gravitational waves in numerical relativity

Adaptive techniques are crucial for successful numerical modeling of gravitational waves from astrophysical sources such as coalescing compact binaries, since the radiation typically has wavelengths much larger than the scale of the sources. We have carried out an important step toward this goal: the evolution of weak gravitational waves using adaptive mesh refinement in the Einstein equations. The 2-level adaptive simulation is compared with unigrid runs at coarse and fine resolution, and is shown to track closely the features of the fine grid run.

A Performance Evaluation of the Convex SPP-1000 Scalable Shared Memory Parallel Computer

The Convex SPP-1000 is the first commercial implementation of a new generation of scalable shared memory parallel computers with full cache coherence. It employs a hierarchical structure of processing communication and memory name-space management resources to provide a scalableNUMA environment. Ensembles of 8 HP PA-RISC7100 microprocessorsemploy an internal cross-bar switch and directory based cache coherence scheme to provide a tightly coupled SMP.Up to 16 processing ensembles are interconnected by a 4 ring network incorporating a full hardware implementation of the SCI protocol for a full system configuration of 128 processors. This paper presents the findings of a set of empirical studies using both synthetic test codes and full applications for the Earth and space sciences to characterize the performance properties of this new architecture. It is shown that overhead and latencies of global primitive mechanisms, while low in absolute time, are significantly more costly than similar functions local to an individual processor ensemble.