C. Richard DeVore

Magnetic Helicity Generation by Solar Differential Rotation

Observations of sunspots, active regions, filaments, coronal arcades, and interplanetary magnetic clouds indicate that the Sun preferentially exhibits left-handed, negative-helicity features in its northern hemisphere and their opposite counterparts in the south, independent of sunspot cycle. We investigate quantitatively the generation of magnetic helicity by solar differential rotation acting on emerged bipolar sources of flux, using analytical and numerical methods. We find that the vast majority of bipoles absorb negative helicity in the northern hemisphere and positive helicity in the south, in accord with observations. After 2-4 solar rotation periods have elapsed, the helicity generated by differential rotation amounts to about 10% of the bipoles squared flux. Thus, each of the approximately 1 × 103 large bipolar regions emergent on the Sun during sunspot cycle 21 entrained about 1 × 1043 Mx2 of helicity in its 1 × 1022 Mx of flux. We show further that the roughly 5 × 103 coronal mass ejections and associated interplanetary magnetic clouds that departed the Sun during the cycle carried off about 5 × 1024 Mx of flux and 1 × 1046 Mx2 of helicity, within a factor of 2 of the estimates for solar production of these quantities. Evidently, differential rotation acting on emerged bipolar sources of flux can account quantitatively for the magnetic helicity balance of the Sun and the heliosphere, as well as for the observed prevalence of negative-helicity magnetic features in the north and positive-helicity features in the south.

Flux-corrected transport techniques for multidimensional compressible magnetohydrodynamics

A prescription is given for conservatively integrating generalized hydromagnetic equations using flux-corrected transport (FCT) techniques. By placing the magnetic-field components at the interface locations of the finite-difference grid, the field is kept divergence-free to within machine roundoff error. The use of FCT techniques allows an integration scheme of high accuracy to be employed, while the numerical ripples associated with large dispersion errors are avoided. The method is particularly well suited for problems involving magnetohydrodynamic shocks and other discontinuities.

Dynamical Formation and Stability of Helical Prominence Magnetic Fields

Abstract : We numerically simulated an initially bipolar magnetic field subjected to shear motions concentrated near and parallel to the photospheric polarity inversion line. The simulations yield three principal results: (1) For footprint displacements comparable to the bipoles depth, the sheared core field acquires a dipped geometry that can support cool prominence material against gravity. This confirms previous force-free equilibrium models for forming dipped prominence fields by differential shear, and extends them to much larger applied shears and time-dependent dynamics with dissipation. (2) At larger shears, we discover a new mechanism for forming the helical magnetic fields of prominences. It entails a two-step process of magnetic reconnection in the corona. First, flux in the sheared core reconnects with flux in the unsheared, restraining arcade, producing new pairs of interlinked field lines. Second, as these interlinked fields continue to be sheared, they are brought together and reconnect again, producing helical field threading and enveloping the body of the prominence. This mechanism can account for the twist that is often observed in both quiescent and erupting prominences. (3) Even for very large shears, the dipped, helical structure settles into an apparently stable equilibrium, despite the substantial amount of reconnection and twist in the magnetic field. We conclude that neither a kink instability of the helical core field, nor a tether-cutting instability of the restraining arcade, is operating in our low-lying model prominence. This concurs with both observations and a theoretical model for prominence stability.

Homologous Confined Filament Eruptions via Magnetic Breakout

We describe magnetohydrodynamic simulations of a bipolar active region embedded in the Suns global background field and subjected to twisting footpoint displacements concentrated near its polarity inversion lines to produce strong magnetic shear. The dipole moments of the active region and background field are antiparallel, so that the initially potential magnetic field contains a coronal null. This configuration supports magnetic breakout eruptions in our simulations that exhibit three novel features. First, the eruptions are multiple and homologous: the flare reconnection following each eruption reforms the magnetic null, setting the stage for a subsequent episode of breakout reconnection and eruption driven by the ongoing footpoint motions. Second, the eruptions are confined; that is, their rapidly rising, moderately sheared field lines do not escape the Sun but instead come to rest in the outer corona, comprising a large coronal loop formed by reconnection during the rise phase. Third, the most strongly sheared field lines of the active region are quite flat prior to eruption, expand upward sharply during the event, and lose most of their shear through reconnection with overlying flux, while lower lying field lines survive the eruption and recover their flat configuration within a few hours. These behaviors are consistent with filament disappearance followed by reformation in place. We also find that the upward motion of the erupting sheared flux exhibits a distinct three-phase acceleration profile. All of these features of our simulations—homology, confinement, reformation, and multiphase acceleration—are well established aspects of solar eruptions.

SOLAR PROMINENCE INTERACTIONS

We report numerical simulations of the formation, interaction, and magnetic reconnection between pairs of solar prominences within the sheared-arcade model. Our experiments consider the four possible basic combinations of chiralities (identical or opposite) and axial magnetic fields (aligned or opposed) between the participating prominences. When the topology of the global flux system comprising the prominences and arcades is bipolar, so that a single polarity inversion line is shared by the two structures, then identical chiralities necessarily imply aligned axial fields, while opposite chiralities imply opposed axial fields. In the former case, external magnetic reconnections forming field lines linking the two prominences occur; in the latter, such reconnections are disfavored, and no linkage takes place. These results concur with empirical rules for prominence interactions. When the topology instead is quadrupolar, so that a second polarity inversion line crossing the first lies between the prominences, then the converse relation holds between chirality and axial-field alignment. External reconnections forming linking field lines now occur between prominences with opposite chiralities; they also occur, but result only in footpoint exchanges, between prominences with identical chiralities. These findings conflict with the accepted empirical rules but may not have been tested in observations to date. All of our model prominences, especially those that undergo linking reconnections, contain substantial magnetic shear and twist. Nevertheless, none exhibits any sign of onset of instability or loss of equilibrium that might culminate in an eruption.

Simulations of the mean solar magnetic field during sunspot cycle 21

Regarding new bipolar magnetic regions as sources of flux, we have computed the evolution of the photospheric magnetic field during 1976–1984 and derived the corresponding evolution of the mean line-of-sight field as seen from Earth. We obtained a good, but imperfect, agreement between the observed mean field and the field computed for a nominal choice of flux transport parameters. Also, we determined the response of the computed mean field to variations in the transport parameters and the source properties. The results lead us to regard the mean-field evolution as a random-walk process with dissipation. New eruptions of flux produce the random walk, and together differential rotation, meridional flow (if present), and diffusion provide the dissipation. The net effect of each new source depends on its strength and orientation (relative to the strength and orientation of the mean field) and on the time elapsed before the next eruption (relative to the decay time of the field). Thus the mean field evolves principally due to the contributions of the larger sources, which produce a strong, gradually evolving field near sunspot maximum but a weak, sporadically evolving field near sunspot minimum.

Solar prominence merging

In a recent paper, we described MHD simulations of the interaction between a pair of distinct prominences formed by the photospheric line-tied shearing of two separated dipoles. One case was typical of solar observations of prominence merging, in which the prominences have the same axial field direction and sign of magnetic helicity. For that configuration, we reported the formation of linkages between the prominences due to magnetic reconnection of their sheared fields. In this paper, we analyze the evolution of the plasma-supporting magnetic dips in this configuration. As the photospheric flux is being progressively sheared, dip-related chromospheric fibrils and high-altitude threads form and develop into the two prominences, which undergo internal oscillations. As the prominences are stretched farther along their axes, they come into contact and their sheared fluxes pass each other, and new dips form in the interaction region. The distribution of these dips increasingly fills the volume between the prominences, so that the two progenitors gradually merge into a single prominence. Our model reproduces typical observational properties reported from both high-cadence and daily observations at various wavelengths. We identify the multistep mechanism, consisting of a complex coupling between photospheric shear, coronal magnetic reconnection without null points, and formation of quasi bald patches, that is responsible for the prominence merging through dip creation. The resulting magnetic topology differs significantly from that of a twisted flux tube.

Simulations of the sun's polar magnetic fields during sunspot cycle 21

Regarding new bipolar magnetic regions as sources of flux, we have simulated the evolution of the radial component of the solar photospheric magnetic field during 1976–1984 and derived the corresponding evolution of the line-of-sight polar fields as seen from Earth. The observed timing and strength of the polar-field reversal during cycle 21 can be accounted for by supergranular diffusion alone, for a diffusion coefficient of 800 km2 s-1. For an assumed 300 km2 s-1 rate of diffusion, on the other hand, a poleward meridional flow with a moderately broad profile and a peak speed of 10 m s-1 reached at about 5° latitude is required to obtain agreement between the simulated and observed fields. Such a flow accelerates the transport of following-polarity flux to the polar caps, but also inhibits the diffusion of leading-polarity flux across the equator. For flows faster than about 10 m s-1 the latter effect dominates, and the simulated polar fields reverse increasingly later and more weakly than the observed fields.

Magnetic Free Energies of Breakout Coronal Mass Ejections

A critical issue in understanding and eventually predicting coronal mass ejections (CMEs) is determining the magnetic free energy that can drive the explosive eruption. We present calculations of this free energy for the breakout CME model, which postulates that the preeruption magnetic topology is a multipolar field with a null point in the corona. Using analytical and numerical methods, we determine the free energies for two broad families of photospheric flux distributions, parameterized by the radius of the coronal null and the degree to which flux is concentrated near the poles and equator. The available CME energy attains a broad maximum for distributions whose potential null resides between about 1.25 and 1.75 solar radii, and falls off toward zero as the null approaches the surface or moves out to infinity. These results may explain the wide range of energies observed for CMEs and their associated flares. We find that concentrating the surface flux to narrower latitude bands near the poles and equator, on the other hand, has little effect on the available energy. Our mathematical approach currently is restricted to spherically axisymmetric systems. Its generalization to fully three-dimensional fields might provide the foundation of a first-principles forecasting technique for solar eruptions.

The stability of imploding detonations in the geometrical shock dynamics (CCW) model

The stability of cylindrically and spherically imploding detonations is examined within the theoretical framework of geometrical shock dynamics. The linearized Chester–Chisnell–Whitham (CCW) equations describing the accelerating detonation wave are solved both analytically and numerically to track the evolution of the distorted wave front. As is the case for the corresponding nonreactive shock problem, for harmonic mode numbers greater than unity the perturbation amplitudes decrease as the implosion proceeds, but not as rapidly as the implosion radius itself. Thus, the detonation is relatively unstable in this model, and indeed is more unstable than the imploding shock of the same initial strength. The latter result is due primarily to the slower acceleration of the detonation wave as it implodes, relative to the nonreactive shock wave.