NG41A-01 INVITED
Self-Organization of Braided Coronal Magnetic Fields and the Flare Distribution
First I will discuss braiding of magnetic field lines in solar x-ray loops. Turbulent motions at the surface of the sun randomly move the field line endpoints about each other, braiding the lines above. Braiding can also enter the loops as a consequence of reconnection with network or carpet fields. This braiding is removed by reconnection events, resulting in small solar flares. Balancing random input of braiding with not-so-random reconnection can lead to a self-organized braid structure with power law structural properties. I will also discuss whether braiding can be observed in Trace and Hinode loops. Unfortunately, self- organization is likely to make a clear observation of braid structure more difficult. Secondly I will discuss applications of writhe number to studies of sigmoids and kinked erupting prominences. The sign of writhe for a kinked loop can depend on more than just its helicity!
NG41A-02 INVITED
Magnetic Braiding and the Onset of Reconnection
Parker's original theory of 'topological dissipation', that is the idea that the braiding of coronal loops leads to singular current sheets and subsequently to reconnection, has been often criticised. There is a lack of evidence for the formation of singular current sheets and one can even prove the existence of smooth force- free equilibria for the moderate values of twist consistent with observations. Here we readdress this problem in the light of 3D magnetic reconnection theory where the crucial quantity for reconnection is not the current density itself but the integrated parallel electric current along magnetic field lines. Using examples of an Borromean braid we demonstrate that force-free equilibria can have a smooth current distributions but at the same time an extremely filamentary structure of the parallel current integrated along field lines. With increasing complexity of the braid the length scale associated with the integrated parallel current structure decreases exponentially. Thus these structures are very sensitive to smallest amounts of dissipation and the inevitable consequence of the magnetic braiding process is a loss of equilibrium of the coronal field via magnetic reconnection events.
NG41A-03 INVITED
The Role of Magnetic Reconnection in Self-Organization of the Corona: Theory and Observations
Based on observations that solar flares obey power law statistics, it was suggested that the solar corona is in a state of self-organized criticality [1]. However, the physical mechanism underlying the dynamics is not well understood. A recent model [2] describing the catastrophic onset of fast (Hall) magnetic reconnection in weakly collisional plasmas may potentially contribute to this discussion. We suggest that the condition at which the catastrophic onset of reconnection occurs sets the critical state of the corona and the physics of reconnection organizes the corona into this critical state [3]. (See also [4].) The model makes a quantitative prediction for the conditions of the corona at the onset of eruptions, which is known to be consistent with observations of the solar corona. We present new observational evidence from stellar flares (107 events in 37 sun-like stars) that stellar coronae are near the same critical state at flare onset. This provides observational evidence in support of the model and suggests that magnetic reconnection plays an active role in constraining the conditions in solar and stellar coronae. Implications for self-organization in coronal heating and solar eruptions will be discussed. [1] E. T. Lu and R. J. Hamilton, Ap. J., 380, L89, 1991; [2] P. A. Cassak et al., Phys. Rev. Lett., 95, 235002, 2005; P. A. Cassak et al., Ap. J. Lett., 644, L145, 2006; [3] P. A. Cassak et al., Ap. J. Lett., 676, L69, 2008; [4] D. A. Uzdensky, Ap. J., 671, 2139, 2007.
NG41A-04 INVITED
Using topological invariants to estimate magnetic free energy release from solar flares
Solar flares and eruptions are believed to occur when energy stored as electric currents (i.e magnetic free
energy) is suddenly converted into radiation, thermal and kinetic energy. Energy accumulated throughout an
active region over days is released in a matter of minutes through a process most likely involving magnetic
reconnection. Topological analysis is an ideal tool for bridging the great time-scale and size-scale disparities
intrinsic to this scenario. The storage process is believed to preserve the topology of coronal field lines, so
the free magnetic energy may be bounded from below by its minimum subject to one or more topological
constraints. Different global constraints, such as additive relative helicity or the fluxes interconnecting
unipolar photospheric regions, lead to different free energy bounds. These different bounds can be
arranged in a hierarchy due to the inter-relations of their associated constraints. Magnetic reconnection
produces sudden topological change to a certain amount of magnetic flux, eliminating the related constraints
and thereby opening the field to a lower energy state. The energy release may be estimated in practice by
the difference in minima when the affected constraints are relaxed. The requirement that a small-scale
process affect the field-line topology within a significant amount of magnetic flux, provides insight into how
and where magnetic reconnection might occur.
This work was supported by funding from the LWS TR&T program.
NG41A-05 INVITED
Magnetic twist, writhe, and helicity at coronal mass ejection onset and their initial evolution
Observations of filament/prominence eruptions, usually the best tracer of a coronal mass ejection's onset, indicate that the erupting magnetic flux consists of a single expanding flux rope anchored in the solar surface at both ends. Twisted strands of emission or absorption and the writhing of the erupting flux suggest the helical kink instability as the trigger in a number of cases, consistent also with the typically exponential or exponential-like initial rise profile. High values of the twist, about three, possibly up to up to about five field line turns, have been inferred from observations and numerical simulations. These exceed the often cited value of about one turn for the threshold of the instability. It is therefore of interest whether such highly twisted flux ropes can indeed be formed on the Sun and how high the threshold for onset of kinking can lie. I will present a parametric study of the instability for a realistic arched and line tied flux rope to demonstrate that the threshold falls in a wide range, consistent with the inferred range of twist. Simulations of unstable equilibria reproduce the strongly helical shapes in a number of well-observed eruptions, strengthening the case for the instability further. The direction of writhing is one of the few available unambiguous diagnostics for the chirality of the erupting flux. The amount of writhing, however, is not simply related to the pre-eruption twist. It depends also on the properties of the surrounding field and on the amount of reconnection, so that the ability to forecast this space weather-relevant quantity will require further study. Finally, the outward transport of helicity by the ejected magnetic flux will be estimated.
NG41A-06 INVITED
Nonlinear Consequences of Interchange Reconnection
Interchange reconnection is defined as reconnection between an open and a closed magnetic field line, where the former extends from its footpoint on some source--e.g., the Sun or Earth--to infinity and the latter has the shape of a loop with both footpoints rooted in the source. A consequence of interchange reconnection is transport of the open field line footpoint by saltation, or leaping. Although this nonlinear form of transport can be part of a steady-state process, it is considerably different from the steady-state footpoint circulation in convection cells that is usually assumed to occur in Earth's magnetosphere. Interchange reconnection has been used in solar and heliospheric physics to explain a wide range of phenomena, but its role in magnetospheric physics has received little attention. A recent explanation for the solar-cycle reversal of the heliospheric magnetic field in terms of interchange reconnection is briefly reviewed, as are the efforts of M. Watanabe et al. to understand interchange reconnection in the magnetosphere. Finally, a new technique developed by V. G. Merkin is presented that uniquely demonstrates footpoint saltation generated by interchange reconnection in an MHD simulation of the magnetosphere using the Lyon-Fedder-Mobarry model.
NG41A-07 INVITED
New Insights into the Observable Characteristics of Reconnection Layers
In the past few years, large-scale fully kinetic particle-in-cell (PIC) simulations have offered a wealth of new predictions regarding the structure and time-dependence of reconnection layers. In contrast to previous two- fluid models, kinetic simulations demonstrate a basic tendency for the electron diffusion region to form highly elongated current sheets in both neutral sheet geometry as well as guide field reconnection. These elongated layers have important implications for the large-scale magnetic structure and time-dependence including (1) strong modifications to the out-of-plane field structure at large distances from the x-line, (2) the repeated formation of secondary magnetic islands with complicated flux-rope geometry and (3) significant electron heating in the downstream region. In addition, these highly elongated electron layers offer a number of distinct signatures that may be observable by a single spacecraft with sufficient time resolution. These properties include: (i) the demagnetization parameter for thermal electrons, (ii) perpendicular electron mach number, (iii) electron anisotropy and (iv) electron agyrotropy. These features may be useful for rapidly identifying these electron layers and/or triggering burst mode data recovery on future space missions such as MMS or Cross-Scale.
NG41A-08 INVITED
The role of magnetic reconnection in solar wind-magnetosphere coupling
Dungey's classic reconnecting magnetosphere model still provides the basic context for most theoretical and observational discussions of magnetopause reconnection. The two-dimensional version of Dungey's model seems to naturally explain the half-wave rectifier response of geomagnetic activity to the orientation of the Interplanetary Magnetic Field (IMF): When the IMF is southward, reconnection occurs near the subsolar magnetopause, generating a global magnetospheric convection pattern which is thought to be the ultimate cause of magnetospheric storms and substorms; when the IMF is northward, however, subsolar reconnection is "switched off", and reconnection occurs poleward of the cusps. Unfortunately, the two-dimensional version of Dungey's model does not generalize in a straightforward way to three dimensions. In three dimensions, nearly steady subsolar reconnection is topologically possible for all non-vanishing IMF clock angles (note that while the pure northward and pure southward orientations are topologically stable in two dimensions, they are unstable and, thus, not likely to ever be observed in three dimensions). Three-dimensional magnetohydrodynamics (MHD) simulations, on the other hand, demonstrate that the subsolar magnetopause stagnation flow becomes unstable as the IMF turns southward: Flux Transfer Events (FTEs) are generated, producing changes in the global magnetopause topology. This result suggests that the transition from steady to time-dependent reconnection may play an important role in changing the global convection pattern of the magnetosphere as the IMF turns southward. We explore this hypothesis using three-dimensional MHD simulations.