D. W. Longcope

Flux-Tube Twist Resulting from Helical Turbulence: The Σ-Effect

Recent observational studies suggest that active region magnetic flux emerges in a twisted state and that the sense of twist depends weakly on solar hemisphere. We propose that this twist is imparted to the flux through its interaction with turbulent velocities in the convection zone. This process, designated the Σ-effect, operates on isolated magnetic flux tubes subjected to buffeting by turbulence with a nonvanishing kinetic helicity

The Relationship Between X-Ray Radiance and Magnetic Flux

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INJECTION OF MAGNETIC ENERGY AND MAGNETIC HELICITY INTO THE SOLAR ATMOSPHERE BY AN EMERGING MAGNETIC FLUX TUBE

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Topology and current ribbons: A model for current, reconnection and flaring in a complex, evolving corona

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Current sheet formation along three‐dimensional magnetic separators

-->. The Σ-effect leads to twist of the same sense inferred from observation and opposite to that predicted by the α-effect. A series of numerical calculations are performed to estimate the magnitude of the Σ-effect in the solar convective zone. The results compare favorably with observations in both mean value and statistical dispersion. We find a further relationship with total magnetic flux that can be tested in future observations. The model also predicts that twist is uncorrelated with the tilt angle of the active region.

RECONNECTION OUTFLOWS AND CURRENT SHEET OBSERVED WITH HINODE/XRT IN THE 2008 APRIL 9 'CARTWHEEL CME' FLARE

We use soft X-ray and magnetic field observations of the Sun (quiet Sun, X-ray bright points, active regions, and integrated solar disk) and active stars (dwarf and pre-main-sequence) to study the relationship between total unsigned magnetic flux, � , and X-ray spectral radiance, LX. We find thatand LX exhibit a very nearly linear relationship over 12 orders of magnitude, albeit with significant levels of scatter. This suggests a universal relationship between magnetic flux and the power dissipated through coronal heating. If the relationship can be assumed linear, it is consistent with an average volumetric heating rate � Q � �=L, where � B is the average field strength along a closed field line and L is its length between footpoints. The �- LX relationship also indicates that X-rays provide a useful proxy for the magnetic flux on stars when magnetic measurements are unavailable. Subject headings: stars: coronae — stars: magnetic fields — Sun: corona — Sun: magnetic fields — Sun: X-rays, gamma rays

Tests and Comparisons of Velocity-Inversion Techniques

We present a detailed investigation of the dynamical behavior of emerging magnetic flux using three-dimensional MHD numerical simulation. A magnetic flux tube with a left-handed twist, initially placed below the photosphere, emerges into the solar atmosphere. This leads to a dynamical expansion of emerging field lines as well as an injection of magnetic energy and magnetic helicity into the atmosphere. The field-aligned distributions of forces and plasma flows show that emerging field lines can be classified as either expanding field lines or undulating field lines. A key parameter determining the type of emerging field line is the aspect ratio of its shape (the ratio of height to footpoint distance). The emergence generates not only vertical but also horizontal flows in the photosphere, both of which contribute to injecting magnetic energy and magnetic helicity. The contributions of vertical flows are dominant at the early phase of flux emergence, while horizontal flows become a dominant contributor later. The emergence starts with a simple dipole structure formed in the photosphere, which is subsequently deformed and fragmented, leading to a quadrupolar magnetic structure.

Observations of Separator Reconnection to an Emerging Active Region

Magnetic field enters the corona from the interior of the Sun through isolated magnetic features on the solar surface. These features correspond to the tops of submerged magnetic flux tubes, and coronal field lines often connect one flux tube to another, defining a pattern of inter-linkage. Using a model field, in which flux tubes are represented as point magnetic charges, it is possible to quantify this inter-linkage. If the coronal field were current-free then motions of the magnetic features would change the inter-linkage through implicit (vacuum) magnetic reconnection. Without reconnection the conductive corona develops currents to avoid changing the flux linkage. This current forms singular layers (ribbons) flowing along topologically significant field lines called separators. Current ribbons store magnetic energy as internal stress in the field: the amount of energy stored is a function of the flux tube displacement. To explore this process we develop a model called the minimum-current corona (MCC) which approximates the current arising on a separator in response to displacement of photospheric flux. This permits a model of the quasi-static evolution of the corona above a complex active region. We also introduce flaring to rapidly change the flux inter-linkage between magnetic features when the internal stress on a separator becomes too large. This eliminates the separator current and releases the energy stored by it. Implementation of the MCC in two examples reveals repeated flaring during the evolution of simple active regions, releasing anywhere from 1027–1029 ergs, at intervals of hours. Combining the energy and frequency gives a general expression for heat deposition due to flaring (i.e., reconnection).

TRACE and Yohkoh Observations of a White-Light Flare

It was shown by Syrovatskii [Sov. Phys. JETP 33, 933 (1971)] that a perfectly conducting two‐dimensional magnetic field stressed externally develops a current sheet at an X point. A generalization of this analysis shows that a generic three‐dimensional magnetic field develops a closed ribbon of current along separators already existing in the field. A separator is a field line that begins and ends at different magnetic null points. A current ribbon will occur if there are two distinct separators beginning and ending at the same two nulls, thus forming a loop. The magnetic field containing the current ribbon is in force‐free equilibrium. An expression is found for the net current induced in the ribbon, and the magnetic energy stored by it, in terms of the amount of external stress. An electric field parallel to the current will facilitate reconnection and will dissipate the current and release the stored energy.

IMPLEMENTING A MAGNETIC CHARGE TOPOLOGY MODEL FOR SOLAR ACTIVE REGIONS

Supra-arcade downflows (SADs) have been observed with Yohkoh/SXT (soft X-rays (SXR)), TRACE (extreme ultraviolet (EUV)), SOHO/LASCO (white light), SOHO/SUMER (EUV spectra), and Hinode/XRT (SXR). Characteristics such as low emissivity and trajectories, which slow as they reach the top of the arcade, are consistent with post-reconnection magnetic flux tubes retracting from a reconnection site high in the corona until they reach a lower-energy magnetic configuration. Viewed from a perpendicular angle, SADs should appear as shrinking loops rather than downflowing voids. We present X-ray Telescope (XRT) observations of supra-arcade downflowing loops (SADLs) following a coronal mass ejection (CME) on 2008 April 9 and show that their speeds and decelerations are consistent with those determined for SADs. We also present evidence for a possible current sheet observed during this flare that extends between the flare arcade and the CME. Additionally, we show a correlation between reconnection outflows observed with XRT and outgoing flows observed with LASCO.