Terry G. Forbes

Energy partition in two solar flare/CME events

Using coordinated observations from instruments on the Advanced Composition Explorer (ACE), the Solar and Heliospheric Observatory (SOHO), and the Ramaty High Energy Solar Spectroscopic Imager (RHESSI), we have evaluated the energetics of two well-observed flare/CME events on 21 April 2002 and 23 July 2002. For each event, we have estimated the energy contents (and the likely uncertainties) of (1) the coronal mass ejection, (2) the thermal plasma at the Sun, (3) the hard X-ray producing accelerated electrons, (4) the gamma-ray producing ions, and (5) the solar energetic particles. The results are assimilated and discussed relative to the probable amount of nonpotential magnetic energy available in a large active region.

The effect of curvature on flux-rope models of coronal mass ejections

The large-scale curvature of a flux rope can help propel it outward from the Sun. Here we extend previous two-dimensional flux-rope models of coronal mass ejections to include the curvature force. To obtain analytical results, we assume axial symmetry and model the flux rope as a torus that encircles the Sun. Initially, the flux rope is suspended in the corona by a balance between magnetic tension, compression, and curvature forces, but this balance is lost if the photospheric sources of the coronal field slowly decay with time. The evolution of the system shows catastrophic behavior as occurred in previous models, but, unlike the previous models, flux ropes with large radii are more likely to erupt than ones with small radii. The maximum total magnetic energy that can be stored before equilibrium is lost is 1.53 times the energy of the potential field, and this value is less than the limiting value of 1.662 for the fully opened field. As a consequence, the loss of ideal MHD equilibrium that occurs in the model cannot completely open the magnetic field. However, the loss of equilibrium does lead to the sudden formation of a current sheet, and if rapid reconnection occurs in this sheet, then the flux rope can escape from the Sun. We also find that the held can gradually become opened without suffering any loss of equilibrium if the photospheric field strength falls below a critical value. This behavior is analogous to the opening of a spherically symmetric arcade in response to a finite amount of shear.

A THREE-DIMENSIONAL FLUX ROPE MODEL FOR CORONAL MASS EJECTIONS BASED ON A LOSS OF EQUILIBRIUM

A series of simulation runs are carried out to investigate the loss of equilibrium of the three-dimensional flux rope configuration of Titov & Demoulin as a suitable mechanism for the initiation of coronal mass ejections. By means of these simulations, we are able to determine the conditions for which stable equilibria no longer exist. Our results imply that it is possible to achieve a loss of equilibrium even though the ends of the flux rope are anchored to the solar surface. However, in order to have the flux rope escape, it is necessary to modify the configuration by eliminating the arcade field.

Catastrophic evolution of a force-free flux rope : a model for eruptive flares

We present a self-consistent, two-dimensional, magnetohydrodynamic model of an eruptive flare based on an ideal-MHD coronal magnetic field configuration which is line-tied at the photosphere and contains a force-free flux rope. If the flux rope is not too large, the gradual disappearance of the photospheric field causes the flux rope to lose equilibrium catastrophically and jump to a higher altitude, releasing magnetic energy in the process. During the jump, an extended current sheet forms below the flux rope, and subsequent reconnection of this current sheet allows the flux rope to escape into the outer corona. A critical flux-rope radius, which depends on the form of the photospheric field, divides configurations which undergo a catastrophic loss of equilibrium from those which do not

A NUMERICAL MODEL OF A CORONAL MASS EJECTION: SHOCK DEVELOPMENT WITH IMPLICATIONS FOR THE ACCELERATION OF GeV PROTONS

The initiation and evolution of the coronal mass ejection, which occurred on 1998 May 2 in NOAA Active Region 8210, are modeled using a fully three-dimensional, global MHD code. The initial magnetic field for the model is based on magnetogram data from the Wilcox Solar Observatory, and the solar eruption is initiated by slowly evolving the boundary conditions until a critical point is reached where the configuration loses equilibrium. At this time, the field erupts, and a flux rope is ejected that achieves a maximum speed in excess of 1000 km s-1. The shock that forms in front of the rope reaches a fast-mode Mach number in excess of 4 and a compression ratio greater than 3 by the time it has traveled a distance of 5 R☉ from the surface. For such values, diffusive shock acceleration theory predicts a distribution of solar energetic protons with a cutoff energy of about 10 GeV. For this event, there appears to be no need to introduce an additional acceleration mechanism to account for solar energetic protons with energies below 10 GeV.

A Three-dimensional Line-tied Magnetic Field Model for Solar Eruptions

We introduce a three-dimensional analytical model of a coronal flux rope with its ends embedded in the solar surface. The model allows the flux rope to move in the corona while maintaining line-tied conditions at the solar surface. These conditions ensure that the normal component of the coronal magnetic field at the surface remains fixed during an eruption and that no magnetic energy enters the corona through the surface to drive the eruption. The model is based on the magnetic configuration of Titov & Demoulin, where a toroidal flux rope is held in equilibrium by an overlying magnetic arcade. We investigate the stability of this configuration to specific perturbations and show that it is subject to the torus instability when the flux rope length exceeds a critical value. A force analysis of the configuration shows that flux ropes are most likely to erupt in a localized region near the apex, while the regions near the surface remain relatively undisturbed. Thus, the flux rope will tend to form an aneurysm-like structure once it erupts. Our analysis also suggests how the flux rope rotation seen in some eruptions and simulations may be related to the observed orientation of the overlying arcade field. This model exhibits the potential for catastrophic loss of equilibrium as a possible trigger for eruptions, but further study is required to prove this property.

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

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.

What can we learn about reconnection from coronal mass ejections

Abstract It may be possible to calculate the rate of reconnection in the corona by measuring the rate at which the temporary coronal hole formed by a coronal mass ejection (CME) disappears. This calculation is possible if the disappearance of the hole is caused by the same reconnection process which creates the giant X-ray arches associated with CMEs. These arches form just below the vertical current sheet that is created as the CME drags magnetic field lines out into interplanetary space, and they are similar in form to ‘post’-flare loops, except that they often have an upward motion that is different. Instead of continually slowing with time as ‘post’-flare loops do, they move upwards at a rate which increases, or remains nearly constant, with time. This difference has raised doubts about the relevance of reconnection to the formation and propagation of the arches. Using a two-dimensional flux rope model to calculate the size and location of the current sheet as a function of time, we find that the difference between the motion of ‘post’-flare loops and giant arches can be explained simply by the variation of the coronal Alfven speed with height.

The formation of flare loops by magnetic reconnection and chromospheric ablation

Slow-mode shocks produced by reconnection in the corona can provide the thermal energy necessary to sustain flare loops for many hours. These slow shocks have a complex structure because strong thermal conduction along field lines dissociates the shocks into conduction fronts and isothermal subshocks. Heat conducted along field lines mapping from the subshocks to the chromosphere ablates chromospheric plasma and thereby creates the hot flare loops and associated flare ribbons. Here we combine a non-coplanar compressible reconnection theory with simple scaling arguments for ablation and radiative cooling, and predict average properties of hot and cool flare loops as a function of the coronal vector magnetic field. For a coronal field strength of 100 G the temperature of the hot flare loops decreases from 1.2 × 107 K to 4.0 × 106 K as the component of the coronal magnetic field perpendicular to the plane of the loops increases from 0% to 86% of the total field. When the perpendicular component exceeds 86% of the total field or when the altitude of the reconnection site exceeds 106km, flare loops no longer occur. Shock enhanced radiative cooling triggers the formation of cool Hα flare loops with predicted densities of ≈ 1013 cm−3, and a small gap of ≈ 103 km is predicted to exist between the footpoints of the cool flare loops and the inner edges of the flare ribbons.

Magnetic Flipping' Reconnection in Three Dimensions Without Null Points

In three dimensions, magnetic reconnection may take place in a sheared magnetic field at any singular field line, where the nearby field has X-type topology in planes perpendicular to the field line and where an electric field is present parallel to the field line. In the ideal region around the singular line there will, in general, be singularities in the plasma flow and electric field, both at the singular line and at “magnetic flipping layers,” which are remnants of local magnetic separatrices. In the absence of a three-dimensional magnetic neutral point or null point, reconnection of field lines can still occur by a process of magnetic flipping, in which the plasma crosses the flipping layers but the field lines rapidly flip along them by magnetic diffusion. Depending on the boundary conditions, there may be two or four flipping layers which converge on the singular line. A boundary layer analysis of a flipping layer is given, in which the magnetic field parallel to the layer decreases as one crosses it while the plasma pressure (or magnetic pressure associated with the field along the singular line) increases. The width of the flipping layer decreases with distance from the singular line.