It is clear that the solar corona is being heated and that coronal magnetic fields undergo reconnection all the time. Here we attempt to show that these two facts are in fact related - i.e. coronal reconnection generates heat. This attempt must addre
ss the fact that topological change of field lines does not automatically generate heat. We present one case of flux emergence where we have measured the rate of coronal magnetic reconnection and the rate of energy dissipation in the corona. The ratio of these two, $P/dot{Phi}$, is a current comparable to the amount of current expected to flow along the boundary separating the emerged flux from the pre-existing flux overlying it. We can generalize this relation to the overall corona in quiet Sun or in active regions. Doing so yields estimates for the contribution to corona heating from magnetic reconnection. These estimated rates are comparable to the amount required to maintain the corona at its observed temperature.
Magnetic energy released in the corona by solar flares reaches the chromosphere where it drives characteristic upflows and downflows known as evaporation and condensation. These flows are studied here for the case where energy is transported to the c
hromosphere by thermal conduction. An analytic model is used to develop relations by which the density and velocity of each flow can be predicted from coronal parameters including the flares energy flux $F$. These relations are explored and refined using a series of numerical investigations in which the transition region is represented by a simplified density jump. The maximum evaporation velocity, for example, is well approximated by $v_esimeq0.38(F/rho_{co,0})^{1/3}$, where $rho_{co,0}$ is the mass density of the pre-flare corona. This and the other relations are found to fit simulations using more realistic models of the transition region both performed in this work, and taken from a variety of previously published investigations. These relations offer a novel and efficient means of simulating coronal reconnection without neglecting entirely the effects of evaporation.
We present a simplified analytic model of a quadrupolar magnetic field and flux rope to model coronal mass ejections. The model magnetic field is two-dimensional, force-free and has current only on the axis of the flux rope and within two currents sh
eets. It is a generalization of previous models containing a single current sheet anchored to a bipolar flux distribution. Our new model can undergo quasi-static evolution due either to changes at the boundary or to magnetic reconnection at either current sheet. We find that all three kinds of evolution can lead to a catastrophe known as loss of equilibrium. Some equilibria can be driven to catastrophic instability either through reconnection at the lower current sheet, known as tether cutting, or through reconnection at the upper current sheet, known as breakout. Other equilibria can be destabilized through only one and not the other. Still others undergo no instability, but evolve increasingly rapidly in response to slow steady driving (ideal or reconnective). One key feature of every case is a response to reconnection different from that found in simpler systems. In our two-current sheet model a reconnection electric field in one current sheet causes the current in that sheet to {em increase} rather than decrease. This suggests the possibility for the microscopic reconnection mechanism to run away.
Using a simple two-dimensional, zero-beta model, we explore the manner by which reconnection at a current sheet releases and dissipates free magnetic energy. We find that only a small fraction (3%-11% depending on current sheet size) of the energy is
stored close enough to the current sheet to be dissipated abruptly by the reconnection process. The remaining energy, stored in the larger-scale field, is converted to kinetic energy in a fast magnetosonic disturbance propagating away from the reconnection site, carrying the initial current and generating reconnection-associated flows (inflow and outflow). Some of this reflects from the lower boundary (the photosphere) and refracts back to the X-point reconnection site. Most of this inward wave energy is reflected back again, and continues to bounce between X-point and photosphere until it is gradually dissipated, over many transits. This phase of the energy dissipation process is thus global and lasts far longer than the initial purely local phase. In the process a significant fraction of the energy (25%-60%) remains as undissipated fast magnetosonic waves propagating away from the reconnection site, primarily upward. This flare-generated wave is initiated by unbalanced Lorentz forces in the reconnection-disrupted current sheet, rather than by dissipation-generated pressure, as some previous models have assumed. Depending on the orientation of the initial current sheet the wave front is either a rarefaction, with backward directed flow, or a compression, with forward directed flow.
Super-hot looptop sources, detected in some large solar flares, are compact sources of HXR emission with spectra matching thermal electron populations exceeding 30 megakelvins. High observed emission measure, as well as inference of electron thermali
zation within the small source region, both provide evidence of high densities at the looptop; typically more than an order of magnitude above ambient. Where some investigators have suggested such density enhancement results from a rapid enhancement in the magnetic field strength, we propose an alternative model, based on Petschek reconnection, whereby looptop plasma is heated and compressed by slow magnetosonic shocks generated self-consistently through flux retraction following reconnection. Under steady conditions such shocks can enhance density by no more than a factor of four. These steady shock relations (Rankine-Hugoniot relations) turn out to be inapplicable to Petscheks model owing to transient effects of thermal conduction. The actual density enhancement can in fact exceed a factor of ten over the entire reconnection outflow. An ensemble of flux tubes retracting following reconnection at an ensemble of distinct sites will have a collective emission measure proportional to the rate of flux tube production. This rate, distinct from the local reconnection rate within a single tube, can be measured separately through flare ribbon motion. Typical flux transfer rates and loop parameters yield emission measures comparable to those observed in super-hot sources.
We present a quantitative model of the magnetic energy stored and then released through magnetic reconnection for a flare on 26 Feb 2004. This flare, well observed by RHESSI and TRACE, shows evidence of non-thermal electrons only for a brief, early p
hase. Throughout the main period of energy release there is a super-hot (T>30 MK) plasma emitting thermal bremsstrahlung atop the flare loops. Our model describes the heating and compression of such a source by localized, transient magnetic reconnection. It is a three-dimensional generalization of the Petschek model whereby Alfven-speed retraction following reconnection drives supersonic inflows parallel to the field lines, which form shocks heating, compressing, and confining a loop-top plasma plug. The confining inflows provide longer life than a freely-expanding or conductively-cooling plasma of similar size and temperature. Superposition of successive transient episodes of localized reconnection across a current sheet produces an apparently persistent, localized source of high-temperature emission. The temperature of the source decreases smoothly on a time scale consistent with observations, far longer than the cooling time of a single plug. Built from a disordered collection of small plugs, the source need not have the coherent jet-like structure predicted by steady-state reconnection models. This new model predicts temperatures and emission measure consistent with the observations of 26 Feb 2004. Furthermore, the total energy released by the flare is found to be roughly consistent with that predicted by the model. Only a small fraction of the energy released appears in the super-hot source at any one time, but roughly a quarter of the flare energy is thermalized by the reconnection shocks over the course of the flare. All energy is presumed to ultimately appear in the lower-temperature T<20 MK, post-flare loops.
In models of fast magnetic reconnection, flux transfer occurs within a small portion of a current sheet triggering stored magnetic energy to be thermalized by shocks. When the initial current sheet separates magnetic fields which are not perfectly an
ti-parallel, i.e. they are skewed, magnetic energy is first converted to bulk kinetic energy and then thermalized in slow magnetosonic shocks. We show that the latter resemble parallel shocks or hydrodynamic shocks for all skew angles except those very near the anti-parallel limit. As for parallel shocks, the structures of reconnection-driven slow shocks are best studied using two-fluid equations in which ions and electrons have independent temperature. Time-dependent solutions of these equations can be used to predict and understand the shocks from reconnection of skewed magnetic fields. The results differ from those found using a single-fluid model such as magnetohydrodynamics. In the two-fluid model electrons are heated indirectly and thus carry a heat flux always well below the free-streaming limit. The viscous stress of the ions is, however, typically near the fluid-treatable limit. We find that for a wide range of skew angles and small plasma beta an electron conduction front extends ahead of the slow shock but remains within the outflow jet. In such cases conduction will play a more limited role in driving chromospheric evaporation than has been predicted based on single-fluid, anti-parallel models.
Magnetic null points can be located numerically in a potential field extrapolation or their average density can be estimated from the Fourier spectrum of a magnetogram. We use both methods to compute the null point density from a quiet Sun magnetogra
m made with Hinodes NFI and from magnetograms from SOHOs MDI in both its high-resolution and low-resolution modes. All estimates of the super-chromospheric column density (z>1.5 Mm) agree with one another and with the previous measurements: 0.003 null points per square Mm of solar surface.
Coronal magnetic field may be characterized by how its field lines interconnect regions of opposing photospheric flux -- its connectivity. Connectivity can be quantified as the net flux connecting pairs of opposing regions, once such regions are iden
tified. One existing algorithm will partition a typical active region into a number of unipolar regions ranging from a few dozen to a few hundred, depending on algorithmic parameters. This work explores how the properties of the partitions depend on some algorithmic parameters, and how connectivity depends on the coarseness of partitioning for one particular active region magnetogram. We find the number of connections among them scales with the number of regions even as the number of possible connections scales with its square. There are several methods of generating a coronal field, even a potential field. The field may be computed inside conducting boundaries or over an infinite half-space. For computation of connectivity, the unipolar regions may be replaced by point sources or the exact magnetogram may be used as a lower boundary condition. Our investigation shows that the connectivities from these various fields differ only slightly -- no more than 15%. The greatest difference is between fields within conducting walls and those in the half-space. Their connectivities grow more different as finer partitioning creates more source regions. This also gives a quantitative means of establishing how far away conducting boundaries must be placed in order not to significantly affect the extrapolation. For identical outer boundaries, the use of point sources instead of the exact magnetogram makes a smaller difference in connectivity: typically 6% independent of the number of source regions.
We present a novel model in which shortening of a magnetic flux tube following localized, three-dimensional reconnection generates strong gas-dynamic shocks around its apex. The shortening releases magnetic energy by progressing away from the reconne
ction site at the Alfven speed. This launches inward flows along the field lines whose collision creates a pair of gas-dynamic shocks. The shocks raise both the mass density and temperature inside the newly shortened flux tube. Reconnecting field lines whose initial directions differ by more that 100 degrees can produce a concentrated knot of plasma hotter that 20 MK, consistent with observations. In spite of these high temperatures, the shocks convert less than 10% of the liberated magnetic energy into heat - the rest remains as kinetic energy of bulk motion. These gas-dynamic shocks arise only when the reconnection is impulsive and localized in all three dimensions; they are distinct from the slow magnetosonic shocks of the Petschek steady-state reconnection model.
