Interpretation of the observed motions of hard X-ray sources in solar flares

In connection with the RHESSI satellite observations of solar flares, which have revealed new properties of hard X-ray sources during flares, we offer an interpretation of these properties. The observed motions of coronal and chromospheric sources are shown to be the consequences of three-dimensional magnetic reconnection at the separator in the corona. During the first (initial) flare phase, the reconnection process releases an excess of magnetic energy related predominantly to themagnetic tensions produced before the flare by shear plasma flows in the photosphere. The relaxation of a magnetic shear in the corona also explains the downward motion of the coronal source and the decrease in the separation between chromospheric sources. During the second (main) flare phase, ordinary reconnection dominates; it describes the energy release in the terms of the “standard model” of large eruptive flares accompanied by the rise of the coronal source and an increase in the separation between chromospheric sources.     

On Solving the Coronal Heating Problem

The question of what heats the solar corona remains one of the most important problems in astrophysics. Finding a definitive solution involves a number of challenging steps, beginning with an identification of the energy source and ending with a prediction of observable quantities that can be compared directly with actual observations. Critical intermediate steps include realistic modeling of both the energy release process (the conversion of magnetic stress energy or wave energy into heat) and the response of the plasma to the heating. A variety of difficult issues must be addressed: highly disparate spatial scales, physical connections between the corona and lower atmosphere, complex microphysics, and variability and dynamics. Nearly all of the coronal heating mechanisms that have been proposed produce heating that is impulsive from the perspective of elemental magnetic flux strands. It is this perspective that must be adopted to understand how the plasma responds and radiates. In our opinion, the most promising explanation offered so far is Parker's idea of nanoflares occurring in magnetic fields that become tangled by turbulent convection. Exciting new developments include the identification of the “secondary instability” as the likely mechanism of energy release and the demonstration that impulsive heating in sub-resolution strands can explain certain observed properties of coronal loops that are otherwise very difficult to understand. Whatever the detailed mechanism of energy release, it is clear that some form of magnetic reconnection must be occurring at significant altitudes in the corona (above the magnetic carpet), so that the tangling does not increase indefinitely. This article outlines the key elements of a comprehensive strategy for solving the coronal heating problem and warns of obstacles that must be overcome along the way.     

Reconnection of a Kinking Flux Rope Triggering the Ejection of a Microwave and Hard X-Ray Source II. Numerical Modeling

Numerical simulations of the helical (m=1) kink instability of an arched, line-tied flux rope demonstrate that the helical deformation enforces reconnection between the legs of the rope if modes with two helical turns are dominant as a result of high initial twist in the range Φ≳6π. Such a reconnection is complex, involving also the ambient field. In addition to breaking up the original rope, it can form a new, low-lying, less twisted flux rope. The new flux rope is pushed downward by the reconnection outflow, which typically forces it to break as well by reconnecting with the ambient field. The top part of the original rope, largely rooted in the sources of the ambient flux after the break-up, can fully erupt or be halted at low heights, producing a “failed eruption.” The helical current sheet associated with the instability is squeezed between the approaching legs, temporarily forming a double current sheet. The leg – leg reconnection proceeds at a high rate, producing sufficiently strong electric fields that it would be able to accelerate particles. It may also form plasmoids, or plasmoid-like structures, which trap energetic particles and propagate out of the reconnection region up to the top of the erupting flux rope along the helical current sheet. The kinking of a highly twisted flux rope involving leg – leg reconnection can explain key features of an eruptive but partially occulted solar flare on 18 April 2001, which ejected a relatively compact hard X-ray and microwave source and was associated with a fast coronal mass ejection.     

Transition region and coronal plasmas: instrumentation and spectral analysis

The plasma conditions in the solar atmosphere and, in particular, in coronal holes are summarized, before space-borne instrumentation for observing these regions in vacuum-ultraviolet light is briefly introduced with the Solar Ultraviolet Measurements of Emitted Radiation (SUMER) spectrometer on the Solar and Heliospheric Observatory (SOHO) as example. Spectroscopic measurements of small plasma jets are then analyzed in detail. Magnetic reconnection is thought to be responsible for heating the corona of the Sun as well as accelerating the solar wind by converting magnetic energy into thermal and kinetic energies. The continuous outflow of the fast solar wind from coronal holes on ‘open’ field lines, which reach out into interplanetary space, then requires many reconnection events of very small scale sizes – most of them probably below the resolution capabilities of present-day instruments. Our observations of such an event have been obtained with the Solar and Heliospheric Observatory (SOHO) providing both high-resolution imaging and spectral information for structural and dynamical studies. We find whirling or rotating motions as well as jets with acceleration along their propagation paths in close spatial and temporal vicinity to the coronal jet. This revised version was published online in July 2006 with corrections to the Cover Date.     

Quadrupolar Dimmings During a Partial Halo Coronal Mass Ejection Event

We present detailed observations of the formations of four distinct coronal dimmings during a flare of 17 September 2002, which was followed by an eruption of a huge coronal loop system, and then an over-and-out partial halo coronal mass ejection (CME), with the same direction as the loop system eruption but laterally far offset from the flare site. Among the four dimmings, two compact ones were symmetrically located in the opposite polarity regions immediately adjacent to the highly sheared magnetic polarity inversion line in the flare region, and hence were probably composed of bipolar double dimmings due to a flux-rope eruption and represented its evacuated footpoints. However, another nearby compact dimming and a remote diffuse one were formed in the opposite polarity footpoint regions of the eruptive loop system, and thus probably consisted of a pair of dimmings magnetically linked by the erupting loop system and also indicated its evacuated footpoints. The loop system might have played a role in guiding the erupting flare field and producing the over-and-out CME, but its eruption might simply have been pushed out by the erupting flare field, because there was no reconnection signature between them. From comparison with a derived potential-field source-surface (PFSS) magnetic configuration, our observations consistently suggest that the dimmings were formed in pairs and originated from the eruptions of the two different magnetic systems. We thus define them as “quadrupolar dimmings.”     

Intensity oscillations at the feet of coronal holes

We investigate the regime of chromospheric oscillations at the bases of coronal holes and compare them with the oscillations in the quiet chromosphere outside coronal holes using time series of spectrograms taken at different times in eight quiet regions on the Sun. As the oscillation parameter being studied, we have chosen the central intensity of the chromospheric Ca II K and H and 849.8-nm lines. The intensity measurements at all spatial points (along the spectrograph slit) have been subjected to a standard Fourier analysis. For the identified areas of the networks, cells, and network boundaries, we have calculated the integrated oscillation powers in several frequency bands. For all frequency bands, the powers of the intensity oscillations at the formation level of the Ca II resonance doublet line cores have been found to be enhanced at the bases of coronal holes approximately by a factor of 1.5. For the “three-minute” band, this enhancement is more pronounced in the network than in the cell, while the opposite is true for the “five-minute” band. The power in the five-minute band is higher than that in the three-minute one both at the bases of coronal holes and outside them, but this ratio in the network for a coronal hole is higher (1.40 ± 0.25 and 1.30 ± 0.10). We interpret this fact and the fact that the power of the three-minute oscillations for nonmagnetic regions changes with height differently at the base of a coronal hole and outside it as an increase in the importance of magnetoacoustic portals at the chromospheric base of the coronal hole.     

Evidence for Tether-Cutting Reconnection in a Quadrupole Magnetic Configuration in the April 9, 2001, M7.9 Flare

We studied the M7.9 flare on April 9, 2001 that occurred within a δ-sunspot of active region NOAA 9415. We used a multi-wavelength data set, which includes Yohkoh, TRACE, SOHO, and ACE spacecraft observations, Potsdam and Ondřejov radio data and Big Bear Solar Observatory (BBSO) images in order to study the large-scale structure of this two-ribbon flare that was accompanied by a very fast coronal mass ejection (CME). We analyzed light curves of the flare emission as well as the structure of the radio emission and report the following: the timing of the event, i.e., the fact that the initial brightenings, associated with the core magnetic field, occurred earlier than the remote brightening (RB), argue against the break-out model in the early phase of this event. We thus conclude that the M7.9 flare and the CME were triggered by a tether-cutting reconnection deep in the core field connecting the δ-spot and this reconnection formed an unstable flux rope. Further evolution of the erupted flux rope could be described either by the “standard“ flare model or a break-out type of the reconnection. The complex structure of flare emission in visible, X-ray, and radio spectral ranges point toward a scenario which involves multiple reconnection processes between extended closed magnetic structures.     

<Emphasis Type="Italic">In Situ</Emphasis> Signatures of Interchange Reconnection between Magnetic Clouds and Open Magnetic Fields: A Mechanism for the Erosion of Polar Coronal Holes?

We outline a method to determine the direction of solar open flux transport that results from the opening of magnetic clouds (MCs) by interchange reconnection at the Sun based solely on in-situ observations. This method uses established findings about i) the locations and magnetic polarities of emerging MC footpoints, ii) the hemispheric dependence of the helicity of MCs, and iii) the occurrence of interchange reconnection at the Sun being signaled by uni-directional suprathermal electrons inside MCs. Combining those observational facts in a statistical analysis of MCs during solar cycle 23 (period 1995 – 2007), we show that the time of disappearance of the northern polar coronal hole (1998 – 1999), permeated by an outward-pointing magnetic field, is associated with a peak in the number of MCs originating from the northern hemisphere and connected to the Sun by outward-pointing magnetic field lines. A similar peak is observed in the number of MCs originating from the southern hemisphere and connected to the Sun by inward-pointing magnetic field lines. This pattern is interpreted as the result of interchange reconnection occurring between MCs and the open field lines of nearby polar coronal holes. This reconnection process closes down polar coronal hole open field lines and transports these open field lines equatorward, thus contributing to the global coronal magnetic field reversal process. These results will be further constrainable with the rising phase of solar cycle 24.     

The Gradual Phase of the X17 Flare on October 28, 2003

We present SOHO/CDS observations taken during the gradual phase of the X17 flare that occurred on October 28, 2003. The CDS data are supplemented with TRACE and ground-based observations. The spectral observations allow us to determine velocities from the Doppler shifts measured in the flare loops and in the two ribbon kernels, one hour and a half after the flare peak. Strong downflows (>70 km s⁻¹) are observed along the loop legs at transition-region temperatures. The velocities are close to those expected for free fall. Observations and results from a hydrodynamic simulation are consistent with the heating taking place for a short time near the top of the arcade. Slight upflows are observed in the outer edges of the ribbons (<60 km s⁻¹) in the EUV lines formed at log T < 6.3. These flows could correspond to the so-called “gentle evaporation.” At “flare” temperatures (Fe xix, log T = 6.9), no appreciable flows are observed. The observations are consistent with the general standard reconnection models for two-ribbons flares.     

Classification of magnetic reconnection during two current-loop coalescence

We present a classification of magnetic reconnection during two current loop coalescence, which may be quite important for the physical process of both solar flares and coronal loop heating in the solar active region. It is suggested that different kinds of the current loop coalescence processes could be identified from the soft X-ray telescope(SXT) of the Yohkoh satellite and the magnetic field data in the active region.     

Avalanche models for solar flares (Invited Review)

This paper is a pedagogical introduction to avalanche models of solar flares, including a comprehensive review of recent modeling efforts and directions. This class of flare model is built on a recent paradigm in statistical physics, known as self-organized criticality. The basic idea is that flares are the result of an ‘avalanche’ of small-scale magnetic reconnection events cascading through a highly stressed coronal magnetic structure, driven to a critical state by random photospheric motions of its magnetic footpoints. Such models thus provide a natural and convenient computational framework to examine Parker's hypothesis of coronal heating by nanoflares. Supplementary material to this paper is available in electronic form at http://dx.doi.org/10.1023/A:1013301521745     

Nonlinear excitation of small-scale Alfvén waves by fast waves and plasma heating in the solar atmosphere

We study a nonlinear mechanism for the excitation of kinetic Alfvén waves (KAWs) by fast magneto-acoustic waves (FWs) in the solar atmosphere. Our focus is on the excitation of KAWs that have very small wavelengths in the direction perpendicular to the background magnetic field. Because of their small perpendicular length scales, these waves are very efficient in the energy exchange with plasmas and other waves. We show that the nonlinear coupling of the energy of the finite-amplitude FWs to the small-scale KAWs can be much faster than other dissipation mechanisms for fast wave, such as electron viscous damping, Landau damping, and modulational instability. The nonlinear damping of the FWs due to decay FW = KAW + KAW places a limit on the amplitude of the magnetic field in the fast waves in the solar corona and solar-wind at the level B/B ₀∼10⁻². In turn, the nonlinearly excited small-scale KAWs undergo strong dissipation due to resistive or Landau damping and can provide coronal and solar-wind heating. The transient coronal heating observed by Yohkoh and SOHO may be produced by the kinetic Alfvén waves that are excited by parametric decay of fast waves propagating from the reconnection sites.     

The dynamics of driven magnetic reconnection in coronal arcades

The dynamics of interacting coronal loops and arcades have recently been highlighted by observations from theYohkoh satellite and may represent a viable mechanism for heating the solar corona. Here such an interaction is studied using two-dimensional resistive magnetohydrodynamic (MHD) simulations. Initial potential field structures evolve in response to imposed photospheric flows. In addition to the anticipated current sheet about theX-point separating the colliding flux systems, significant current layers are found to lie all the way along the separatrices that intersect at theX-point and divide the coronal magnetic field into topologically distinct regions. Shear flows across the separatrices are also observed. Both of these features are shown to be compatible with recent analytical studies of two-dimensional linear steady-state magnetic reconnection, even though the driven system that has been simulated is not strictly ‘open’ in the sense implied by steady-state calculations. The implications for future steady-state models are also discussed. The presence of the neutral point also brings into question any constant-density approximations that have previously been used for such quasi-steady coronal evolution models. This results from the intimate coupling between the neutral point and its separatrices communicated via the gas pressure. In terms of the detailed energetics during the arcade evolution, preliminary results reveal that on the order of 3% of the energy injected by the footpoint motions is lost purely through ohmic dissipation. We would therefore anticipate a local hot spot between the interacting flux systems, and a brightening distributed along the length of any separatrix field lines. Furthermore, as the resistivityη is reduced, the flux annihilation rate and the ohmic dissipation rate are found to scale independently ofη.     

Slow-shock heating in post-flare arches

The heating of a coronal arch, following the occurrence of a dynamic (two-ribbon) flare, is discussed. We investigate whether slow-shock heating, occurring during the reconnection process in the dynamic flare and responsible for the heating of the post-flare loops, is also a workable proposition for the heating of a coronal arch. Contrary to the flare loops, the shock structure in the arch is generally not modified greatly by thermal conduction effects. As a result slow-shock heating may be investigated in terms of the familiar MHD shock jump relations. The observed enhanced arch density with respect to the surrounding corona is explained as a direct consequence of the reconnection process. For a combination of high arch temperatures and low values of coronal magnetic field and density thermal conduction may become important and will lead to an extra density enhancement in the arch. Our interpretation of the arch of 21–22 May, 1980 suggests that the formation of the arch took approximately one hour, and that observed temperature, density and maximum energy content can be consistently explained by the slow-shock heating mechanism.Currently: Center for Astrophysics and Space Sciences, C-011, University of California at San Diego, La Jolla, CA 92093, U.S.A.     

Observations of Low-Latitude Coronal Plumes

Using Fe ix/x 17.1 nm observations from the Extreme-Ultraviolet Imaging Telescope (EIT) on the Solar and Heliospheric Observatory (SOHO), we have identified many coronal plumes inside low-latitude coronal holes as they transited the solar limb during the late declining phase of cycle 23. These diffuse, linear features appear to be completely analogous to the familiar polar plumes. By tracking them as they rotate from the limb onto the disk (or vice versa), we confirm that EUV plumes seen against the disk appear as faint, diffuse blobs of emission surrounding a brighter core. When the EIT images are compared with near-simultaneous magnetograms from the SOHO Michelson Doppler Imager (MDI), the low-latitude, on-disk plumes are found to overlie regions of mixed polarity, where small bipoles are in contact with unipolar flux concentrations inside the coronal hole. The birth and decay of the plumes are shown to be closely related to the emergence of ephemeral regions, their dispersal in the supergranular flow field, and the cancellation of the minority-polarity flux against the dominant-polarity network elements. In addition to the faint polar and nonpolar plumes associated with ephemeral regions, we note the existence of two topologically similar coronal structures: the giant plume-like features that occur above active regions inside coronal holes, and the even larger scale “pseudostreamers” that separate coronal holes of the same polarity. In all three cases, the basic structure consists of open field lines of a given polarity overlying a photospheric region of the opposite polarity; ongoing interchange reconnection at the X-point separating the open field domains from the underlying double-arcade system appears to result in the steady evaporation of material from the closed into the open region.     

Heating the Solar Corona by Magnetic Reconnection

Here I review briefly the theory of magnetohydrodynamic reconnection and ask what observational evidence is there that it is heating the corona. In particular, the new directions in which three-dimensional theory for reconnection is heading are outlined. Part of the coronal heating problem has been solved with the identification of reconnection driven by converging flux motions as the key for x-ray bright points. Furthermore, it has been shown that the large-scale diffuse corona is heated rather uniformly, so that turbulent reconnection by braiding or ion-cyclotron waves driven by network micro-flares are prime candidates. Finally, reconnection is the natural explanation for a wide variety of phenomena discovered by SOHO including explosive events, blinkers, the magnetic carpet and even possibly tornadoes. This revised version was published online in July 2006 with corrections to the Cover Date.     

Streamer Belt and Chains as the Main Sources of Quasi-Stationary Slow Solar Wind

Synoptic maps of white-light coronal brightness from SOHO/LASCO C2 and distributions of solar wind velocity obtained from interplanetary scintillation are studied. Regions with velocity V≈300 – 450 km s⁻¹ and increased density N>10 cm⁻³, typical of the “slow” solar wind originating from the belt and chains of streamers, are shown to exist at Earth’s orbit, between the fast solar wind flows (with a maximum velocity V _max≈450 – 800 km s⁻¹). The belt and chains of streamers are the main sources of the “slow” solar wind. As the sources of “slow” solar wind, the contribution from the chains of streamers may be comparable to that from the streamer belt.     

The Implications of 3D for Solar MHD Modelling

The effects of three-dimensionality on the modelling of solar magnetic fields are described. We focus on two processes that are believed to play an important role in coronal heating – the braiding of field lines by photospheric motions and the reconnection of colliding flux tubes. First, it is shown that a proper treatment of boundary conditions at the photosphere in 3D entails qualitatively new physical processes that are not present in 2D. The numerical resolution of even simple boundary velocity patterns in 3D leads to obstacles which have no counterpart in the 2D case. We conclude that adaptive mesh refinement is necessary for capturing the essential 3D physics of a braiding motion at the photosphere. Next, the effects of 3D on magnetic reconnection are discussed. Reconnection in 3D can lead to an evolution of interacting flux tubes, magnetic tunneling, that is not only impossible in lower dimensionality, but is strikingly counterintuitive. The implications of these results for the structure of the solar magnetic field and for coronal heating are described.     

The rate of flux pile-up magnetic reconnection in reduced MHD

The rate of two-dimensional flux pile-up magnetic reconnection is known to be severely limited by gas pressure in a low-beta plasma of the solar corona. As earlier perturbational calculations indicated, however, the pressure limitation should be less restrictive for three-dimensional flux pile-up. In this paper the maximum rate of reconnection is calculated in the approximation of reduced magnetohydrodynamics (RMHD), which is valid in the solar coronal loops. The rate is calculated for finite-magnitude reconnecting fields in the case of a strong axial field in the loop. Gas pressure effects are ignored in RMHD but a similar limitation on the rate of magnetic merging exists. Nevertheless, the magnetic energy dissipation rate and the reconnection electric field can increase by several orders of magnitude as compared with strictly two-dimensional pile-up. Though this is still not enough to explain the most powerful solar flares, slow coronal transients with energy release rates of order 10²⁵– 10²⁶ erg s^–1and heating of quiet coronal loops are within the compass of the model.     

Laboratory Simulation of Magnetospheric Plasma Shocks

An experimental simulation of planetary magnetospheres is being developed to investigate the formation of collisionless shocks and their effects. Two experimental situations are considered. In both, the solar wind is simulated by laser ablation plasmas. In one case, the “solar wind” flows across the magnetic field of a high-current discharge. In the other, a transverse magnetic field is embedded in the plasma flow, which interacts with a conductive obstacle. The ablation plasma is created using the “Tomcat” laser, currently emitting 5 J in a 6 ns pulse at 1 μm wavelength and irradiance above 10¹³ W/cm². The “Zebra” z-pinch generator, with load current up to 1 MA and voltage up to 3.5 MV produces the magnetic fields. Hydrodynamic modeling is used to estimate the plasma parameters achievable at the front of the plasma flow and to optimize the experiment design. Particle-in-cell simulations reveal details of the interaction of the “solar wind” with an external magnetic field, including flow collimation and heating effects at the stopping point. Hybrid simulations show the formation of a bow shock at the interaction of a magnetized plasma flow with a conductor. The plasma density and the embedded field have characteristic spatial modulations in the shock region, with abrupt jumps and fine structure on the skin depth scale.