The effects of magnetic structure on the conduction cooling of flare loops

A model of the sheared magnetic field in a coronal loop is used to evaluate the average cross-field suppression of axial thermal conduction. If the energy source is uniform in radius, this can lead to heat-flux reduction by a factor greater than three. When the source is annular, in a region of radius where the current density and shear are peaked, the effect can be significantly larger. In one extreme case, however, in which magnetic tearing provides the heating in a very narrow layer, the spatial resonance of the source excitation in a long loop leads to approximately axial conduction.     

Loss of equilibrium in coronal loops

The loss of equilibrium in coronal magnetic field structures is a possible source of energy for coronal heating and solar flares. We investigate whether such a loss of equilibrium occurs when a coronal loop is progressively twisted by photospheric motions. In studies of 2-D cylindrical equilibria, long loops have been found to be of constant cross-sectional area along most of their length, with axial variations being confined to narrow boundary layers. We use this information to develop a 1-D line-tied model, for a 2-D coronal loop. We specify the twist in terms of the azimuthal field and more physically, in terms of the photospheric footpoint displacement. In the former case we find a loss of equilibrium, but not in the latter. We also examine a twisted loop with a non-zero plasma pressure. The loss of equilibrium is only found at high-plasma . It is conjectured that such high- can occur in flare loops and prior to a prominence eruption. However, when the plasma evolves adiabatically, there is no loss of equilibrium.     

How Accurately Can We Determine the Coronal Heating Mechanism in the Large-Scale Solar Corona?

In recent papers by Priest et al., the nature of the coronal heating mechanism in the large-scale solar corona was considered. The authors compared observations of the temperature profile along large coronal loops with simple theoretical models and found that uniform heating along the loop gave the best fit to the observed data. This then led them to speculate that turbulent reconnection is a likely method to heat the large-scale solar corona. Here we reconsider their data and their suggestion about the nature of the coronal heating mechanism. Two distinct models are compared with the observations of temperature profiles. This is done to determine the most likely form of heating under different theoretical constraints. From this, more accurate judgments on the nature of the coronal heating mechanism are made. It is found that, due to the size of the error estimates in the observed temperatures, it is extremely difficult to distinguish between some of the different heat forms. In the initial comparison the limited range of observed temperatures (T>1.5 MK) in the data sets suggests that heat deposited in the upper portions of the loop, fits the data more accurately than heat deposited in the lower portions. However if a fuller model temperature range (T<1.0 MK) is used results in contridiction to this are found. In light of this several improvements are required from the observations in order to produce theoretically meaningful results. This gives serious bounds on the accuracy of the observations of the large-scale solar corona in future satellite missions such a Solar-B or Stereo.     

Energy source of the solar wind

A direct transfer of energy from photospheric activity to the solar wind by means of electric currents is discussed. Currents are assumed to flow in quiescent prominences which occasionally erupt and give rise to expanding loop-like structures in the corona, as observed from Skylab. Due to expansion, the legs of the loops are transformed into coronal rays which carry currents from the photosphere to the outer parts of the corona or interplanetary medium and then back again to the photosphere. It is proposed that energy is transferred from photospheric activity to the solar wind in the following ways: (1) as kinetic energy of the ejected loop matter; (2) as electric power directly fed into the extended loops; and (3) as torsional waves produced by fluctuations in the loop currents.     

Acceleration and Storage of Energetic Electrons in Magnetic Loops in the Course of Electric Current Oscillations

A mechanism of electron acceleration and storage of energetic particles in solar and stellar coronal magnetic loops, based on oscillations of the electric current, is considered. The magnetic loop is presented as an electric circuit with the electric current generated by convective motions in the photosphere. Eigenoscillations of the electric current in a loop induce an electric field directed along the loop axis. It is shown that the sudden reductions that occur in the course of type IV continuum and pulsating type III observed in various frequency bands (25?–?180 MHz, 110?–?600 MHz, 0.7?–?3.0 GHz) in solar flares provide evidence for acceleration and storage of the energetic electrons in coronal magnetic loops. We estimate the energization rate and the energy of accelerated electrons and present examples of the storage of energetic electrons in loops in the course of flares on the Sun or on ultracool stars. We also discuss the efficiency of the suggested mechanism as compared with the electron acceleration during the five-minute photospheric oscillations and with the acceleration driven by the magnetic Rayleigh–Taylor instability.     

Model calculations of the rising motion of a prominence loop

Model calculations are presented for the rising motion of the top section of a prominence loop, which is represented by a straight flux rope immersed in a coronal medium permeated with a bipolar magnetic field. Initially the prominence is at rest, in equilibrium with the surrounding coronal medium. When the magnetic monopoles that account for the source current for the bipolar field strengthen, the upward hydromagnetic buoyancy force overcomes the downward gravitational force so that the prominence is initiated into rising motion. The illustrative examples show that prominences can move away from the solar surface by the action of the hydromagnetic buoyancy force, which is preponderant with the diamagnetic force due to the current carried by the prominence interacting with the coronal magnetic field produced by the photospheric currents, if the changes in the photospheric magnetic field are sufficiently large.     

The topology of a mixed-polarity potential field,and inferences for the heating of the quiet solar corona

We study the statistical properties of the connectivity of the corona over the quiet Sun by analyzing the potential magnetic field above the central area of source planes sprinkled randomly with some 300 magnetic monopoles each. We find that the field is generally more complex than one might infer from a study of the field within the source plane alone, or from a study of the 3D field around a small number of sources. Whereas a given source most commonly connects to only its nearest neighbors, it may connect to up to several dozen sources; only a weak trend relates the source strength and the number of connections. The connections between pairs of sources define volumes, or domains, of connectivity. Domains that have a finite cross section with the source plane are enclosed by surfaces that contain a pair of null points. In contrast, most of the bounding surfaces of domains that lie above the source plane appear not to contain null points. We argue that the above findings imply (i) that we should expect at best a weak correlation between coronal brightness and the flux in an underlying flux concentration, and (ii) that the low-lying chromospheric field lines (such as are observable in H) provide information on source connections that are largely complementary to those traced by the higher-reaching coronal field lines (observable in the extreme ultraviolet). We compare sample TRACE and SOHO/MDI observations of the quiet corona and photosphere with our finding that the number density of null points within the source plane closely matches that of the sources; because we find essentially no foci of coronal brightening away from significant photospheric magnetic flux concentrations, we conclude that coronal heating at such null points does not contribute significantly to the overall heating. We argue that the divergence of field lines towards multiple sources restricts the propagation of braids and twists, so that any coronal heating that is associated with the dissipation of braids induced by footpoint shuffling in mixed-polarity network is likely (a) to occur predominantly low in the corona, and (b) to be relatively more efficient in quiet Sun than in active regions for a given field strength and loop length.     

Simple tests for the ideal MHD stability of line-tied coronal magnetic fields

Methods for investigating the stability of line-tied, cylindrically-symmetric magnetic fields are presented. The energy method is used and the perturbed potential energy integral is manipulated to produce simple tests that predict either stability to general coronal disturbances or instability to localized modes, both satisfying photospheric line-tying. Using these tests the maximum amount of magnetic energy, that can be stored in the coronal magnetic field prior to an instability, can be estimated. The tests are applied to four different classes of equilibria and results are obtained for both arcade and loop geometries.     

Magnetic reconnection and energy release in the solar corona by Taylor relaxation

The heating of the solar corona by resistive turbulence of coronal magnetic fields is considered. The theory of this process, based on the Taylor-Heyvaerts-Priest hypothesis and a magnetic relaxation equation, is developed. Such an approach allows one to obtain the successive magnetic reconnection configurations and energy balance of the coronal magnetic field in response to prescribed motions of the photospheric footpoints. Two specific models of the coronal magnetic configuration are investigated, namely an array of closely packed flux tubes and a two-dimensional magnetic arcade.     

Implications of rapid footpoint motions of photospheric flux tubes for coronal heating

Some recent observations at Pic-du-Midi (Mulleret al., 1992a) suggest that the photospheric footpoints of coronal magnetic field lines occasionally move rapidly with typical velocities of the order 3 km s^–1 for about 3 or 4 min. We argue that such occasional rapid footpoint motions could have a profound impact on the heating of the quiet corona. Qualitative estimates indicate that these occasional rapid motions can account for the entire energy flux needed to heat the quiet corona. We therefore carry out a mathematical analysis to study in detail the response of a vertical thin flux tube to photospheric footpoint motions in terms of a superposition of linear kink modes for an isothermal atmosphere. We find the resulting total energy that is asymptotically injected into an isothermal atmosphere (i.e., an atmosphere without any back reflection). By using typical parameter values for fast and slow footpoint motions, we show that, even if the footpoints spend only 2.5% of the time undergoing rapid motions, still these rapid motions could be more efficient in transporting energy to the corona than the slow motions that take place most of the time.     

Intermittent heating in a model of solar coronal loops

X-ray and EUV observations of the solar corona reveal a very complex and dynamic environment where there are many examples of structures that are believed to outline the Sun's magnetic field. In this present study, the authors investigate the temporal response of the temperature, density and pressure of a solar coronal plasma contained within a magnetic loop to an intermittent heating source generated by Ohmic dissipation. The energy input is produced by a one-dimensional MHD flare model. This model is able to reproduce some of the statistical properties derived from X-ray flare observations. In particular the heat deposition consists of both a sub-flaring background and much larger, singular dissipative events. Two different heating profiles are investigated: (a) the spatial average of the square of the current along the loop and (b) the maximum of the square of the current along the loop. For case (a), the plasma parameters appear to respond more to the global variations in the heat deposition about its average value rather than to each specific event. For case (b), the plasma quantities are more intermittent in their evolution. In both cases the density response is the least bursty signal. It is found that the time-dependent energy input can maintain the plasma at typical coronal temperatures. Implications of these results upon the latest coronal observations are discussed.     

Energy released by the interaction of coronal magnetic fields

Comparisons between coronal spectroheliograms and photospheric magnetograms are presented to support the idea that as coronal magnetic fields interact, a process of field line reconnection usually takes place as a natural way of preventing magnetic stresses from building up in the lower corona. This suggests that the energy which would have been stored in stressed fields is continuously released as kinetic energy of material being driven aside to make way for the reconnecting fields. However, this kinetic energy is negligible compared to the thermal energy of the coronal plasma. Therefore, it appears that these slow adjustments of coronal magnetic fields cannot account for even the normal heating of the corona, much less the energetic events associated with solar flares.Visiting Scientist, Kitt Peak National Observatory, Tucson Arizona.Operated by the Association of Universities for Research in Astronomy, Inc., under contract with the National Science Foundation.     

High-resolution observations of solar radio bursts at 2, 6, and 20 cm wavelength

The Very Large Array and the Westerbork Synthesis Radio Telescope have been used to observe eight solar bursts at 2, 6, or 20 cm wavelength with second-of-arc angular resolution. The regions of burst energy were all resolved with angular sizes between 5″ and 30″, brightness temperatures between 2 × 10⁷ K and 2 x 10⁸ K, and degrees of circular polarization between 10 and 90%. A series of 10 s snapshot maps are presented for the more intense bursts, and superimposed on photospheric magnetograms or Hα photographs. The impulsive phase of the radio bursts is located near the magnetic neutral line of the active regions, and between the flaring Hα kernels which mark the footpoints of magnetic loops. The impulsive phase of one 6 cm burst was smaller and spatially separated from both the preburst radio emission and the gradual decay phase of the burst. Another 6 cm burst exhibited preburst heating of the coronal loop in which the burst occurred. The plasma was probably heated at a lower level in the loop, while the burst energy was released several minutes later at a higher level. A multiple-spike 20 cm burst exhibited polarity inversions with degrees of circular polarization of 90%. The rapid changes in circular polarization are attributed to either a magnetically complex region or the emersion of new magnetic flux at coronal heights where magnetic field strengths H ≈ 300 to 400 G.     

Analysis of EUV limb brightening observations from ATM

Magnetic fields in the low corona are the only plausible source of energy for solar flares. Other energy sources appear inadequate or uncorrelated with flares. Low coronal magnetic fields cannot be measured accurately, so most attention has been directed toward measurements of the photospheric magnetic fields from which coronal developments may be inferred. Observations of these magnetic fields are reviewed. It is concluded that, except possibly for the largest flares, changes in the photospheric magnetic fields in flaring centers are confined to evolutionary changes associated with emergence of new magnetic flux. Flare observations with the 10830 Å line of helium, in particular, are discussed. It is concluded that the brightest flare knots appear near points of emergent magnetic flux. Pre-flare activation and eruptions of H filaments are discussed. It is concluded that the rapid motions in filaments indicate unambiguously that the magnetic fields in the low corona are severely disrupted prior to most flares. The coronal signature of H filament eruptions is illustrated with soft X-ray photographs from the S-054 experiment of the NASA Skylab mission. An attempt is made, by studying X-ray flare morphology, to determine whether flares grow by reconnections between adjacent or intertwined magnetic elements or by triggering, in which each flaring loop drives adjacent loops to unstable states. It is concluded that successive loop brightenings are most easily interpreted as the result of magnetic field reconnections, although better time resolution is required to settle the question. A model of magnetic field reconnections for flares associated with filament activation and emerging magnetic flux is presented.     

Solar Magnetic Carpet III: Coronal Modelling of Synthetic Magnetograms

This article is the third in a series working towards the construction of a realistic, evolving, non-linear force-free coronal-field model for the solar magnetic carpet. Here, we present preliminary results of 3D time-dependent simulations of the small-scale coronal field of the magnetic carpet. Four simulations are considered, each with the same evolving photospheric boundary condition: a 48-hour time series of synthetic magnetograms produced from the model of Meyer et al. (Solar Phys. 272, 29, 2011). Three simulations include a uniform, overlying coronal magnetic field of differing strength, the fourth simulation includes no overlying field. The build-up, storage, and dissipation of magnetic energy within the simulations is studied. In particular, we study their dependence upon the evolution of the photospheric magnetic field and the strength of the overlying coronal field. We also consider where energy is stored and dissipated within the coronal field. The free magnetic energy built up is found to be more than sufficient to power small-scale, transient phenomena such as nanoflares and X-ray bright points, with the bulk of the free energy found to be stored low down, between 0.5?–?0.8 Mm. The energy dissipated is currently found to be too small to account for the heating of the entire quiet-Sun corona. However, the form and location of energy-dissipation regions qualitatively agree with what is observed on small scales on the Sun. Future MHD modelling using the same synthetic magnetograms may lead to a higher energy release.     

Observations of Coronal Structures Above an Active Region by Eit and Implications for Coronal Energy Deposition

Solar EUV images recorded by the EUV Imaging Telescope (EIT) on SOHO have been used to evaluate temperature and density as a function of position in two largescale features in the corona observed in the temperature range of 1.0–2.0 MK. Such observations permit estimates of longitudinal temperature gradients (if present) in the corona and, consequently, estimates of thermal conduction and radiative losses as a function of position in the features. We examine two relatively cool features as recorded in EIT's Feix/x (171 Å) and Fexii (195 Å) bands in a decaying active region. The first is a long-lived loop-like feature with one leg, ending in the active region, much more prominent than one or more distant footpoints assumed to be rooted in regions of weakly enhanced field. The other is a near-radial feature, observed at the West limb, which may be either the base of a very high loop or the base of a helmet streamer. We evaluate energy requirements to support a steady-state energy balance in these features and find in both instances that downward thermal conductive losses (at heights above the transition region) are inadequate to support local radiative losses, which are the predominant loss mechanism. The requirement that a coronal energy deposition rate proportional to the square of the ambient electron density (or pressure) is present in these cool coronal features provides an additional constraint on coronal heating mechanisms.     

Plasma waves caused by transient heat conduction in a coronal loop and anomalous resistivity

Numerical simulation is made of the transient heat conduction during local heating in a model coronal magnetic loop with an axial electric current. It is assumed that a segment near the top of the normal coronal loop is heated to above 10⁷ K by a sufficiently small heat input as compared with the total flare energy. A hump appears in the velocity distribution of electrons moving down the temperature gradient with speeds slightly below the thermal one. Consequently, electron plasma waves are excited. The high intensity of the waves persists in the upper region of the loop for more than a second until the termination of the simulation. The energy density of the plasma waves normalized with respect to thermal density is 10^–3.5 at maximum. A theoretical estimate gives an anomalous resistivity 5 orders of magnitude greater than an initial value. Based on the above result, we propose a model for impulsive loop flares.     

Coronal loop heating by discrete Alfvén waves

We have modeled the solar coronal active loop heating by discrete Alfvén waves. Discrete Alfvén waves (DAW) are a new class of Alfvén waves which can be described by the two-fluid model with finite ion-cyclotron frequency, or the MHD model with plasma current along the magnetic field line as shown by Appert, Vaclavik, and Villar (1984). We have modeled the coronal loop as a semi-toroidal plasma with the major toroidal radius much larger than the plasma radius. We have shown that the absorption of discrete Alfvén waves by the plasma through viscosity can account for at least 30% of the coronal heating rate density of 10^–4 J m^–3 s^–1.     

Small-Scale Energy Release Driven by Supergranular Flows on the Quiet Sun

We present data and modelling for the quiet Sun that strongly suggest a ubiquitous small-scale atmospheric heating mechanism that is driven solely by converging supergranular flows. A possible energy source for such events is the power transfer to the plasma via the work done on the magnetic field by photospheric convective flows, which exert drag on the footpoints of magnetic structures. We present evidence of small-scale energy release events driven directly by the hydrodynamic forces that act on the magnetic elements in the photosphere, as a result of supergranular-scale flows. We show strong spatial and temporal correlation between quiet-Sun soft X-ray emission (from Yohkoh SXT) and SOHO MDI-derived flux removal events driven by deduced photospheric flows. We also present a simple model of heating generated by flux submergence, based on particle acceleration by converging magnetic mirrors. In the near future, high resolution soft X-ray images from XRT on the Hinode satellite will allow definitive, quantitative verification of our results. Electronic Supplementary Material The online version of this article () contains supplementary material, which is available to authorized users.     

太阳大气中动力学阿尔文波的产生与加热研究进展

动力学阿尔文波是垂直波长接近离子回旋半径或者电子惯性长度的色散阿尔文波.由于波的尺度接近粒子的动力学尺度,动力学阿尔文波在太阳和空间等离子体加热、加速等能化现象中起重要作用.因此,动力学阿尔文波通常被认为是日冕加热的候选者.本研究工作深入、系统地调研了太阳大气中动力学阿尔文波的激发和耗散机制.基于日冕等离子体环境,介绍了几种常见的动力学阿尔文波激发机制:温度各向异性不稳定性、场向电流不稳定性、电子束流不稳定性、密度非均匀不稳定性以及共振模式转换.还介绍了太阳大气中动力学阿尔文波的耗散机制,并讨论了这些耗散机制对黑子加热、冕环加热以及冕羽加热的影响.不仅为认识太阳大气中动力学阿尔文波的驱动机制、动力学演化特征以及波粒相互作用提供合理的理论依据,而且有助于揭示日冕等离子体中能量储存和释放、粒子加热等能化现象的微观物理机制.