Magnetic Relaxation and Particle Acceleration in a Flaring Twisted Coronal Loop

In the present work we aim to study particle acceleration in twisted coronal loops. For this purpose, an MHD model of magnetic reconnection in a linearly unstable twisted magnetic fluxtube is considered. Further, the electric and magnetic fields obtained in the MHD simulations are used to calculate proton and electron trajectories in the guiding-centre approximation. It is shown that particle acceleration in such a model is distributed rather uniformly along the coronal loop and the high-energy population remains generally neutral. It also follows from the model that the horizontal cross-section of the volume occupied by high-energy particles near the loop footpoints increases with time, which can be used as an observational proxy.     

The shape of twisted,line-tied coronal loops

The magnetostatic equilibrium of a coronal loop in response to slow twisting of the photospheric footpoints is investigated. A numerical code is used to solve the full non-linear 2-D axisymmetric problem, extending earlier linearised models which assume weak twist and large aspect ratio. It is found that often the core of the loop tends to contract into a region of strong longitudinal field while the outer part expands. It is shown that, away from the photospheric footpoints, the equilibrium is very well approximated by a straight 1-D cylindrical model. This idea is used to develop a simple method for prescribing the footpoint angular displacement and calculating the equilibrium.     

Spatially Resolved Microwave Observations of Multiple Periodicities in a Flaring Loop

Quasi-periodic pulsations (QPPs) with at least three simultaneously existing spectral components with periods P≥30 s, P≈20 s, and about P≈10 s were detected during the decay phase of a solar flare on 3 July 2002, observed with the Nobeyama Radioheliograph (NoRH). A detailed study of the spatial structure of the Fourier amplitudes of QPPs along a flaring loop has revealed different spatial distributions of the three components. It is shown that the source of the QPPs with period P≥30 s has its maximum amplitude in the inner region of the loop, between the footpoints. QPPs with period P≈20 s are localized at the periphery of the loop, mainly in the outer parts of the footpoints. The spatial distribution of oscillations with period about P≈10 s contains three regions of high QPP amplitudes: two near the footpoints and one in the middle of the flaring region. It is shown that the observed properties of the spectral components are most accurately described by the fundamental, second, and third harmonics of the kink mode standing waves. This is the first identification of the kink mode in flare loops which is based on strict limitations derived from data on the spatial structure of a pulsating flare region.     

A model of solar flares triggered by interactions between force-free current loops and plasmoids

We present a model of solar flares triggered by collisions between current loops and plasmoids. We investigate a collision process between a force-free current loop and a plasmoid, by using 3-D resistive MHD code. It is shown that a current system can be induced in the front of a plasmoid, when it approaches a force-free current loop. This secondary current produced in the front of the plasmoid separates from the plasmoid and coalesces to the force-free current loop associated with the magnetic reconnection. The core of the plasmoid stays outside the reconnection region, maintaining high density. The core can be confined by the current system produced around the plasmoid. This collison process between a current loop and a plasmoid may explain the triggering of solar flares observed byYohkoh.     

耦合热传导的磁重联的数值模拟

磁重联被认为是太阳耀斑的产生机制,本文数值模拟在日冕中发生在磁重联过程,结果表明耀斑环的表观运动是磁重联的自洽结果;由重联点发出的慢激波对耀斑环的加热有贡献;耀斑环的上升并不意味着重联点的上升。     

MHD equilibrium and stability properties of a bipolar current loop

A study is made of equilibrium and stability properties of a semi-toroidal current loop imbedded in a high temperature plasma. The loop carries a toroidal current density J _t and poloidal current density J _p. By explicity including the global curvature of the loop, the net Lorentz and pressure forces acting along the major radius are calculated. Requirement of equilibrium force-balance gives rise to conditions that must be satisfied by the physical parameters and geometry. On the basis of these conditions, we deduce a class of equilibrium semi-toroidal current loops satisfying c ^#X2212;1 J × B ? ▽p = 0. It is found that the averge pressure inside the loop is less than the ambient coronal pressure in equilibrium. Furthermore, this class of equilibria is shown to be stable to a number of destructive MHD modes. The theoretical results are discussed in the context of solar bipolar current loops.     

On the location of energy release and temperature profiles along coronal loops

Several mechanisms have been suggested to contribute to the heating of the solar corona, each of which deposits energy along coronal loops in a characteristic way. To compare the theoretical models with observations one has to derive observable quantities from the models. One such parameter is the temperature profile along a loop. Here numerical experiments of flux braiding are used to provide the spatial distribution of energy deposition along a loop. It is found that braiding produces a heat distribution along the loop which has slight peaks near the footpoints and summit and whose magnitude depends on the driving time. Using different examples of the heat deposition, the temperature profiles along the loop are determined assuming a steady state. Along with this, different methods for providing average temperature profiles from the time-series have been investigated. These give summit temperatures within approximately 10% of each other. The distribution of the heating has a significant impact on both the summit temperature and the temperature distribution along the loop. In each case the ratio between the heat deposited and radiation provides a scaling for the summit temperature.     

Electron acceleration by electric fields near the footpoints of current-carrying coronal magnetic loops

We analyze the electric fields that arise at the footpoints of a coronal magnetic loop from the interaction between a convective flow of partially ionized plasma and the magnetic field of the loop. Such a situation can take place when the loop footpoints are at the nodes of several supergranulation cells. In this case, the neutral component of the converging convective flows entrain electrons and ions in different ways, because these are magnetized differently. As a result, a charge-separating electric field emerges at the loop footpoints, which can efficiently accelerate particles inside the magnetic loop under appropriate conditions. We consider two acceleration regimes: impulsive (as applied to simple loop flares) and pulsating (as applied to solar and stellar radio pulsations). We have calculated the fluxes of accelerated electrons and their characteristic energies. We discuss the role of the return current when dense beams of accelerated particles are injected into the corona. The results obtained are considered in light of the currently available data on the corpuscular radiation from solar flares.     

MICROWAVE EMISSION FROM CORONAL HEIGHTS: STUDY OF A NON-THERMAL RADIO FLARE

Two small radio flares following the great gamma-ray burst on 11 June 1991 are studied. We analyse the different association of emission features at microwaves, decimeter waves, and soft and hard X-rays for the events. The first flare has well-defined emission features in microwaves and soft and hard X-rays, and a faint decimetric signature well after the hard X-ray burst. It is not certain if the decimetric event is connected to the burst features. The second event is characterized by an almost simultaneous appearance of hard X-ray burst maxima and decimetric narrowband drift bursts, but soft X-ray emission is missing from the event. With the exception of the possibility that the soft X-ray emission is absorbed along the way, the following models can explain the reported differences in the second event: (1) Microwave emission in the second event is produced by 150 keV electrons spiraling in the magnetic field relatively low in the corona, while the hard X-ray emission is produced at the beginning of the burst near the loop top as thick-target emission. If the bulk of electrons entered the loop, the low-energy electrons would not be effectively mirrored and would eventually hit the footpoints and cause soft X-ray emission by evaporation, which was not observed. The collisions at the loop top would not produce observable plasma heating. The observed decimetric type III bursts could be created by plasma oscillations caused by electron beams traveling along the magnetic field lines at low coronal heights. (2) Microwave emission is caused by electrons with MeV energies trapped in the large magnetic loops, and the electrons are effectively mirrored from the loop footpoints. The hard X-ray emission can come both from the loop top and the loop footpoints as the accelerated lower energy electrons are not mirrored. The low-energy electrons are not, however, sufficient to create observable soft X-ray emission. The type III emission in this case could be formed either at low coronal heights or in local thick regions in the large loops, high in the corona.     

Modeling Images and Spectra of a Solar Flare Observed by RHESSI on 20 February 2002

We have analyzed a C7.5 limb flare observed by RHESSI on 20 February 2002. The RHESSI images appear to show two footpoints and a loop-top source. Our goal was to determine if the data are consistent with a simple steady-state model in which high-energy electrons are continuously injected at the top of a semicircular flare loop. A comparison of the RHESSI images with simulated images from the model has made it possible for us to identify spurious sources and fluxes in the RHESSI images. We find that the RHESSI results are in many aspects consistent with the model if a thermal source is included between the loop footpoints, but there is a problem with the spectral index of the loop-top source. The thermal source between the footpoints is likely to be a low-lying loop interacting with the northern footpoint of a higher loop containing the loop-top source.     

The rotation of magnetic loop systems in the solar atmosphere

Eclipse photographs indicate that large regions of the inner solar corona are confined in various types of closed magnetic configurations and, as a result, do not participate in the general solar wind expansion. In this paper, the rotation of initially poloidal loop configurations of this type, as influenced by differential rotation of the footpoints, is investigated. The analysis is restricted to axially symmetric fields and it is assumed that the toroidal magnetic field induced by differential rotation is small as compared to the initial poloidal field. This restricts the validity of the analysis to times less than about one month.The most interesting physical situation is that of flux tubes existing in one solar hemisphere only, one end of the tube being fixed in the photosphere at a higher latitude than the other. As a consequence, the lower end of the tube rotates at a faster rate than the upper end. Solution of the pertinent equations reveals that the angular velocity measured along a field line increases monotonically from its value at the poleward footpoint to that at the lower footpoint. The variation of angular velocity along the field depends upon the field geometry only and is not directly related to the variation of angular velocity along the solar surface between the footpoints. Depending upon the field configuration, both outward radial increases and decreases are possible. Using the Newton and Nunn model for the surface differential rotation rate, the angular velocity distribution on two particularly simple types of closed magnetic loop systems is determined analytically. It is shown that the angular velocity increases outward in the polar regions but decreases outward near the equator - leading to a decrease in differential rotation with height.The National Center for Atmospheric Research is sponsored by the National Science Foundation.     

Heating of chromospheric magnetic features by direct current dissipation

It is shown that the direct current dissipation is very unlikely to be the heat source of the coronal loop, because it accompanies unacceptably high heating rate in the chromospheric portion of the loop. This also suggests that a rather weak current density can supply the heat to a small (R < 10⁷ cm) chromospheric magnetic features. A larger magnetic element may be heated by the direct current dissipation only if the current changes directions within a single element so that the generated magnetic field is sufficiently weak to insure MHD stability.     

Dynamical interpretation of the very hot region appearing at the top of the loop

In order to explain the appearance of a hard X-ray source at the top of a loop, we present a model in which the dynamical effects of the dark filament mass infallng along the loop in association with the “disparition brusque” plays an important role. The crash of the infalling mass produces high temperature regions in the low corona above the two footpoints of the loop, and the up-going shocks, created in the crash and strengthened in propagating upwards along the steep density gradient in the tail of the infalling mass, produce a very high temperature (10⁸ K) region upon colliding with each other near the top of the loop. Successive occurrence of this process in successively higher loops in magnetic arcade may account for the sources of gradual hard X-ray bursts appearing at the top of the loop-like structure.     

Thermal equilibria of coronal magnetic arcades

A coronal magnetic arcade can be thought of as consisting of an assembly of coronal loops. By solving equations of thermal equilibrium along each loop and assuming a base temperature of 2 × 10⁴ K, the thermal structure of the arcade can be found. By assuming a form for the plasma pressure in the arcade, the possible thermal structures can be shown to depend on three parameters. Arcades can contain hot loops with summits hotter than 400 000 K, cool loops at temperatures less than 80 000 K along their lengths, hot-cool loops with cool summits and cool footpoints but hotter intermediate portions, and warm loops, cooler than 80 000 K along most of their lengths but with summits as hot as 400 000 K. For certain arcades, there exist regions where more than one kind of loop is possible. If the parameters describing the arcade are varied, it is possible for non-equilibrium to occur when a type of solution ceases to exist. For example, hot or warm loops can cease to exist so that only cool solutions are possible when the arcade size or pressure is decreased, while warm or cool loops may give way to hot-cool loops when the heating is reduced or the pressure is increased.     

Flow in coronal loops with a mass source

This research studies the flow of plasma inside a coronal loop in which an injection of plasma through the lateral surface is permitted. The flow is assumed steady and polytropic. The problem covers two cases: (a) upflow at one footpoint, downflow at the other; (b) downflow at both footpoints. The first case can be shown to be quite similar to that of a mass-conserving flow with variable cross section; the second, instead, is characterized by solutions with a different type of topology; its main new feature is the obvious fact that all the solutions pass through a single point going from negative to positive velocities. In this second case the density ratio between footpoints and top can be much smaller than in a mass conserving flow. This can explain some properties of observed loops.     

Determination of the True Shape of Coronal Loops

Using line of sight velocity measurements from the SUMER and CDS instruments aboard SOHO, in conjunction with a simple geometrical model, we reconstructed the true, 3D shape and the velocity of plasma flow along coronal loops. The projection of the loop on the sky and the position of the footpoints define a family of curves. Assuming that the loop is located on a plane, the line of sight velocity can be used to select the most plausible solution. For two loops, observed in the Ne viii? 770 Å and O v? 630 Å spectral lines, we find asymmetric, subsonic uni-directional flows, with velocity maxima of ≈?80 km?s^?1 near the footpoints. The loops are highly inclined with respect to the vertical, by 55^○ and 70^○, respectively; thus the true height of the loop tops from the photospheric level is ≈?20^′′, comparable to the isothermal scale height.     

The magnetic non-equilibrium of buoyant flux tubes in the solar corona

The equilibrium shape of a slender flux tube in the stratified solar atmosphere is studied. The path is determined by a balance between the downwards magnetic tension, which depends on the curvature of the loop, and the upwards buoyancy force. Previous results for untwisted slender tubes are extended to include twisted tubes embedded in an external magnetic field.The path of an untwisted tube in an atmosphere with an ambient magnetic field is calculated. For a given footpoint separation, the height of the tube is lowered by increasing the strength of the external magnetic field. If the footpoints are slowly moved apart, the tube rises, until a threshold separation is reached beyond which there is no possible equilibrium height. This threshold width does not depend on the strength of the external field.The effects of twisting up a curved loop are studied, using an extension of results obtained for slender curved tubes with a straight axis. It is shown that for a twisted tube of given width, there can be two possible values of the equilibrium height. If, however, the tube is twisted more than a certain amount or if the footpoints are too widely separated there is no equilibrium. The critical footpoint separation for non-equilibrium is smaller for a twisted tube that an untwisted one.Twisting a tube or moving its feet apart is thus likely to result in non-equilibrium, causing the tube to rise indefinitely under the influence of the unbalanced buoyant force. It is suggested that this phenomenon could be important in the preflare stage of a large two-ribbon solar flare, by causing the initial slow rise of an active region filament. As well as being involved in the onset of an erupting prominence, this non-equilibrium may also be relevant to the formation of coronal loop transients.     

Hard X-ray characteristics of solar flares using electron Monte-Carlo calculations and beamed thick target model

The experimental results of X-ray bursts with spectral characteristics, spatial distribution, fast time variations, polarization, and directivity measurements carried out with Intercosmos, PVO/ISEE-3 spacecrafts, imaging instrument observations of Hard X-ray (HXIS) and Hard X-ray Burst Spectrometers (HXRBS) during solar maximum mission have been reviewed. The observed results about the above characteristics are discussed in detail in terms of non-thermal and thermal models. It is shown that the results can be interpreted in terms of beamed thick-target model in which electrons stream down to the loop footpoints and produce hard X-rays through electron-ion bremsstrahlung.     

Thermal equilibria of coronal magnetic loops with non-constant cross-sectional area

Equations of thermal equilibrium along coronal loops are solved in the absence of gravity but where the cross-sectional area changes along the loop. The footpoint temperature is assumed to be 2 × 10⁴ K. Several fundamental types of solution are found, namely hot loops, cool loops, hot-cool loops (where the footpoints and summits are cool but the intermediate parts are hotter) and warm loops (cool along most of their lengths except the summits). On increasing the cross-sectional area the summit temperature generally increases slightly except for warm loops where no increase in temperature is recorded and hot-cool loops where a dramatic increase in summit temperature may occur. The cool and hot-cool loops may model elementary fibril structures within prominences.     

1986年2月4日太阳耀斑的演化研究

本文根据乌鲁木齐天文站的H_α耀斑及3.2cm射电流量观侧资料、云南天文台的黑子精细结构照相和Marshall Space Flight Center的向量磁场图,对1986年2月4日的六个耀斑的形态相关及演化联系,特别是0736UT 4B/3X大耀斑的发展过程进行了综合分析。主要结果是: 1.4日大耀斑的初始亮点和闪光相的主要形态演化,与活动区中沿中性线新浮现的强大电流/磁环系密切相关。后者的主要标志是沿中性线的长的剪切半影纤维及它两端的偶极旋涡黑子群(1_3F_3)。 2.上述大耀斑与1972年8月4日0624 UT大耀斑爆发的磁场背景及主要形态特征相似,表明两者的储能和触发机制可能相同。 3.大耀斑爆发的H_α初始亮点,双带出现,环系形成,亮物质抛射和吸收冕珥等现象同3.2cm射电流量的变化在时间上有较好的对应关系。 4.重复性的前期小耀斑爆发位置和发展趋势与大耀斑的主要形态及演化特征相似。它们相对于剪切的纵场中性线两侧的位置相近或相同。因而,可以看作上述强大电流/磁环系不稳性发展过程中的前置小爆发。