Catastrophe of Coronal Magnetic Flux Ropes Caused by Photospheric Motions

Using a 2.5-D, time-dependent ideal MHD model in Cartesian coordinates, we carried out numerical simulations to investigate the equilibrium and evolution properties of a magnetic configuration that consists of a coronal magnetic flux rope and a partly open photospheric background field, which is equivalent to that produced by a two-patch magnetic source on the photospheric surface. The axial and annular magnetic fluxes of the flux rope are given and fixed. The global magnetic configuration evolves in response to three types of changes of the background field: decreasing of the distance between the two sources, shrinking of the size of each source, and increasing of the shear in the closed component of the background field. As a result, the geometrical parameters of the flux rope, i.e. the height of the rope axis, the half-width of the rope and the length of the vertical current sheet below the rope, change due to the variation of the background field. It is shown that for a given coronal magnetic flux rope in a partly open background field, the variation of the geometrical parameters of the flux rope displays a catastrophic behavior, namely, there exists a critical point for each case, at which an infinitesimal change of the background field leads to a loss of equilibrium, and thus a jump of the flux rope. The implication of such a catastrophe in solar active phenomena is briefly discussed.     

The Coronal Emission of Photospheric Magnetic Fragments

This paper examines the relationship between magnetic dipoles in the photosphere and X-ray bright points (XBPs) in the corona, using an XBP special campaign dataset obtained by the Yohkoh SXT and the NSO/Kitt Peak magnetograph. We find that for the cases where a simple dipole exists in the photosphere, the condition that they are separated by a distance less than the interaction distance defined by Longcope1998 is favorable for an XBP to be observed. For the cases where the magnetic topology is more complicated due to the addition of an extra fragment, we find that the geometry of the magnetic fragments is a major factor that determines if an XBP is observed. XBPs are more likely to be formed above magnetic fragments arranged in such a way that photospheric motions giving rise to reconnection between any two fragments will also give rise to reconnection with the remaining fragment.     

Numerical Simulations of the Flux Tube Tectonics Model for Coronal Heating

In this paper we present results from 3D MHD numerical simulations based on the flux tube tectonics method of coronal heating proposed by Priest, Heyvaerts, and Title (2002). They suggested that individual coronal loops connect to the photosphere in many different magnetic flux fragments and that separatrix surfaces exist between the fingers connecting a loop to the photosphere and between individual loops. Simple lateral motions of the flux fragments could then cause currents to concentrate along the separatrices which may then drive reconnection contributing to coronal heating. Here we have taken a simple configuration with four flux patches on the top and bottom of the numerical domain and a small background axial field. Then we move two of the flux patches on the base between the other two using periodic boundary conditions such that when they leave the box they re-enter it at the other end. This simple motion soon causes current sheets to build up along the quasi-separatrix layers and subsequently magnetic diffusion/reconnection occurs.     

太阳光球磁通量南北不对称性研究

运用统计方法系统研究了1978-2002年太阳光球磁通量南北不对称性变化特征，发现其与太阳活动周有关．不对称值在太阳活动极小年要明显高于太阳活动极大年，并且磁通量变化总是由上升段的北半球占优逐渐过渡到下降段的南半球占优．另外运用小波变换方法详细讨论了这种不对称性变化可能存在的周期信息．     

Formation of Intensive Magnetic Flux Tubes in a Converging Flow of Partially Ionized Solar Photospheric Plasma

Theoretical model, explaining a phenomenon of formation of Intensive Magnetic Flux Tube (IMFT) in a converging flow of partially ionized solar photospheric plasma is considered. Special attention is paid to the fact of weak ionization (n/n _n ∼ 10^-4) of plasma in the photosphere. The cases of 2D magnetic slab and cylindric magnetic tube are considered. It was shown that in a converging flow of photospheric plasma thin magnetic tubes, or slabs with the characteristic scale L ₀ ∼ (1 ÷ 5) ċ 10⁷ cm and magnetic field 1000 ÷ 2000 G can be generated. By this 2D magnetic slabs could be unstable with respect to an exchange instability and appear as an intermediate step during IMFT formation on the boundary of two supergranulation cells. Formation of compact strong magnetic field structures, and their energy balance are discussed. Stationary Joule energy dissipation taking place on the photospheric levels in the models of magnetic slab or IMFT under consideration increases towards the periphery of these objects and can exceed radiation looses. This can cause the occurrence of magnetic tubes with hot external envelopes, and modification of plasma temperature and density distribution, with respect to ones in a quiet atmosphere. This revised version was published online in July 2006 with corrections to the Cover Date.     

An Evolving Synoptic Magnetic Flux map and Implications for the Distribution of Photospheric Magnetic Flux

We describe a procedure intended to produce accurate daily estimates of the magnetic flux distribution on the entire solar surface. Models of differential rotation, meridional flow, supergranulation, and the random emergence of background flux elements are used to regularly update unobserved or poorly observed portions of an initial traditional magnetic synoptic map that acts as a seed. Fresh observations replace model estimates when available. Application of these surface magnetic transport models gives us new insight into the distribution and evolution of magnetic flux on the Sun, especially at the poles where canopy effects, limited spatial resolution, and foreshortening result in poor measurements. We find that meridional circulation has a considerable effect on the distribution of polar magnetic fields. We present a modeled polar field distribution as well as time series of the difference between the northern and southern polar magnetic flux; this flux imbalance is related to the heliospheric current sheet tilt. We also estimate that the amount of new background magnetic flux needed to sustain the `quiet-Sun' magnetic field is about 1.1×10²³ Mx d^–1 (equivalent to several large active regions) at the spatial resolution and epoch of our maps. We comment on the diffusive properties of supergranules, ephemeral regions, and intranetwork flux. The maps are available on the NSO World Wide Web page.     

Latent Heating of Coronal Loops

This paper is aimed at establishing the relationship between the large-scale magnetic fields (LSMF), coronal holes (CH), and active regions (AR) in the Sun. The LSMF structure was analyzed by calculating the vector photospheric magnetic field under a potential approximation. Synoptic maps were drawn to study the distribution of the B field component and to isolate regions where the open field lines of the unipolar magnetic field are most radial. These are the sites of occurrence of X-ray and Hei 10830 Å coronal holes detected from the SXT/Yohkoh images. It is shown that coronal holes are usually located in LSMF regions with a typical pattern of divergentB vectors and a so-called saddle configuration.B vectors from the conjugate (spaced by 90°) coronal holes converge towards the active regions between CH. Variations in AR distort coronal holes and change their boundaries. This implies that the energy regime in CH depends on the energy supply from the active region. The LSMF structure is more stable than coronal holes, remaining practically unchanged during tens of rotations of the Sun. Thus, a peculiar magnetically coupled system of LSMF/CH/AR has been revealed. A model has been suggested to describe the interaction of the emerging toroids in the convection zone and in the photosphere. The cellular convection, that develops at the center of the toroids, is responsible for the occurrence of active regions. The model qualitatively describes the observed particularities of the LSMF/CH/AR system.     

The Parker Problem and the Theory of Coronal Heating

To illustrate his theory of coronal heating, Parker initially considers the problem of disturbing a homogeneous vertical magnetic field that is line-tied across two infinite horizontal surfaces. It is argued that, in the absence of resistive effects, any perturbed equilibrium must be independent of z. As a result random footpoint perturbations give rise to magnetic singularities, which generate strong Ohmic heating in the case of resistive plasmas. More recently these ideas have been formalized in terms of a magneto-static theorem but no formal proof has been provided. In this paper we investigate the Parker hypothesis by formulating the problem in terms of the fluid displacement. We find that, contrary to Parker's assertion, well-defined solutions for arbitrary compressibility can be constructed which possess non-trivial z-dependence. In particular, an analytic treatment shows that small-amplitude Fourier disturbances violate the symmetry ∂_z = 0 for both compact and non-compact regions of the (x, y) plane. Magnetic relaxation experiments at various levels of gas pressure confirm the existence and stability of the Fourier mode solutions. More general footpoint displacements that include appreciable shear and twist are also shown to relax to well-defined non-singular equilibria. The implications for Parker's theory of coronal heating are discussed.     

Photospheric Injection of Magnetic Helicity: Connectivity-Based Flux Density Method

Magnetic helicity quantifies the degree to which the magnetic field in a volume is globally sheared and/or twisted. This quantity is believed to play a key role in solar activity due to its conservation property. Helicity is continuously injected into the corona during the evolution of active regions (ARs). To better understand and quantify the role of magnetic helicity in solar activity, the distribution of magnetic helicity flux in ARs needs to be studied. The helicity distribution can be computed from the temporal evolution of photospheric magnetograms of ARs such as the ones provided by SDO/HMI and Hinode/SOT. Most recent analyses of photospheric helicity flux derived a proxy to the helicity-flux density based on the relative rotation rate of photospheric magnetic footpoints. Although this proxy allows a good estimate of the photospheric helicity flux, it is still not a true helicity flux density because it does not take into account the connectivity of the magnetic field lines. For the first time, we implement a helicity density that takes this connectivity into account. To use it for future observational studies, we tested the method and its precision on several types of models involving different patterns of helicity injection. We also tested it on more complex configurations – from magnetohydrodynamics (MHD) simulations – containing quasi-separatrix layers. We demonstrate that this connectivity-based proxy is best-suited to map the true distribution of photospheric helicity injection.     

细磁通量管运动的特征

从细磁通量管运动方程组导出了特征速度、特征线及其相容关系。这些结果是用特征线法研究细磁通量管运动的基础，也是正确提出定解问题的依据。表征细磁通量管横向波传播的特征速度与管内流动的ＡｌｆｖｅｎＭａｃｈ数有关。当管内流速超过ｋｅｌｖｉｎ－Ｈｅｌｍｈｏｌｔｚ不稳定性临界值时，不存在横向波模式。     

Scaling Law for the Heating of Solar Coronal Loops

We report preliminary results from a series of numerical simulations of the reduced magnetohydrodynamic equations used to describe the dynamics of magnetic loops in active regions of the solar corona. A stationary velocity field is applied at the photospheric boundaries to imitate the driving action of granule motions. A turbulent stationary regime is reached, characterized by a broadband power spectrum Ek approximately k-3&solm0;2 and heating rate levels compatible with the energy requirements of active region loops. A dimensional analysis of the equations indicates that their solutions are determined by two dimensionless parameters: the Reynolds number and the ratio between the Alfvén time and the photospheric turnover time. From a series of simulations for different values of this ratio, we determine how the heating rate scales with the physical parameters of the problem, which might be useful for an observational test of this model.     

Observational Evidence for Rising Penumbral Flux Tubes?

On 13 May 2000 parts of a penumbra were observed in an active region NOAA 8990 with the La Palma Stokes Polarimeter attached to the Swedish Vacuum Solar Telescope. The stratification over the solar atmosphere of different physical parameters is retrieved from these data by using the Stokes inversion based on response functions. The results confirm the previous findings of the penumbral structure. In general, the magnetic field becomes weaker and more horizontal with increasing distance from the umbra and the line-of-sight velocities are increasing towards the outer boundary of the penumbra. The results also suggest the existence of the unresolved fine structure of the penumbra. The stratifications of the temperature and of the magnetic field strength indicate the presence of rising flux tubes, which were predicted theoretically by Schlichenmaier, Jahn and Schmidt (1998, Astron. Astrophys. 337, 897).     

On Analysis of Dual Spacecraft Stereoscopic Observations to Determine the Three-Dimensional Morphology and Plasma Properties of Solar Coronal Flux Tubes

By using two spacecraft equipped with multi-bandpass X-ray telescopes, it is possible to obtain direct 3-dimensional morphology of coronal structures which is essential for understanding the energetics and dynamics of the solar atmosphere. X-ray observations taken only in orbit about the Earth are inadequate to fully resolve the 3-dimensional nature of the solar corona. These Earth-orbit observations produce 2-dimensional images and an appropriate model must be included to derive the 3-dimensional structures from the line-of-sight information. Stereoscopic observations from space will remove this limitation and are needed if we are to improve our knowledge of the 3-dimensional morphology of the corona.Several important points regarding a stereoscopic mission are investigated and illustrated using model coronal flux tubes and image-rendering techniques. Synthesized images are formed by integrating the emission from volume elements along the line-of-sight path through a 3-dimensional volume in which a set of model flux tubes are located. The flux tubes are defined by (1) a plasma model defining the emissivity for a specific density, temperature, and pressure distribution, and (2) a magnetic field model from which a set of field lines are selected to define the geometry of the flux tubes. The field lines are used to define the flux-tube volume by assuming an initial base radius and conservation of flux. An effective instrumental spectral-response function is folded into the integration. Analysis of pairs of these synthesized images with various angular perspectives are used to investigate the effect of angular separation on mission objectives. The resulting images and analysis provide guidelines for developing a stereoscopic mission.Our study produced four important results, namely: (1) An angular separation of 30 degrees maximizes the scientific return by direct triangulation analysis because of the tradeoff between increased line-of-sight resolution of position and decreased recognition of individual loop structures arising from the overlapping of multiple loops with increasing angular separation. (2) The analysis benefits from the use of time-differential images to select flux tubes from the collection of numerous overlapping systems by selecting only recently heated or cooled flux tubes. (3) An analysis needs to be developed for algebraic reconstruction techniques applying a priori information, specific to the solar coronal structures, i.e., flux-tube continuity, maximum emission strength, non-negative emission, previous history, and maximum gradients of emission. (4) An analysis strategy combining triangulation, modeling techniques, and algebraic restoration is necessary to derive a complete understanding of the 3-dimensional morphology of the magnetic field. In the same way that helioseismology is classical viewing of the Sun with a tailored set of analysis tools for probing the interior of the Sun, heliostereoscopy is classical viewing of the X-ray emitting corona and requires a tailored set of analysis tools to deduce the true 3-dimensional structure of the corona.     

Magnetic Null Points due to Multiple Sources of Solar Photospheric Flux

How common are magnetic null points in the highly complex magnetic field of the solar atmosphere? In this work we seek to model the magnetic structure of quiet regions by placing magnetic sources and sinks on a hexagonal network of supergranule cells to represent the intense magnetic fields that occur at the boundaries of these cells. The resulting potential coronal magnetic field is then computed analytically and searched numerically for magnetic null points, which are classified according to their types and spine directions. Two relations from the theory of vector fields relate the numbers of null points to the numbers of sources and sinks and these are used to check the numerical results. Previous results relating these quantities for monopolar and dipolar magnetic fields are described and a new one for a particular class of quadrupolar fields arising in this study is derived. We model a three-cell configuration and study the effects of increasing the strength of a central sink and of moving the central sink. A twelve-cell configuration is studied in lesser detail.

     

色球和日冕的MHD加热机制

扼要地介绍了色球和日冕加热问题的研究历史。随着空间太阳观测技术的进步，人们认识到色球和日冕加热机制主要与MHD过程有关。因此，在本文中着重介绍四种MHD色球和日冕加热机制：（1）阿尔芬波；（2）MHD湍动；（3）场向电流；（4）磁重联。由于这四种加热机制的有效性都需要通过高分辨率观测来判定，所以空间太阳观测对于研究色球和日冕加热问题具有重大意义。     

Catastrophic Behavior of Multiple Coronal Flux Rope System

A major solar active event called Bastille Day Event occurred in AR 9077 on July 14, 2000. Simultaneous occurrence of a filament eruption, a flare and a coronal mass ejection was observed in this event. Previous analyses of this event show that before the event, there existed an activation and eruption of a huge trans-equatorial filament, which might play a crucial role in triggering the Bastille Day event. This implies that independent flux systems are closely related to and affect each other, which has encouraged us to investigate the catastrophic behavior of a multiple coronal flux rope system with the use of a 2.5-D time-dependent MHD model. A force-free field that contains three separate coronal flux ropes is taken to be the initial state. Starting from this state, we increase either the annular or the axial flux of a certain flux rope to examine the catastrophic behavior of the system in two regimes, the ideal MHD regime and the resistive MHD regime. It is found that a catastrophe occurs if the flux exceeds a certain critical value, or the magnetic energy of the system exceeds a certain threshold: the rope of interest breaks away from the base and escapes to infinity, leaving a current sheet below. Moreover, the destiny of the remainder flux ropes relies on whether reconnection takes place across the current sheet. In the ideal MHD regime, i.e., in the absence of reconnection, these ropes remain to be attached to the base in equilibrium, whereas in the resistive MHD regime they abruptly erupt upward during reconnection and escape to infinity. Reconnection causes the field lines to close back to the base and thus changes the background field outside the attached flux ropes in such a way that the constraint on these ropes is substantially relaxed and the corresponding catastrophic energy threshold is reduced accordingly, leading to a catastrophic eruption of these ropes. Since magnetic reconnection is generally inevitable when a current sheet forms and develops through an eruption of one flux rope, the eruption of this flux rope must lead to an eruption of the others. This provides an example to demonstrate the interaction between several independent magnetic flux systems in different regions, as implied by the Bastille Day event, and may serve as a possible mechanism for sympathetic events occurring on the Sun.     

Parameters of the Magnetic Flux inside Coronal Holes

The parameters of the magnetic flux distribution inside low-latitude coronal holes (CHs) were analyzed. A statistical study of 44 CHs based on Solar and Heliospheric Observatory (SOHO)/MDI full disk magnetograms and SOHO/EIT 284?Å images showed that the density of the net magnetic flux, B _net, does not correlate with the associated solar wind speeds, V _x . Both the area and net flux of CHs correlate with the solar wind speed and the corresponding spatial Pearson correlation coefficients are 0.75 and 0.71, respectively. A possible explanation for the low correlation between B _net and V _x is proposed. The observed non-correlation might be rooted in the structural complexity of the magnetic field. As a measure of the complexity of the magnetic field, the filling factor, f(r), was calculated as a function of spatial scales. In CHs, f(r) was found to be nearly constant at scales above 2 Mm, which indicates a monofractal structural organization and smooth temporal evolution. The magnitude of the filling factor is 0.04 from the Hinode SOT/SP data and 0.07 from the MDI/HR data. The Hinode data show that at scales smaller than 2 Mm, the filling factor decreases rapidly, which means a multifractal structure and highly intermittent, burst-like energy release regime. The absence of the necessary complexity in CH magnetic fields at scales above 2 Mm seems to be the most plausible reason why the net magnetic flux density does not seem to be related to the solar wind speed: the energy release dynamics, needed for solar wind acceleration, appears to occur at small scales below 1 Mm.     

An Impulsive Heating Model for the Evolution of Coronal Loops

It was suggested by Parker that the solar corona is heated by many small energy release events generally called microflares or nanoflares. More and more observations showed flows and intensity variations in nonflaring loops. Both theories and observations have indicated that the heating of coronal loops should actually be unsteady. Using SOLFTM (Solar Flux Tube Model), we investigate the hydrodynamics of coronal loops undergoing different manners of impulsive heating with the same total energy deposition. The half length of the loops is 110 Mm, a typical length of active region loops. We divide the loops into two categories: loops that experience catastrophic cooling and loops that do not. It is found that when the nanoflare heating sources are in the coronal part, the loops are in non-catastrophic-cooling state and their evolutions are similar. When the heating is localized below the transition region, the loops evolve in quite different ways. It is shown that with increasing number of heating pulses and inter-pulse time, the catastrophic cooling is weakened, delayed, or even disappears altogether.     

Numerical Solutions of Three-Dimensional Pressure-Bounded Magnetohydrostatic Flux Tubes

We present a three-dimensional technique for the solution of the magnetohydrostatic equations when we are modeling structures bounded by a current sheet that is free to move to satisfy pressure balance. The magnetic field is expressed in terms of Euler potentials and the equations are transformed to flux coordinates, greatly simplifying the problem of locating the free boundary. Multi-grid techniques are used to rapidly solve the resulting nonlinear elliptic partial differential equations. The method is tested against Low's (1982) exact solution of a bipolar plasma loop. It is shown that fast, accurate solutions can be found.