Coronal Magnetic Flux Rope Equilibria and Magnetic Helicity

1 INTRODUCTIONObservations show that the magnetic helicity of solar magnetic structures has a predominantsign in each hemisphere of the Sun, positive in the southern hemisphere and negative in thenorthern, regardless of the solar cycle (Rust, 1994). The magnetic helicity is strictly conservedin the frame of ideal MHD (WOltjer, 1958), and approximately conserved in the presence ofresistive dissipation and magnetic reconnection in a highly conductive plajsma (Taylor, 1974;Berger, 1984; H…     

A New Method of Identifying 3D Null Points in Solar Vector Magnetic Fields

Employing the Poincare index of isolated null-points in a vector field, we worked out a mathematical method of searching for 3D null-points in coronal magnetic fields. After introducing the relevant differential topology, we test the method by using the analytical model of Brown & Priest. The location of null-point identified by our method coincides precisely with the analytical solution. Finally we apply the method to the 3D coronal magnetic fields reconstructed from an observed MDI magnetogram of a super-active region (NOAA 10488). We find that the 3D null-point seems to be a key element in the magnetic topology associated with flare occurrence.     

Determination of the Topology Skeleton of Magnetic Fields in a Solar Active Region

Magnetic topology has been a key to the understanding of magnetic energy re-lease mechanism. Based on observed vector magnetograms, we have determined the three-dimensional (3D) topology skeleton of the magnetic fields in the active region NOAA 10720.The skeleton consists of six 3D magnetic nulls and a network of corresponding spines, fans,and null-null lines. For the first time, we have identified a spiral magnetic null in Sun's corona.The magnetic lines of force twisted around the spine of the null, forming a 'magnetic wreath'with excess of free magnetic energy and resembling observed brightening structures at extra-ultraviolet (EUV) wavebands. We found clear evidence of topology eruptions which are re-ferred to as catastrophic changes of topology skeleton associated with a coronal mass ejection(CME) and an explosive X-ray flare. These results shed new lights on the structural complex-ity and its role in explosive magnetic activity. The concept of flux rope has been widely used in modelling explosive magnetic activity, although their observational identity is rather ob-scure or, at least, lacking of necessary details up to date. We suggest that the magnetic wreath associated with the 3D spiral null is likely an important class of the physical entity of flux ropes.     

Distribution of Helical Properties of Solar Magnetic Fields

We summarize studies of helical properties of solar magnetic fields such as current helicity and twist of magnetic fields in solar active regions (ARs), that are observational tracers of the alpha-effect in the solar convective zone (SCZ). Information on their spatial distribution is obtained by analysis of systematic mag-netographic observations of active regions taken at Huairou Solar Observing Station of National Astronomical Observatories of Chinese Academy of Sciences. The main property is that the tracers of the alpha-effect are antisymmetric about the solar equator. Identifying longitudinal migration of active regions with their individual rotation rates and taking into account the internal differential rotation law within the SCZ known from helioseismology, we deduce the distribution of the effect over depth. We have found evidence that the alpha-effect changes its value and sign near the bottom of the SCZ, and this is in accord with the theoretical studies and numerical simulations. We discuss     

Coronal Mass Ejections,Magnetic Fields,and the Green Corona in Cycle 23

We study a time – latitudinal distribution of CMEs observed by the SOHO spacecraft, their projected speeds and associated magnetic fields, as well as the north – south (N – S) asymmetry of solar surface magnetic fields, and the coronal green line intensities. We have found that (a) there exists an intricate relation between the average projected velocity of CMEs and the mean value of large-scale magnetic fields; (b) there exists a pronounced N – S asymmetry in both the distribution and the number of CMEs; (c) this asymmetry is in favor of the northern hemisphere at the beginning of the cycle, and of the southern hemisphere from 2001 onward, being, in fact, (d) closely related with the N – S asymmetry in the distribution of large-scale magnetic fields and the coronal green line intensities.     

日冕磁场重建方法在研究太阳爆发活动中的应用

太阳是与地球关系最为密切的天体.发生在日面上的剧烈爆发性活动可能对人类的生存环境产生巨大影响甚至是灾难性后果.包含太阳耀斑、暗条爆发和日冕物质抛射在内的太阳爆发活动是同一物理过程的不同表现形式,其能量来源于爆发前储存在日冕中的磁场自由能.因此,了解日冕磁场的3维结构是理解太阳爆发的触发机制以及活动区的稳定性等现象的前提.由于观测技术限制,目前尚无法对日冕磁场进行常规观测,因此发展了多种利用可常规观测的光球磁场来重建日冕磁场的方法.主要评述近10 yr来各种日冕磁场重建方法在研究太阳爆发活动中的应用.     

Transient Coronal Sigmoids and Rotating Erupting Flux Ropes

To determine the relationship between transient coronal (soft X-ray or EUV) sigmoids and erupting flux ropes, we analyse four events in which a transient sigmoid could be associated with a filament whose apex rotates upon eruption and two further events in which the two phenomena were spatially but not temporally coincident. We find the helicity sign of the erupting field and the direction of filament rotation to be consistent with the conversion of twist into writhe under the ideal MHD constraint of helicity conservation, thus supporting our assumption of flux rope topology for the rising filament. For positive (negative) helicity the filament apex rotates clockwise (counterclockwise), consistent with the flux rope taking on a reverse (forward) S shape, which is opposite to that observed for the sigmoid. This result is incompatible with two models for sigmoid formation: one identifying sigmoids with upward arching kink-unstable flux ropes and one identifying sigmoids with a current layer between two oppositely sheared arcades. We find instead that the observations agree well with the model by Titov and Démoulin (Astron. Astrophys. 351, 707, 1999), which identifies transient sigmoids with steepened current layers below rising flux ropes.     

Transequatorial Filament Eruption and Its Link to a Coronal Mass Ejection

We revisit the Bastille Day flare/CME Event of 2000 July 14, and demonstrate that this flare/CME event is not related to only one single active region (AR). Activation and eruption of a huge transequatorial filament are seen to precede the simultaneous filament eruption and flare in the source active region, NOAA AR 9077, and the full halo-CME in the high corona. Evidence of reconfiguration of large-scale magnetic structures related to the event is illustrated by SOHO EIT and Yohkoh SXT observations, as well as, the reconstructed 3D magnetic lines of force based on the force-free assumption. We suggest that the AR filament in AR9077 was connected to the transequatorial filament. The large-scale magnetic composition related to the transequatorial filament and its sheared magnetic arcade appears to be an essential part of the CME parent magnetic structure. Estimations show that the filament-arcade system has enough magnetic helicity to account for the helicity carried by the related CMEs. In addition, rather global magnetic connectivity, covering almost all the visible range in longitude and a huge span in latitude on the Sun, is implied by the Nancay Radioheliograph (NRH) observations. The analysis of the Bastille Day event suggests that although the triggering of a global CME might take place in an AR, a much larger scale magnetic composition seems to be the source of the ejected magnetic flux, helicity and plasma. The Bastille Day event is the first described example in the literature, in which a transequatorial filament activity appears to play a key role in a global CME. Many tens of halo-CME are found to be associated with transequatorial filaments and their magnetic environment.     

Energetics and Propagation of Coronal Mass Ejections in Different Plasma Environments

Based on previous work, we investigate the propagation of CMEs in a more realistic plasma environment than the isothermal atmosphere, and find that it is a slightly faster reconnection for flux ropes to break free. The average Alfven Mach number MA for the inflow into the reconnection site has to be at least 0.013 in order to give a plausible eruption (compared to MA = 0.005 for the isothermal atmosphere). Taking MA = 0.1, we find that the energy output and the electric field induced inside the current sheet match the temporal behavior inferred from the energetic, long duration, CME-associated X-ray events. The results indicate that catastrophic loss of equilibrium in the coronal magnetic field provides the most promising mechanism for major solar eruptions, and that the more energetic the eruption is, the earlier the associated flare peaks. The variation of the output power with the background field strength revealed by our calculations implies the poor correlation between slow CMEs and solar flares. Th     

Coronal Flux Rope Catastrophe in Octapole Magnetic Fields

As demonstrated by many previous studies, a system consisting of an isolated coronal flux rope and a surrounding background magnetic field exhibits a catastrophic behavior. In particular, if the magnetic field of the system is force-free and axisymmetric in spherical geometry, the magnetic energy at the catastrophic point, referred to as the catastrophic energy threshold, is found to be larger than the corresponding partly or fully open field energy. This paper takes an octapole field as the background and introduces a flux rope within the central arcade of the octapole field. A relaxation method based on time-dependent ideal magnetohydrodynamic (MHD) simulations is used to find axisymmetric force-free field solutions in spherical geometry associated with the flux rope system. With respect to an increase of either the annular flux Φ_p or the axial flux Φ_ϕ of the rope, the system exhibits a catastrophic behavior as expected, and the catastrophic energy threshold is larger than that of the corresponding partly open field, in which the central arcade is opened up, but the remainder remains closed. For a given octapole field, the energy threshold depends on either Φ_p or Φ_ϕ at the catastrophic point, and it increases with increasing Φ_p or decreasing Φ_ϕ. On the other hand, the extent to which the central bipolar component of the octapole field is open also affects the energy threshold. These results differ from those for the bipolar background field case, in which the catastrophic energy threshold is almost independent of the magnetic properties of the flux rope at the catastrophic points and the extent to which the background field is open. The reason for such a difference is briefly discussed.     

Milestones in the Observations of Cosmic Magnetic Fields

Magnetic fields are observed everywhere in the universe. In this review, we concentrate on the observational aspects of the magnetic fields of Galactic and extragalactic objects. Readers can follow the milestones in the observations of cosmic magnetic fields obtained from the most important tracers of magnetic fields, namely, the star-light polarization, the Zeeman effect, the rotation measures (RMs, hereafter) of extragalactic radio sources, the pulsar RMs, radio polarization observations, as well as the newly implemented sub-mm and mm polarization capabilities. The magnetic field of the Galaxy was first discovered in 1949 by optical polarization observations. The local magnetic fields within one or two kpc have been well delineated by starlight polarization data. The polarization observations of diffuse Galactic radio background emission in 1962 confirmed unequivocally the existence of a Galactic magnetic field. The bulk of the present information about the magnetic fields in the Galaxy comes from anal     

Magnetic Properties of Metric Noise Storms Associated with Coronal Mass Ejections

Using Nancay Radioheliograph (NRH) imaging observations, combined with SOHO/Michelson Doppler Imager (MDI) magnetogram observations and coronal magnetic field extrapolation, we studied the magnetic nature of metric noise storms that are associated with coronal mass ejections (CMEs). Four events are selected: the events of 2000 July 14, 2001 April 26, 2002 August 16 and 2001 March 28. The identified noise storm sources cover or partially cover the active regions (ARs), but the centers of storm sources are offset from the ARs. Using extrapolated magnetic field lines, we find that the noise storm sources trace the boundary between the open and closed field lines. We demonstrate that the disappearance of noise storm source is followed by the appearance of the burst source. The burst sources spread on the solar disk and their distributions correspond to the extent of the CME in LASCO C2 field of view. All the SOHO/Extreme Ultraviolet Imaging Telescope (EIT) dimmings associ- ated with noise storm sources are located at the periphery of noise storms where the magnetic lines of force were previously closed and low-lying. When the closed field becomes partially or fully open, the basic configurations of noise storm sources are changed, then the noise storm sources are no longer observed. These observations provide the information that the variations of noise storms manifest the restructuring or reconfiguring of the coronal magnetic field.     

Magnetic Flux Imbalance of the Solar and Heliospheric Magnetic Fields

A comparative analysis of solar and heliospheric magnetic fields in terms of their cumulative sums reveals cyclic and long-term changes that appear as a magnetic flux imbalance and alternations of dominant magnetic polarities. The global magnetic flux imbalance of the Sun manifests itself in the solar mean magnetic field (SMMF) signal. The north – south asymmetry of solar activity and the quadrupole mode of the solar magnetic field contribute the most to the observed magnetic flux imbalance. The polarity asymmetry exhibits the Hale magnetic cycle in both the radial and azimuthal components of the interplanetary magnetic field (IMF). Analysis of the cumulative sums of the IMF components clearly reveals cyclic changes in the IMF geometry. The accumulated deviations in the IMF spiral angle from its nominal value also demonstrate long-term changes resulting from a slow increase of the solar wind speed over 1965 – 2006. A predominance of the positive IMF B _z with a significant linear trend in its cumulative signal is interpreted as a manifestation of the relic magnetic field of the Sun. Long-term changes in the IMF B _z are revealed. They demonstrate decadal changes owing to the 11/22-year solar cycle. Long-duration time intervals with a dominant negative B _z component were found in temporal patterns of the cumulative sum of the IMF B _z .     

Magnetic Energy of Force-Free Fields with Detached Field Lines

Using an axisymmetrical ideal MHD model in spherical coordinates, we present a numerical study of magnetic configurations characterized by a levitating flux rope embedded in a bipolar background field whose normal field at the solar surface is the same or very close to that of a central dipole. The characteristic plasma β (the ratio between gas pressure and magnetic pressure) is taken to be sosmall (β= 10^-4) that the magnetic field is close to being force-free. The system as a whole is then let evolve quasi-statically with a slow increase of either the annular magnetic flux or the axial magnetic flux of the rope, and the total magneticenergy of the system grows accordingly. It is found that there exists an energy threshold: the flux rope sticks to the solar surface in equilibrium if the magneticenergy of the system is below the threshold, whereas it loses equilibrium if the threshold is exceeded. The energy threshold is found to be larger than that of thecorresponding fully-open magnetic field by a factor of nearly 1.08 irrespective as towhether the background field is completely closed or partly open, or whether the magnetic energy is enhanced by an increase of annular or axial flux of the rope.This gives an example showing that a force-free magnetic field may have an energy larger than the corresponding open field energy if part of the field lines is allowed tobe detached from the solar surface. The implication of such a conclusion in coronal mass ejections is briefly discussed and some comments are made on the maximum energy of force-free magnetic fields.     

The Hβ Chromospheric Magnetic Field in a Quiescent Filament

We observed the line-of-sight magnetic field in the chromosphereand photosphere of a large quiescent filament on the solar disk on September 6, 2001 using the Solar Magnetic Field Telescope in Huairou Solar Observing Station. The chromospheric and photospheric magnetograms together with Hβ filtergrams of the filament were examined. The filament was located on the neutral line of the large scale longitudinal magnetic field in the photosphere and the chromosphere. The lateral feet of the filament were found to be related to magnetic structures with opposite polarities. Two small lateral feet are linked to weak parasitic polarity. There is a negative magnetic structure in the photosphere under a break of the filament. At the location corresponding to the filament in the chromospheric magnetograms, the magnetic strength is found to be about 40-70 Gauss (measuring error about 39 Gauss). The magnetic signal indicates the amplitude and orientation of the internal magnetic field in the filament. We discuss several possible causes which may produce such a measured signal. A twisted magnetic configuration inside the filament is suggested .     

Studying Solar Eruptions from Reconstructed Coronal Magnetic Field

The Sun is the celestial body in the sky with the closest relationship with the Earth. The violent eruptive activities happening on the Sun can greatly impact the human living environment and lead to disastrous consequences. It is well accepted that solar eruptions including the solar flare, prominence eruption and coronal mass ejection are the different manifestations of a single physical process powered by the magnetic free energy gradually stored in the corona prior to eruptions. Therefore, mapping the three-dimensional structure of coronal magnetic field is a prerequisite to understand the initiation mechanism of solar eruptions. Due to the technological and methodological difficulties, routine observations of the coronal magnetic field are still unavailable. Therefore, a number of methods have been developed to reconstruct the coronal magnetic field. This paper mainly reviews the applications of various reconstruction methods to the studies of the solar eruptions in the recent ten years.     

Coronal activity from dynamos in astrophysical rotators

We show that a steady mean-field dynamo in astrophysical rotators leads to an outflow of relative magnetic helicity and thus magnetic energy available for particle and wind acceleration in a corona. The connection between energy and magnetic helicity arises because mean-field generation is linked to an inverse cascade of magnetic helicity. To maintain a steady state in large magnetic Reynolds number rotators, there must then be an escape of relative magnetic helicity associated with the mean field, accompanied by an equal and opposite contribution from the fluctuating field. From the helicity flow, a lower limit on the magnetic energy deposited in the corona can be estimated. Steady coronal activity including the dissipation of magnetic energy, and formation of multi-scale helical structures therefore necessarily accompanies an internal dynamo. This highlights the importance of boundary conditions which allow this to occur for non-linear astrophysical dynamo simulations. Our theoretical estimate of the power delivered by a mean-field dynamo is consistent with that inferred from observations to be delivered to the solar corona, the Galactic corona, and Seyfert 1 AGN coronae.     

Formation of Solar Delta Active Regions： Twist and Writhe of Magnetic Ropes

We analyze the process of formation of delta configuration in some well-known super active regions based on photospheric vector magnetogram observations. It is found that the magnetic field in the initial developing stage of some delta active regions shows a potential-like configuration in the solar atmosphere, the magnetic shear develops mainly near the magnetic neutral line with magnetic islands of opposite polarities, and the large-scale photospheric twisted field forming gradually later. Some results are obtained: (1) The analysis of magnetic writhe of whole active regions cannot be limited in the strong field of sunspots, because the contribution of the fraction of decayed magnetic field is non-negligible. (2) The magnetic model of kink magnetic ropes, supposed to be generated in the subatmosphere, is not consistent with the evolution of large-scale twisted photospheric transverse magnetic field and not entirely consistent with the relationship with magnetic shear in some delta active regions. (3) T     

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.     

Eruption of an Active-Region Filament Driven by an Emerging Bipole

1 INTRODUCTION Filaments are cool, dense material suspended in the hot, tenuous corona. It is widely accepted that the global magnetic field surrounding the filaments plays a key role in their formation, structure and stability (Tandberg-Hanssen1995). Fil…