Grad–Shafranov Reconstruction of Magnetic Clouds: Overview and Improvements

The Grad–Shafranov reconstruction is a method of estimating the orientation (invariant axis) and cross section of magnetic flux ropes using the data from a single spacecraft. It can be applied to various magnetic structures such as magnetic clouds (MCs) and flux ropes embedded in the magnetopause and in the solar wind. We develop a number of improvements of this technique and show some examples of the reconstruction procedure of interplanetary coronal mass ejections (ICMEs) observed at 1 AU by the STEREO, Wind, and ACE spacecraft during the minimum following Solar Cycle 23. The analysis is conducted not only for ideal localized ICME events but also for non-trivial cases of magnetic clouds in fast solar wind. The Grad–Shafranov reconstruction gives reasonable results for the sample events, although it possesses certain limitations, which need to be taken into account during the interpretation of the model results.     

Solar Cycle Variation of Magnetic Flux Ropes in a Quasi-Static Coronal Evolution Model

The structure of electric current and magnetic helicity in the solar corona is closely linked to solar activity over the 11-year cycle, yet is poorly understood. As an alternative to traditional current-free “potential-field” extrapolations, we investigate a model for the global coronal magnetic field which is non-potential and time-dependent, following the build-up and transport of magnetic helicity due to flux emergence and large-scale photospheric motions. This helicity concentrates into twisted magnetic flux ropes, which may lose equilibrium and be ejected. Here, we consider how the magnetic structure predicted by this model – in particular the flux ropes – varies over the solar activity cycle, based on photospheric input data from six periods of cycle 23. The number of flux ropes doubles from minimum to maximum, following the total length of photospheric polarity inversion lines. However, the number of flux rope ejections increases by a factor of eight, following the emergence rate of active regions. This is broadly consistent with the observed cycle modulation of coronal mass ejections, although the actual rate of ejections in the simulation is about a fifth of the rate of observed events. The model predicts that, even at minimum, differential rotation will produce sheared, non-potential, magnetic structure at all latitudes.     

A statistical study of flux ropes in the Martian magnetosphere

Using minimum variance analysis of the circular mapping data from the Mars Global Surveyor (MGS) spacecraft during four selected weeks of observation, we identify 360 magnetic field structures in the Martian topside ionosphere with characteristic signatures of flux ropes. Physical parameters including size, peak field strength, helicity, orientation, and external conditions at the time of each observation are compiled for the events in each population. We observe that Martian flux ropes typically have a peak field amplitude of ∼15 nT and a diameter of ∼80–100 km assuming they are stationary. Flux ropes tend to be aligned approximately parallel to the planetary surface, and perpendicular to the direction from which the solar wind flows. They are more frequently observed during times of low solar wind pressure, but do not show a clear preference for a particular Interplanetary Magnetic Field (IMF) draping direction. Flux rope characteristics of peak field amplitude, diameter, and helicity vary with solar zenith angle. Amplitudes tend to be higher during periods of high solar wind pressure. The events are sorted into three populations based on the location at which they were observed, possibly corresponding to distinct formation mechanisms. Flux ropes observed in eclipse tend to have smaller peak amplitudes and are larger than those observed in sunlight, and are less likely to be oriented parallel to the planetary surface. Proximity to crustal fields does not appear to influence the characteristics of flux ropes observed at the 400 km spacecraft altitude. The frequent observation of flux rope structures near Mars in a variety of locations suggests that the low-altitude plasma environment is quite dynamic, with magnetic shear playing a prominent role in determining magnetic field structure near the planet.     

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.     

Comparison study of magnetic flux ropes in the ionospheres of Venus, Mars and Titan

Magnetic flux ropes are created in the ionosphere of Venus and Mars during the interaction of the solar wind with their ionospheres and also at Titan during the interaction of the Saturnian magnetospheric plasma flow with Titan’s ionosphere. The flux ropes at Venus and Mars were extensively studied from Pioneer Venus Orbiter and Mars Global Surveyor observations respectively during solar maximum. Based on the statistical properties of the observed flux ropes at Venus and Mars, the formation of a flux rope in the ionosphere is thought first to arise near the boundary between the magnetic barrier and the ionosphere and later to sink into the lower ionosphere. Venus flux ropes are also observed during solar minimum by Venus Express and the observations of developing and mature flux ropes are consistent with the proposed mechanism. With the knowledge of flux rope structure in the Venus ionosphere, the twisted fields in the lower ionosphere of Titan from Cassini observations are studied and are found to resemble the Venus flux ropes.     

中尺度磁绳结构的行星际观测

由磁绳结构主导、平均尺度约二、三十个小时的行星际磁云是日冕物质抛射在行星际膨胀、传播的体现。最近，Moldwin等人报道在太阳风中还观测到一些尺度在几十分钟的小尺度磁绳结构，并认为太阳风中的磁绳结构在尺度分布上可能具有双峰特征，在全面检视了WIND卫星(1995年-2000年)和ACE卫星(1998年-2000年)的观测资料后，发现了在行星际太阳风中一些尺度为几个小时的中尺度磁绳结构，利用初步整理的其中28个中尺度磁绳结构事件，认为太阳风中的磁绳结构在尺度分布上可能是连续的，这对行星际太阳风中磁绳结构物理起源的研究可能提出重要的物理限制。     

Characteristics of active-region sources of solar wind near solar maximum

Previous studies of the source regions of solar wind sampled by ACE and Ulysses showed that some solar wind originates from open magnetic flux rooted in active regions. These solar wind sources were labeled active-region sources when the open flux was from a strong field region with no corresponding coronal hole in the NSO He 10830 Å synoptic coronal-hole maps. Here, we present a detailed investigation of several of these active-region sources using ACE and Ulysses solar wind data, potential field models of the corona, and solar imaging data. We find that the solar wind from these active-region sources has distinct signatures, e.g., it generally has a higher oxygen charge state than wind associated with helium-10830 Å coronal-hole sources, indicating a hotter source region, consistent with the active region source interpretation. We compare the magnetic topology of the open field lines of these active-region sources with images of the hot corona to search for corresponding features in EUV and soft X-ray images. In most, but not all, cases, a dark area is seen in the EUV and soft X-ray image as for familiar coronal-hole sources. However, in one case no dark area was evident in the soft X-ray images: the magnetic model showed a double dipole coronal structure consistent with the images, both indicating that the footpoints of the open field lines, rooted deep within the active region, lay near the separatrix between loops connecting to two different opposite polarity regions.     

Characteristics of active-region sources of solar wind near solar maximum

Previous studies of the source regions of solar wind sampled by ACE and Ulysses showed that some solar wind originates from open magnetic flux rooted in active regions. These solar wind sources were labeled active-region sources when the open flux was from a strong field region with no corresponding coronal hole in the NSO He 10830 Å synoptic coronal-hole maps. Here, we present a detailed investigation of several of these active-region sources using ACE and Ulysses solar wind data, potential field models of the corona, and solar imaging data. We find that the solar wind from these active-region sources has distinct signatures, e.g., it generally has a higher oxygen charge state than wind associated with helium-10830 Å coronal-hole sources, indicating a hotter source region, consistent with the active region source interpretation. We compare the magnetic topology of the open field lines of these active-region sources with images of the hot corona to search for corresponding features in EUV and soft X-ray images. In most, but not all, cases, a dark area is seen in the EUV and soft X-ray image as for familiar coronal-hole sources. However, in one case no dark area was evident in the soft X-ray images: the magnetic model showed a double dipole coronal structure consistent with the images, both indicating that the footpoints of the open field lines, rooted deep within the active region, lay near the separatrix between loops connecting to two different opposite polarity regions.     

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.     

Are There Different Populations of Flux Ropes in the Solar Wind?

Flux ropes are twisted magnetic structures that can be detected by in-situ measurements in the solar wind. However, different properties of detected flux ropes suggest different types of flux-rope populations. As such, are there different populations of flux ropes? The answer is positive and is the result of the analysis of four lists of flux ropes, including magnetic clouds (MCs), observed at 1 AU. The in-situ data for the four lists were fitted with the same cylindrical force-free field model, which provides an estimate of the local flux-rope parameters such as its radius and orientation. Since the flux-rope distributions have a broad dynamic range, we went beyond a simple histogram analysis by developing a partition technique that uniformly distributes the statistical fluctuations across the radius range. By doing so, we found that small flux ropes with radius R<0.1 AU have a steep power-law distribution in contrast to the larger flux ropes (identified as MCs), which have a Gaussian-like distribution. Next, from four CME catalogs, we estimated the expected flux-rope frequency per year at 1 AU. We found that the predicted numbers are similar to the frequencies of MCs observed in-situ. However, we also found that small flux ropes are at least ten times too abundant to correspond to CMEs, even to narrow ones. Investigating the different possible scenarios for the origin of these small flux ropes, we conclude that these twisted structures can be formed by blowout jets in the low corona or in coronal streamers.     

Twists and rotations of solar magnetic fields

Evidence is reviewed and extended that most, if not all, solar magnetic fields emerge as highly concentrated (4000 gauss)helically twisted flux ropes, made up of hundreds or thousands of individually twisted flux fibers. The pitch angles of the twists are estimated as 10° in the submerged flux ropes and roughly 1° in the flux fibers, but increase by large factors during and following emergence. The upward transmission of magnetic stresses and motions from the submerged flux-rope sections are major factors in solar physics. The helical twists account for the creation of sunspots and for their stability, fine structure, and mode of decay. They are basic features of the atmospheric structures, from the largest prominences and flare events down to arch filament systems and the smallest network components.     

行星际磁通量绳尺度及能量研究

行星际磁通量绳是太阳风中一种重要的磁结构.从1995-2001年的Wind卫星的观测资料中认证了144个行星际磁通量绳.其时间尺度介于几十分钟到几十小时之间,其空间尺度呈现连续分布.通过估算磁通量绳单位长度的能量和总能量发现:磁通量绳的能量分布和耀斑的类似都呈现很好的幂率谱.通过讨论行星际磁通量绳和太阳活动爆发的关系,建议所有的小、中、大尺度通量绳都直接起源于太阳上的爆发,和磁云对应于通常的日冕物质抛射一样,中、小尺度的通量绳对应相对较小的日冕物质抛射.     

Coronal Magnetic Field Evolution from 1996 to 2012: Continuous Non-potential Simulations

Coupled flux transport and magneto-frictional simulations are extended to simulate the continuous magnetic-field evolution in the global solar corona for over 15 years, from the start of Solar Cycle 23 in 1996. By simplifying the dynamics, our model follows the build-up and transport of electric currents and free magnetic energy in the corona, offering an insight into the magnetic structure and topology that extrapolation-based models cannot. To enable these extended simulations, we have implemented a more efficient numerical grid, and have carefully calibrated the surface flux-transport model to reproduce the observed large-scale photospheric radial magnetic field, using emerging active regions determined from observed line-of-sight magnetograms. This calibration is described in some detail. In agreement with previous authors, we find that the standard flux-transport model is insufficient to simultaneously reproduce the observed polar fields and butterfly diagram during Cycle 23, and that additional effects must be added. For the best-fit model, we use automated techniques to detect the latitude–time profile of flux ropes and their ejections over the full solar cycle. Overall, flux ropes are more prevalent outside of active latitudes but those at active latitudes are more frequently ejected. Future possibilities for space-weather prediction with this approach are briefly assessed.     

Polarimetric Properties of Flux Ropes and Sheared Arcades in Coronal Prominence Cavities

The coronal magnetic field is the primary driver of solar dynamic events. Linear and circular polarization signals of certain infrared coronal emission lines contain information about the magnetic field, and to access this information either a forward or an inversion method must be used. We study three coronal magnetic configurations that are applicable to polar-crown filament cavities by doing forward calculations to produce synthetic polarization data. We analyze these forward data to determine the distinguishing characteristics of each model. We conclude that it is possible to distinguish between cylindrical flux ropes, spheromak flux ropes, and sheared arcades using coronal polarization measurements. If one of these models is found to be consistent with observational measurements, it will mean positive identification of the magnetic morphology that surrounds certain quiescent filaments, which will lead to a better understanding of how they form and why they erupt.     

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.     

The cyclical variation of energy flux and photospheric magnetic field strength from coronal holes

We measured the average soft X-ray emission from coronal holes observed on images obtained during AS & E rocket flights from 1974 to 1981. The variation of this emission over the solar cycle was then compared with photospheric magnetic flux measurements within coronal holes over the same period. We found that coronal hole soft X-ray emission could be detected and that this emission appeared to increase with the rise of the sunspot cycle from activity minimum to maximum. Our quantitative results confirmed previous suggestions that the coronal brightness contrast between holes and large-scale structure decreased during this period of the cycle. Gas pressures at the hole base were estimated for assumed temperatures and found to vary from about 0.03 dyne cm^–2 in 1974 to 0.35 dyne cm^–2 in 1981. The increase in coronal hole X-ray emission was accompanied by a similar trend in the surface magnetic flux of near-equatorial holes between 1975 and 1980 (Harvey et al., 1982).     

Magnetic flux ropes in the solar corona: structure and evolution toward eruption

Magnetic flux ropes are characterized by coherently twisted magnetic field lines, which are ubiquitous in magnetized plasmas. As the core structure of various eruptive phenomena in the solar atmosphere, flux ropes hold the key to understanding the physical mechanisms of solar eruptions,which impact the heliosphere and planetary atmospheres. The strongest disturbances in the Earth's space environments are often associated with large-scale flux ropes from the Sun colliding with the Earth's magnetosphere, leading to adverse, sometimes catastrophic, space-weather effects. However, it remains elusive as to how a flux rope forms and evolves toward eruption, and how it is structured and embedded in the ambient field. The present paper addresses these important questions by reviewing current understandings of coronal flux ropes from an observer's perspective, with an emphasis on their structures and nascent evolution toward solar eruptions, as achieved by combining observations of both remote sensing and in-situ detection with modeling and simulation. This paper highlights an initiation mechanism for coronal mass ejections(CMEs) in which plasmoids in current sheets coalesce into a 'seed' flux rope whose subsequent evolution into a CME is consistent with the standard model, thereby bridging the gap between microscale and macroscale dynamics.     

Three-Dimensional Evolution of Flux-Rope CMEs and Its Relation to the Local Orientation of the Heliospheric Current Sheet

Flux ropes ejected from the Sun may change their geometrical orientation during their evolution, which directly affects their geoeffectiveness. Therefore, it is crucial to understand how solar flux ropes evolve in the heliosphere to improve our space-weather forecasting tools. We present a follow-up study of the concepts described by Isavnin, Vourlidas, and Kilpua (Solar Phys. 284, 203, 2013). We analyze 14 coronal mass ejections (CMEs), with clear flux-rope signatures, observed during the decay of Solar Cycle 23 and rise of Solar Cycle 24. First, we estimate initial orientations of the flux ropes at the origin using extreme-ultraviolet observations of post-eruption arcades and/or eruptive prominences. Then we reconstruct multi-viewpoint coronagraph observations of the CMEs from ≈?2 to 30 R_⊙ with a three-dimensional geometric representation of a flux rope to determine their geometrical parameters. Finally, we propagate the flux ropes from ≈?30 R_⊙ to 1 AU through MHD-simulated background solar wind while using in-situ measurements at 1 AU of the associated magnetic cloud as a constraint for the propagation technique. This methodology allows us to estimate the flux-rope orientation all the way from the Sun to 1 AU. We find that while the flux-ropes’ deflection occurs predominantly below 30 R_⊙, a significant amount of deflection and rotation happens between 30 R_⊙ and 1 AU. We compare the flux-rope orientation to the local orientation of the heliospheric current sheet (HCS). We find that slow flux ropes tend to align with the streams of slow solar wind in the inner heliosphere. During the solar-cycle minimum the slow solar-wind channel as well as the HCS usually occupy the area in the vicinity of the solar equatorial plane, which in the past led researchers to the hypothesis that flux ropes align with the HCS. Our results show that exceptions from this rule are explained by interaction with the Parker-spiraled background magnetic field, which dominates over the magnetic interaction with the HCS in the inner heliosphere at least during solar-minimum conditions.     

Post-Eruption Arcades and Interplanetary Coronal Mass Ejections

We compare the temporal and spatial properties of posteruption arcades (PEAs) associated with coronal mass ejections (CMEs) at the Sun that end up as magnetic cloud (MC) and non-MC events in the solar wind. We investigate the length, width, area, tilt angle, and formation time of the PEAs associated with 22 MC and 29 non-MC events and we find no difference between the two populations. According to current ideas on the relation between flares and CMEs, the PEA is formed together with the CME flux-rope structure by magnetic reconnection. Our results indicate that at the Sun flux ropes form during CMEs in association with both MC and non-MC events; however, for non-MC events the flux-rope structure is not observed in the interplanetary space because of the geometry of the observation, i.e. the location of the spacecraft when the structure passes through it.     

Heliospheric X-ray Emission Associated with Charge Transfer of the Solar Wind with Interstellar Neutrals

X-rays should be generated throughout the heliosphere as a consequence of charge transfer collisions between heavy (Z>2) solar wind ions and interstellar neutrals. The high charge state solar wind ions resulting from these collisions are left in highly excited states and emit extreme ultraviolet or soft X-ray photons. This solar wind charge exchange mechanism applied to cometary neutrals has been used to explain the soft X-ray emission observed from comets. A simple model demonstrates that heliospheric X-ray emission can account for about 25%-50% of the observed soft X-ray background intensities. The spatial and temporal variations of heliospheric X-ray emission should reflect variations in the solar wind flux and composition as well as variations in the distribution of interstellar neutrals within the heliosphere. The heliospheric X-ray "background" can perhaps be identified with the "long-term enhancements" in the soft X-ray background measured by ROSAT.