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.     

Numerical Magnetohydrodynamic Experiments for Testing the Physical Mechanisms of Coronal Mass Ejections Acceleration

Analysis of observations from both space-borne (LASCO/SOHO, Skylab and Solar Maximum Mission) and ground-based (Mauna Loa Observatory) instruments show that there are two types of coronal mass ejections (CMEs), fast CMEs and slow CMEs. Fast CMEs start with a high initial speed, which remains more or less constant, while slow CMEs start with a low initial speed, but show a gradual acceleration. To explain the difference between the two types of CMEs, Low and Zhang (2002) proposed that it resulted from a difference in the initial topology of the magnetic fields associated with the underlying quiescent prominences, i.e., a normal prominence configuration will lead to a fast CME, while an inverse quiescent prominence results in a slow CME. In this paper we explore a different scenario to explain the existence of fast and slow CMEs. Postulating only an inverse topology for the quiescent prominences, we show that fast and slow CMEs result from different physical processes responsible for the destabilization of the coronal magnetic field and for the initiation and launching of the CME. We use a 2.5-D, time-dependent streamer and flux-rope magnetohydrodynamic (MHD) model (Wu and Guo, 1997) and investigate three initiation processes, viz. (1) injecting of magnetic flux into the flux-rope, thereby causing an additional Lorentz force that will destabilize the streamer and launch a CME (Wu et al., 1997, 1999); (2) draining of plasma from the flux-rope and triggering a magnetic buoyancy force that causes the flux-rope to lift and launch a CME; and (3) introducing additional heating into the flux-rope, thereby simulating an active-region flux-rope accompanied by a flare to launch a CME. We present 12 numerical tests using these three driving mechanisms either alone or in various combinations. The results show that both fast and slow CMEs can be obtained from an inverse prominence configuration subjected to one or more of these three different initiation processes.     

On the maximum energy release in flux-rope models of Eruptive Flares

We determine the photospheric boundary conditions which maximize the magnetic energy released by a loss of ideal-MHD equilibrium in two-dimensional flux-rope models. In these models a loss of equilibrium causes a transition of the flux rope to a lower magnetic energy state at a higher altitude. During the transition a vertical current sheet forms below the flux rope, and reconnection in this current sheet releases additional energy. Here we compute how much energy is released by the loss of equilibrium relative to the total energy release. When the flux-rope radius is small compared to its height, it is possible to obtain general solutions of the Grad-Shafranov equation for a wide range of boundary conditions. Variational principles can then be used to find the particular boundary condition which maximizes the magnetic energy released for a given class of conditions. We apply this procedure to a class of models known as cusp-type catastrophes, and we find that the maximum energy released by the loss of equilibrium is 20.8% of the total energy release for any model in this class. If the additional restriction is imposed that the photospheric magnetic field forms a simple arcade in the absence of coronal currents, then the maximum energy release reduces to 8.6%.     

On current sheet approximations in models of eruptive flares

We consider an approximation sometimes used for current sheets in flux-rope models of eruptive flares. This approximation is based on a linear expansion of the background field in the vicinity of the current sheet, and it is valid when the length of the current sheet is small compared to the scale length of the coronal magnetic field. However, we find that flux-rope models which use this approximation predict the occurrence of an eruption due to a loss of ideal-MHD equilibrium even when the corresponding exact solution shows that no such eruption occurs. Determination of whether a loss of equilibrium exists can only be obtained by including higher order terms in the expansion of the field or by using the exact solution.     

On the Flux-Rope Topology of Ejecta Observed in the Period 1997 – 2006

In the following study our aim is to analyse the magnetic flux-rope topology of some events observed in the interplanetary medium related to ejecta. The magnetic field structures associated with interplanetary coronal mass ejections are globally classified in magnetic clouds and ejecta. One of the main questions regarding these phenomena concerns their flux-rope or non-flux-rope magnetic field line configuration. From the experimental measurements the only way to elucidate such a question is analysing the corresponding data by means of a flux-rope physical model. After selecting the ejecta events observed during the period 1997?–?2006, we have analysed them in light of an analytical model with that topology for the magnetic field components, initially developed for magnetic clouds, and with a non-force-free character; then, incorporating the expansion of the magnetic structure during their evolution in the interplanetary medium. Different parameters obtained from the fitting of the model are related to the orientation of the axis of the magnetic flux-rope structure and, additionally, the closest distance approach of the spacecraft to its axis. One of the main conclusions achieved concerns the fact that the axes of most of those structures are close to the Sun–Earth line, which implies that the passage of the spacecraft through the corresponding ejecta event is by its flank. In general, we show a rough procedure for the analysis and classification of ejecta in terms of their magnetic field topology.     

Initiation of Coronal Mass Ejections by Sunspot Rotation

We study a filament eruption, two-ribbon flare, and coronal mass ejection (CME) that occurred in NOAA Active Region 10898 on 6 July 2006. The filament was located South of a strong sunspot that dominated the region. In the evolution leading up to the eruption, and for some time after it, a counter-clockwise rotation of the sunspot of about 30 degrees was observed. We suggest that the rotation triggered the eruption by progressively expanding the magnetic field above the filament. To test this scenario, we study the effect of twisting the initially potential field overlying a pre-existing flux-rope, using three-dimensional zero-β MHD simulations. We first consider a relatively simple and symmetric system, and then study a more complex and asymmetric magnetic configuration, whose photospheric-flux distribution and coronal structure are guided by the observations and a potential field extrapolation. In both cases, we find that the twisting leads to the expansion of the overlying field. As a consequence of the progressively reduced magnetic tension, the flux-rope quasi-statically adapts to the changed environmental field, rising slowly. Once the tension is sufficiently reduced, a distinct second phase of evolution occurs where the flux-rope enters an unstable regime characterised by a strong acceleration. Our simulations thus suggest a new mechanism for the triggering of eruptions in the vicinity of rotating sunspots.     

A Helicity-Based Method to Infer the CME Magnetic Field Magnitude in Sun and Geospace: Generalization and Extension to Sun-Like and M-Dwarf Stars and Implications for Exoplanet Habitability

Patsourakos et al. (Astrophys. J. 817, 14, 2016) and Patsourakos and Georgoulis (Astron. Astrophys. 595, A121, 2016) introduced a method to infer the axial magnetic field in flux-rope coronal mass ejections (CMEs) in the solar corona and farther away in the interplanetary medium. The method, based on the conservation principle of magnetic helicity, uses the relative magnetic helicity of the solar source region as input estimates, along with the radius and length of the corresponding CME flux rope. The method was initially applied to cylindrical force-free flux ropes, with encouraging results. We hereby extend our framework along two distinct lines. First, we generalize our formalism to several possible flux-rope configurations (linear and nonlinear force-free, non-force-free, spheromak, and torus) to investigate the dependence of the resulting CME axial magnetic field on input parameters and the employed flux-rope configuration. Second, we generalize our framework to both Sun-like and active M-dwarf stars hosting superflares. In a qualitative sense, we find that Earth may not experience severe atmosphere-eroding magnetospheric compression even for eruptive solar superflares with energies \({\approx}\, 10^{4}\) times higher than those of the largest Geostationary Operational Environmental Satellite (GOES) X-class flares currently observed. In addition, the two recently discovered exoplanets with the highest Earth-similarity index, Kepler 438b and Proxima b, seem to lie in the prohibitive zone of atmospheric erosion due to interplanetary CMEs (ICMEs), except when they possess planetary magnetic fields that are much higher than that of Earth.     

Predictions of Energy and Helicity in Four Major Eruptive Solar Flares

In order to better understand the solar genesis of interplanetary magnetic clouds (MCs), we model the magnetic and topological properties of four large eruptive solar flares and relate them to observations. We use the three-dimensional Minimum Current Corona model (Longcope, 1996, Solar Phys. 169, 91) and observations of pre-flare photospheric magnetic field and flare ribbons to derive values of reconnected magnetic flux, flare energy, flux rope helicity, and orientation of the flux-rope poloidal field. We compare model predictions of those quantities to flare and MC observations, and within the estimated uncertainties of the methods used find the following: The predicted model reconnection fluxes are equal to or lower than the reconnection fluxes inferred from the observed ribbon motions. Both observed and model reconnection fluxes match the MC poloidal fluxes. The predicted flux-rope helicities match the MC helicities. The predicted free energies lie between the observed energies and the estimated total flare luminosities. The direction of the leading edge of the MC’s poloidal field is aligned with the poloidal field of the flux rope in the AR rather than the global dipole field. These findings compel us to believe that magnetic clouds associated with these four solar flares are formed by low-corona magnetic reconnection during the eruption, rather than eruption of pre-existing structures in the corona or formation in the upper corona with participation of the global magnetic field. We also note that since all four flares occurred in active regions without significant pre-flare flux emergence and cancelation, the energy and helicity that we find are stored by shearing and rotating motions, which are sufficient to account for the observed radiative flare energy and MC helicity.     

磁场约束的近圆弧形等离子体拱

等离子体弧是日冕中的一种基本结构,其高温观测特性意味着它有较高的等离子体压力。本文在二维近似下,讨论了等离子体拱被两个强磁场区域所约束时的平衡。对于较大的等离子体标高,等离子体具有近似圆弧形的结构。通过求出强磁场区域中的磁场位形,可以得到孤立的等离子体拱的平衡状态。由于总压守恒的边界条件是高度非线性的,整个问题是一类非线性的自由边界问题。在近圆弧形近似下,其基态是一维的非线性问题,而相对于基态的偏离是二维的线性问题。这样,整个问题可以给出分析解。     

Does the region of flare-energy release work as a vacuum-cleaner?

We aim to explore the unusual flare event which took place in the solar atmosphere on September 22, 2011 and propose its theoretical interpretation. We analyze the process of energy release in the twisted magnetic flux-rope associated with the event, assuming the excitation of anomalous resistivity of turbulent plasma in the rope, and solve numerically nonlinear two-dimensional (2D) magnetohydrodynamic (MHD) equations. The analytical approach to the problem of flare-energy release show that the conditions of excitation of anomalous resistivity can be satisfied in the twisted magnetic flux-rope whose parameters fits well the SDO observational findings. One of the most remarkable properties of the flare phenomenon under the present consideration was the permanent sucking of the coronal/chromospheric gas from the very remote points to the flare filament, i.e. into the low-lying hot region of the flare energy release. This unusual phenomenon has been simulated by numerical methods in terms of ideal MHD. The numerical results reveal that siphon back-flow exhibits characteristic spatial signatures which mimic the observational findings. The flare-energy release region, as a part of strongly twisted magnetic flux-rope, is able to work as a vacuum-cleaner.     

Coronal Mass Ejection of 15 May 2001: II. Coupling of the Cme Acceleration and the Flare Energy Release

We analyze the relationship between the dynamics of the coronal mass ejection (CME) of 15 May 2001 and the energy release in the associated flare. The flare took place behind the east limb and was disclosed by a growing system of hot soft X-ray (SXR) loops that appeared from behind the limb around the onset of the rapid acceleration of the CME. The highly correlated behavior of the SXR light-curve derivative and the time profile of the CME acceleration reveals an intrinsic relationship between the CME dynamics and the flare energy release. Furthermore, we found that the CME acceleration peak occurs simultaneously with the fastest growth (100 km s^-1) of X-ray loops, indicating that the reconnection plays an essential role in the eruption. Inspecting the CME/flare morphology we recognized in the Yohkoh-SXT images an oval feature that formed within the rising structure at the onset of the rapid acceleration phase, simultaneously with the appearance of the X-ray loops. The eruptive prominence was imbedded within the lower half of the oval, suggestive of a flux-rope/prominence magnetic configuration. We interpret the observed morphological evolution in terms of a reconnection process in the current sheet that presumably formed below the erupting flux-rope at the onset of the CME acceleration. Measurements of the tip-height of the cusped X-ray loop system and the height of the lower edge of the oval, enable us to trace the stretching of the current sheet. The initial distance between the oval and the loops amounted to 35 – 40 Mm. In about 1 h the inferred length of the current sheet increased to 150 – 200 Mm, which corresponds to a mean elongation speed of 35 – 45 km s^-1. The results are discussed in the framework of CME models that include the magnetic reconnection below the erupting flux-rope.     

On the stationary configuration of the heliospheric sheet

The expansion of solar coronal plasma is considered for the model described in Koutchmy et al. (1999). In addition to a spherical solar surface, the initial configuration represents a heliospheric sheet of dense plasma in the dipole equatorial plane. The heliospheric-sheet current decreases with distance as 1/r ², with its sign being opposite to the sign of the initial-dipole current. The latter follows from the fact that the plasma sheet is denser than the surrounding corona and that the equilibrium condition for the sheet in the gravitational and magnetic fields is satisfied. The field lines of this configuration are nearly straight. We have obtained a general solution of the steady-state MHD equations, which depends not only on distance r but also on latitude θ. Applicability of the solution to interpreting observational data, in particular, those obtained from the Ulysses spacecraft, is discussed.     

An investigation of the large-scale magnetic field variations in the corona prior to and after CME eruptions

The magnetic field changes in the corona at the site of coronal mass ejections (CMEs) have been investigated using the potential field-source surface model. It is shown that a CME is accompanied by the opening of closed field lines that formed the streamer's helmet base prior to the onset of a coronal disturbance. Two to three days after the appearance of the CME, the field configuration at the location of the coronal ejection reverts approximately to the state pre-existing before the generation of the CME. The appearance of small transient open magnetic tubes has been found after eruption of the coronal mass. These magnetic tubes seem to be the analogs for transient coronal holes.Taking into account the results of calculations of the field changes in the neighbourhood of the CME occurrence site, we have suggested a possible mechanism governing the spatio-temporal correlation between some flares and CMEs. Also, a possible mechanism has been proposed for field reconfiguration in the corona, leading to loss of the equilibrium of the magnetic configuration and to the subsequent generation of a CME in the region of coronal streamer chains separating coronal holes with same-polarity magnetic field.     

Coronal MHD perturbation field generated by localized perturbers in a photospheric active region

We investigate the two-dimensional boundary value problem of the linear wave excitation in the solar corona by a pair of periodic perturbers localized at the photosphere. The physical properties of the corona allow us to consider a magnetic configuration such as a potential arcade which is in a magneto-hydrostatic equilibrium with the surrounding plasma. The model excludes the A1fvén mode and since the slow mode is absent in a potential arcade, the excited waves are then the fast magneto-acoustic modes. The characteristic magnetic field scale length is twice the scale height of the coronal plasma, assumed isothermal and the induced fluid motions are in the direction perpendicular to the magnetic field, in the cross-sectional plane of the arcade.A particular example of two localized perturbers in a photospheric active region is given, pointing out the effects produced in the perturbed fields by the variation of the different parameters involved. Such example shows that, while a modification of the linear size or the horizontal wave number of the perturbers does not affect significantly the propagating disturbances, the variation of the perturbers' frequency produces important effects. Such effects can be summarized by saying that low-frequency perturbers are able to disturb the whole coronal magnetic configuration above the active region while high-frequency perturbers only disturb the coronal region just above them, producing a channeling feature. Moreover, for high frequencies the perturbations grow withz all the way from the photosphere while for very low frequencies evanescent waves are dominant, although thanks to the influence of the medium their amplitude starts to grow from somez on.     

Solar Wind and Heavy Ion Properties of Interplanetary Coronal Mass Ejections

Magnetic field and plasma properties of the solar wind measured in near-Earth space are a convolution of coronal source conditions and in-transit processes which take place between the corona and near-Earth space. Elemental composition and heavy ion charge states, however, are not significantly altered during transit to Earth and thus such properties can be used to diagnose the coronal source conditions of the solar wind observed in situ. We use data from the Advanced Composition Explorer (ACE) spacecraft to statistically quantify differences in the coronal source properties of interplanetary coronal mass ejections (ICMEs). Magnetic clouds, ICMEs which contain a magnetic flux-rope signature, display heavy ion properties consistent with significantly hotter coronal source regions than non-cloud ICMEs. Specifically, magnetic clouds display significantly elevated ion charge states, suggesting they receive greater heating in the low corona. Further dividing ICMEs by speed, however, shows this effect is primarily limited to fast magnetic clouds and that in terms of heavy ion properties, slow magnetic clouds are far more similar to non-cloud ICMEs. As such, fast magnetic clouds appear distinct from other ICME types in terms of both ion charge states and elemental composition. ICME speed, rather ICME type, correlates with helium abundance and iron charge state, consistent with fast ICMEs being heated through the more extended corona. Fast ICMEs also tend to be embedded within faster ambient solar wind than slow ICMEs, though this could be partly the result of in-transit drag effects. These signatures are discussed in terms of spatial sampling of ICMEs and from fundamentally different coronal formation and release processes.     

The Solar Connection of Enhanced Heavy Ion Charge States in the Interplanetary Medium: Implications for the Flux-Rope Structure of CMEs

We investigated a set of 54 interplanetary coronal mass ejection (ICME) events whose solar sources are very close to the disk center (within ±?15^° from the central meridian). The ICMEs consisted of 23 magnetic-cloud (MC) events and 31 non-MC events. Our analyses suggest that the MC and non-MC ICMEs have more or less the same eruption characteristics at the Sun in terms of soft X-ray flares and CMEs. Both types have significant enhancements in ion charge states, although the non-MC structures have slightly lower levels of enhancement. The overall duration of charge-state enhancement is also considerably smaller than that in MCs as derived from solar wind plasma and magnetic signatures. We find very good correlation between the Fe and O charge-state measurements and the flare properties such as soft X-ray flare intensity and flare temperature for both MCs and non-MCs. These observations suggest that both MC and non-MC ICMEs are likely to have a flux-rope structure and the unfavorable observational geometry may be responsible for the appearance of non-MC structures at 1 AU. We do not find any evidence for an active region expansion resulting in ICMEs lacking a flux-rope structure because the mechanism of producing high charge states and the flux-rope structure at the Sun is the same for MC and non-MC events.     

Evidence of Magnetic Flux Ropes in the Solar Wind From Sigmoidal and non-Sigmoidal Active Regions

We have examined WIND magnetic field and plasma data during the first half of 1998 in order to find encounters of this spacecraft with magnetic clouds. From the events obtained through this search, we have selected four of them taking into account their solar origin. The four magnetic clouds are related to halo or partial halo CMEs, but the morphology of the active region before the eruption is sigmoidal for three of them and non-sigmoidal for the other one. We have analyzed these events in the solar wind by fitting the experimental data to a non-force-free flux-rope model. We conclude that both kinds of active regions develop in the solar wind an ejection with a flux-rope topology.     

Numerical Experiments Base on the Catastrophe Model of Solar Eruptionstwo

On the basis of the catastrophe model developed by Isenberg et al., we have used the NIRVANA code to perform the magnetohydrodynamics (MHD) numerical experiments to look into the various behaviors of the coronal magnetic configuration that includes a current-carrying flux rope for modelling the prominence levitation in the corona. These behaviors include the evolution of the equilibrium height of magnetic flux rope with the background magnetic field, the corresponding interior equilibrium of magnetic flux rope, the dynamic properties of magnetic flux rope after the system loses equilibrium, as well as the impact of the reference radius on the equilibrium height of magnetic flux rope. In our calculations, an empirical model of the coronal density distribution given by Sittler & Guhathakurta is used, and the physical dissipation is included. Our experiments show that a deviation between the simulated equilibrium height of magnetic flux rope and the theoretical result of Isenberg et al. exists, but it is not apparent, and the evolutionary features of the two results are similar. If the magnetic flux rope is initially located at the stable branch of the theoretical equilibrium curve, the magnetic flux rope will quickly reach the equilibrium position after several rounds of oscillations as a result of the self-adjustment of the system; when the system is located at the critical point it will quickly lose equilibrium and evolve to the eruptive state; the impact of the variation of reference radius on the equilibrium height of magnetic flux rope is consistent with the prediction of the theory; in the eruptive state, the kinetic properties of magnetic flux rope are consistent with the results given by the Lin-Forbes model and observation, and the fast-mode shock in front of the magnetic flux rope is observed in our experiments; furthermore, because that the dissipation is included in our numerical experiments, the energy conversion from the magnetic energy to other forms of energy is very apparent in the eruptive process.     

Physical conditions in the corona for a bipolar magnetic region

We have used the S-056 X-ray data from Skylab to determine quantitative values for the coronal conditions characterizing a new bipolar magnetic region (BMR). In particular, we include: (a) the time variation of the total soft X-ray flux from the BMR as a function of time; (b) the temporal and spatial variation of the temperature and emission measure; (c) the variation with time of thermal energy density; (d) the (calculated) magnetic field configuration and magnetic flux density in the corona; and (e) the temporal variation of the magnetic field energy in the corona. Detailed comparisons are made between the configuration of X-ray features and the magnetic field topology.     

灾变理论在太阳物理和天体物理其他研究领域中的应用

叙述和介绍了太阳爆发的磁通量绳灾变理论和模型的发展过程,强调了建立这样的模型所需要的观测基础。讨论了由模型所预言的爆发磁结构的几个重要特征以及观测结果对这种预言的证实。在此模型的基础上,讨论了一个典型的爆发过程中所出现的不同现象及它们之间的相互关系。最后,介绍了作者的一项最新尝试:将太阳爆发的灾变理论和模型应用到对黑洞吸积盘间歇性喷流的理论研究当中,以及研究所取得的初步结果。