The Magnetic Helicity Injected by Shearing Motions

Photospheric shearing motions are one of the possible ways to inject magnetic helicity into the corona. We explore their efficiency as a function of their particular properties and those of the magnetic field configuration. Based on the work of M. A. Berger, we separate the helicity injection into two terms: twist and writhe. For shearing motions concentrated between the centers of two magnetic polarities the helicity injected by twist and writhe add up, while for spatially more extended shearing motions, such as differential rotation, twist and writhe helicity have opposite signs and partially cancel. This implies that the amount of injected helicity can change in sign with time even if the shear velocity is time independent. We confirm the amount of helicity injected by differential rotation in a bipole in the two particular cases studied by DeVore (2000), and further explore the parameter space on which this injection depends. For a given latitude, tilt and magnetic flux, the generation of helicity is slightly more efficient in young active regions than in decayed ones (up to a factor 2). The helicity injection is mostly affected by the tilt of the AR with respect to the solar equator. The total helicity injected by shearing motions, with both spatial and temporal coherence, is at most equivalent to that of a twisted flux tube having the same magnetic flux and a number of turns of 0.3. In the solar case, where the motions have not such global coherence, the injection of helicity is expected to be much smaller, while for differential rotation this maximum value reduces to 0.2 turns. We conclude that shearing motions are a relatively inefficient way to bring magnetic helicity into the corona (compared to the helicity carried by a significantly twisted flux tube).     

Determining the Intrinsic CME Flux Rope Type Using Remote-sensing Solar Disk Observations

A key aim in space weather research is to be able to use remote-sensing observations of the solar atmosphere to extend the lead time of predicting the geoeffectiveness of a coronal mass ejection (CME). In order to achieve this, the magnetic structure of the CME as it leaves the Sun must be known. In this article we address this issue by developing a method to determine the intrinsic flux rope type of a CME solely from solar disk observations. We use several well-known proxies for the magnetic helicity sign, the axis orientation, and the axial magnetic field direction to predict the magnetic structure of the interplanetary flux rope. We present two case studies: the 2 June 2011 and the 14 June 2012 CMEs. Both of these events erupted from an active region, and despite having clear in situ counterparts, their eruption characteristics were relatively complex. The first event was associated with an active region filament that erupted in two stages, while for the other event the eruption originated from a relatively high coronal altitude and the source region did not feature a filament. Our magnetic helicity sign proxies include the analysis of magnetic tongues, soft X-ray and/or extreme-ultraviolet sigmoids, coronal arcade skew, filament emission and absorption threads, and filament rotation. Since the inclination of the post-eruption arcades was not clear, we use the tilt of the polarity inversion line to determine the flux rope axis orientation and coronal dimmings to determine the flux rope footpoints, and therefore, the direction of the axial magnetic field. The comparison of the estimated intrinsic flux rope structure to in situ observations at the Lagrangian point L1 indicated a good agreement with the predictions. Our results highlight the flux rope type determination techniques that are particularly useful for active region eruptions, where most geoeffective CMEs originate.     

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.     

Solar filaments as tracers of subsurface processes

Solar filaments are discussed in terms of two contrasting paradigms. The standard paradigm is that filaments are formed by condensation of coronal plasma into magnetic fields that are twisted or dimpled as a consequence of motions of the fields’ sources in the photosphere. According to a new paradigm, filaments form in rising, twisted flux ropes and are a necessary intermediate stage in the transfer to interplanetary space of dynamo-generated magnetic flux. It is argued that the accumulation of magnetic helicity in filaments and their coronal surroundings leads to filament eruptions and coronal mass ejections. These ejections relieve the Sun of the flux generated by the dynamo and make way for the flux of the next cycle.     

Helicity as a Component of Filament Formation

In this paper we seek the origin of the axial component of the magnetic field in filaments by adapting theory to observations. A previous paper (Mackay, Gaizauskas, and van Ballegooijen, 2000) showed that surface flows acting on potential magnetic fields for 27 days – the maximum time between the emergence of magnetic flux and the formation of large filaments between the resulting activity complexes – cannot explain the chirality or inverse polarity nature of the observed filaments. We show that the inclusion of initial helicity, for which there is observational evidence, in the flux transport model results in sufficiently strong dextral fields of inverse polarity to account for the existence and length of an observed filament within the allotted time. The simulations even produce a large length of dextral chirality when just small amounts of helicity are included in the initial configuration. The modeling suggests that the axial field component in filaments can result from a combination of surface (flux transport) and sub-surface (helicity) effects acting together. Here surface effects convert the large-scale helicity emerging in active regions into a smaller-scale magnetic-field component parallel to the polarity inversion line so as to form a magnetic configuration suitable for a filament.     

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.     

Magnetic Energy and Helicity Fluxes at the Photospheric Level

The source of coronal magnetic energy and helicity lies below the surface of the Sun, probably in the convective zone dynamo. Measurements of magnetic and velocity fields can capture the fluxes of both magnetic energy and helicity crossing the photosphere. We point out the ambiguities which can occur when observations are used to compute these fluxes. In particular, we show that these fluxes should be computed only from the horizontal motions deduced by tracking the photospheric cut of magnetic flux tubes. These horizontal motions include the effect of both the emergence and the shearing motions whatever the magnetic configuration complexity is. We finally analyze the observational difficulties involved in deriving such fluxes, in particular the limitations of the correlation tracking methods.     

Magnetic instability of coronal arcades as the origin of two-ribbon flares

The generally accepted scenario for the events leading up to a two-ribbon flare is that a magnetic arcade (supporting a plage filament) responds to the slow photospheric motions of its footpoints by evolving passively through a series of (largely) force-free equilibria. At some critical amount of shear the configuration becomes unstable and erupts outwards. Subsequently, the field closes back down in the manner modelled by Kopp and Pneuman (1976); but the main problem has been to explain the eruptive instability.The present paper analyses the magnetohydrodynamic stability of several possible arcade configurations, including the dominant stabilizing effect of line-tying at the photospheric footpoints. One low-lying force-free structure is found to be stable regardless of the shear; also some of the arcades that lie on the upper branch of the equilibrium curves are shown to be stable. However, another force-free configuration appears more likely to represent the preflare structure. It consists of a large flux tube, anchored at its ends and surrounded by an arcade, so that the field transverse to the arcade axis contains a magnetic island. Such a configuration is found to become unstable when either the length of the structure, the twist of the flux tube, or the height of the island becomes too great; the higher the tube is situated, the smaller is the twist required for instability.     

Evolution of fibrils with special reference to flare activity

We show observational results on the pre-flare evolutions of H structures as well as the developments of H flares. It is shown that the chromospheric features are brought to a sheared state before flares due to motions of footpoints which correspond to particular sunspot motions. Generally in evolutions of the chromospheric features it is found that motions and reconnections of the footpoints play essential roles. The following three stages are found for development of the neutral line filament before flares: (1) formation of a filament as a result of reconnection; (2) increase of the shear of the filament due to the shear motion; and (3) reconnection of fine components of the filament to form an elongated component immediately before flares. We further show developments of two particular flares with and without the filament, and point out basic release processes of flares. The flare that occurred at the filament (July 5, 1974) started with the activation of the elongated component of the filament after the process (3). The main phase of a two-ribbon flare is considered as the rises of short components of the filament triggered by the rising motion of the elongated component. The flare of September 10, 1974 occurred at the region where fibrils connect the sunspots in distorted form. Pre-flare distortion was produced by translational rotation of the sunspot. Development of this two-ribbon flare is interpreted as being due to successive rises of the fibrils with a self-trigger mechanism.On leave from Tokyo Astronomical Observatory (present address).     

Implications of rapid footpoint motions of photospheric flux tubes for coronal heating

Some recent observations at Pic-du-Midi (Mulleret al., 1992a) suggest that the photospheric footpoints of coronal magnetic field lines occasionally move rapidly with typical velocities of the order 3 km s^–1 for about 3 or 4 min. We argue that such occasional rapid footpoint motions could have a profound impact on the heating of the quiet corona. Qualitative estimates indicate that these occasional rapid motions can account for the entire energy flux needed to heat the quiet corona. We therefore carry out a mathematical analysis to study in detail the response of a vertical thin flux tube to photospheric footpoint motions in terms of a superposition of linear kink modes for an isothermal atmosphere. We find the resulting total energy that is asymptotically injected into an isothermal atmosphere (i.e., an atmosphere without any back reflection). By using typical parameter values for fast and slow footpoint motions, we show that, even if the footpoints spend only 2.5% of the time undergoing rapid motions, still these rapid motions could be more efficient in transporting energy to the corona than the slow motions that take place most of the time.     

The Magnetic Helicity Budget of a cme-Prolific Active Region

Coronal mass ejections (CMEs) are thought to be the way by which the solar corona expels accumulated magnetic helicity which is injected into the corona via several methods. DeVore (2000) suggests that a significant quantity is injected by the action of differential rotation, however Démoulin et al. (2002b), based on the study of a simple bipolar active region, show that this may not be the case. This paper studies the magnetic helicity evolution in an active region (NOAA 8100) in which the main photospheric polarities rotate around each other during five Carrington rotations. As a result of this changing orientation of the bipole, the helicity injection by differential rotation is not a monotonic function of time. Instead, it experiences a maximum and even a change of sign. In this particular active region, both differential rotation and localized shearing motions are actually depleting the coronal helicity instead of building it. During this period of five solar rotations, a high number of CMEs (35 observed, 65 estimated) erupted from the active region and the helicity carried away has been calculated, assuming that each can be modeled by a twisted flux rope. It is found that the helicity injected by differential rotation (–7×10⁴² Mx²) into the active region cannot provide the amount of helicity ejected via CMEs, which is a factor 5 to 46 larger and of the opposite sign. Instead, it is proposed that the ejected helicity is provided by the twist in the sub-photospheric part of the magnetic flux tube forming the active region.     

Conservation of both current and helicity in a quadrupolar model for solar flares

A model for a solar flare, involving magnetic reconnection transferring flux and current between current-carrying magnetic loops connecting two pairs of footpoints, is generalized to include conservation of magnetic helicity during reconnection, as well as conservation of current at all four footpoints. For a set of force-free loops, with the ith loop having flux F _i and current I _i, the self and mutual helicities are proportional to the self and mutual inductances with the constant of proportionality determined by α_i=F _i/μ₀ I _i. In a constant-α model, the change in magnetic energy is proportional to the change in helicity, and conservation of helicity implies conservation of magnetic energy, so that a flare cannot occur. In a quadrupolar model, with α₁>α₂ initially, α₁ increases and α₂ decreases when flux and current are transferred from loops 1 and 2 to loops 3 and 4. A model that conserves both current and helicity is constructed; it depends on the initial αs, and otherwise is somewhat simpler than when helicity is neglected.     

Determination of magnetic helicity content of solar active regions from SOHO/MDI magnetograms

Chae (2001) first proposed a method of self-consistently determining the rate of change of magnetic helicity using a time series of longitudinal magnetograms only, such as taken by SOHO/MDI. Assuming that magnetic fields in the photosphere are predominantly vertical, he determined the horizontal component of velocity by tracking the displacements of magnetic flux fragments using the technique of local correlation tracking (LCT). In the present paper, after briefly reviewing the recent advance in helicity rate measurement, we argue that the LCT method can be more generally applied even to regions of inclined magnetic fields. We also present some results obtained by applying the LCT method to the active region NOAA 10365 under emergence during the observable period, which are summarized as follows. (1) Strong shearing flows were found near the polarity inversion line that were very effective in helicity injection. (2) Both the magnetic flux and helicity of the active region steadily increased during the observing period, and reached 1.2 × 10²² Mx and 8 ×10⁴² Mx², respectively, 4.5 days after the birth of the active region. (3) The corresponding ratio of the helicity to the square of the magnetic flux, 0.05, is roughly compatible with the values determined by other studies using linear-force-free modeling. (4) A series of flares took place while the rate of helicity injection was high. (5) The choice of a smaller window size or a shorter time interval in the LCT method resulted in a bigger value of the LCT velocity and a bigger value of the temporal fluctuation of the helicity rate. (6) Nevertheless when averaged over a time period of about one hour or longer, the average rate of helicity became about the same within about 10%, almost irrespective of the chosen window size and time interval, indicating that short-lived, fluctuating flows may be insignificant in transferring magnetic helicity. Our results suggest that the LCT method may be applied to 96-minute cadence full-disk MDI magnetograms or other data of similar kind, to provide a practically useful, if not perfect, way of monitoring the magnetic helicity content of active regions as a function of time.     

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.     

Determination of magnetic helicity content of solar active regions from SOHO/MDI magnetograms

Chae (2001) first proposed a method of self-consistently determining the rate of change of magnetic helicity using a time series of longitudinal magnetograms only, such as taken by SOHO/MDI. Assuming that magnetic fields in the photosphere are predominantly vertical, he determined the horizontal component of velocity by tracking the displacements of magnetic flux fragments using the technique of local correlation tracking (LCT). In the present paper, after briefly reviewing the recent advance in helicity rate measurement, we argue that the LCT method can be more generally applied even to regions of inclined magnetic fields. We also present some results obtained by applying the LCT method to the active region NOAA 10365 under emergence during the observable period, which are summarized as follows. (1) Strong shearing flows were found near the polarity inversion line that were very effective in helicity injection. (2) Both the magnetic flux and helicity of the active region steadily increased during the observing period, and reached 1.2 × 10²² Mx and 8 ×10⁴² Mx², respectively, 4.5 days after the birth of the active region. (3) The corresponding ratio of the helicity to the square of the magnetic flux, 0.05, is roughly compatible with the values determined by other studies using linear-force-free modeling. (4) A series of flares took place while the rate of helicity injection was high. (5) The choice of a smaller window size or a shorter time interval in the LCT method resulted in a bigger value of the LCT velocity and a bigger value of the temporal fluctuation of the helicity rate. (6) Nevertheless when averaged over a time period of about one hour or longer, the average rate of helicity became about the same within about 10%, almost irrespective of the chosen window size and time interval, indicating that short-lived, fluctuating flows may be insignificant in transferring magnetic helicity. Our results suggest that the LCT method may be applied to 96-minute cadence full-disk MDI magnetograms or other data of similar kind, to provide a practically useful, if not perfect, way of monitoring the magnetic helicity content of active regions as a function of time.     

Are CME-Related Dimmings Always a Simple Signature of Interplanetary Magnetic Cloud Footpoints?

Coronal dimmings are often present on both sides of erupting magnetic configurations. It has been suggested that dimmings mark the location of the footpoints of ejected flux ropes and, thus, their magnetic flux can be used as a proxy for the flux involved in the ejection. If so, this quantity can be compared to the flux in the associated interplanetary magnetic cloud to find clues about the origin of the ejected flux rope. In the context of this physical interpretation, we analyze the event, flare, and coronal mass ejection (CME) that occurred in active region 10486 on 28 October 2003. The CME on this day is associated with large-scale dimmings, located on either side of the main flaring region. We combine SOHO/Extreme Ultraviolet Imaging Telescope data and Michelson Doppler Imager magnetic maps to identify and measure the flux in the dimming regions. We model the associated cloud and compute its magnetic flux using in situ observations from the Magnetometer Instrument and the Solar Wind Electron Proton Alpha Monitor aboard the Advance Composition Explorer. We find that the magnetic fluxes of the dimmings and magnetic cloud are incompatible, in contrast to what has been found in previous studies. We conclude that, in certain cases, especially in large-scale events and eruptions that occur in regions that are not isolated from other flux concentrations, the interpretation of dimmings requires a deeper analysis of the global magnetic configuration, since at least a fraction of the dimmed regions is formed by reconnection between the erupting field and the surrounding magnetic structures.     

The Magnetic Field, Horizontal Motion and Helicity in a Fast Emerging Flux Region which Eventually forms a Delta Spot

We studied the behavior of magnetic field, horizontal motion and helicity in a fast emerging flux region NOAA 10488 which eventually forms a δ spot. It is found that the rotation of photospheric footpoints forms in the earlier stage of magnetic flux emergence and the relative shear motion of different magnetic flux systems appears later in this active region (AR). Therefore the emerging process of the AR can be separated into two phases: rotation and shear. We have computed the magnetic helicity injected into the corona using the local correlation tracking (LCT) technique. Furthermore we determined the vertical component of current helicity density and the vertical component of induction electric fields E_z = (V× B)_z in the photosphere. Particularly we have presented the comparison of the injection rate of magnetic helicity and the variation of the current helicity density. The main results are as follows: (1) The strong shear motion (SSM) between the new emerging flux system and the old one brings more magnetic helicity into the corona than the twisting motions. (2) After the maturity of the main bipolar spots, their twist decreases and the SSM becomes dominant and the major contributor of magnetic non-potentiality in the solar atmosphere in this AR. (3) The positions of the maxima of E_z (about 0.1 ∼ 0.2 V cm⁻¹) shift from the twisting areas to the areas showing SSMs as the AR evolved from the rotation phase to the shear one, but no obvious correlation is found between the kernels of Hα flare and E_z for the M1.6 flare in this AR. (4) The coronal helicity inferred from the horizontal motion of this AR amounts to −6 × 10⁴³ Mx². It is comparable with the coronal helicity of ARs producing flares with coronal mass ejections (CMEs) or helicity carried away by magnetic clouds (MCs) reported in previous studies (Nindos, Zhang, and Zhang, 2003; Nindos and Andrews, 2004). In addition, the formation of the δ configuration in this AR belongs to the third formation type indicated by Zirin and Liggett (1987), i.e., collision of opposite polarities from different dipoles, and can be naturally explained by the SSM.     

The eruption of a small filament in the quiet Sun

We analyzed multi-wavelength observations of the eruption of a small-scale filament on the quiet Sun. The filament first became thicker, then broke into two, and eventually underwent a partial eruption with possible rotating motion. The eruption was followed by a small flare with three bright kernels on either side of the eruptive section in Hα and a small coronal dimming near one end of this section in EUV and soft X-ray. On the photosphere, MDI magnetograms show the flux emergence or motions and cancellation between opposite polarities before and during the filament eruption. We find that this small-scale filament shows the similar characteristics as the previous findings in the large-scale filament eruptions on the multi-wavelength, indicating the common nature.     

The Interplanetary Responses to the Great Solar Activities in Late October 2003

Based on the observations of the Sun and the interplanetary medium, a series of solar activities in late October 2003 and their consequences are studied comprehensively. Thirteen X-ray flares with importance greater than M-class, six frontside halo coronal mass ejections (CMEs) with span angle larger than 100 and three associated eruptions of filament materials are identified by examining lots of solar observations from October 26 to 29. All these flares were associated with type III radio bursts, all the frontside halo CMEs were accompanied by type II or type II-like radio bursts. Particularly, among these activities, two major solar events caused two extraordinary enhancements (exceeding 1000 particles/(cm²s^–1sterMev^–1) of solar energetic particle (SEP) flux intensity near the Earth, two large ejecta with fast shocks preceding, and two great geomagnetic storms with Dst peak value of –363 and –401 nT, respectively. By using a cross correlation technique and a force-free cylindrical flux rope model, the October 29 magnetic cloud associated with the largest CME are analyzed, including its orientation and the sign of its helicity. It is found that the helicity of the cloud is negative, contrary to the regular statistical pattern that negative- and positive-helical interplanetary magnetic clouds would be expected to come from northern and southern solar hemisphere. Moreover, the relationship between the orientation of magnetic cloud and associated filament is discussed. In addition, some discussion concerning multiple-magnetic-cloud structures and SEP events is also given.