Conditions for the Formation and Maintenance of Filaments – (Invited Review)

Observational conditions for the formation and maintenance of filaments are reviewed since 1989 in the light of recent findings on their structure, chirality, inferred magnetic topology, and mass flows. Recent observations confirm the necessary conditions previously cited: (1) their location at a boundary between opposite-polarity magnetic fields (2) a system of overlying coronal loops, (3) a magnetically-defined channel beneath, (4) the convergence of the opposite-polarity network magnetic fields towards their common boundary within the channel and (5) cancellation of magnetic flux at the common polarity boundary. Evidence is put forth for three additional conditions associated with fully developed filaments: (A) field-aligned mass flows parallel with their fine structure (B) a multi-polar background source of small-scale magnetic fields necessary for the formation of the filament barbs and (C) a handedness property known as chirality which requires them to be either of two types, dextral or sinistral. One-to-one relationships have been established between the chirality of filaments and the chirality of their filament channels and overlying coronal arcades. These findings reinforce earlier evidence that every filament magnetic field is separate from the magnetic field of the overlying arcade but both are parts of a larger magnetic field system. The larger system has at least quadrupolar footprints in the photosphere and includes the filament channel and subphotospheric magnetic fields, This ‘systems’ view of filaments and their environment enables new perspectives on why arcades and channels are invariable conditions for their existence. Supplementary material to this paper is available in electronic form at http://dx.doi.org/10.1023/A:1005026814076     

Morphology of H-alpha filaments and filament channel systems

Ring-like filaments have been detected on the spectroheliograms in the H-alpha line. Inside these filaments the magnetic field flux has a predominant polarity. Some of the dark filaments are connected by filament channels which can be seen at the limb either as (a) weak prominences or (b) dense low chromospheric features or (c) multi-channel system of matter flow between two prominences or (d) common quiescent prominences. The filament and the filament channel together form a continuous closed contour and outline the region of thef polarity particularly at the beginning of the solar cycle. The change in sign of the polar field of the Sun is associated with the drift of the filament band to high latitudes.     

A potential-field model for dextral and sinistral filament channels

Recent observations of Martin, Bilimoria, and Tracadas (1995) have revealed two new magnetic and structural classes for solar filaments and filament channels. The magnetic classes are called sinistral and dextral, while the structural classes are left-bearing and right-bearing. Dextral filaments dominate in the northern hemisphere and sinistral in the southern. A model consistent with the observations is developed with magnetic sources that represent the network flux on both sides of the channel and extra concentrations of flux that produce the strong field component along the channel. We suggest that it is the imbalance of flux locations along the channel that creates the field of a filament channel. The resulting separatrix surfaces have distinct upper and lower boundaries that may produce the upper boundary of the filament cavity or filament and the lower boundary of the filament. The model is applied to a specific filament channel, with discrete sources and sinks that represent the flux observed in a photospheric magnetogram. The resulting three-dimensional field lines near the filament location are low-lying and possess dips.     

A model combining the polar and the sector structured solar magnetic fields

A phenomenological model of the interplay between the polar magnetic fields of the Sun and the solar sector structure is discussed. Current sheets separate regions of opposite polarity and mark the sector boundaries in the corona. The sheets are visible as helmet streamers. The solar sector boundary is tilted with respect to central meridian, and boundaries with opposite polarity change are oppositely tilted. The tilt of a given type of boundary [(+, ?) or (?, +)] changes systematically during the sunspot cycle as the polarity of the polar fields reverses. Similar reversals of the position of the streamers at the limbs takes place. If we consider (a) a sunspot cycle where the northern polar field is inward (?) during the early part of the cycle and (b) a (+, ?) sector boundary at central meridian then the model predicts the following pattern; a streamer at high northern latitudes should be observed over the west limb together with a corresponding southern streamer over the east limb. The current sheet runs now NW-SE. At sunspot maximum the boundary is more in the N-S direction; later when the polar fields have completed their reversal the boundary runs NE-SW and the northern streamer should be observed over the east limb and the southern streamer over the west limb. Observational evidence in support of the model is presented, especially the findings of Hansen, Sawyer and Hansen and Koomen and Howard that the K-corona is highly structured and related to the solar sector structure.     

Three-Dimensional Nonlinear Force-Free Field Reconstruction of Solar Active Region 11158 by Direct Boundary Integral Equation

A three-dimensional coronal magnetic field is reconstructed for the NOAA active region 11158 on 14 February 2011. A GPU-accelerated direct boundary integral equation (DBIE) method is implemented which is approximately 1000 times faster than the original DBIE used on solar non-linear force-free field modeling. Using the SDO/HMI vector magnetogram as the bottom boundary condition, the reconstructed magnetic field lines are compared with the projected EUV loop structures as observed in the front-view (SDO/AIA) and the side-view (STEREO-A/B) images for the first time; they show very good agreement three-dimensionally. A quantitative comparison with some stereoscopically reconstructed coronal loops shows that the average misalignment angles in our model are at the same order as the state-of-the-art results obtained from reconstructed coronal loops. It is found that the observed coronal loop structures can be grouped into a number of closed and open field structures with some central bright coronal loop features around the polarity inversion line. The reconstructed highly sheared magnetic field lines agree very well with the low-lying sigmoidal filament along the polarity inversion line. This central low-lying magnetic field loop system must have played a key role in powering the flare. It should be noted that while a strand-like coronal feature along the polarity inversion line may be related to the filament, one cannot simply interpret all the coronal bright features along the polarity inversion line as manifestation of the filament without any stereoscopic information.     

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.     

Stereoscopic Analysis of the 31 August 2007 Prominence Eruption and Coronal Mass Ejection

The spectacular prominence eruption and CME of 31 August 2007 are analyzed stereoscopically using data from NASA??s twin Solar Terrestrial Relations Observatory (STEREO) spacecraft. The technique of tie pointing and triangulation (T&T) is used to reconstruct the prominence (or filament when seen on the disk) before and during the eruption. For the first time, a filament barb is reconstructed in three-dimensions, confirming that the barb connects the filament spine to the solar surface. The chirality of the filament system is determined from the barb and magnetogram and confirmed by the skew of the loops of the post-eruptive arcade relative to the polarity reversal boundary below. The T&T analysis shows that the filament rotates as it erupts in the direction expected for a filament system of the given chirality. While the prominence begins to rotate in the slow-rise phase, most of the rotation occurs during the fast-rise phase, after formation of the CME begins. The stereoscopic analysis also allows us to analyze the spatial relationships among various features of the eruption including the pre-eruptive filament, the flare ribbons, the erupting prominence, and the cavity of the coronal mass ejection (CME). We find that erupting prominence strands and the CME have different (non-radial) trajectories; we relate the trajectories to the structure of the coronal magnetic fields. The possible cause of the eruption is also discussed.     

Modelling the Global Solar Corona II: Coronal Evolution and Filament Chirality Comparison

This paper considers the hemispheric pattern of solar filaments using newly developed simulations of the real photospheric and 3D coronal magnetic fields over a six-month period, on a global scale. The magnetic field direction in the simulation is compared directly with the chirality of observed filaments, at their observed locations. In our model the coronal field evolves through a continuous sequence of nonlinear force-free equilibria, in response to the changing photospheric boundary conditions and the emergence of new magnetic flux. In total 119 magnetic bipoles with properties matching observed active regions are inserted. These bipoles emerge twisted and inject magnetic helicity into the solar atmosphere. When we choose the sign of this active-region helicity to match that observed in each hemisphere, the model produces the correct chirality for up to 96% of filaments, including exceptions to the hemispheric pattern. If the emerging bipoles have zero helicity, or helicity of the opposite sign, then this percentage is much reduced. In addition, the simulation produces a higher proportion of filaments with the correct chirality after longer times. This indicates that a key element in the evolution of the coronal field is its long-term memory, and the build-up and transport of helicity from low to high latitudes over many months. It highlights the importance of continuous evolution of the coronal field, rather than independent extrapolations at different times. This has significant consequences for future modelling such as that related to the origin and development of coronal mass ejections.     

Properties of filaments in solar cycle 20-23 from McIntosh Archive

A filament is a cool, dense structure suspended in the solar corona. The eruption of a filament is often associated with a coronal mass ejection(CME), which has an adverse effect on space weather. Hence,research on filaments has attracted much attention in the recent past. The tilt angle of active region(AR)magnetic bipoles is a crucial parameter in the context of the solar dynamo, which governs the conversion efficiency of the toroidal magnetic field to poloidal magnetic field. Filaments always form over polarity inversion lines(PILs), so the study of tilt angles for these filaments can provide valuable information about generation of a magnetic field in the Sun. We investigate the tilt angles of filaments and other properties using McIntosh Archive data. We fit a straight line to each filament to estimate its tilt angle. We examine the variation of mean tilt angle with time. The latitude distribution of positive tilt angle filaments and negative tilt angle filaments reveals that there is a dominance of positive tilt angle filaments in the southern hemisphere and negative tilt angle filaments dominate in the northern hemisphere. We study the variation of the mean tilt angle for low and high latitudes separately. Investigations of temporal variation with filament number indicate that total filament number and low latitude filament number vary cyclically, in phase with the solar cycle. There are fewer filaments at high latitudes and they also show a cyclic pattern in temporal variation. We also study the north-south asymmetry of filaments with different latitude criteria.     

Non-radial motion of eruptive filaments

We develop a simple model to explain the non-radial motion of eruptive solar filaments under solar minimum conditions. The global magnetic field is derived from the first and third components of the spherical harmonic expansion of a magnetic scalar potential. The filament is modeled as a toroidal current located above the mid-latitude polarity inversion line. We investigate the stability of the filament against changes in the filament current and attempt to explain the non-radial motion and acceleration of the eruptive filament. We also discuss the limitations of this model.     

Modelling the Global Solar Corona: III. Origin of the Hemispheric Pattern of Filaments

We consider the physical origin of the hemispheric pattern of filament chirality on the Sun. Our 3D simulations of the coronal field evolution over a period of six months, based on photospheric magnetic measurements, were previously shown to be highly successful at reproducing observed filament chiralities. In this paper we identify and describe the physical mechanisms responsible for this success. The key mechanisms are found to be (1) differential rotation of north – south polarity inversion lines, (2) the shape of bipolar active regions, and (3) evolution of skew over a period of many days. As on the real Sun, the hemispheric pattern in our simulations holds in a statistical sense. Exceptions arise naturally for filaments in certain locations relative to bipolar active regions or from interactions among a number of active regions.     

The height stratification of solar magnetic fields in cycles 21–23

The radial component of the solar magnetic field, Br, was calculated in the potential approximation in the height range from 1 to 2.5 solar radii, Ro. According to these data, synoptic maps of the magnetic field for solar cycles 21–23 were constructed. For each 10-degree latitudinal zone, the proportion of its area, S _+field, that was occupied by the “+” field in each rotation was found. In the entire latitudinal zone, the radial component of the field is assumed to be positive if S_+field ≥ 80% and negative if S _+field ≤ 20%. The field proved to be virtually unipolar at the level of the photosphere (R = Ro) during most of the cycle, from the poles to the north and south latitude ≈60°. In the vicinity of minimums between cycles 21 and 22, as well as cycles 22 and 23, for a few rotations of the Sun, the field was almost unipolar within the range of latitudes (?40°)-90°. At R = 2.5 Ro, for most of each cycle, the field was unipolar in the range of latitudes (?20°-(-90°)) and (20°–90°). According to our interpretation, the shift of the polar-field boundary to the equator with height reflects superradial expansion of open magnetic flux tubes from the polar coronal holes. It was found that the reversal of the polar fields began with 1–2 rotations and ended from 2 to 14 solar rotations earlier at great heights than at the surface of the Sun. This indicates that the reversal of the large-scale field occurs first and then that of the small-scale one. In the study of the sectoral structure of the magnetic field at different heights it was found that the boundaries that rotate with a period of less than the Carrington revolution extend to greater heights than the boundaries with a Carrington or longer period. We assume that the boundaries of the first type are formed by the large-scale structures of the magnetic field and the boundaries of the second type are determined by the active regions.     

Modelling the Global Solar Corona: Filament Chirality Observations and Surface Simulations

The hemispheric pattern of solar filaments is considered in the context of the global magnetic field of the solar corona. In recent work Mackay and van Ballegooijen have shown how, for a pair of interacting magnetic bipoles, the observed chirality pattern could be explained by the dominant range of bipole tilt angles and helicity in each hemisphere. This study aims to test this earlier result through a direct comparison between theory and observations, using newly developed simulations of the actual surface and 3D coronal magnetic fields over a 6-month period, on a global scale. We consider two key components: (1) observations of filament chirality for the sample of 255 filaments and (2) our new simulations of the large-scale surface magnetic field. Based on a flux-transport model, these will be used as the lower boundary condition for the future 3D coronal simulations. Our technique differs significantly from those of other authors, where the coronal field is either assumed to be purely potential or has to be reset back to potential every 27 days for the photospheric field to remain accurate. In our case we ensure accuracy by the insertion of newly emerging bipolar active regions, based on observed photospheric synoptic magnetograms. The large-scale surface field is shown to remain accurate over the 6-month period, without any resetting. This new technique will enable future simulations to consider the long-term buildup and transport of helicity and shear in the coronal magnetic field over many months or years.     

Dynamics of the circumpolar magnetic field of the Sun at a maximum of cycle 24

Data on the value and sign of the circumpolar magnetic field of the Sun at a maximum of its activity in cycle 24 have been analyzed. The data were obtained from observations at the Wilcox Solar Observatory and from synoptic maps of the magnetic field built in the SOLIS project (SOLIS stands for Synoptic Optical Long-term Investigations of the Sun) and with the Helioseismic and Magnetic Imager (HMI). We studied the dynamics of the total magnetic fields in the circumpolar latitudinal zones of different extension in the northern and southern hemispheres. The epochs of the sign reversal of the polar magnetic field were determined. It was found that, in cycle 24, the magnetic field polarity changed three times in the northern hemisphere and only once in the southern one. In the northern hemisphere, the reversal of the polar magnetic field finished approximately a year earlier than that in the southern one. The obtained results are compared to the data on the sign reversal of the polar magnetic field of the Sun reported for the previous solar cycles.     

Polarity Reversal Time of the Magnetic Dipole Component of the Sun in Solar Cycle 24

The Sun’s general magnetic field has shown polarity reversal three times during the last three solar cycles. We attempt to estimate the upcoming polarity reversal time of the solar magnetic dipole by using the coronal field model and synoptic data of the photospheric magnetic field. The scalar magnetic potential of the coronal magnetic field is expanded into a spherical harmonic series. The long-term variations of the dipole component ( $g^{0}_{1}$ ) calculated from the data of National Solar Observatory/Kitt Peak and Wilcox Solar Observatory are compared with each other. It is found that the two $g^{0}_{1}$ values show a similar tendency and an approximately linear increase between the Carrington rotation periods CR 2070 and CR 2118. The next polarity reversal is estimated by linear extrapolation to be between CR 2132.2 (December 2012) and CR2134.8 (March 2013).     

Observations of the reappearance of polar coronal holes and the reversal of the polar magnetic field

We examine observations relating to the evolution of the polar magnetic field around sunspot maximum, when the net polar flux reverses polarity and coronal holes redevelop around the poles. Coronal hole observations during the last two solar maxima are examined in detail. Long-term averages of the latitudinal dependence of the photospheric magnetic field and the evolutionary pattern of the polar crown filaments are used to trace the poleward motion of the reversal of the large-scale surface field, and are compared to the redevelopment of the polar holes. The polar holes evolve from small, mid-latitude holes of new-cycle polarity which expand poleward until they join and cover the pole. We find that the appearance of these mid-latitude holes, the peak of flux emergence at low latitudes, and the polar polarity reversal all occur within a few solar rotations. Lagging 6 months to 1 1/2 yr after this time, the polar crown disappears and the polar holes redevelop.These results are examined in the context of phenomenological models of the solar cycle. We believe the following results in particular must be accounted for in successful models of the solar cycle: (1) The process of polarity reversal and redevelopment of the polar holes is discontinuous, occurring in 2 or 3 longitude bands, with surges of flux of old-cycle polarity interrupting the poleward migration of new-cycle flux. There is a persistent asymmetry in these processes between the two hemispheres; the polarity reversal in the two hemispheres is offset by 6 months to 1 1/2 yr. (2) Contrary to the Babcock hypothesis, the polar crown disappears months after the magnetic polar reversal. We suggest one possible scenario to explain this effect. (3) Our observations support suggestions of a poleward meridional flow around solar maximum that cannot be accounted for by Leighton-type diffusion.     

Global Magnetic Patterns of Chirality

During the past five years at least six manifestations of a global organization of solar magnetic fields have been recognized. The magnetic chirality (handedness) of the following features shows a hemispheric preference: filament channels, quiescent filaments, sunspot whorls, superpenumbral fibrils, coronal arcades, and interplanetary clouds associated with CMEs. Although the patterns are clear in the data, their interpretation and their possible connection to the dynamo is open to question. This paper reviews the observations of the patterns, corrects some misinterpretations, and offers a scenario for the origin of the most marked pattern, the chirality of filaments. We suggest the pattern arises from the reconnection of coronal loops, under the influence of supergranulation and differential rotation. Unlike alternative scenarios, ours relies only on observable surface motions and fields.     

Investigation of the solar differential rotation by hydrogen filaments in 1976–1986

Based on observational data on chromosphere filaments, certain characteristics of solar differential rotation during solar activity cycle No. 21 are determined at Abastumani Astrophysical Observatory.In the northern hemisphere of the Sun, propagation of a quasi-bi-annual impulse of the rotation residual from high latitudes to the equator is found in 1979–1981. It is supposed that this phenomenon might be related to the polarity reversal in the northern hemisphere of the Sun in 1981.0.     

A Non-Linear Force-Free Field Model for the Evolving Magnetic Structure of Solar Filaments

In this paper the effect of a small magnetic element approaching the main body of a solar filament is considered through non-linear force-free field modeling. The filament is represented by a series of magnetic dips. Once the dips are calculated, a simple hydrostatic atmosphere model is applied to determine which structures have sufficient column mass depth to be visible in Hα. Two orientations of the bipole are considered, either parallel or anti-parallel to the overlying arcade. The magnetic polarity that lies closest to the filament is then advected towards the filament. Initially for both the dominant and minority polarity advected elements, right/left bearing barbs are produced for dextral/sinsitral filaments. The production of barbs due to dominant polarity elements is a new feature. In later stages the filament breaks into two dipped sections and takes a highly irregular, non-symmetrical form with multiple pillars. The two sections are connected by field lines with double dips even though the twist of the field is less than one turn. Reconnection is not found to play a key role in the break up of the filament. The non-linear force-free fields produce very different results to extrapolated linear-force free fields. For the cases considered here the linear force-free field does not produce the break up of the filament nor the production of barbs as a result of dominant polarity elements.     

The dipole-quadrupole cycle of the background solar magnetic field

The evolution of the background magnetic field with the solar cycle has been studied using the dipole-quadrupole magnetic energy behaviour in a cycle. The combined energy of the axisymmetric dipole, non-axisymmetric quadrupole, and equatorial dipole is relatively lowly variable over the solar cycle. The dipole field changed sign when the quadrupole field was near a maximum, andvice versa. A conceptual picture involving four meridional magnetic polarity sectors proposed to explain these features may be in agreement with equatorial coronal hole observations. The rate of sector rotation is estimated to be 8 heliographic degrees per year faster than the Carrington rotation (P = 27.23^d synodic). Polarity boundaries of sectors located 180° apart show meridional migrations in one direction, while the boundaries of the other two sectors move in the opposite direction. A simple model of how the magnetic field energy varies, subject to specifying reasonable initial photospheric magnetic and velocity field patterns, follows the observed evolution of the dipole and quadrupole field energies quite nicely.