In recent years, solar filaments and their birth grounds called filament channels (Gaizauskas, 1998), which always overlie photospheric polarity inversion lines (PILs), have been classified by the orientation of their main axial magnetic field. This orientation, named the filament chirality (Martin et al., 1994) may take one of two forms: dextral or sinistral. Dextral/sinistral filaments have an axial magnetic field that points to the right/left when the main axis of the filament is viewed from the positive polarity side of the PIL. In force-free field models (Aulanier and Démoulin, 1998; Mackay et al., 1999; van Ballegooijen et al., 2000; Mackay and van Ballegooijen, 2005) this chirality is directly related to the dominant sign of magnetic helicity that is contained within the filament and filament channel. A dextral filament will contain dominantly negative helicity, a sinistral filament positive helicity. As filaments and their channels form over a wide range of latitudes on the Sun, ranging from the active belts to the polar crown, they may be regarded as useful indicators of sheared non-potential fields and magnetic helicity within the solar corona.
A surprising feature of the chirality of filaments is that it displays a large-scale hemispheric pattern: dextral/sinistral filaments dominate in the northern/southern hemispheres, respectively (Martin et al., 1994; Zirker et al., 1997; Pevtsov et al., 2003; Yeates et al., 2007). This pattern is intriguing as it is exactly opposite to that expected from differential rotation acting on a North-South coronal arcade. Although dextral/sinistral filaments dominate in the northern/southern hemisphere, observations show that exceptions to this pattern do occur. Therefore any model which tries to explain the formation of filaments and their dominant axial magnetic fields must explain not only the origin of this hemispheric pattern but also why exceptions to it arise.
Since filament chirality is directly related to magnetic helicity (dextral negative, sinistral positive) the formation and transport of filaments across the solar surface is an indication of the global pattern of magnetic helicity transport on the Sun (Yeates et al., 2008a), a key feature in explaining many eruptive phenomena. Static extrapolation techniques (including MHD models of the relaxation type) cannot study the generation nor transport of this helicity across the surface of the Sun. This can only be achieved with models that couple the evolution of both photospheric and coronal fields over long periods of time.
The first attempt to explain the hemispheric pattern of filaments using global magnetic flux transport models was carried out by van Ballegooijen et al. (1998). By using observed magnetic flux distributions and initial coronal fields which were potential, they simulated the non-equilibrium evolution of the coronal field. They found that the flux transport effects acting alone on potential fields create approximately equal numbers of dextral and sinistral channels in each hemisphere, in contradiction with observations. Following this, Mackay and van Ballegooijen (2005) re-considered the origin of the hemispheric pattern through combined flux transport and magneto-frictional relaxation simulations (Section 3.2.3), where the coronal field responds to surface motions by relaxing to a nonlinear force-free equilibrium. In the simulations the authors considered an idealised setup of initially isolated bipoles. Therefore, in contrast to the study of van Ballegooijen et al. (1998), they did not use initial potential fields. The authors demonstrate that the hemispheric pattern of filaments may be explained through the observational properties of newly-emerging bipoles such as (i) their dominant tilt angles (–10°:30°, Wang and Sheeley Jr, 1989), and (ii) the dominant helicity with which they emerge in each hemisphere (Pevtsov et al., 1995). A key feature of these simulations was that the possible occurrence of exceptions to the hemispheric pattern was quantified for the first time, arising from large positive bipole tilt angles and minority helicity.
In a more conclusive study, the results of Mackay and van Ballegooijen (2005) have been tested through a direct comparison between theory and observations by Yeates et al. (2007, 2008b). First, they used H observations from BBSO over a 6 month period to determine the location and chirality of 109 filaments (Yeates et al., 2007) relative to the underlying magnetic flux. In the second stage they used combined magnetic flux transport and magneto-frictional simulations (Section 3.2.3), based on actual photospheric magnetic distributions found on the Sun. Unlike previous studies, these were run for the whole six month period without ever resetting the surface field back to that found in observations or the coronal field to potential. To maintain accuracy over this time, 119 bipoles had to be emerged with properties determined from observations. Hence, the simulations were able to consider long term helicity transport across the solar surface from low to high latitudes. Yeates et al. (2008b) carried out a direct one-to-one comparison of the chirality produced by the model with the observed chirality of the filaments. An example of this can be seen in Figure 17, where Figure 17a shows the global field distribution after 108 days of evolution. The enlargement in Figure 17b shows a simulated flux rope structure with an axial field of dextral chirality. The real H filament that formed at this location can be seen in Figure 17c. Through studying the barbs and applying a statistical technique, the filament was determined to be of dextral chirality so the chirality formed in the simulation matches that of the filament.
Through varying the sign and amount of helicity emerging within the bipoles, Yeates et al. (2008b) (see their Figure 5b) show that by emerging dominantly negative helicity in the northern hemisphere and positive in the southern, a 96% agreement can be found between the observations and simulations. An important feature is that the agreement is equally good for minority chirality filaments as well as for dominant chirality filaments. Therefore, the global coronal model applied was equally good in producing positive and negative helicity regions at the correct times and spatial locations to represent solar filaments. Another key feature of the simulations is that a better agreement between the observations and simulations is found the longer the simulations are run. This indicates that the Sun has a long term memory of the transport of helicity from low to high latitudes. The reason for this high agreement is described in the paper of Yeates and Mackay (2009b) where seven different mechanisms are involved in producing the observed chiralities. The results demonstrate that the combined effects of differential rotation, meridional flow, supergranular diffusion, and emerging twisted active regions are sufficient to produce the observed hemispheric pattern of filaments. While the model of Yeates et al. (2008b) obtained an excellent agreement with the observed chirality of filaments, the 6 month simulation was unable to reproduce dextral/sinistral chirality along the polar crown PILs in the northern/southern hemispheres. The cause was that the simulation was not run for long enough to allow meridional flow, which acts on a time scale of 2 yr (see Section 2.2.1), to transport the helicity produced at low latitudes up into the polar regions. A later simulation running for a full 11-year solar cycle (see Figure 4a of Yeates and Mackay, 2012) was able to obtain the correct dextral/sinistral chirality along the polar crown PILs in each hemisphere, once the duration of the simulation exceeded the meridional flow timescale. This shows that, at least in the context of solar filaments, the flux transport and magneto-frictional model adequately describes the build-up and transport of helicity from low to high latitudes on the Sun. The model has subsequently been applied to the formation of magnetic flux ropes and their subsequent loss of equilibrium (Yeates and Mackay, 2009a; Yeates et al., 2010a), a possible mechanism for the initiation of coronal mass ejections.
Living Rev. Solar Phys. 9, (2012), 6
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