and sinistral in the southern hemisphere. Figure5.2shows one of their plots, illustrating this hemi- spheric pattern. The work ofMartin, Bilimoria, and Tracadas(1994), using Hαimages to infer the magnetic structure of 154 filaments, showed the same global pattern independent of solar cycle,
i.e. the chiralities in each hemisphere do not reverse along with the magnetic polarities every 11
years. They found that the pattern held in a statistical sense, i.e. with exceptions, and held for qui- escent filaments but not “active region filaments” (by which they appear to mean filaments inside or bordering on regions of high magnetic flux density, rather than the “active filaments” referred to above).
Pevtsov, Balasubramaniam, and Rogers(2003) have more recently studied 2310 filaments in the years 2000 and 2001, also using Hαimages from BBSO. They measure the fractional chirality for each filament, defined as
Cf =
Nright−Nleft
Nright+Nleft
, (5.1)
whereNrightandNleftare the number of apparently right-bearing and left-bearing barbs respect- ively. A dextral filament would thus score close toCf = 1, while a sinistral filament would have
Cf ∼ −1. They find that80.2%of quiescent filaments follow the pattern in the northern hemi-
sphere and85.5% in the southern hemisphere. UnlikeMartin, Bilimoria, and Tracadas (1994) they find that the pattern still holds for filaments in active regions, but more weakly (74.9%and 76.7%in the two hemispheres). Note that polar crown filaments were excluded entirely from this study, owing presumably to the difficulty in determining their chirality at the necessary viewing angle.
5.2
Previous Theoretical Models
In this section we review the theories which have been suggested to account for the observed hemispheric pattern in filament chirality. For space reasons we do not describe all models for the formation of filaments; for a recent summary see Mackay, Gaizauskas, and Yeates(2008). Those models, as in this thesis, consider primarily the formation of the magnetic structure. The thermodynamics of prominence plasma are discussed inTandberg-Hanssen(1974) orHeinzel and Anzer(2005).
An influential model for the production of helical magnetic fields by photospheric flux cancellation was proposed byvan Ballegooijen and Martens(1989). The idea, reproduced here in Figure5.3, is a fundamental process which occurs in the simulations described in this thesis. Starting with an initial arcade of potential loops across a photospheric PIL (Figure5.3a), surface motions shear the loops along the PIL (Figure5.3b) and the loop footpoints converge toward the PIL under supergranular diffusion (Figure 5.3c). Reconnection between the two loops (at the point * in Figure5.3d) leads to the formation of a long loop along the PIL, and a short loop perpendicular to
5.2 Previous Theoretical Models 86
Figure 5.3: Formation of helical magnetic fields by flux cancellation and reconnection (Figure 1 ofvan Ballegooijen and Martens,1989, reproduced by permission of the AAS). The rectangle represents the solar photosphere and the dashed line is the PIL.
it. The short loop has sufficient curvature to overcome magnetic buoyancy and submerges beneath the photosphere, while the long loop does not. Subsequent loops (Figure5.3e) then reconnect beneath the long loop and form a helical field structure along the PIL (Figure5.3f). As more flux reconnects and submerges, the flux in the helical field increases and the axis moves higher. A following paper (van Ballegooijen and Martens,1990) tried to apply the model to explain the hemispheric chirality pattern. They pointed out that shearing by differential rotation would pro- duce the correct chirality only for a PIL that makes a large angle with the east-west direction, and then only for a short time. In particular the wrong chirality would form on the east-west directed high-latitude PILs. They suggested instead that differential rotation acting on subsurface fields would produce the correct sign of chirality, if such fields could emerge along the PIL as smaller magnetic bipoles with opposite polarity to the main region. Then reconnection of these bipoles with the overlying field would produce a helical field of the observed chirality. The same idea of differential rotation acting on a subsurface field which then emerges and reconnects was used in the model ofPriest, van Ballegooijen, and Mackay(1996). In contrast to advective motions,Rust and Kumar(1994) invoke the emergence of already helical fields from the convection zone. However, Zirker et al. (1997) argue that we should “resist the temptation to ascribe patterns to unobservable subsurface phenomena”. They disagree with Rust and Kumar(1994) because no Hα fine structure is seen to cross the PIL, and with the emerging bipole theory of Priest, van Ballegooijen, and Mackay(1996) because the emergence of systematically aligned small bipoles along the PIL is not observed either. Instead they suggest that the hemispheric pattern can be explained purely by the observable surface motions. In particular:
5.2 Previous Theoretical Models 87
Figure 5.4: The head-to-tail linkage model ofMartens and Zwaan(2001) for filament formation between two bipoles: (a) configuration leading to dextral chirality, and (b) configuration leading to sinistral chirality (in the northern hemisphere). The dashed lines show the photospheric PILs and thick lines show coronal field lines.
arcade of loops with the correct skew.
2. Diffusion of lower loops towards the PIL and the tilt angle of bipolar regions leads to the formation of helical fields of the correct chirality, by the van Ballegooijen and Martens
(1989) mechanism.
3. Polar crown filaments do not form in situ, but migrate slowly poleward under the meridional flow and grow in size through linking.
The third point is argued also byMartens and Zwaan(2001) in their “head-to-tail linkage” scen- ario. Unlike the above models this assumes that the flux concentrations on either side of the PIL are not part of the same bipolar region, so are not connected above the photosphere prior to the diffusive cancellation and reconnection. The basic mechanism is shown in Figure5.4, which shows their two suggested configurations of two bipoles. The two configurations produce oppos- ite chirality along the PIL between them when loops from the two bipoles reconnect. Martens and Zwaan(2001) suggest that configuration (a), producing the correct chirality, dominates for higher-latitude filaments, supported by observations that filaments tend to go from a leading spot to poleward faculae (i.e. remnants of an older region). They suggest that configuration (b) would be unlikely above the sunspot belts because older regions would have lost their initial tilt due to differential rotation. Thus the hemispheric pattern for mid- to high-latitude filaments is caused by a combination of Hale’s Law (sunspot polarities), Joy’s Law (tilt angles), and differential rota- tion. In this chapter we test the theory for a large sample of filaments, and find there to be other important factors. In particular, filaments do not always occur in the two-bipole configurations of
Martens and Zwaan(2001).
The 3D coronal model in this thesis owes its origins tovan Ballegooijen, Cartledge, and Priest
5.2 Previous Theoretical Models 88
Figure 5.5: Magnetic field structure for two bipoles interacting in the northern hemisphere (Figure 2 ofMackay and van Ballegooijen, 2005, reproduced by permission of the AAS): (a) on day 2 after the bipoles have made cross connections, and (b) after 46 days of evolution, when dextral skew has formed between the two bipoles. The initial bipoles here haveβ =−0.2and tilt angle 10◦. Solid lines represent positive flux, dashed lines negative flux, and dotted lines the PIL. Thick lines are coronal field lines.
produced by the surface motions of differential rotation, meridional flow, and supergranular diffu- sion. However, although the correct chirality was produced on north-south PILs, the opposite chir- ality was produced on east-west PILs, in conflict with observations of polar crown filaments. The magneto-frictional model used in this thesis was developed originally byvan Ballegooijen, Priest, and Mackay(2000) and applied byMackay, Gaizauskas, and van Ballegooijen(2000) to model the formation of filaments in an observed activity complex. They found that continuous shearing over several solar rotations was required to develop the correct chirality, although the photospheric field lost accuracy in their longer runs. The new photospheric simulations developed in Chapter3 of this thesis have enabled us to overcome this difficulty.Mackay, Gaizauskas, and van Ballegoo- ijen(2000) also found that developing skew quickly enough to match observed filaments required additional axial flux emergence (the small bipoles ofvan Ballegooijen and Martens,1990again), for which there is no observational evidence. A more satisfactory alternative was developed by
Mackay and van Ballegooijen(2001) who studied the interaction of two idealised bipoles which were given an initial helicity/twist, as used in this thesis (Chapter4). This study however had a background polar field which led to the wrong chirality being produced in the declining phase of the solar cycle.
By removing the dominant polar field, Mackay and van Ballegooijen (2005) demonstrated the dominant hemispheric pattern for their idealised two-bipolar configurations, in a parameter study varying the twist and tilt angle of the bipoles. Their results demonstrate the hemispheric pat- tern, and show how exceptions would occur for highly tilted bipoles with either weak twist or the minority sign for their hemisphere. One of their runs is reproduced here in Figure5.5, showing