The Hemispheric Pattern of Filaments and Consequences for Filament Formation Duncan H Mackay Solar Physics Group University of St. Andrews
Contents. • Solar Prominences – properties and hemispheric pattern. • Flux Transport Simulations. • Coronal Arcade Observations. • Consequences for Filament Formation.
Solar Prominences. Found in the solar corona. Temp 500 times less. Density 100 times greater. Very Stable Length 60-600,000km Height 10-100,000km Width 4-15,000km B ~ 5-30G (along main axis) • Existence due to magnetic fields.
Two types of chirality: Sinistral and Dextral. • Sun rotates differentially – faster at the equator than at the poles. Observations (Martin et al. 1995) show opposite is true : NorthernHemisphere - Dextral Southern Hemisphere - Sinistral
Previous Models and Mechanisms • Many new theories of filament formation have been put forward (include a variety of mechanisms), differential rotation, shear flows, Subsurface motions, converging flows, Magnetic reconnection (above and below surface), Flux emergence (bipoles or twisted flux ropes). • Subsurface Models : Rust and Kumar 1995 Priest, van Ballegooijen and Mackay 1996 • Surface Models : Kuperus 1996, Zirker et al. 1997 Martens and Zwaan 2001 • van Ballegooijen et al.1998 constructed a flux transport model which evolved initial potential fields :equal numbers of sinistral/dextral filaments in each hemisphere.
Aims of present work. • Use a flux transport model to explain the hemispheric pattern of filaments (Mackay and van Ballegooijen 2001). Coronal field relaxes to equilibrium. Initial fields non-potential (independent bipoles). Simple theoretical configurations (single bipole interacting with a polar field). Rising and Declining phases.
The Model • Use flux transport code (photospheric/coronal field) to explain hemispheric pattern (van Ballegooijen et al 2000). • Evolve, B through the induction equation. • At the photosphere the field is subject to differential rotation, meridonal flows and supergranular diffusion. • Reconnections only occur in the photosphere. In the corona use ideal induction equation with magneto-frictional method.
Rising Phase • Consider interaction of single bipole with polar field. • Graph of Skew vs Initial Tilt Angle. Tilt angle has strong effect. Equal length of D/S in range -10:30 Sinistral dominant <-20,>30. No Hemispheric Pattern.
New initial condition of independent untwisted bipole. • Graph of Skew vs Initial Tilt Angle. Dextral skew dominant -20:30. Observed Bipole Tilt angles 80% -10:30 (Wang and Sheeley 1989). Dominant tilt angles give hemispheric pattern.
Initial condition of independent twisted bipole (-ve helicity). • Graph of Skew vs Initial Tilt Angle. Dextral skew dominant. -ve helicity dominant type for northern hemisphere (Pevtsov et al. 1995). +ve helicity gives opposite result.
Declining Phase • Polar fields of opposite sign to the rising phase. • Graph of Skew vs Initial Tilt Angle. Equal amounts of dextral and sinistral skew. No Hemispheric Pattern.
Independent untwisted bipole within polar field. • Graph of Skew vs Initial Tilt Angle. No hemispheric pattern In Declining Phase.
Independent twisted bipole (-ve helicity). • Graph of Skew vs Initial Tilt Angle. Natural connectivity of bipole flux difficult to break.
Summary of Results. • Easy to reproduce a hemispheric pattern in rising phase but not in declining phase. • Rising phase : Isolated untwisted/-ve helicity bipoles. Declining phase: No definite hemispheric pattern, mid-latitude return arm - dextral skew. high-latitude lead arm - sinistral skew • Martin et al. 1995 observations include both rising and declining phases but are weighted towards mid-latitudes. • Need new filament observations to clarify the results. • Distinction of type of skew produced on different orientations of PIL can be used to check validity of results.
Skew of Coronal Arcades. • Coronal arcades have a one-to-one relationship with underlying filaments (Martin and McAllister 1997). +ve dextral (left skewed) -ve sinistral (right skewed) • Surface models assume filament forms out of sheared coronal arcade. • McAllister et al. (2002) considered the skew of high latitude arcades from October 1991-August 1994 (Declining phase of cycle 22).
PIL was split into distinct groups to compare with theory. PIL Type North/South Total Number +ve I -ve LA/PC N 1 211 S 32 1 0 RAN 21 1 1 S 0 0 38 Other N 28 1 5 S 0 020 • Agreement of Yohkoh observations with models. • Strong indications from theory and observations that in the declining phase there is alatitudinal pattern NOT A hemispheric pattern.
Consequences for Filament Formation • It remains unclear how the chirality of filaments behave in the declining phase : three obvious possibilities. Surface ModelsSubsurface Models Global chirality patternD/S chirality patternFilament form by in rising phase. both phases.emerging flux ropes. Not for declining phase.Filaments have preferredOn return arm flux rope site of formation.and arcade match. Latitudinal Pattern.Return Arm ????On lead arm flux rope Dextral - mid latitudeand arcade have return arm.opposite orientation. Sinistral - high-latitudeN-S filaments then lead arm.E-W ones after d.rBreak one-to-one and m.f. acted. correspondence.