twist & writhe of kink-unstable magnetic flux ropes I

1. twist & writhe of kink-unstable magnetic flux ropes I • flux rope: helicity sum of twist and writhe: • twist and writhe often confused: • twist = winding of field lines about flux rope axis • writhe = winding (kinking) of rope itself • kink instability: twist  and writhe  (sum is constant) • aim: first study of twist & writhe evolution during instability

2. twist & writhe of kink-unstable magnetic flux ropes II observational problems: • helicity cannot be measured (coronal field not known) • twist: measure from helical fine structures (difficult) • writhe: measure from sigmoidal shape (not done yet) problems with writhe: • we have only 2D observations (STEREO will help) • difficult to compute (Mitch will help): so far: 2D integral; now: 1D integral (Berger & Prior, submitted)

3. twist & writhe of kink-unstable magnetic flux ropes III • writhe = local writhe + non-local writhe • non-local writhe depends only on angle between tangent at apex • and line connecting the footpoints of filament/sigmoid • local writhe depends also on apex height (unknown, but can be • estimated) possible application: measure writhe from 2D observations

4. twist & writhe of kink-unstable magnetic flux ropes IV I study evolution twist & writhe in different numerical configurations

5. twist & writhe of kink-unstable magnetic flux ropes V confined ejective • writhe  0.5  twist of  1 pi converted during instability • non-local writhe dominates for greater heights

6. transient soft X-ray Sigmoids I 1997 May 12 • forward or backward S-shape (indicator of helicity) • brighten at start of eruption; often “transition” to cusp • what are Sigmoids ? • kink-unstable flux ropes (Rust & Kumar 1996, Török & Kliem 2003) • field lines sheared by photospheric motions(Aulanier et al. 2005) • “current sheets” (Titov & Démoulin 1999; Low & Berger 2003)

7. transient soft X-ray Sigmoids II Fan & Gibson 2003 Kliem et al. 2004 • numerical simulations suggest “current sheet model” because • kinking flux rope has the wrong sigmoidal shape • how to confirm: find event with simultaneous observations • of Sigmoid and (kinking) filament eruption • study of temporal relation Sigmoid — flare also planned …

8. bipolar / quadrupolar active region eruptions I • 2 CME classes: impulsive (active region; fast & strong acc.; flare) • gradual (quiet Sun; slow & weak acc.; prominence) Vršnak et al., 2005 (statistical study of CME kinematics): • indicates that two classes of CMEs do not exist • but: flare CMEs on average faster than non/weak-flare CMEs strongest flares occur in quadrupolar or delta-spot active regions CME from quadrupolar AR faster than from bipolar AR ?

9. bipolar / quadrupolar active region eruptions II bipolarAR: slower CME ? quadrupolar AR: faster CME ?

10. bipolar / quadrupolar active region eruptions III Kliem & Török, in preparation quadrupolar field drops faster with height than bipolar field  from torus instability we expect faster and stronger acceleration of flux rope in quadrupolar AR  faster CMEs different configurations …

11. bipolar / quadrupolar active region eruptions IV • “quadrupolar CME” faster • (n=3.44 in right plot) • continuum of acceleration profiles • for different overlying fields • 2 CME classes do not exist ! relation to flare strength ?

12. flare / CME – relationship I Zhang et al. 2001 observation: close correlation between CME velocity and soft X-ray flux

13. flare / CME – relationship II • vertical current sheet (CS) formed behind erupting flux rope • reconnection in CS (flare) and instability (CME) closely coupled • instability drives eruption (flux rope velocity always higher • than upward directed reconnection outflow !) to be done: reconnection rate & light curve (how ?)

14. nearly constant loop cross sections I • observed loop expansion factors as low as 1.1 – 1.3 in both • soft X-ray and EUV (for both non-flare and post-flare loops). • cannot be explained with potential or sheared force-free fields are such loops highly twisted?

15. nearly constant loop cross sections II Klimchuk et al., 2000 • found some constriction, but not sufficiently strong • could only consider twists up to one turn (relaxation method) • recent lfff extrapolations also find too large expansion factors • (Lopez-Fuentes et al., ApJ, accepted)

16. nearly constant loop cross sections III radial force in flux rope (0,B_phi,B_z): 1st term: always constriction 2nd term: constriction or expansion Klimchuk et al., 2000 differences to Klimchuk et al., 2000: • photospheric motions  larger twist • new twist profile  stronger constriction? • planned: twist more concentrated

17. nearly constant loop cross sections IV • maybe thermal pressure necessary ? (Bellan, 2003) • what is the role of temperature / heating ?

18. flux rope extrapolation Valori & Kliem, in preparation • non-linear force-free field extrapolation of T&D flux rope model • magnetofrictional method  no equation of motion • two ropes don’t merge anymore if box height is increased due to lack of full MHD or due to boundary conditions ?

19. partial filament eruptions Gibson et al. 2004; Fan 2005; Gibson & Fan, submitted BPSS carrying filament partly remains after eruption other possible scenarios: • “asymmetric” eruption of kink-unstable flux rope • flux rope legs reconnect to form new flux rope