twist writhe of kinkunstable magnetic flux ropes I

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

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 2 D observations (STEREO will help) difficult to compute (Mitch will help): so far: 2 D integral; now: 1 D integral (Berger & Prior, submitted)

twist & writhe of kink-unstable magnetic flux ropes III writhe = 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 2 D observations

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

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

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)

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 …

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 ?

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

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 …

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 ?

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

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 ? )

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?

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. , Ap. J, accepted)

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

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

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 ?

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 legs reconnect to form new flux rope