twist & writhe of kink-unstable magnetic flux ropes I

)(2 WrTwHm flux rope: helicity sum of twist and writhe:

kink instability: twist and writhe (sum is constant)

twist and writhe often confused: twist = winding of field lines about flux rope axis writhe = winding (kinking) of rope itself

aim: first study of twist & writhe evolution during instability

twist & writhe of kink-unstable magnetic flux ropes II

helicity cannot be measured (coronal field not known)

observational problems:

twist: measure from helical fine structures (difficult)

writhe: measure from sigmoidal shape (not done yet)

problems with writhe:

difficult to compute (Mitch will help):

we have only 2D observations (STEREO will help)

so far: 2D integral; now: 1D integral (Berger & Prior, submitted)

twist & writhe of kink-unstable magnetic flux ropes III

possible application: measure writhe from 2D observations

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)

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

5|| loop Φ

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)

“current sheets” (Titov & Démoulin 1999; Low & Berger 2003)

field lines sheared by photospheric motions (Aulanier et al. 2005)

transient soft X-ray Sigmoids II

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 …

Kliem et al. 2004

Fan & Gibson 2003

bipolar / quadrupolar active region eruptions I

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 ?

2 CME classes: impulsive (active region; fast & strong acc.; flare) gradual (quiet Sun; slow & weak acc.; prominence)

bipolar / quadrupolar active region eruptions II

quadrupolar AR: faster CME ?bipolar AR: slower CME ?

bipolar / quadrupolar active region eruptions III

from torus instability we expectfaster and stronger accelerationof flux rope in quadrupolar AR

Kliem & Török, in preparation

faster CMEs

quadrupolar field drops fasterwith height than bipolar field

)(0)( hnhBhB

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

reconnection in CS (flare) and instability (CME) closely coupled

instability drives eruption (flux rope velocity always higher than upward directed reconnection outflow !)

vertical current sheet (CS) formed behind erupting flux rope

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

recent lfff extrapolations also find too large expansion factors (Lopez-Fuentes et al., ApJ, accepted)

could only consider twists up to one turn (relaxation method)

nearly constant loop cross sections III

22

2

11BB

rf rr

radial force in flux rope (0,B_phi,B_z):

1st term: always constriction

2nd term: constriction or expansion

differences to Klimchuk et al., 2000:

new twist profile stronger constriction?

photospheric motions larger twist

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

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

Gibson et al. 2004; Fan 2005; Gibson & Fan, submitted