Twist & writhe of kink-unstable magnetic flux ropes I flux rope: helicity sum of twist and writhe:...
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Transcript of Twist & writhe of kink-unstable magnetic flux ropes I flux rope: helicity sum of twist and writhe:...
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