Active Region Evolution and the Removal of Magnetic Helicity by

CMEs

Len Culhane

Mullard Space Science Laboratory

University College London

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SUMMARY

Results of two investigations are presented:

I. Long-term Evolution of Sigmoidal Structures and Related CME Activity

(Glover, Harra, Matthews, Hori, Culhane, 2001, In Press, A&A)

Morphological study of an AR complex over three rotations from 9-Mar-00 to

11-May-00

II. Magnetic Evolution of a Long-lived AR: the Source of Magnetic Helicity(Mandrini, Demoulin, van Driel-Gesztelyi, Plunkett, Thompson, Kovari, Aulanier, 2001, Submitted, A&A)

Quantitative study of the magnetic helicity budget of AR 7978 over seven rotationsfrom 6-Jul-96 to 16-Dec-96

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I. Evolution of the AR 8906 Activity Complex - Sigmoids and CMEs(Glover et al., 2001, Astron. & Astrophys., In Press)

Recent studies suggesthigh probability of eruption and associatedCMEs(Hudson et al., 1998,GRL., Canfield et al., 1999, GRL., Glover et al., 2000, GRL.)

Sigmoids – possibleprediction of CMEs?(Sterling and Hudson1997, Ap.J. Lett.)

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Activity evolution isfollowed for three solar rotations (Glover et al.)

SXT and MDI full disk observations arefor each central meridian passage: 13-Mar-2000 (a, b), 10-Apr-2000 (c, d) 7-May-2000 (e, f).

Arrows indicate a small emerging flux region – designated AR 8984 (e, f). A filament channel is seen in frames d and f.

Evolution of the Activity Complex AR 8906

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Time Distribution of GOES Events (> B1.0) and CME Onsets

Numbers of X-ray eventsand CME launches that originated in the AR 8906 activity complex during three solar rotations in theinterval 9 March to 12 May 2000.

Central meridian passagesare: 13 Mar, 10 Apr and7 May.

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Formation of a Sigmoidal Feature on 10-Apr-00Full disk SXT (a,b,c) and MDI (d)images on 10-Apr-00 (Rotation 2)

Flux emergence is seen at 19:28 U.T. along with the formation of a sigmoidal feature stretching from the emerging flux region to the filament channel

The sigmoid is fully developed by22:15 U.T. and remains visible for ~ 12 hours.

The most CME-active period during the second rotation seems associated with the appearance of the sigmoid.

Did newly emerging twisted flux increase the helicity content which was then shed by CMEs?

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Yohkoh SXT full-disk image of a sigmoid on 8-May-00 at 09:45 UT

Structure links remnants of earlier ARs associated withAR 8906

Inset shows the same region prior to eruption at 04:36 UT

Sigmoid Structure formed on Rotation 3 between the Dispersed Remnants of Earlier Active Regions

8-May-00 04:36 UT

8-May-00 09:45 UT

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Activity during Rotation 3 on 8 May-00

SXT

EIT 195

H

Images taken before (a, c, e) and after(b, d, f) the eruption on 8 May. In theSXT images (a, b), several diffuseS-shaped loops are gradually replaced by a single twisted flux-rope

Arrows in c and d show position of post-flare loops in the Southern halfof the filament channel

Arrows in e and f show the S-shapedfilament underlying the soft X-rayArcade.

Events on 8 May are:B6.8 flare with peak at 06:23 U.T.Partial Halo CMEPartial filament eruption

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SXT image shows the sigmoid formed on 8 May (inset) while the full-disk image shows the situation on 10 May when a less sheared arcade replaced the sigmoid

Events on 10 May are:Unclassified GOES flare with peak at 22:16 U.T.Expanding loop CMEFilament eruption

Formation of the less shearedstructure coincides with an eruption and the launch of the last CME – are we again seeing helicity removal?

Sigmoid replaced by less sheared Arcade following a CME

8-May-00 09:45 UT

10-May-00 12:28 UT

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SXT Observations of Activity Evolution on 10-May-01

SXT images showing the region pre- andpost eruption on 8 May.

Pre-eruption (a), a highly sheared arcadeis indicated by the arrow. Gradual riseand expansion of the arcade is shown in(b) and (c).

Following a filament eruption, a muchless sheared arcade is seen in (d)

A loop-like CME is observed by LASCOC2 at 19:26 U.T. The height-time plot isconsistent with with the gradual rise ofthe SXT arcade. Big Bear H data showsa filament eruption.

MDI data are consistent with helical fielderupting with the filament material.

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II. Source of Magnetic Helicity Shed by CMEs

• Demoulin, Mandrini, Van Driel-Gesztelyi, Plunkett et al. (2001) studied the Helicity budget of AR 7978 for 7 rotations from Jul-1996

• Procedure:

Extrapolate (LFF) photospheric field (MDI) into corona/derive Compute coronal AR helicity for each rotation Calculate helicity due to differential rotation Identify all AR 7978 CMEs and from average magnetic cloud

properties, estimate the helicity shed by the CMEs Compare the three helicity values to check if differential rotation

could be the helicity source

• For the field extrapolation, xB = B so: Compute field as f() and match structures with observed loops Repeat for different values of to find best global fit

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Magnetic Field Extrapolations

N-S shear gradient usually requires two values

= 1.4.10-2 Mm-1

Mm-1

Parameter determined by iteration

Coronal field is computed fora given and a match sought between field lines and SXT loops

Repeated for a range of values to find the best one for a global fit

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Magnetic Helicity• Magnetic Helicity is a globally conserved quantity: - Convection zone → Corona → Interplanetary Medium

• Helicity H = ∫V A.B dV where A is the vector potential with B = xA

• Requirement for V to be arbitrarily large posed a problem until:

– Berger and Field (1984) defined relative magnetic helicity or

where Hr is gauge invariant and is independent of B and B0 outside V V V

r dVBABdVAH 00..

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x

x

y

y

yxN

n

N

n yx

nn

r kkl

BH

1 122

2,

)(2

Production and Removal of Magnetic Helicity

1. Coronal Helicity is given by

where B is the Fourier amplitude of the harmonic (nx,ny), kx = nx /L,

ky = 2ny /L, l = (k2x + k2

y – 2)1/2 and L represents the horizontal extent

of the computational box

The size and complexity of the AR require a large number of harmonicsor Nx = Ny = 256

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Production and Removal of Magnetic Helicity

2. Helicity generated by Differential Rotation has two terms or:

where twist relates to the rotation of each magnetic polarity andwrithe involves the relative rotation of positive and negative polarities.However the writhe term has always the opposite sign from the twistterm for solar differential rotation so the two contributions oppose

Helicity generation is affected by:• Latitude of the AR• Degree of magnetic field dispersion• Tilt of the bipole

writhertwistrr HtHtH )()(

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Production and Removal of Magnetic Helicity3. Helicity in Ejected Magnetic Clouds

Magnetic clouds are twisted flux tubes expanding as they move out from the Sun in a CME so assume a one-to-one association.Following Berger (1999), the relative helicity per unit length for a twisted flux tube is of the form

where Baxial is the cloud axial field and R the cloud radius.

Following Lepping et al. (1990), Baxial ~ 2.10-4 G and R ~ 2.1012 cm

For L ~ 0.5 AU (assumes disconnection from Sun, DeVore, 2000), Hr ~ 20.1041Mx2/cloud or per CME

For L ~ 2 AU (assumes connection to Sun, Richardson, 1997)Hr ~ 80.1041Mx2/cloud or per CME

327.0~ RBdz

dHaxial

r

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Evolution of AR 7987Flares and CMEs in AR 7978

Rot. Date of CMP Flares CMEs

no. X M C B

Helicity Budget of AR 7978

Coronal Diff. Rot. Mag. Clouds (1042 Mx2) (1042 Mx2) (1042 Mx2)

1 7-July-1996 1 2 14 16 82 3-Aug-1996 - - 1 17 53 30-Aug-1996 - - - 2 14 25-Sep-1996 - - - - 75 23-Oct-1996 - - - 1 36 18-Nov-1996 - - - - 4

- 2 [16, 64] [ 5, 11] 3 [10, 40] [17, 23] 3 [ 2, 8] [ 9, 12] 1 [14, 56] [ 4, 6] 0.8 [ 6, 24] 4 0.3 [ 8, 32]

• Differential rotation generally fails to provide sufficient helicity for either the coronal field or the CMEs

• Ejected helicity is equivalent to that of a flux tube with the same flux as AR 7978 and having between 0.6 and 2.4 turns

OUTCOME

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CONCLUSIONS

• For the AR 8906 activity complex, S-shaped structures appear to form due to increasing shear leading to a build-up of helicity

• This build-up could be due to differential rotation or to the emergence of already sheared flux tubes

• S-like morphology is reduced by continued CME activity and is finally removed by CMEs in the third rotation when flare activity has almost ceased

• Main source of helicity is probably due to the emergence of twisted magnetic flux tubes that form the active region

• Following the work of Berger and others, relative magnetic helicity is defined and calculated for finite volumes related to AR 7968• After field extrapolations and calculation of the helicity i) stored in the corona and ii) injected by differential rotation, it is found that CMEs shed more helicity than is provided by i) and ii)

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