Asymmetry of helicity injection in emerging active regions

Helicity Thinkshop 2009, Beijing

Asymmetry of helicity injection in emerging active regions

L. Tian, D. Alexander Rice University, USA

Y. Liu Yunnan Astronomical Observatory, China


Background - observations

Well observed on solar photosphere, chromosphere and corona in many different wave-lengths.


Why we study helicity ?

It is conserved in large scale. It can be traced as the magnetic field flux when it

(a) appears as an emerging flux region; (b) forms new loops to fill the corona; (c) erupts to be a flare or a coronal mass ejection (CME); (d) becomes a magnetic cloud when reaches the Earth.

Understanding of flare and CME formation mechanism (a) Overload helicity accumulation will inevitably cause a CME occurrence; (b) Different helical flux systems can trigger magnetic reconnection.

Helicity output is the key to the solar dynamo Constraints on the dynamo models if take into account the helicity conservation.


Helicity measurements - Hc

Current helicity

Hc =∫v B • J dV, and

J = ∇ x B

Only the vertical component (z)

of J can be directly derived from the photospheric magnetic field observations.

Sample of vertical current helicity density (hc) map. From H.Zhang

(2001)


Helicity measurements - Hm

Magnetic helicity

Hm=∫vA • B dV, and

B = ∇ x A

Only the transport rate (dHm/dt) can be derived from the photospheric magnetic field observations.

Sample of time series magnetic flux change associated with magnetic helicity change. From J.Chae (2001)


Analysis of helicity injection rate (dHm/dt)

Definition

or, simply, ∫ S

m dSGdt

dH

∫'

'')(

2)(

S nn dSB

dt

rdBxG

nn uurrdt

rdr

rdt

rd))'((

1)(

1)(22

tn

nt BB

u

i.e., helicity density

by LCT method (FWHM=10”, dt=96min)

∫∫ ∫ S nPS S ntPntP

m dSBAudSBAdSBAdt

dH)2()(2)(2

(Pariat 2005)


Analysis of helicity injection rate (dHm/dt)

Note, using LCT method we can only obtain the total map. Therefore only the total helicity flux density can be obtained, no information is obtained regarding to the contribution from either the advection terms (magnetic field emergence), or from the shear terms (horizontal motions) .

tn

nt BB

u

tn

nt BB

u

by horizontal mass motions

by emerging flux motions


Amount of helicity flux change

The amount of helicity flux estimated from the formula should both contributions from the emerging motions and the shear motions.

However, many observations display that the surface differential rotation and/or the overall horizontal motions contribute minor to the helicity flux injected from below into the corona (see review in Tian and Alexander 2009), indicating that the flux emergence is the most important origin for the coronal helcity accumulations.

∫ dtdt

dHH )(


Topic : asymmetry of helicity injection flux in emerging active regions

Purposes :

(1)To physically study why the leading magnetic field of bipolar ARs is often more compact, while the following one, more dispersed.

(2)To clear the relation between asymmetry of helicity flux and asymmetry of magnetic flux.


First, how about the asymmetry in magnetic flux evolution

AR 8227AR 8214

May-02 03:12UT

May-06 03:12UT Jun.-03 03:15UT

May-30 03:12UT

after one solar rotation cycle

MDI data (96m)

sample 1


The leading polarities always remain more cohesive than the following ones during long-term evolution

AR 0656 AR 0667

Aug.-10 03:11UT

Aug.-13 19:11UT

AR 0670

Sep.-06 03:11UT

Sep.-09 19:11UT

after one solar rotation cycle

sample 2


Database containing 15 emerging ARsand analysis results


Four emerging ARs in southern hemisphere

The magnetic flux increase for N and P is imbalanced /asymmetry. The same for the helicity flux.

Magnetic flux vs date helicity flux increase Magnetic flux helicity flux increase


Four emerging ARs in northern hemisphere

The magnetic flux increase for N and P is imbalanced /asymmetry. The same for the helicity flux.


The higher proper motion in the leading polarity, the larger helicity injection by it

The correlation between helicity flux increase and magnetic flux increase is very poor.

This has two important physical implications: emerging of asymmetric Ω-loop, and more twisted in the leading polarity.


In the following work, we use the normalized parameter ΔH/Φ2, Instead of ΔH, to examine the twist and helicity injection for per unit emerging flux.

dH 2

2

2/

22 d

H


We select 11 ARs (whose magnetic flux maps were shown in the previous work)

AR 0381 (Demoulin & Pariat 2009) is added in the database for comparison. Totally, there are 11 emerging ARs for this analysis.

small

small


In the 1st –3rd columns are ΔΗ/Φ2 vs. date, d vs. date, andΔΗ/Φ2 vs. Φ for every AR

The helicity injection is found to saturate when d separation stops.


ΔΗ/Φ2 vs. d, αvs. date

The helicity injection is found to delay about 1-2 days after flux emergence.

The helicity injection delay may be linked to the emergence of the periphery of the flux rope which contains a low amount of helicity even very twisted.

Four ARs with observations at their very beginning to emerge.


(1) The leading leg of a presumed Ω-shaped flux tube possesses more twist than that of the following leg prior to its emergence from the interior.

(2) The behavior of twist depending on the rate of the flux tube emergence, i.e., the level of rotation of the footpoint of the flux tube will depend upon the rapidity of flux emergence.

(3) the leading polarity possesses more helicity so that the leading flux is maintained to be compact and cohesive, due to a stronger tension of the magnetic field, and consequently,is less affected by the convective motions.

Does the leading polarity moves and emerges faster ? Seems yes (because as the field strength in the leading leg becomes

proportionately stronger, it becomes more buoyant). It needs MHD simulation to confirm.

Discussion: The physical origin of the helicity flux asymmetry


(1) The helicity asymmetry, between the leading and following magnetic field, results in the observed magnetic field asymmetry of the two polarities (due to an imbalance in the magnetic tension of the emerging flux tube);

(2) The observed imbalance in the helicity asymmetry results from a difference in the speed of emergence between the leading and following legs of an inclined Ω-shaped flux tube;

(3) The imbalance in the normalized helicity does not have a relation with the imbalance of opposite-sign magnetic flux.

Main conclusions


Questions remained

(1) Magnetic Helicity would be saturation in some time. However, it is possibly true (?).

(2) Injection of magnetic helicity has 1-2 days delay. Why?

(3)The force-free parameter (alpha) is too small comparing with observation of vector magnetograms. Why?

dH 2

2


Questions remained

………….

(N) The origin of coronal helicity is still not clear by now; Sunspot rotation possibly plays a very important role in producing and injecting magnetic helicity. (Better methods to measure magnetic helicity need to be developed urgently.)

Obviously, more Helicity Thinkshops are expected in the future…

And….


Thanks!

Asymmetry of helicity injection in emerging active regions

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