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Mei Zhang

（ National Astronomical Observatory, Chinese Academy of Sciences）

Helicity Transport from the convection zone

to interplanetary space

Collaborators:

Boon Chye Low, Natasha Flyer, Mark Miesch (NCAR, Boulder, USA)

Yin Zhang, Chuanyu Wang, Juan Hao (NAOC, Beijing, China)

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Helicity Transport from the convection zone to interplanetary space

--- How do we know?

Can we measure (or monitor) it?

Plan of the Talk

1. Why helicity?

2. Helicity Transport

(Physical process: convection zone – photosphere – corona – interplanetary space)

1) Observation on the photosphere

2) Creation in the convection zone

3) Consequences in the corona

4) In the interplanetary space

3. Concluding remarks

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Magnetic helicity:

Magnetic helicity quantifies the twist (self-helicity)

and linkage (mutual-helicity) of magnetic field lines.

Ｈ＝０

Ｈ＝ＴΦ2

Ｈ＝ ± ２ Φ1Φ2

Magnetic helicity is a quantity that describes field topology.

(A ： vector potential)

(Image credit:

T. Sakurai)

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Magnetic helicity:

Helicity much less dissipative than energy rather transported or redistributed than dissipated magnetic field (flux and energy) then transported together avoid treating the difficult process of magnetic reconnection

Magnetic helicity is a conserved physical quantity.

(A ： vector potential)

• The total magnetic helicity is still conserved in the corona even when there is a fast magnetic reconnection (Berger 1984).

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Observation on the photosphere:

--- Hemispheric helicity sign rule

(Image credit: A. Pevtsov)

Magnetic fields are

observed to emerge into

each hemisphere with a

preferred helicity sign:

Positive in southern

hemisphere;

Negative in northern

hemisphere.

(Pevtsov et al. 1995, Bao & Zhang

1998, Hagino & Sakurai 2005)

Hemispheric rule in global magnetic field

Left: MDI; (September 1996) Right: KPVT

(Wang & Zhang 2010, ApJ, 720, 632)

The same hemispheric helicity sign rule exists, extending to 60

degrees high in latitudes, and is preserved through the whole

solar-cycle.

(Following the approach in Petvsov & Latushko 2000)

Hemispheric helicity sign rule by SP/Hinode

observation

Do not follow:

end of cycle 23

Follow: beginning

of cycle 24

(Hao & Zhang 2011, ApJ, 733, L27)

However, complication actually comes in with active regions….

NOAA 10940

(Feb 1, 2007)

by SP/Hinode

Strong (umbra) and weak (penumbra) fields

show opposite helicity signs.

(Hao & Zhang 2011, ApJ, 733, L27)

How to understand this

hemispheric helicity sign rule and

its solar cycle variation?

Example: Making use of Dynamo models

Hemispheric helicity sign rule shows up clearly in magnetic helicity density map.

Current helicity does

show cycle variation,

with opposite-sign

patches presenting.

Bφ

A Convective Babcock-Leighton Dynamo Model (Miesch & Brown 2012)

hm

hc

(More analysis in progress)

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=> Magnetic helicity is accumulating

in the corona !

1. Hemispheric helicity

sign rule

2. Berger (1984)’s

conservation law

In the corona:

(Image credit: A. Pevtsov)

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What are the

consequences of magnetic

helicity accumulation

in the corona?

Consequences of helicity accumulation (1):

Formation of Flux Ropes in the Corona

Taylor relaxation (1972): Turbulent reconnections take place to relax the

field to Woltjer minimum-energy state under helicity conservation.

As a result of Taylor relaxation, magnetic flux ropes will form in the corona, as long as enough total magnetic helicity has been transported into the corona.

(Zhang & Low 2003, ApJ, 584, 479)

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Nonlinear force-free field calculations indicate that there may be an upper bound on the total magnetic helicity that force-free fields can contain.

(Zhang, Flyer & Low 2006, ApJ, 644, 575)

Consequences of helicity accumulation (2):

CME takes place

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The existence of total magnetic

helicity upper bound means

Expulsion becomes

unavoidable.

The essence of helicity bound:

The azimuthal field needs confinement that is provided by the anchored poloridal field. Certain amount of poloridal flux can only confine a certain amount of toroidal flux.

(Zhang, Flyer & Low 2006, ApJ, 644, 575)

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Helicity bound: Compare with observations

Our upper bound (for dipolar boundary): 0.35 Φp2

Observations: 0.2 – 0.4 Φp2 (Demoulin 2007 in a review)

Boundary condition:

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• The upper bound of total magnetic helicity (HR/Φp2) of multipolar fields

is 10 times smaller. Explain why complicated regions easier to erupt.(Zhang & Flyer 2008, ApJ, 683, 1160 )

~ 0.2 Φp2 (bipolar)

~ 0.035 Φp2 (multipolar)

• The upper bound of total magnetic helicity depends on boundary condition. --- Understand those flux-emergence-triggered or other boundary-variation-associated CMEs.

Consequences of helicity accumulation (3):

flux-emergence can trigger CME

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However, helicity accumulation is still important.

(for boundary variation to trigger CMEs)

91% of 189 CME-source regions are found to have small-scale flux emergence, whereas the same percentage of small-scale flux emergence is identified in active regions during periods with no solar surface activity.

This means that flux emergence alone is not a sufficient condition to trigger CMEs.

(Zhang Yin et al. 2008, Sol. Phys., 250, 75)

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1. Why CME takes place? • Because the corona has accumulated enough total

magnetic helicity for the eruption.

2. Why occasionally, not continuously?• Because the corona needs time to accumulate enough total

magnetic helicity for the eruption.

3. Why erupts from previously closed regions?• Because this is where magnetic helicity can be

accumulated.

4. Why initiation often associates with surface field variations such as flux emergence?• Because for the changed boundary condition the helicity

upper bound may be reduced, making the already accumulated total helicity exceeding the new upper bound.

Understanding CMEs in terms of magnetic helicity accumulation:

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In the interplanetary space

With more helicity (increasing the index n), the field becomes fully opened up, forming a current sheet at the equator.

(Zhang, Flyer & Low 2012, ApJ, 755, 78)

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The field presents

Parker-spiral-like

structures in the

interplanetary space, to

accommodate the large

amount of magnetic

helicity released from

low corona.

(Zhang, Flyer & Low 2012, ApJ, 755, 78)

(Field lines with θ=0.5o, 1o, 2o, 20o above the equator. )

(Purple: self-similar; Blue: Aly. )

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1. Hemispheric helicity sign rule is observed on the photosphere.

• In both global Sun and active regions.

• The rule shows solar cycle variation in sunspots.

2. Dynamo models (at least some of them) produce magnetic field consistent with the observed rule.

• Magnetic helicity better preserved than current helicity.

3. The accumulation of magnetic helicity in the corona

• Can give rise to flux ropes in the corona.

• Result in CME as a natural product of coronal evolution.

4. When helicity is dumped into the interplanetary space

• Parker-spiral-like structures will form.

Concluding Remarks

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1. Hemispheric helicity sign rule is observed on the photosphere.

• In both global Sun and active regions.

• The rule shows solar cycle variation in sunspots.

2. Dynamo models (at least some of them) produce magnetic field consistent with the observed rule.

• Magnetic helicity better preserved than current helicity.

Measure by SP/Hinode etc.

3. The accumulation of magnetic helicity in the corona

• Can give rise to flux ropes in the corona.

• Result in CME as a natural product of coronal evolution.

4. When helicity is dumped into the interplanetary space

• Parker-spiral-like structures will form.

Measure (or monitor) by coronal magnetism?

Concluding Remarks

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Thank you for your attention!

Huairou Solar Observing Station, NAOC

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We try to understand this by studying families of nonlinear force-free fields.

Force-free: Because the corona is very tenuous, the large-scale field is usually regarded as force-free.

Boundary condition:

Governing equation:

A family: With the same boundary condition and a specific n, different γ values give fields with different magnetic energy and total magnetic helicity.

(in Zhang et al. 2006)

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• The central part of the field (flux rope) becomes exceeding kink instability criteria in the process of helicity accumulation.

(Zhang & Flyer 2008, ApJ, 683, 1160 )

Consequence of helicity accumulation (4):

~ 0.2 Φp2 (bipolar)

~ 0.035 Φp2 (multipolar)

Eruptions by kink

instability and by

exceeding helicity

upper bound do not

exclude each other.

(Even the field is allowed to relax to its

minimum-energy state, it cannot relax to

a potential field!)

Woltjer (1958) Theorem:

E 0H Epot

Consequences of Helicity Accumulation (6):

This implies a storage of a “flare un-releasable” magnetic energy,

increasing with the increasingly accumulated total magnetic helicity.

This is the energy that corona stores uniquely for CMEs!

Magnetic Energy Storage as a natural product of coronal evolution

(Zhang & Low 2005, ARAA, 43, 103)

E = E – Epot=(E - 0H )+( )+( 0H - -

Epot)

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Can we monitor the evolution of magnetic helicity and use it to predict the eruption of CMEs?

In principle: Yes, by observing the photosphere…

--- We can calculate the helicity transfer rate on the photosphere to monitor the helicity accumulation in the corona.

--- We can estimate the helicity upper bound corresponding to current boundary flux distribution.

For space weather?

However, needs to fight for accuracy (of vector magnetic field measurement etc.) and speed (of upper bound calculation).

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Example ： Calibrating MDI magnetograms

using SP/Hinode observations

1 、 Compared to

SP/Hionde

observations ， MDI also

underestimates magnetic

flux, for both 2007 and 2008

calibration versions.

2 、 2008 version has

successfully removed the

center-to-limb variation,

whereas 2007 version did

not.(Wang Dong et al., 2009, Solar Physics, 260, 233）