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Solar cycle variation of kinetic helicity. Mei Zhang ( National Astronomical Observatory, Chinese Academy of Sciences ). Collaborators : Junwei Zhao (Stanford, USA) Mark Miesch (HAO/NCAR, USA). Plan of the Talk. Motivation: Solar-cycle variation of current helicity

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Solar cycle variation of kinetic helicity

Mei Zhang

(National Astronomical Observatory, Chinese Academy of Sciences)


Junwei Zhao (Stanford, USA)

Mark Miesch (HAO/NCAR, USA)


Plan of the Talk

  • Motivation:
  • Solar-cycle variation of current helicity
  • 2. Solar-cycle variation of kinetic helicity
    • 1) In dynamo model
    • 2) By helioseismology

Hemispheric helicity sign rule

Magnetic fields are observed to emerge into each hemisphere with a preferred helicity sign:

Positive in southern hemisphere;

Negative in northern hemisphere.

(e.g. Seehafer 1990, Pevtsov et al. 1995, Bao & Zhang 1998)

(Image credit: A. Pevtsov)

No argument on the existence of this hemispheric helicity sign rule.


However, there is an argument on Is this rule preserved for the whole solar cycle?


Longcope et al. (1998): YES:solar-cycle independent

--- Helicity is produced in the process of magnetic flux tubes rising through the solar convection zone and being buffeted by turbulence with a non-vanishing kinetic helicity (Σ-effect)

Choudhuri et al. (2004): NO:solar-cycle dependent

--- Poloridal flux getting warped around a toroidal flux tube rising through the convection zone to give rise to the helicity

--- Deviations from the usual sign rule at the beginning of a solar cycle


Is this rule preserved for the whole solar cycle?


Bao et al. (2000): NO (of hc) for the ascending phase of cycle 23

(Huairou data)

Pevtsov et al. (2001): Yes for the first four years of cycle 23

(Mees data)

Hagino & Sakurai (2005): Yes for maximums; NO for minimums

(Mitaka data, 1983-2000)

Pevtsov et al. (2008): No agreement on the ‘wrong-sign’ years

(19 years’ data of different instruments)


Hemispheric helicity sign rule by SP/Hinode

(Hao & Zhang 2011, ApJ, 733, L27 and Juan Hao’s talk tomorrow for more development)

End of cycle 23:

do not follow

Beginning of cycle 24:


Hint: Choudhuri et al. (2004) may be right in its physical picture but wrong in phase prediction.

Despite with the accurate measurement by SP/Hinode, the scatter is still very large.

Hint: The scatter is an inherent property, not induced by measurement error. Consistent with Longcope et al. (1998).


How to understand this hemispheric helicity sign rule and its solar cycle variation?

Solar cycle variation in a convective dynamo model



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


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

Current helicity does show cycle variation, with opposite-sign patches presenting.


(More analysis in progress)

(r=0.96, 28Mm)


In the model:No solar-cycle variation on kinetic helicity

(Only vertical component, to compare with observation)



Solar cycle variation of kinetic helicity

Subsurface velocity field obtained

through time-distance helioseismology

using HMI/SDO data


No solar-cycle variation of kinematic helicity

Each line: one-month averaged

(r= 0 - 1 Mm)


Consistency in model and observation: tendency + magnitude

in HMI data, time distance method

in Model: Miesch et al. (2006)

(produce solar-like differential rotation)

(r = 21 Mm)

(r = 0 - 1 Mm)


meridional flow

with error bars


Solar-cycle variation of meridional flow?

Yes, as reported before in Zhao & Kosovichev (2004).

Means that previous non-detection on Hk is not by noise.



  • Hemispheric helicity sign rule is observed on the photosphere and shows solar cycle variation.
  • Dynamo models (at least one of them) produce magnetic field consistent with the observed rule.
    • Magnetic helicity better preserved than current helicity.
  • Both the dynamo model and helioseismology observation show no solar-cycle variation of kinetic helicity.

These give constrains on the mechanism of helicity production as well as dynamo models.


Thank you for your attention!

Huairou Solar Observing Station, NAOC



We calculate two helicity parameters:

1. average local twist

2. normalized average current helicity

With two vector B representatives:

1. flux density map (B1)

2. true field strength (B2)

hemispheric rule in global magnetic field
Hemispheric rule in global magnetic field

The same hemispheric helicity sign rule exists, extending to 60 degrees high in latitudes, and is preserved through the whole solar-cycle.

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

Left: MDI; (September 1996) Right: KPVT

(Following the approach in Petvsov & Latushko 2000)