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Chuanyu Wang & Mei Zhang

(National Astronomical observatories,

Chinese Academy of Sciences)

Current Helicity Pattern in Large-scale

Photospheric Magnetic Field

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Magnetic fields are observed to e

merge into each hemisphere with

a preferred helicity sign:

Positive in southern hemisphere

Negative in northern hemisphere

Introduction: Hemispheric rule of helicity

(Image credit: A. Pevtsov)

However, most observations are made in active regions.

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The same rule exists outside active regions?

Pevtsov & Latushko (2000) were the first to study the current helicity of the global Sun outside active regions, by applying a reconstruction technique to full-disk longitudinal magnetograms.

Pevtsov & Latushko., 2000, ApJ,528： 999-1003

We use the same reconstruction technique, but apply

different analysis method which strengthens the

results.

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Reconstruction of vector magnetic field

Suppose that large-scale magnetic fields are evolving rather slowly

and the variations of longitudinal magnetic fields within certain time

duration are caused by the changing positions on the solar disk only.

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Parameters used

Spatial resolution: △S=184’’

Time interval: △t=5 days

Differential rotation:

Reference: Pevtsov & Latushko., 2000, ApJ,528： 999-1003

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Snapshot heliographic maps

We combine observations of the solar magnetic fields made at different t

imes into a representation of the whole solar surface at a particular spec

ified time which referred to as a “snapshot heliographic map’’ (different fr

om tranditional Carrington map).

Roger K. Ulrich & John E. Boyden., 2006, Sol. phys.,235:17-29

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Obtained vector magnetic fields

Constructed snapshot heliogr

aphic maps of Br, Bθ , Bφ from t

op to bottom panels respectiv

ely, of one solar rotation (~ CR

1914).

White background represents positiv

e values of Br (pointing up), Bθ (pointi

ng to the north) and Bφ (pointing to th

e left) respectively. Contours corresp

ond to ± 2, 4, 8, 16, 32, 64G for Br an

d Bθ , and ±0.5, 1, 2G for Bφ .

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The calculation of current helicity:

Our method: calculating the hc map and then averaging along longitudinal direction to get hc profile

Pevtsov & Latushko (2000) method: averaging along longitudinal direction before calculating hc profile

√

√

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Current helicity map

The current helicity density hc map. White background represents positive

values of hc. Contours correspond to hc = ±0.1,0.2, 0.4, 0.8 ×10-5G2m-1.

It is interesting to see that the active region in the southern hemisphere shows a bulk area of negative hc values, which are opposite to that of surrounding regions. This seems to be consistent with the result of Zhang (2006) where strong and weak fields are found to have opposite helicity signs.

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Hemispheric rule

The profile of averaged hc with the l

atitude, using our method.

The profile of hc with the latitude, usin

g Pevtsov & Latushko’s approach.

Our plot shows clearly the hemispheric rule, that is, positive helic

ity sign in the southern hemisphere and negative helicity sign in t

he northern hemisphere, for all latitudes, including the latitudes b

elow 40 degrees.

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A few notes:1. We have used only one MDI magnetogram each day, h

aving done none of smoothing between different magnetograms. The plot (right bottom) in Pevtsov & Latushko (2000) was obtained using a few months’ MDI data.

2. We estimate that our method gives a clearer tendency because:

First, there may be some very useful information of hc

contained in the Bθ magnetogram that Pevtsov & Latu

shko (2000) ignored. We noticed that Bθ are usually lar

ger than Bφ and have a strong variation in longitudinal

direction. This indicates that the second term may be a larger term in the equation. Pevtsov & Latushko.(2000)

Second, our method gives each point on the synoptic map an equal weight whereas theirs are more heavily influenced by strong fields because they averaged the

Br and Bφ before calculating hc. Particularly, the difference may become more evid

ent if the strong and weak fields show opposite helicity signs as reported in Zhan

g (2006) and also indicated in our hc figure.

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Check the dependence of the result ondifferent magnetograms used

In the above figure we have used the first magnetogam of each day (solid line in this figure). Now we have used other magnetograms of each day and constructed other 14 different synoptic maps of vector magnet

ic field and hence get other 14 hc profiles (dotted lines).

They all clearly show the same hemispheric rule.

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Check the dependence of the result on different time interval & different sliding square window size

We changed the △t and △S, and get similar profiles. This means that

our result is also independent of the parameters we chose.

The solid line shows the profile using △t=5 days, and the dotted and dashed linesshow the profiles using △t=3 and 4 days respectively.

The solid line shows the profile using △S=184”, and the dotted and dashed lines show the profiles using △S=90” and 224” respectively.

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Conclusion:

We concluded that the large-scale magnetic fields show clear

and consistent current helicity pattern that follows the establi

shed hemispheric rule, that is, positive helicity sign in the so

uthern hemisphere and negative helicity sign in the northern

hemisphere.

This hemispheric sign pattern is everywhere in the global ma

gnetic field, including weak fields outside active regions, ind

ependent of the longitudinal magnetograms and the paramet

ers we have used.

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Thank You !Thank You !