BCAS
Vol.25 No.3 2011
Solar Magnetic Helicity
ZHANG Hongqi1
National Astronomical Observatories, CAS, Beijing, 100012
Helicities is topologically a measure of the structural
complexity of the corresponding fields. The magnetic
helicity can be separated into two kinds. One is the self
helicity, which relates to the magnetic flux tubes twisted
themselves. This helicity may be used to analyze the twisted
magnetic flux loops. Another one is the mutual helicity,
which relates to the different magnetic flux tubes linked to
each other.
The magnetic helicity H m and current helicity Hc
can be written in the form H m =∫ v h m d 3 x=∫ v A•Bd 3 x and
Hc=∫vhcd3x=∫vB•▽×Bd3x where A is the magnetic potential,
B is the magnetic field and hc is defined as current helicity
density.
It is known that most of the magnetic helicity in the solar
atmosphere concentrates in the solar active regions. Since
the operation of the Huairou Solar Observing Station of the
CAS National Astronomical Observatories took off in 1984,
a series of vector magnetograms of solar active regions
have been observed by the Solar Magnetic Field Telescope.
Hence, we have seized a chance to study the magnetic
helicity of solar active regions systematically (Figure 1).
The synthetic analysis of magnetic helicity in solar active
regions is important for understanding the basic topology
of magnetic field in solar atmosphere and the relationship
with solar flare-coronal mass ejections process (cf. Bao et
al., 1999; Deng et al., 2001; Liu and Zhang, 2002; Zhang et
al., 2006) and also solar active cycles (cf. Bao and Zhang,
1989; Zhang et al., 2010).
From a series of photospheric vector magnetograms, it
is found that the newly emerging magnetic flux associates the
current helicity from the subatmosphere in the active regions
with the redistribution of the current helicity density in the
upper atmosphere, i.e. it provides observational evidence that
flux and helicity emerge together. It is found that the strong
shear motion between the new emerging flux system and the
old one brings more magnetic helicity into the corona than
the twisting motions (Liu and Zhang, 2006), and the magnetic
helicity carried away from the Sun by CMEs comes from
helicity injected to the corona by such motions or by emerging
magnetic flux (Liu and Zhang, 2006; Zhang et al., 2008).
It is found that the electric current helicity is
predominantly negative in the Northern Hemisphere and
positive in the Southern Hemisphere (hemispheric rule
of helicity) (cf. Bao and Zhang, 1989). For estimating
the accuracy on the measurements of current helicity
in the solar active regions, a series of pairs of vector
magnetograms observed by Solar Magnetic Field Telescope
(SMFT) of Huairou Solar Observing Station and Solar
Flare Telescope (SFT) at Mitaka (MTK) of the National
Astronomical Observatory of Japan have been used to
compare mean current helicity density of solar active
regions, and also with a series of magnetograms observed
Prof. ZHANG Hongqi
Professor with the CAS National Astronomical Observatories
Major research directions: solar activities and magnetic fields
A series of results have been achieved in the diagnostics of solar vector magnetic fields,
formation of magnetic field (current and helicity) in solar atmosphere and eruption of the solar
flare-Coronal Mass Ejections, etc.
1
220
Correspondence and requests for materials should be addressed to [email protected].
Bulletin of the Chinese Academy of Sciences
Vol.25 No.3 2011
Solar Physics
Fig.2 Comparison on the statistical variation of mean α (helicity
parameter) of same solar active regions with latitude from
different data sets between Huairou Solar Observing Station
of National Astronomical Observatories of China (black) and
National Astronomical observatory of Japan (yellow), and also
that between Mees Solar Observatory (blue) and National
Astronomical observatory of Japan (red).
Fig.1 Active region NOAA 6619 taken at Huairou Solar Observing
Station on May 11, 1991, at 03:26UT. Top: the photospheric vector
magnetogram taken. Positive/negative values of longitudinal
components of the magnetic field are shaded white/black. The
transverse magnetic field is shown by blue arrows; the magnitude
of the field is proportional to the length of the arrows. Bottom: the
contours of electric current helicity are plotted over the filtergram
of this active region; positive (negative) values are shown by red
(green) contours corresponding to 0.01, 0.05, 0.1, 0.5 G2m−1,
respectively. The average values of current helicity and twist
are -8.7×10−3 G2m−1 and -3.2 ×10−8 m−1, the standard deviations
0.08G2m−1 and 1.1×10−6 m−1, respectively. One can see that the
quantities are highly fluctuating. The field of view is 2.6″×1.8″.
by the Haleakala Stokes Polarimeter (HSP). Figure 2 shows
the comparing results by Xu et al. (2007). The basic trend
of statistical current helicity of solar active regions with
solar cycles can be found.
It is suggested a dynamo mechanism in the solar
interior based on the combined action of differential rotation
and cyclonic convective vortices as a viable way to generate
magnetic fields capable of driving the activity cycle.
According to mean field dynamo theory, the electromotive
force E averaged over convective eddies has a component
parallel to the magnetic field, E = α < B > +..., where the
pseudo scalar α is related to kinetic and electric current
helicities. The statistical imbalance of magnetic helicity of
solar active regions in both hemispheres with solar cycles
Fig.3 Top: the distribution of the averaged twist αff and bottom:
electric current helicity Hcz of solar active regions in the 22nd and
23rd solar cycles. Superimposed, the underlying coloured “butterfly
diagram” shows how sunspot density varies with latitude over
the solar cycle. Vertical axis gives the latitude and the horizontal
gives the time in years. The circle sizes give the magnitude of the
displayed quantity. The bars to the right of the circles show the
level of error bars computed as 95% confidence intervals, scaled
to the same units as the circles. 72 out of 88 groups for current
helicity (82%) as well as 67 out of 88 groups for twist (74%) have
the error bars lower than the signal level.
was discovered by Zhang et al. (2010), who analyzed
a series of vector magnetograms of solar active regions
observed at Huairou Solar Observing Station in China
for nearly 20 years in Figure 3. They found the following
Bulletin of the Chinese Academy of Sciences
221
BCAS
Vol.25 No.3 2011
observational evidence: magnetic (electric current) helicity
and twist patterns are, in general, anti-symmetric with
respect to the solar equator. The helicity pattern is more
complicated than Hale’s polarity law for sunspots. Areas of
the “wrong” sign relative to the hemispheric rule of helicity
have been found at the ends of the butterfly wings as well
as at their very beginnings. The maximum value of helicity,
at the surface at least, seems to occur near the edges of the
butterfly diagram of sunspots. The possibility of the reverse
of hemispheric helicity rule in some periods of solar cycle
has been proposed (Xu et al., 2009) in the framework of
Parker’s very simple model for the solar dynamo.
A statistical relationship between photospheric
current helicity and subsurface kinetic helicity in solar
active regions has been analyzed by Gao et al. (2009).
The parameters are employed: average value of vertical
component of mean current helicity density and mean
subsurface kinetic helicity density, both data were observed
at Huairou Solar Observing Station and SOHO/MDI. It
is found that although there is an opposite hemispheric
preponderance between the signs of current helicity and
that of kinetic helicity at the solar surface, the uncertain
correlations between them do not support that the
photospheric current helicity has a cause and effect relation
with the kinetic helicity at 0-12 Mm beneath the solar
surface.
Moreover, a possible correlation between the magnetic
and velocity fields has been analyzed based on the SOHO/
MDI magnetograms and Dopplergrams was reported by
Zhao et al. (2011). It is found that the observed large-scale
weak magnetic field, which is weaker than 50 G (gauss), is
correlated with the velocity statistically.
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