Hemispheric Sign Rule Research Articles

Spectral Magnetic Helicity of Solar Active Regions between 2006 and 2017

Abstract We compute magnetic helicity and energy spectra from about 2485 patches of about 100 Mm side length on the solar surface using data from Hinode during 2006–2017. An extensive database is assembled where we list the magnetic energy and helicity, large- and small-scale magnetic helicity, mean current helicity density, fractional magnetic helicity, and correlation length along with the Hinode map identification number (MapID), as well as the Carrington latitude and longitude for each MapID. While there are departures from the hemispheric sign rule for magnetic and current helicities, the weak trend reported here is in agreement with the previous results. This is argued to be a physical effect associated with the dominance of individual active regions that contribute more strongly in the better-resolved Hinode maps. In comparison with earlier work, the typical correlation length is found to be 6– , while the length scale relating the magnetic and current helicities to each other is around .

EVOLUTION OF MAGNETIC HELICITY AND ENERGY SPECTRA OF SOLAR ACTIVE REGIONS

ABSTRACT We adopt an isotropic representation of the Fourier-transformed two-point correlation tensor of the magnetic field to estimate the magnetic energy and helicity spectra as well as current helicity spectra of two individual active regions (NOAA 11158 and NOAA 11515) and the change of the spectral indices during their development as well as during the solar cycle. The departure of the spectral indices of magnetic energy and current helicity from 5/3 are analyzed, and it is found that it is lower than the spectral index of the magnetic energy spectrum. Furthermore, the fractional magnetic helicity tends to increase when the scale of the energy-carrying magnetic structures increases. The magnetic helicity of NOAA 11515 violates the expected hemispheric sign rule, which is interpreted as an effect of enhanced field strengths at scales larger than 30–60 Mm with opposite signs of helicity. This is consistent with the general cycle dependence, which shows that around the solar maximum the magnetic energy and helicity spectra are steeper, emphasizing the large-scale field.

A statistical analysis of current helicity and twist in solar active regions over the phases of the solar cycle using the spectro-polarimeter data of Hinode

Abstract Current helicity and twist of solar magnetic fields are important in characterizing the dynamo mechanism working in the convection zone of the Sun. We have carried out a statistical study on the current helicity of solar active regions observed with the spectro-polarimeter (SP) of the Hinode Solar Optical Telescope (SOT). We used SOT-SP data of 558 vector magnetograms of a total of 80 active regions obtained during the period from 2006 to 2012. We have applied spatial smoothing and division of data points into weak and strong field ranges to compare the contributions from different scales and field strengths. We found that the current helicity follows the “hemispheric sign rule” when weak magnetic fields (absolute field strength < 300 gauss) are considered and no smoothing is applied. On the other hand, the pattern of current helicity fluctuates and violates the hemispheric sign rule when stronger magnetic fields are considered and smoothing of 2${^{\prime\prime}_{.}}$0 (modeled on ground-based observations) is applied. Furthermore, we found a tendency that weak and inclined fields conform to the hemispheric sign rule and strong and vertical fields violate it. These different properties of helicity through the strong and weak magnetic field components give important clues in understanding the solar dynamo as well as the mechanism of formation and evolution of solar active regions.

The origin of the helicity hemispheric sign rule reversals in the mean-field solar-type dynamo

Observations of proxies of the magnetic helicity in the Sun over the past two solar cycles revealed reversals of the helicity hemispheric sign rule (negative in the North and positive in the South hemispheres). We apply the mean-field solar dynamo model to study the reversals of the magnetic helicity sign for the dynamo operating in the bulk of the solar convection zone. The evolution of the magnetic helicity is governed by the conservation law. We found that the reversal of the sign of the small-scale magnetic helicity follows the dynamo wave propagating inside the convection zone. Therefore, the spatial patterns of the magnetic helicity reversals reflect the processes which contribute to generation and evolution of the large-scale magnetic fields. At the surface the patterns of the helicity sign reversals are determined by the magnetic helicity boundary conditions at the top of the convection zone. We demonstrate the impact of fluctuations in the dynamo parameters and variability in dynamo cycle amplitude on the reversals of the magnetic helicity sign rule. The obtained results suggest that the magnetic helicity of the large-scale axisymmetric field can be treated as an additional observational tracer for the solar dynamo.

Statistical distribution of current helicity in solar active regions over the magnetic cycle

The current helicity in solar active regions derived from vector magnetograph observations for more than 20 years indicates the so-called hemispheric sign rule; the helicity is predominantly negative in the northern hemisphere and positive in the southern hemisphere. In this paper we revisit this property and compare the statistical distribution of current helicity with Gaussian distribution using the method of normal probability paper. The data sample comprises 6630 independent magnetograms obtained at Huairou Solar Observing Station, China, over 1988-2005 which correspond to 983 solar active regions. We found the following. (1) For the most of cases in time-hemisphere domains the distribution of helicity is close to Gaussian. (2) At some domains (some years and hemispheres) we can clearly observe significant departure of the distribution from a single Gaussian, in the form of two- or multi-component distribution. (3) For the most non-single-Gaussian parts of the dataset we see co-existence of two or more components, one of which (often predominant) has a mean value very close to zero, which does not contribute much to the hemispheric sign rule. The other component has relatively large value of helicity that often determines agreement or disagreement with the hemispheric sign rule in accord with the global structure of helicity reported by Zhang et al. (2010).

Magnetic Helicity of Solar Active Regions as Revealed by Vector Magnetograms and Coronal X-Ray Images

Abstract We have used photospheric vector magnetograms of 15 different solar active regions to calculate the current helicity parameter, $ \alpha _{\rm av}$ , and the linear force-free field (LFFF) parameter, $ \alpha _{\rm best}$ , that fits best the observed transverse field. The data were obtained with the Solar Magnetic Field Telescope at the Huairou Solar Observing Station, the National Astronomical Observatories of China, the Solar Flare Telescope of the National Astronomical Observatory of Japan, and the Haleakala Stokes Polarimeter at the Mees Solar Observatory, University of Hawaii, from 1997 to 2000. The agreement in sign of $ \alpha _{\rm av}$ between three vector magnetographs is better than 90%. For $ \alpha _{\rm best}$ , the agreement is 80%–90%. The line-of-sight magnetograms observed with the Michelson–Doppler Imager (MDI) on SOHO and coronal X-ray images observed with the Soft X-ray Telescope (SXT) on Yohkoh have been used to determine the constant $ \alpha _{\rm c}$ of the LFFF in the corona. The value of $ \alpha _{\rm c}$ corresponds to the extrapolated coronal field whose field lines best match, by visual inspection, the structure of coronal loops in X-ray images. It is found that the sign agreement between photospheric $ \alpha _{\rm av}$ or $ \alpha _{\rm best}$ and coronal $ \alpha _{\rm c}$ is lower (60%–85%). We consider the differences in measurements, observing conditions, data reduction methods, and limitation in LFFF extrapolation, and discuss their contributions to the dispersions in the hemispheric sign rule of helicity.

A HEMISPHERIC HELICITY SIGN RULE INDICATED BY LARGE-SCALE PHOTOSPHERIC MAGNETIC FIELDS AT THREE PHASES OF SOLAR CYCLE 23

The hemispheric sign rule of current helicity is examined for large-scale magnetic fields, extending to 60° high in solar latitudes, at three different phases of solar cycle 23 and using three different instruments. The current helicity is calculated from the vector magnetic fields derived respectively from the longitudinal full-disk magnetograms obtained by the Michelson Doppler Imager on board the Solar and Heliospheric Observatory as well as the Kitt Peak Vacuum Telescope and the Synoptic Long-term Investigations of the Sun at the National Solar Observatory at Kitt Peak. We have used the same technique introduced by Pevtsov & Latushko to retrieve the vector magnetic field but have applied a different method to calculate the current helicity. Our analysis strengthens evidence that the large-scale magnetic fields show a clear and consistent current helicity pattern that follows the established hemispheric rule, that is, a positive helicity sign in the southern hemisphere and a negative helicity sign in the northern hemisphere. This hemispheric sign pattern is present everywhere in the global magnetic field, extending to 60° high in solar latitudes, independent of the instruments and parameters used, and is evident at both solar maximum and minimum phases.

Some basic questions on helicity inferred from vector magnetograms

This paper summarizes current helicity measurements in the solar active regions (ARs). There is a basic agreement with the “hemispheric sign rule (HSR)” of the current helicity among different vector magnetographs through two solar cycles, but there is a large dispersion of the fraction of ARs following the HSR. In our sample, there are 50%–78% ARs in solar cycle 22 and 44%–79% ARs in cycle 23 following the HSR. A variation is also found in the fraction of the ARs following the HSR between different instruments even when the same ARs are selected. The difference also exists for the same instrument when the selected ARs are different. There are some differences in the variation of HSR with solar cycle for the individual helicity parameter inferred from different instruments. Factors which influence the correlation of different data sets are analyzed.

Current helicity pattern of large-scale magnetic field on the photosphere

Following Pevtsov and Latushko, we study the current helicity pattern of the large-scale magnetic field on the photosphere. We use the same technique as theirs to derive the vector magnetic field (Br, Bθ, Bϕ) from full-disk longitudinal magnetograms based on the assumption that large-scale magnetic fields evolve rather slowly and the variations of the longitudinal magnetic fields within certain time duration are caused by the changing position angles only. Different from their study, we have calculated the current helicity maps directly from the derived vector magnetograms, rather than from obtaining the latitudinal variation of hc by ignoring the role of Bθ component and averaging Br and Bϕ over all solar longitudes. This approach significantly strengthens the evidence of the hemispheric rule presented in the reconstructed vector magnetic field. Our study shows that the established hemispheric sign rule, that is, positive helicity sign in the southern hemisphere and negative helicity sign in the northern hemisphere, is applicable everywhere in the global magnetic field, namely, also evident in weak fields outside active regions, and that the obtained sign pattern is independent of the longitudinal magnetograms and the parameters that we have used.

Solar-Cycle Variation of Magnetic Helicity in Active Regions

Abstract The hemispheric sign rule of helicity and its long-term variation were studied. The data were obtained from the Solar Flare Telescope at Mitaka and the 65-cm solar telescope at Okayama. The data covered the period of 1983–2001, from the declining phase of solar cycle 21 to the rising phase of cycle 23. Although the hemispheric sign rule of helicity generally holds, we also found significant time variations in the yearly values of helicity during the observation period. The hemispheric sign rule of helicity is satisfied in the solar maximum phase, but may not be so in the solar minimum phase.

The Current Helicity Parameter Hc is More Sensitive than αbest to Faraday Rotation

Observations have indicated that the net helicity sign of active regions is predominantly negative in the northern hemisphere and positive in the southern (see Table 1). From Table 1, we find that the hemispheric sign rule of helicity parameter αbest does not change with another solar cycle; but the helicity parameter Hc seems to show a weak opposite hemispheric preference for Huairou data in the solar cycle 23 and no preference for Mees data. How to explain such a phenomenon? We think one reason may be from the action of Faraday rotation. Faraday rotation will cause a counterclockwise rotation of the azimuth for a positive polarity field and vice versa. During the cycle 22, the polarity of leading sunspots is dominantly negative in the northern hemisphere and positive in the southern. The effect of Faraday rotation, which is determined mostly by a leading polarity sunspot, has a positive contribution to the percentage of current helicity signs in active regions and leads to the increase of the strength of the hemispheric sign rule. In the cycle 23, the polarity of most leading sunspots is positive in the northern hemisphere and Faraday rotation will decrease the percentage of current helicity signs. Consequently, the strength of the hemispheric rule should be weakened. On the other hand, Hc is more susceptible to Faraday rotation than αbest because it is mainly related to the areas where the line-of-sight field is strong. Therefore, if the effect of Faraday rotation is not completely removed in our observations, the hemispheric sign rule showed is weak in the cycle 23 than in the cycle 22 (for αbest), even opposite (for Hc).

MAGNETIC HELICITY OF SOLAR ACTIVE REGIONS AND ITS IMPLICATIONS

We have studied the magnetic helicity of active regions by using the data from (1) the photo-electric magnetograph of the Okayama Observatory (1983-1995) and (2) the video magnetograph of NAOJ/Mitaka (1992-2000). The latitude distribution of helicity showed a tendency that the regions in the north (south) hemisphere have negative (positive) helicities, respectively, which is already known as the hemispheric sign rule. If we look into the sign of helicity as a function of time, the sign rule was less definite or was reversed sometimes in the sunspot minimum phase. We also studied the relation between the magnetic helicity and the sunspot tilt angles, and found that these two quantities are positively correlated, which is opposite to the expectation of a theoretical model. The implications of this cycle-phase dependence of helicity signs and the correlation between magnetic he Ii city and sunspot tilt angles are discussed.

The hemispheric sign rule of current helicity during the rising phase of cycle 23

We compute the signs of two different current helicity parameters (i.e., αbest andH c) for 87 active regions during the rise of cycle 23 The results indicate that 59% of the active regions in the northern hemisphere have negative αbest and 65% in the southern hemisphere have positive. This is consistent with that of the cycle 22. However, the helicity parameterH cshows a weaker opposite hemispheric preference in the new solar cycle. Possible reasons are discussed.

Studies of solar intranetwork fields and current helicity in active regions

In this paper we begin with a brief review of the most recent observational studies of intranetwork elements. Next by analyzing well observed quantities of other magnetic elements, we suggest that the magnetic flux of all elements is proportional to its lifetime, mainly depending on each size. Then we present an empirical way to extrapolate the size and magnetic field of intranetwork elements, and find that their average size is about 210 km and the corresponding field strength is 350 G. Finally, our studies of current helicity in active regions are summarized as follows: (1) most of the active regions in solar cycle 22 follow the hemispheric helicity sign rule, and the evolution of surface large-scale current helicity has a good correlation with solar activity; (2) the active regions with reversed helicity sign tend to emerge at certain longitudes; (3) the rapid and substantial changes of current helicity in an area or in its vicinity are most likely to trigger flares.

The Hemispheric Sign Rule of Current Helicity during the Rising Phase of Cycle 23

AbstractWe compute the signs of two different current helicity parameters (i.e., αbestandHc) for 87 active regions during the rise of cycle 23. The results indicate that 59% of the active regions in the northern hemisphere have negative αbestand 65% in the southern hemisphere have positive. This is consistent with that of the cycle 22. However, the helicity parameterHcshows a weaker opposite hemispheric preference in the new solar cycle. Possible reasons are discussed.