Hemispheric Rule Research Articles

Evolution of force‐free field parameter in active regions with major eruptive events

Using a nonlinear force‐free field (NLFFF) method to extrapolate photospheric magnetic fields, we compute the force‐free field parameter (α), which is a measure of torsion of the magnetic field lines. We calculated the α parameter for 62 active regions that produced major eruptive events in solar cycle 24. We verified statistically how the 62 studied active regions obey the hemispheric rule of helicity. In agreement with previous studies, we found that 67% of active regions located in the northern hemisphere have a negative sign for the global alpha parameter αg, and 69% of the active regions situated in the southern hemisphere have a positive sign. We have identified and analyzed five cases of evolution of αg at times when eruptive phenomena occurred in the selected active regions. We find that 52% of cases show an increase of torsion during flares, while only 22% show a decrease. This shows that increasing torsion plays an important role in flare ignition. For the other cases, a definitive conclusion cannot be reached because of multiple variations.

Distributed Electric Currents in Solar Active Regions

Using magnetographic data provided by the Helioseismic and Magnetic Imager on board the Solar Dynamics Observatory, we analyzed the structure of magnetic fields and vertical electric currents in six active regions (ARs) with different level of flare activity. We found that electric currents are well balanced over the entire AR: for all of them the current imbalance is below 0.1%, which means that any current system is closed within an AR. Decomposition of the transverse magnetic field vector into two components allowed us to reveal the existence of large-scale vortex structures of the azimuthal magnetic field component around main sunspots of ARs. In each AR, we found a large-scale electric current system occupying a vast area of an AR, which we call distributed electric current. For ARs obeying the Hale polarity law and the hemispheric helicity sign rule, the distributed current is directed upward in the leading part of an AR and it appears to be closing back to the photosphere in the following part of an AR through the corona and chromosphere. Our analysis of the time variations of the magnitude of the distributed electric currents showed that low-flaring ARs exhibit small variations of the distributed currents in the range of $\pm 20 \times 10^{12}$ A, whereas the highly flaring ARs exhibited significant slow variations of the distributed currents in the range of $30-95 \times 10^{12}$ A. Intervals of the enhanced flaring appear to be co-temporal with smooth enhancements of the distributed electric current.

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 .

A Systematic Study of Hale and Anti-Hale Sunspot Physical Parameters

Abstract We present a systematic study of sunspot physical parameters using full-disk magnetograms from the Michelson Doppler Imager/Solar and Heliospheric Observatory and the Helioseismic and Magnetic Imager/Solar Dynamic Observatory. Our aim is to use uniform data sets and analysis procedures to characterize the sunspots, paying particular attention to the differences and similarities between “Hale” and “anti-Hale” spots. Included are measurements of the magnetic tilt angles, areas, fluxes, and polarity pole separations for 4385 sunspot groups in Cycles 23 and 24 each measured, on average, at ∼66 epochs centered on meridian crossing. The sunspots are classified as either “Hale” or “anti-Hale,” depending on whether their polarities align or anti-align with Hale’s hemispheric polarity rule. We find that (1) the “anti-Hale” sunspots constitute a fraction (8.1 ± 0.4)% of all sunspots, and this fraction is the same in both hemispheres and cycles; (2) “Hale” sunspots obey Joy’s law in both hemispheres and cycles but “anti-Hale” sunspots do not—three equivalent forms of Joy’s law are derived: γ = (0.39 ± 0.06) ϕ, and , where γ is the tilt angle and ϕ is the heliospheric latitude; (3) the average Hale sunspot tilt angle is and (4) the tilt angles, magnetic fluxes, and pole separations of sunspots are interrelated, with larger fluxes correlated with larger pole separations and smaller tilt angles. We present empirical relations between these quantities. Cycle 24 is a much weaker cycle than Cycle 23 in sunspot numbers, cumulative magnetic flux, and average sunspot magnetic flux. The “anti-Hale” sunspots are also much weaker than “Hale” sunspots in those parameters, but they share similar magnetic flux distributions and average latitudes. We characterize the two populations, and aim to shed light on the origin of “anti-Hale” sunspots.

A quantity characterizing variation of observed magnetic twist in solar active regions

An alternative parameter RJz is introduced as the ratio of one of two kinds of opposite-sign current to the total current and is used to investigate the relationship between this quantity and the hemispheric helicity sign rule (HSR) that has been established by a series of previous statistical studies. The classification of current in each hemisphere obeys the following rule: if the product of the current and the corresponding longitudinal field component contributes a consistent sign with respect to the HSR, it is called “HSR-compliant” current, otherwise it is called “HSR-noncompliant” current. Firstly, consistency between the butterfly diagram of RJz and current helicity was obtained in a statistical study. Active regions with RJz smaller than 0.5 tend to obey the HSR whereas those with RJz greater than 0.5 tend to disobey it. The “HSR-compliant” current systems have a 60% probability of realization compared to 40% for “HSR-noncompliant” current systems. Overall, the HSR is violated for active regions in which the “HSR-noncompliant” current is greater than the “HSR-compliant” current. Secondly, the parameter RJz was subsequently used to study the evolution of current systems in the case analyses of flare-productive active regions NOAA AR 11158 and AR 11283. It is found that there is a “RJz-quasi-stationary” phase that is relatively flare quiescent and “RJz-dynamic” phase that is characterized by the occurrence of large flares.

CHIRALITY AND MAGNETIC CONFIGURATIONS OF SOLAR FILAMENTS

ABSTRACT It has been revealed that the magnetic topology in the solar atmosphere displays hemispheric preference, i.e., helicity is mainly negative/positive in the northern/southern hemispheres, respectively. However, the strength of the hemispheric rule and its cyclic variation are controversial. In this paper, we apply a new method based on the filament drainage to 571 erupting filaments from 2010 May to 2015 December in order to determine the filament chirality and its hemispheric preference. It is found that 91.6% of our sample of erupting filaments follows the hemispheric rule of helicity sign. It is also found that the strength of the hemispheric preference of the quiescent filaments decreases slightly from ∼97% in the rising phase to ∼85% in the declining phase of solar cycle 24, whereas the strength of the intermediate filaments keeps a high value around 96 ± 4% at all times. Only the active-region filaments show significant variations. Their strength of the hemispheric rule rises from ∼63% to ∼95% in the rising phase, and keeps a high value of 82% ± 5% during the declining phase. Furthermore, during a half-year period around the solar maximum, their hemispheric preference totally vanishes. Additionally, we also diagnose the magnetic configurations of the filaments based on our indirect method and find that in our sample of erupting events, 89% are inverse-polarity filaments with a flux rope magnetic configuration, whereas 11% are normal-polarity filaments with a sheared arcade configuration.

MAGNETIC HELICITY REVERSALS IN A CYCLIC CONVECTIVE DYNAMO

ABSTRACT We investigate the role of magnetic helicity in promoting cyclic magnetic activity in a global, 3D, magnetohydrodynamic (MHD) simulation of a convective dynamo. This simulation is characterized by coherent bands of toroidal field that exist within the convection zone, with opposite polarities in the northern hemisphere (NH) and southern hemisphere (SH). Throughout most of the cycle, the magnetic helicity in these bands is negative in the NH and positive in the SH. However, during the declining phase of each cycle, this hemispheric rule reverses. We attribute this to a global restructuring of the magnetic topology that is induced by the interaction of the bands across the equator. This band interaction appears to be ultimately responsible for, or at least associated with, the decay and subsequent reversal of both the toroidal bands and the polar fields. We briefly discuss the implications of these results within the context of solar observations, which also show some potential evidence for toroidal band interactions and helicity reversals.

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.

Magnetic Flux Emergence Along the Solar Cycle

Flux emergence plays an important role along the solar cycle. Magnetic flux emergence builds sunspot groups and solar activity. The sunspot groups contribute to the large scale behaviour of the magnetic field over the 11 year cycle and the reversal of the North and South magnetic polarity every 22 years. The leading polarity of sunspot groups is opposite in the North and South hemispheres and reverses for each new solar cycle. However the hemispheric rule shows the conservation of sign of the magnetic helicity with positive and negative magnetic helicity in the South and North hemispheres, respectively. MHD models of emerging flux have been developed over the past twenty years but have not yet succeeded to reproduce solar observations. The emergence of flux occurs through plasma layers of very high gradients of pressure and changing of modes from a large β to a low β plasma (<1). With the new armada of high spatial and temporal resolution instruments on the ground and in space, emergence of magnetic flux is observed in tremendous detail and followed during their transit through the upper atmosphere. Signatures of flux emergence in the corona depend on the pre-existing magnetic configuration and on the strength of the emerging flux. We review in this paper new and established models as well as the recent observations.

MAGNETIC HELICITY IN EMERGING SOLAR ACTIVE REGIONS

Using vector magnetic field data from the Helioseismic and Magnetic Imager instrument aboard the Solar Dynamics Observatory, we study magnetic helicity injection into the corona in emerging active regions (ARs) and examine the hemispheric helicity rule. In every region studied, photospheric shearing motion contributes most of the helicity accumulated in the corona. In a sample of 28 emerging ARs, 17 follow the hemisphere rule (61% ± 18% at a 95% confidence interval). Magnetic helicity and twist in 25 ARs (89% ± 11%) have the same sign. The maximum magnetic twist, which depends on the size of an AR, is inferred in a sample of 23 emerging ARs with a bipolar magnetic field configuration.

Hemispheric Distribution of Subsurface Kinetic Helicity and Its Variation with Magnetic Activity

We study the hemispheric distribution of the kinetic helicity of subsurface flows in the near-surface layers of the solar convection zone and its variation with magnetic activity. We determine subsurface flows with a ring-diagram analysis applied to Global Oscillation Network Group (GONG) Dopplergrams and Dynamics Program data from the Michelson Doppler Imager (MDI) instrument onboard the Solar and Heliospheric Observatory (SOHO). We determine the average kinetic helicity density as a function of Carrington rotation and latitude. The average kinetic helicity density at all depths and the kinetic helicity, integrated over 2 – 7 Mm, follow the same hemispheric rule as the current/magnetic helicity proxies with predominantly positive values in the southern and negative ones in the northern hemisphere. This holds true for all levels of magnetic activity from quiet to active regions. However, this is a statistical result; only about 55 % of all locations follow the hemispheric rule. But these locations have larger helicity values than those that do not follow the rule. The average values of helicity density increase with depth for all levels of activity, which might reflect an increase of the characteristic size of convective motions with greater depth. The average helicity of subsets of high magnetic activity is about five times larger than that of subsets of low activity. The solar-cycle variation of helicity is thus mainly due to the presence or absence of active regions. During the rising phase of cycle 24, locations of high magnetic activity at low latitudes show a weaker hemispheric behavior compared to the rising phase of cycle 23.

ON THE STRENGTH OF THE HEMISPHERIC RULE AND THE ORIGIN OF ACTIVE-REGION HELICITY

Vector magnetograph and morphological observations have shown that the solar magnetic field tends to have negative (positive) helicity in the northern (southern) hemisphere, although only ~60%-70% of active regions appear to obey this In contrast, at least ~80% of quiescent filaments and filament channels that form during the decay of active regions follow the rule. We attribute this discrepancy to the difficulty in determining the helicity sign of newly emerged active regions, which are dominated by their current-free component; as the transverse field is canceled at the polarity inversion lines, however, the axial component becomes dominant there, allowing a more reliable determination of the original active-region chirality. We thus deduce that the hemispheric rule is far stronger than generally assumed, and cannot be explained by stochastic processes. Earlier studies have shown that the twist associated with the axial tilt of active regions is too small to account for the observed helicity; here, both tilt and twist are induced by the Coriolis force acting on the diverging flow in the emerging flux tube. However, in addition to this east-west expansion about the apex of the loop, each of its legs must expand continually in cross section during its rise through the convection zone, thereby acquiring a further twist through the Coriolis force. Since this transverse pressure effect is not limited by drag or tension forces, the final twist depends mainly on the rise time, and may be large enough to explain the observed active-region helicity.

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.

FIRST SYNOPTIC MAPS OF PHOTOSPHERIC VECTOR MAGNETIC FIELD FROM SOLIS/VSM: NON-RADIAL MAGNETIC FIELDS AND HEMISPHERIC PATTERN OF HELICITY

We use daily full-disk vector magnetograms from Vector Spectromagnetograph (VSM) on Synoptic Optical Long-term Investigations of the Sun (SOLIS) system to synthesize the first Carrington maps of the photospheric vector magnetic field. We describe these maps and make a comparison of observed radial field with the radial field estimate from LOS magnetograms. Further, we employ these maps to study the hemispheric pattern of current helicity density, Hc, during the rising phase of the solar cycle 24. Longitudinal average over the 23 consecutive solar rotations shows a clear signature of the hemispheric helicity rule, i.e. Hc is predominantly negative in the North and positive in South. Although our data include the early phase of cycle 24, there appears no evidence for a possible (systematic) reversal of the hemispheric helicity rule at the beginning of cycle as predicted by some dynamo models. Further, we compute the hemispheric pattern in active region latitudes (-30 deg \le \theta \le 30 deg) separately for weak (100< |B_r| <500 G)and strong (|B_r|>1000 G) radial magnetic fields. We find that while the current helicity of strong fields follows the well-known hemispheric rule (i.e., \theta . Hc < 0), H_c of weak fields exhibits an inverse hemispheric behavior (i.e., \theta . Hc > 0) albeit with large statistical scatter. We discuss two plausible scenarios to explain the opposite hemispheric trend of helicity in weak and strong field region.

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).

Hemispheric Patterns in Filament Chirality and Sigmoid Shape over the Solar Cycle

AbstractThe motivation for our research was to study the correlation between the chirality of filaments and the handedness (S- or Z-shape) of sigmoids. It was assumed that sigmoids would mostly coincide with filaments and that the S-shaped sigmoids would correlate well with filaments of sinistral chirality, which we found that to be at best a very weak relation. Since we had a full solar cycle of filament metadata at hand it was easy to verify the supposedly known hemispheric preference of filament chirality. We discovered that the hemispheric chirality rule was confirmed for the epoch where a thorough manual study had been performed, but that at other phases of the solar cycle the rule seems to disappear and sometimes even reverse.

Fe XII STALKS AND THE ORIGIN OF THE AXIAL FIELD IN FILAMENT CHANNELS

Employing Fe XII images and line-of-sight magnetograms, we deduce the direction of the axial field in high-latitude filament channels from the orientation of the adjacent stalklike structures. Throughout the rising phase of the current solar cycle 24, filament channels poleward of latitude 30° overwhelmingly obeyed the hemispheric chirality rule, being dextral (sinistral) in the northern (southern) hemisphere, corresponding to negative (positive) helicity. During the deep minimum of 2007-2009, the orientation of the Fe XII stalks was often difficult to determine, but no obvious violations of the rule were found. Although the hemispheric trend was still present during the maximum and early declining phase of cycle 23 (2000-2003), several high-latitude exceptions were identified at that time. From the observation that dextral (sinistral) filament channels form through the decay of active regions whose Fe XII features show a counterclockwise (clockwise) whorl, we conclude that the axial field direction is determined by the intrinsic helicity of the active regions. In contrast, generation of the axial field component by the photospheric differential rotation is difficult to reconcile with the observed chirality of polar crown and circular filament channels, and with the presence of filament channels along the equator. The main role of differential rotation in filament channel formation is to expedite the cancellation of flux and thus the removal of the transverse field component. We propose further that, rather than being ejected into the heliosphere, the axial field is eventually resubmerged by flux cancellation as the adjacent unipolar regions become increasingly mixed.

Active Regions with Superpenumbral Whirls and Their Subsurface Kinetic Helicity

We search for a signature of helicity flow from the solar interior to the photosphere and chromosphere. For this purpose, we study two active regions, NOAA 11084 and 11092, that show a regular pattern of superpenumbral whirls in chromospheric and coronal images. These two regions are good candidates for comparing magnetic/current helicity with subsurface kinetic helicity because the patterns persist throughout the disk passage of both regions. We use photospheric vector magnetograms from SOLIS/VSM and SDO/HMI to determine a magnetic helicity proxy, the spatially averaged signed shear angle (SASSA). The SASSA parameter produces consistent results leading to positive values for NOAA 11084 and negative ones for NOAA 11092 consistent with the clockwise and counter-clockwise orientation of the whirls. We then derive the properties of the subsurface flows associated with these active regions. We measure subsurface flows using a ring-diagram analysis of GONG high-resolution Doppler data and derive their kinetic helicity, h z . Since the patterns persist throughout the disk passage, we analyze synoptic maps of the subsurface kinetic helicity density. The sign of the subsurface kinetic helicity is negative for NOAA 11084 and positive for NOAA 11092; the sign of the kinetic helicity is thus anticorrelated with that of the SASSA parameter. As a control experiment, we study the subsurface flows of six active regions without a persistent whirl pattern. Four of the six regions show a mixture of positive and negative kinetic helicity resulting in small average values, while two regions are clearly dominated by kinetic helicity of one sign or the other, as in the case of regions with whirls. The regions without whirls follow overall the same hemispheric rule in their kinetic helicity as in their current helicity with positive values in the southern and negative values in the northern hemisphere.

Solar cycle variation of helicity characteristics indicated by SP/Hinode

AbstractHelicity characteristics in active regions (ARs) are studied, using so far the most accurate vector magnetic field measurements obtained with SP/Hinode. Our sample includes all ARs observed by SP/Hinode, up to June 2012. The sample is divided into three sub-samples: Cycle 23 (from 2006.11 to 2008.06), Cycle 24a (from 2008.10 to 2010.09) and Cycle 24b (from 2010.10 to 2012.06). We confirm our previous findings that the usual hemispheric helicity sign rule is not obeyed in the descending phase of solar cycle 23 and is obeyed in the ascending phase of solar cycle 24. And we find that the second phase of the solar cycle 24 (Cycle 24b) shows an even stronger evidence of the usual hemispheric helicity sign rule than its first phase (Cycle 24a). It is also found that our previous finding that the strong and weak fields possess the opposite helicity signs is not followed in Cycle 24b, whereas it is weakly followed in Cycle 24a and strongly followed in the descending phase of Cycle 23. This means that this rule also has a solar cycle variation, in addition to the solar cycle variation of the usual hemispheric helicity sign rule, and there is a roughly 2-years time delay between the two.