Hale's Polarity Law Research Articles

Signature of the turbulent component of the solar dynamo on active region scales and its association with flaring activity

ABSTRACT It is a challenging problem to obtain observational evidence of the turbulent component of solar dynamo operating in the convective zone because the dynamo action is hidden below the photosphere. Here we present results of a statistical study of flaring active regions (ARs) that produced strong solar flares of an X-ray class X1.0 and higher during a time period that covered solar cycles 23 and 24. We introduced a magneto-morphological classification of ARs, which allowed us to estimate the possible contribution of the turbulent component of the dynamo into the structure of an AR. We found that in 72 per cent of cases, flaring ARs do not comply with the empirical laws of the global dynamo (frequently they are not bipolar ARs or, if they are, they violate the Hale polarity law, the Joy law, or the leading sunspot prevalence rule). This can be attributed to the influence of the turbulent dynamo action inside the convective zone on spatial scales of typical ARs. Thus, it appears that the flaring is governed by the turbulent component of the solar dynamo. The contribution into the flaring from these AR ‘violators’ (irregular ARs) is enhanced during the second maximum and the descending phase of a solar cycle, when the toroidal field weakens and the influence of the turbulent component becomes more pronounced. These observational findings are in consensus with a concept of the essential role of non-linearities and turbulent intermittence in the magnetic fields generation inside the convective zone, which follows from dynamo simulations.

A Catalog of Bipolar Active Regions Violating the Hale Polarity Law, 1989 – 2018

There is no list of bipolar active regions (ARs) with reverse polarity (anti-Hale regions), although statistical investigations of such ARs (bearing the imprint of deep subphotospheric processes) are important for understanding solar-cycle mechanisms. We studied 8606 ARs from 1 January 1989 to 31 December 2018 to detect anti-Hale regions and to compile a catalog. The Solar and Heliospheric Observatory (SOHO) and the Solar Dynamics Observatory (SDO) data, as well as the Debrecen Photoheliographic Data, the Mount Wilson Observatory catalog and drawings, and the USAF/NOAA Solar Region Summary were used. Complex, ambiguous cases related to anti-Hale region identification were analyzed. Two basic and four additional criteria to identify an AR as an anti-Hale region were formulated. The basic criteria assume that: i) dominating features of an AR have to form a bipole of reverse polarity with sunspots/pores of both polarities being present; ii) magnetic connections between the opposite polarities has to be observed. A catalog of anti-Hale regions (275 ARs) is compiled. The catalog contains: NOAA number, date of the greatest total area of sunspots, coordinates, and corrected sunspot area for this date. The tilt and the most complex achieved Mount Wilson magnetic class are also provided. The percentage of anti-Hale groups meeting the proposed criteria is ~3.0% from all studied ARs, which is close to early estimations by authors who had examined each AR individually: ~2.4% by Hale and Nicholson (Ap.J. 62, 270, 1925) and ~3.1% by Richardson (Ap.J. 107, 78, 1948). The enchancement of the anti-Hale percentage in later research might be related to: i) increasing sensitivity of instruments (considering smaller and smaller bipoles); ii) the ambiguities in the anti-Hale region identification.

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.

Contributions from Different-Type Active Regions Into the Total Solar Unsigned Magnetic Flux

Data set acquired by the Helioseismic and Magnetic Imager (HMI) onboard the Solar Dynamics Observatory (SDO) during 2010–2017 allowed us to classify active regions (ARs) into three categories: A-type— regular bipolar ARs; U-type—unipolar spots; B-type—irregular ARs, violating either Hale polarity law or Joy’s law or having the leading spot less than the main following spot. A separate subset of anti-Hale ARs was formed. We selected 1494 ARs in total and found the following: (i) Pearson correlation coefficient r between the total unsigned flux for a given category and the International Sunspot Number smoothly decreases with transition from A-type (r = 0.57) to B-type (r = 0.53) to anti-Hale ARs (r = 0.31) to U-type (r = 0.18); (ii) yearly contributions into the total flux from categories also gradually decreases: from 50–70% from A-type ARs to 20–40% from B‑type ARs to 10–20% from U-type ARs to 5–11% from anti-Hale ARs. (iii) At the beginning of the solar minimum, the fraction of flux from anti-Hale groups increased from 5 to 9% and amount of flux per magnetogram was constant at about 1021 Mx level. The data are compatible with a concept that generation of the magnetic field on the Sun occurs as a united process in a non-linear dynamical dissipative system, i.e., global and local (fluctuation) dynamos are inseparable and operate together. The observed enhancement of the anti-Hale flux during the solar maximum can be due to the combined mechanisms of global mean-field and local fluctuation dynamos.

Solar small-scale dynamo and polarity of sunspot groups

In order to clarify a possible role of small-scale dynamo in formation of solar magnetic field, we suggest an observational test for small-scale dynamo action based on statistics of anti-Hale sunspot groups. As we have shown, according to theoretical expectations the small-scale dynamo action has to provide a population of sunspot groups which do not follow the Hale polarity law, and the density of such groups on the time-latitude diagram is expected to be independent on the phase of the solar cycle. Correspondingly, a percentage of the anti-Hale groups is expected to reach its maximum values during solar minima. For several solar cycles, we considered statistics of anti-Hale groups obtained by several scientific teams, including ours, to find that the percentage of anti-Hale groups becomes indeed maximal during a solar minimum. Our interpretation is that this fact may be explained by the small-scale dynamo action inside the solar convective zone.

How much more can sunspots tell us about the solar dynamo?

AbstractSunspot observations inspired solar dynamo theory and continue to do so. Simply counting them established the sunspot cycle and its period. Latitudinal distributions introduced the tough constraint that the source of sunspots moves equator-ward as the cycle progresses. Observations of Hale's polarity law mandated hemispheric asymmetry. How much more can sunspots tell us about the solar dynamo? We draw attention to a few outstanding questions raised by inherent sunspot properties. Namely, how to explain sunspot rotation rates, the incoherence of follower spots, the longitudinal spacing of sunspot groups, and brightness trends within a given sunspot cycle. After reviewing the first several topics, we then present new results on the brightness of sunspots in Cycle 24 as observed with the Helioseismic Magnetic Imager (HMI). We compare these results to the sunspot brightness observed in Cycle 23 with the Michelson Doppler Imager (MDI). Next, we compare the minimum intensities of five sunspots simultaneously observed by the Hinode Solar Optical Telescope Spectropolarimeter (SOT-SP) and HMI to verify that the minimum brightness of sunspot umbrae correlates well to the maximum field strength. We then examine 90 and 52 sunspots in the north and south hemisphere, respectively, from 2010 - 2012. Finally, we conclude that the average maximum field strengths of umbra 40 Carrington Rotations into Cycle 24 are 2690 Gauss, virtually indistinguishable from the 2660 Gauss value observed at a similar time in Cycle 23 with MDI.

BIPOLAR MAGNETIC REGIONS ON THE SUN: GLOBAL ANALYSIS OF THESOHO/MDI DATA SET

The magnetic flux that is generated by dynamo inside the Sun emerges in the form of bipolar magnetic regions. We have analyzed the whole set of solar magnetograms obtained with the SOHO/MDI instrument in 1995-2011, and automatically identified 160,079 bipolar magnetic regions that span a range of scale sizes across nearly four orders of magnitude. Their properties have been statistically analyzed, in particular with respect to the polarity orientations of the bipolar regions, including their tilt angle distributions. The latitude variation of the average tilt angles (with respect to the E-W direction), known as Joy's law, is found to closely follow the relation 32.1*sin(latitude)[deg]. There is no indication of a dependence on region size that one may expect if the tilts were produced by the Coriolis force during the buoyant rise of flux loops from the tachocline region. A few percent of all regions have orientations that violate Hale's polarity law. We show examples, from different phases of the solar cycle, where well defined medium-size bipolar regions with opposite polarity orientations occur side by side in the same latitude zone. Such oppositely oriented large bipolar regions cannot be part of the same toroidal flux system, but different flux systems must coexist in the same latitude zones. These examples are incompatible with the paradigm of coherent, subsurface toroidal flux ropes as the source of sunspots, and instead show that fluctuations must play a major role at all scales for the turbulent dynamo. We see no observational support for a separation of scales or a division between a global and a local dynamo, since also the smallest scales in the data set retain a non-random component that significantly contributes to the accumulated emergence of a N-S dipole moment that leads to the replacement of the old global poloidal field with a new one that has the opposite orientation.

Cluster analysis for pattern recognition in solar butterfly diagrams

AbstractWe investigate to what extent the wings of solar butterfly diagrams can be separated without an explicit usage of Hale's polarity law as well as the location of the solar equator. We apply two algorithms of cluster analysis for this purpose, namely DBSCAN and C‐means, and demonstrate their ability to separate the wings of contemporary butterfly diagrams based on the sunspot group density in the diagram only. Then we apply the method to historical data concerning the solar activity in the 18th century (Staudacher data). The method separates the two wings for Cycle 2, but fails to separate them for Cycle 1. In our opinion, this finding supports the interpretation of the Staudacher data as an indication of the unusual nature of the solar cycle in the 18th century (© 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

The solar dynamo in the light of the distribution of various sunspot magnetic classes over butterfly diagram

AbstractWe present the data concerning the distribution of various sunspot magnetic classes over the solar butterfly diagram and discuss how this data can inform solar dynamo models. We use the statistics of sunspots that violate the Hale polarity law to estimate the ratio of the fluctuating and mean components of the toroidal magnetic field inside the solar convective zone. An analysis of the spatial distribution of bipolar, unipolar and complex sunspot groups in the context of simple dynamo models results in the conclusion that the mean toroidal field is relatively simple and maintains its shape during the course of the solar cycle (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

The distribution of current helicity at the solar surface at the beginning of the solar cycle

A fraction of solar active regions are observed to have current helicity of a sign that contradicts the polarity law for magnetic helicity; this law corresponds to the well-known Hale polarity law for sunspots. A significant excess of active regions with the sign of helicity is seen to occur just at the beginning of the cycle. We compare these observations with predictions from a dynamo model based on principles of helicity conservation, discussed by Zhang et al. (2006). This model seems capable of explaining only a fraction of the regions with the wrong sign of the helicity. We attribute the remaining excess to additional current helicity production from the twisting of rising magnetic flux tubes, as suggested by Choudhuri et al. (2004). We estimate the relative contributions of this effect and that connected with the model based on magnetic helicity conservation.

The Orientational Relaxation of Bipolar Active Regions

In the mean, bipolar active regions are oriented nearly toroidally, according to Hale's polarity law, with a latitude-dependent tilt known as Joy's Law. The tilt angles of individual active regions deviate from this mean behavior and change over time. It has been found that on average the change is toward the mean angle at a rate characteristic of 4.37 days (Howard, 1996). We show that this orientational relaxation is consistent with the standard model of flux tube emergence from a deep dynamo layer. Under this scenario Joy's law results from the Coriolis effect on the rising flux tube (D'Silva and Choudhuri, 1993), and departures from it result from turbulent buffeting of the tubes (Longcope and Fisher, 1996). We show that relaxation toward Joy's angle occurs because the turbulent perturbations relax on shorter time scales than the perturbations from the Coriolis force. The turbulent perturbations relax more rapidly because they are localized to the topmost portion of the convection zone while the Coriolis perturbations are more widely distributed. If a fully-developed active region remains connected to the strong toroidal magnetic field at the base of the convection zone, its tilt will eventually disappear, leaving it aligned perfectly toroidally. On the other hand, if the flux becomes disconnected from the toroidal field the bipole will assume a tilt indicative of the location of disconnection. We compare models which are connected and disconnected from the toroidal field. Only those disconnected at points very deep in the convection zone are consistent with observed time scale of orientational relaxation.

Origin and Evolution of Filament‐Prominence Systems

We present a head-to-tail linkage model for the formation, evolution, and eruption of solar filaments. The magnetic field structure of our model is based on the observation that filaments form exclusively in filament channels with no apparent magnetic connections above the polarity inversion line. The formation of a filament in this configuration is driven by flux convergence and cancellation, which produces looplike filament segments with a half-turn. Filament segments of like chirality may connect and form long quiescent filaments. Such filaments are stabilized through footpoint anchoring until further cancellation at the footpoints causes their eruption. The eruption restores the original filament channel so that filament formation may resume immediately. We then demonstrate that the combined workings of Hale's polarity law, Joy's law, and differential rotation introduce a strong hemispheric preference in the chirality of filaments formed poleward of the sunspot belt, which is in agreement with observations. We analyze the magnetic fine structure of filaments formed through our model and find consistency with the observed hemispheric preference for barb orientation and a simple explanation for barb formation. Finally, we consider the flux tubes retracted below the surface in the process of filament formation. We show that every cancellation event that generates a filament obeying the hemispheric chirality preference injects a flux tube below the surface with a poloidal field opposite that of the ongoing cycle. We suggest that this pattern of submergence of flux represents the specific mechanism for the reversal of the poloidal flux in a Babcock-Leighton-Durney-type model for the solar dynamo.

Phenomena in an Emerging Active Region. II. Properties of the Dynamic Small‐Scale Structure

The magnetic flux emergence in growing active region NOAA 5617, when it is about 8 hr old, shows an intricate fine structure. The small-scale emergence events are characterized by a coincident upflow and transient darkening (of about 2 Mm and 10 minutes) in the continuum and line-center intensity followed by the appearance of one, or in some cases two, new bright grains flanking the line-center darkening. The bright grains (faculae) coincide with magnetic flux concentrations and downflows. The footpoints move apart at on average 1.4 km s-1. Flux emergence happens recurrently in a number of locations widely distributed over the active region, which appear to form a pattern with a wavelength of about 8 Mm. A preferred orientation that fits Hale's polarity law is displayed by the spatial pattern in the emergence locations, the emergence events themselves, subsequent footpoint motion, and the Hα arch filament system. We find long (~15 Mm) alignments of unipolar faculae of each magnetic polarity that also follow the preferred orientation. We adapt the model for flux emergence to accommodate the observed dynamic fine structure. Essential new features are (1) the emerging bundle of flux tubes is frayed in two systems, in vertical stacks, arranged in slightly curved, nearly parallel sheets; and (2) many flux tubes emerge in multiple locations.

The Rise of Kink‐unstable Magnetic Flux Tubes and the Origin of δ‐Configuration Sunspots

We perform three-dimensional simulations of the rise of twisted magnetic —ux tubes in an adiabatically strati—ed model solar convection zone. The initial —ux tube in our simulations is a uniformly twisted, buoyant, horizontal tube located near the bottom of the strati—ed layer. The twist of the initial —ux tube is described by a parameter a, which is de—ned as the angular rate of —eld-line rotation about the tube axis per unit length of the tube. We study the nonlinear evolution of the helical kink instability of the —ux tube as it rises through the strati—ed layer. We —nd from our simulations that in order for the tube to develop signi—cant kinking during its rise, the initial twist of the tube needs to be close to or greater than the critical limit for the onset of the kink instability. If the initial twist is signi—cantly below the (a c ) critical limit (a below about 50% of we —nd essentially no kink development and the evolution is a c ), similar to the results from previous two-dimensional simulations of the rise of twisted, horizontal —ux tubes. On the other hand, if the initial twist is sufficiently greater than the critical limit such that the e-folding period of the fastest growing kink mode is small compared to the rise time of the tube, we —nd sharp bending and distortion of the tube as a result of the nonlinear evolution of the kink instability. In this case, we —nd that due to the eUect of gravitational strati—cation, the kinked —ux tube arches upward and evolves into a buckled loop with a local change of tube orientation at the loop apex that exceeds 90i from the original direction of the tube. The emergence of this buckled loop can give rise to a compact magnetic bipole with polarity order inverted from the Hale polarity law, similar to the con—gu- ration often seen in d spots. Furthermore, our simulations show that the writhing of the tube axis as a result of the kink instability stretches the —ux tube and increases its buoyancy. Hence, the development of the kink instability can speed up the overall rise of the —ux tube. Subject headings: MHDSun: magnetic —eldssunspots

The Rise of Kink-Unstable Magnetic Flux Tubes in the Solar Convection Zone

We report preliminary results of a three-dimensional simulation of the buoyant rise of a strongly twisted, kink-unstable magnetic flux tube through a gravitationally stratified layer representing the solar convection zone. The numerical calculations employ the well-known anelastic approximation, which is suitable for studying slow, subsonic dynamical processes in the pressure-dominated, high-β plasma of the solar interior. This Letter investigates the case in which the initial twist of the buoyant flux tube is sufficiently high that the e-folding growth times of the unstable kink modes are short in comparison to the rise time of the flux tube. Our simulation shows that the flux tube becomes kinked and that the top portion of the flux tube evolves into a buckled shape with the tube axis being deflected by more than 90° from its original orientation. We suggest that the emergence of this buckled flux tube can give rise to a compact magnetic bipole with polarity order inverted from Hale's polarity law, similar to the configuration often seen in δ spots.

The relationship between solar flares and solar sector boundaries

A superposed epoch analysis of 1964–1970 solar flares shows a marked increase in flare occurrence within a day (13° of longitude) of (- +) solar sector boundaries as well as a local minimum in flare occurrence near (+ -)sector boundaries. This preference for (- +) boundaries is more noticeable for northern hemisphere flares, where these polarities match the Hale polarity law, but is not reversed in the south. Plage regions do not show such a preference.