The Observed Long- and Short-Term Phase Relation between the Toroidal and Poloidal Magnetic Fields in Cycle 23

The observed phase relations between the weak background solar magnetic (poloidal) field and strong magnetic field associated with sunspots (toroidal field) measured at different latitudes are presented. For measurements of the solar magnetic field (SMF) the low-resolution images obtained from Wilcox Solar Observatory are used and the sunspot magnetic field was taken from the Solar Feature Catalogues utilizing the SOHO/MDI full-disk magnetograms. The quasi-3D latitudinal distributions of sunspot areas and magnetic fields obtained for 30 latitudinal bands (15 in the northern hemisphere and 15 in the southern hemisphere) within fixed longitudinal strips are correlated with those of the background SMF. The sunspot areas in all latitudinal zones (averaged with a sliding one-year filter) reveal a strong positive correlation with the absolute SMF in the same zone appearing first with a zero time lag and repeating with a two- to three-year lag through the whole period of observations. The residuals of the sunspot areas averaged over one year and those over four years are also shown to have a well defined periodic structure visible in every two – three years close to one-quarter cycle with the maxima occurring at − 40° and + 40° and drifts during this period either toward the equator or the poles depending on the latitude of sunspot occurrence. This phase relation between poloidal and toroidal field throughout the whole cycle is discussed in association with both the symmetric and asymmetric components of the background SMF and relevant predictions by the solar dynamo models.     

Prospects for predicting cycle 24

Although we have reliable data of solar polar fields only from the mid-1970s, it seems that the polar field at a minimum is well correlated with the next cycle, but the strength of the cycle is not correlated with the polar field produced at its end. We explain this by suggesting that the Babcock-Leighton mechanism of poloidal field generation from tilted active regions involves randomness, whereas the other aspects of the dynamo process are more ordered. To model actual cycles, we have to ‘correct’ our theoretical dynamo model by ‘feeding’ information about the polar field at the minima. Following this process, we find that our model fits the observed sunspot numbers of cycles 21–23 reasonably well and predicts that cycle 24 will be the weakest in a century.     

High-Resolution Vector Magnetograms of the Sun’s Poles from Hinode: Flux Distributions and Global Coronal Modeling

The Sun’s polar fields play a leading role in structuring the large-scale solar atmosphere and in determining the interplanetary magnetic field. They are also believed to supply the seed field for the subsequent solar activity cycle. However, present-day synoptic observations do not have sufficient spatial resolution or sensitivity to diagnose accurately the high-latitude magnetic vector field. The high spatial resolution and sensitivity of the full-Stokes observations from the Hinode Solar Optical Telescope Spectro-Polarimeter, observing the poles long-term, allows us to build up a detailed picture of the Cycle 24 polar field reversal, including the changing latitude distribution of the high-latitude flux, and to study the effect on global coronal field models. The Hinode observations provide detailed information on the dominant facular-scale magnetic structure of the polar fields, and their field inclination and flux distribution. Hybrid synoptic magnetograms are constructed from Hinode polar measurements and full-disk magnetograms from the Synoptic Optical Long-term Investigations of the Sun (SOLIS) Vector Spectro-Magnetograph (VSM), and coronal potential field models are calculated. Loss of effective spatial resolution at the highest latitudes presents complications. Possible improvements to synoptic polar data are discussed.     

Dynamics of the solar magnetic field from SOHO/MDI

The investigation of the dynamics of magnetic fields from small scales to the large scales is very important for the understanding of the nature of solar activity. It is also the base for producing adequate models of the solar cycle with the purpose to predict the level of solar activity. Since December 1995 the Michelson Doppler Imager (MDI) on board of the Solar and Heliospheric Observatory (SOHO) provides full disk magnetograms and synoptic maps which cover the period of solar cycle 23 and the current minimum. In this paper, I review the following important topics with a focus on the dynamics of the solar magnetic field. The synoptic structure of the solar cycle; the birth of the solar cycle (overlapping cycles 23 and 24); the relationship of the photospheric magnetic activity and the EUV solar corona, polar magnetic fields and dynamo theory (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

North-South asymmetry of solar dynamo in the current activity cycle

An explanation is suggested for the north-south asymmetry of the polar magnetic field reversal in the current cycle of solar activity. The contribution of the Babcock-Leighton mechanism to the poloidal field generation is estimated using sunspot data for the current activity cycle. Estimations are performed separately for the northern and southern hemispheres. The contribution of the northern hemisphere exceeded considerably that of the southern hemisphere during the initial stage of the cycle. This is the probable reason for the earlier reversal of the northern polar field. The estimated contributions of the Babcock-Leighton mechanism are considerably smaller than similar estimations for the previous activity cycles. A relatively weak (<1 G) large-scale polar field can be expected for the next activity minimum.     

Solar cycle general magnetic fields of 1959–1974 and dynamical structure of the convection zone

The concept of the solar general magnetic field is extended from that of the polar fields to the concept of any axisymmetric fields of the whole Sun. The poloidal and toroidal general magnetic fields are defined and diagrams of their evolutionary patterns are drawn using the Mount Wilson magnetic synoptic chart data of Carrington rotation numbers from 1417 to 1620 covering approximately half of cycle 19 and cycle 20. After averaging over many rotations long-term regularities appear in the patterns. The diagrams of the patterns are compared with the Butterfly Diagram of sunspots of the same period. The diagram of the poloidal field shows that the Sun behaves like a magnetic quadrupole, each hemisphere having two branches of opposite polarities with mirror images on the other hemisphere. This was predicted by a solar cycle model driven by the dynamo action of the global convection by Yoshimura and could serve as a verification of the model. The diagram of the toriodal field is similar to the Butterfly Diagram of sunspots. The slight differences which do exist between the two diagrams seems to show that the fields responsible for the two may originate from different zones of the Sun. Common or different characteristics of the three diagrams are examined in terms of dynamical structure of the convection zone referring to the theoretical model of the solar cycle driven by the dynamo action of the global convection.     

Solar activity forecast with a dynamo model

Although systematic measurements of the Sun's polar magnetic field exist only from mid-1970s, other proxies can be used to infer the polar field at earlier times. The observational data indicate a strong correlation between the polar field at a sunspot minimum and the strength of the next cycle, although the strength of the cycle is not correlated well with the polar field produced at its end. This suggests that the Babcock–Leighton mechanism of poloidal field generation from decaying sunspots involves randomness, whereas the other aspects of the dynamo process must be reasonably ordered and deterministic. Only if the magnetic diffusivity within the convection zone is assumed to be high (of order  10¹² cm² s⁻¹  ), we can explain the correlation between the polar field at a minimum and the next cycle. We give several independent arguments that the diffusivity must be of this order. In a dynamo model with diffusivity like this, the poloidal field generated at the mid-latitudes is advected toward the poles by the meridional circulation and simultaneously diffuses towards the tachocline, where the toroidal field for the next cycle is produced. To model actual solar cycles with a dynamo model having such high diffusivity, we have to feed the observational data of the poloidal field at the minimum into the theoretical model. We develop a method of doing this in a systematic way. Our model predicts that cycle 24 will be a very weak cycle. Hemispheric asymmetry of solar activity is also calculated with our model and compared with observational data.     

High-resolution observations of the polar magnetic fields of the sun

High-resolution magnetograms of the solar polar region were used for the study of the polar magnetic field. In contrast to low-resolution magnetograph observations which measure the polar magnetic field averaged over a large area, we focused our efforts on the properties of the small magnetic elements in the polar region. Evolution of the filling factor - the ratio of the area occupied by the magnetic elements to the total area - of these magnetic elements, as well as the average magnetic field strength, were studied during the maximum and declining phase of solar cycle 22, from early 1991 to mid-1993.We found that during the sunspot maximum period, the polar regions were occupied by about equal numbers of positive and negative magnetic elements, with equal average field strength. As the solar cycle progresses toward sunspot minimum, the magnetic field elements in the polar region become predominantly of one polarity. The average magnetic field of the dominant polarity elements also increases with the filling factor. In the meanwhile, both the filling factor and the average field strength of the non-dominant polarity elements decrease. The combined effects of the changing filling factors and average field strength produce the observed evolution of the integrated polar flux over the solar cycle.We compared the evolutionary histories of both filling factor and average field strength, for regions of high (70°–80°) and low (60°–70°) latitudes. For the south pole, we found no significant evidence of difference in the time of reversal. However, the low-latitude region of the north pole did reverse polarity much earlier than the high-latitude region. It later showed an oscillatory behavior. We suggest this may be caused by the poleward migration of flux from a large active region in 1989 with highly imbalanced flux.     

Polar fields during the rising phase of cycle 22

High-resolution magnetograph observations of the polar magnetic fields have been obtained at intervals of time since the end of 1986 at Big Bear Solar Observatory. The Big Bear data differ from the low-resolution, full-disk magnetograph observations in that the 2 arc sec resolution makes it possible to resolve concentrated field upward of 100 G. The purpose of this ongoing observation is to examine the evolution of polar fields during the expected polarity reversal as cycle 22 passes its maximum phase, and secondly, to study the polar magnetic field: its true field strength, distribution, and how it compares to other parts of the quiet Sun.We find that the >70° net polar flux of both poles has not reversed as of the end of 1989. However, in the lower latitudes of both poles, 50° to 70°, there are signs reminiscent of those preceding the reversals in cycles 19 and 20. These include: decreasing field intensity in the old polarity fluctuations in net flux between the old and new polarities.We find that the net average longitudinal polar fields (above 50°) are 1–2 G, in agreement with results found in cycles 19 and 20. For individual elements, however, the strongest observed field strength poleward of 70° is over 100 G.We compare the polar fields with the equatorial limb as a function of latitute and longitude, respectively, and find the polar fields are comparable to (or stronger than) the quiet equatorial limb. When the observed mean flux density of the polar field as a function of latitude is corrected for limb-darkening and projection effects (assuming the field is radial), the result is nearly constant. These results suggest that despite the high latitudes, the polar fields have field strength and distribution similar to other parts of the quiet Sun.     

Dynamics of the circumpolar magnetic field of the Sun at a maximum of cycle 24

Data on the value and sign of the circumpolar magnetic field of the Sun at a maximum of its activity in cycle 24 have been analyzed. The data were obtained from observations at the Wilcox Solar Observatory and from synoptic maps of the magnetic field built in the SOLIS project (SOLIS stands for Synoptic Optical Long-term Investigations of the Sun) and with the Helioseismic and Magnetic Imager (HMI). We studied the dynamics of the total magnetic fields in the circumpolar latitudinal zones of different extension in the northern and southern hemispheres. The epochs of the sign reversal of the polar magnetic field were determined. It was found that, in cycle 24, the magnetic field polarity changed three times in the northern hemisphere and only once in the southern one. In the northern hemisphere, the reversal of the polar magnetic field finished approximately a year earlier than that in the southern one. The obtained results are compared to the data on the sign reversal of the polar magnetic field of the Sun reported for the previous solar cycles.     

Solar Polar Fields During Cycles 21 – 23: Correlation with Meridional Flows

We have examined polar magnetic fields for the last three solar cycles, viz. Cycles 21, 22, and 23 using NSO/Kitt Peak synoptic magnetograms. In addition, we have used SOHO/MDI magnetograms to derive the polar fields during Cycle 23. Both Kitt Peak and MDI data at high latitudes (78° – 90°) in both solar hemispheres show a significant drop in the absolute value of polar fields from the late declining phase of the Solar Cycle 22 to the maximum of the Solar Cycle 23. We find that long-term changes in the absolute value of the polar field, in Cycle 23, are well correlated with changes in meridional-flow speeds that have been reported recently. We discuss the implication of this in influencing the extremely prolonged minimum experienced at the start of the current Cycle 24 and in forecasting the behavior of future solar cycles.     

The reversal of the solar polar magnetic fields

It is a basic feature of the Babcock-Leighton model of the solar cycle that the polar field reversal is due to the diffusive decay and poleward drift of the active region fields. The flux from follower regions moves preferentially polewards in each hemisphere, where it cancels with, and then replaces, the previously existing polar fields. A number of workers have attempted to model this process by numerical solutions of the flux transport equation, which include the surface effects of supergranule diffusion, differential rotation and meridional flow, with conflicting results.Here we describe recent changes in the polar fields using synoptic magnetic data provided by the Mount Wilson Observatory, and compare them with simulations using the flux transport equation and based on the observed fields for Carrington rotation 1815. These changes include a part-reversal of the north polar field. It is shown that the evolution of the polar fields cannot be reproduced accurately by simulations of the diffusion and poleward drift of the emerging active regions at sunspot latitudes.Histograms of the distribution of the field intensities derived from the daily magnetograms obtained at the Kitt Peak Station of the National Solar Observatory provide independent evidence that flux is emerging at high latitudes and that this flux makes a contribution to the evolution of these patterns. This implies the presence of some form of sub-surface dynamo action at high latitudes.On leave from the School of Mathematics, University of Sydney.     

A Comparison Between Nonlinear Force-Free Field and Potential Field Models Using Full-Disk SDO/HMI Magnetogram

Measurements of magnetic fields and electric currents in the pre-eruptive corona are crucial to the study of solar eruptive phenomena, like flares and coronal mass ejections (CMEs). However, spectro-polarimetric measurements of certain photospheric lines permit a determination of the vector magnetic field only at the photosphere. Therefore, there is considerable interest in accurate modeling of the solar coronal magnetic field using photospheric vector magnetograms as boundary data. In this work, we model the coronal magnetic field above multiple active regions with the help of a potential field and a nonlinear force-free field (NLFFF) extrapolation code over the full solar disk using Helioseismic and Magnetic Imager (SDO/HMI) data as boundary conditions. We compare projections of the resulting magnetic field lines with full-disk coronal images from the Atmospheric Imaging Assembly (SDO/AIA) for both models. This study has found that the NLFFF model reconstructs the magnetic configuration closer to observation than the potential field model for full-disk magnetic field extrapolation. We conclude that many of the trans-equatorial loops connecting the two solar hemispheres are current-free.     

Ephemeral active regions during solar minimum

Ephemeral active regions (ER) identified on Kitt Peak daily full-disk magnetograms from April through November 1975 were analyzed and compared with larger active regions during the same interval. The 1975 ER were also compared with ER data from 1970, 1973, 1976, and 1977. ER were found to vary approximately with the sunspot cycle. However, a minimum in the number of ER occurred at least one year prior to sunspot minimum. All evidence to date indicates that the early ER minimum was due to the rise of solar cycle 21 primarily in the form of ER. ER were statistically identified as belonging to both outgoing solar cycle 20 and incoming cycle 21 by maxima in their distribution in latitude and by their statistically dominant orientation as a function of latitude. From the identification of ER with specific solar cycles and the persistent presence of high latitude ER maxima since 1970, it is suggested that the outgoing and incoming solar cycles may co-exist on the sun longer than the 0–3 year period of overlap between successive cycles already known from the properties of large sunspot-producing active regions.Presently associated with Solar Physics Research Corporation, Tucson, Arizona and Visiting Astronomer at Kitt Peak National Observatory, operated by the Association of Universities for Research in Astronomy, Inc., under contract with the National Science Foundation.     

High latitude solar magnetic fields

We use Kitt Peak magnetograms to measure polar magnetic fields. The polar mean absolute field increases at the same time as the polar mean field decreases. That is, the polar mean absolute field varies in phase with solar activity, in contrast to the out of phase variation of the mean polar field. We find that the polar fields have a large bipolar component even at solar minimum, with a magnitude equal to that found at low latitudes outside the active latitude bands.     

Magnetic Helicity as a Predictor of the Solar Cycle

It is well known that the polar magnetic field is at its maximum during solar minima, and that the behaviour during this time acts as a strong predictor of the strength of the following solar cycle. This relationship relies on the action of differential rotation (the Omega effect) on the poloidal field, which generates the toroidal flux observed in sunspots and active regions. We measure the helicity flux into both the northern and the southern hemispheres using a model that takes account of the Omega effect, which we apply to data sets covering a total of 60 years. We find that the helicity flux offers a strong prediction of solar activity up to five years in advance of the next solar cycle. We also hazard an early guess as to the strength of Solar Cycle 25, which we believe will be of similar amplitude and strength to Cycle 24.     

Extrapolation of the solar magnetic field within the potential-field approximation from full-disk magnetograms

This paper is concerned with the Laplace boundary-value problem with the directional derivative, corresponding to the specific nature of measurements of the longitudinal component of the photospheric magnetic field. The boundary conditions are specified by a distribution on the sphere of the projection of the magnetic field vector into a given direction, i.e., they exactly correspond to the data of daily magnetograms distributed across the full solar disk. It is shown that the solution of this problem exists in the form of a spherical harmonic expansion, and uniqueness of this solution is proved. A conceptual sketch of numerical determination of the harmonic series coefficients is given. The field of application of the method is analyzed with regard to the peculiarities of actual data. Results derived from calculating magnetic fields from real magnetograms are presented. Finally, we present differences in results derived from extrapolating the magnetic field from a synoptic map and a full-disk magnetogram.     

Determination of the Coronal and Interplanetary Magnetic Field Strength and Radial Profiles from Large-Scale Photospheric Magnetic Fields

We propose a new model for the magnetic field at different distances from the Sun during different phases of the solar cycle. The model depends on the observed large-scale non-polar (\({\pm}\, 55^{\circ }\)) photospheric magnetic field and on the magnetic field measured at polar regions from \(55^{\circ }\) N to \(90^{\circ }\) N and from \(55^{\circ }\) S to \(90^{\circ }\) S, which are the visible manifestations of cyclic changes in the toroidal and poloidal components of the global magnetic field of the Sun. The modeled magnetic field is determined as the superposition of the non-polar and polar photospheric magnetic field and considers cycle variations. The agreement between the model predictions and magnetic fields derived from direct in situ measurements at different distances from the Sun, obtained with different methods and at different solar activity phases, is quite satisfactory. From a comparison of the magnetic fields as observed and calculated from the model at 1 AU, we conclude that the model magnetic field variations adequately explain the main features of the interplanetary magnetic field (IMF) radial, \(B_{\mathrm{x}}\), component cycle evolution at Earth’s orbit. The modeled magnetic field averaged over a Carrington rotation (CR) correlates with the IMF \(B_{\mathrm{x}}\) component also averaged over a CR at Earth’s orbit with a coefficient of 0.691, while for seven CR-averaged data, the correlation reaches 0.81. The radial profiles of the modeled magnetic field are compared with those of already existing models. In contrast to existing models, ours provides realistic magnetic-field radial distributions over a wide range of heliospheric distances at different cycle phases, taking into account the cycle variations of the solar toroidal and poloidal magnetic fields. The model is a good approximation of the cycle behavior of the magnetic field in the heliosphere. In addition, the decrease in the non-polar and polar photospheric magnetic fields is shown. Furthermore, the magnetic field during solar cycle maxima and minima decreased from Cycle 21 to Cycle 24. This implies that both the toroidal and poloidal components, and therefore the solar global magnetic field, decreased from Cycle 21 to Cycle 24.     

The hemispheric asymmetry of solar activity during the last century and the solar dynamo

We believe the Babcock-Leighton process of poloidal field generation to be the main source of irregularity in the solar cycle. The random nature of this process may make the poloidal field in one hemisphere stronger than that in the other hemisphere at the end of a cycle. We expect this to induce an asymmetry in the next sunspot cycle. We look for evidence of this in the observational data and then model it theoretically with our dynamo code. Since actual polar field measurements exist only from the 1970s, we use the polar faculae number data recorded by Sheeley (1991, 2008) as a proxy of the polar field and estimate the hemispheric asymmetry of the polar field in different solar minima during the major part of the twentieth century. This asymmetry is found to have a reasonable correlation with the asymmetry of the next cycle. We then run our dynamo code by feeding information about this asymmetry at the successive minima and compare the results with observational data. We find that the theoretically computed asymmetries of different cycles compare favorably with the observational data, with the correlation co-efficient being 0.73. Due to the coupling between the two hemispheres, any hemispheric asymmetry tends to get attenuated with time. The hemispheric asymmetry of a cycle ei-ther from observational data or from theoretical calculations statistically tends to be less than the asymmetry in the polar field (as inferred from the faculae data) in the preceding minimum. This reduction factor turns out to be 0.43 and 0.51 respectively in observational data and theoretical simulations.     

Variations of magnetic fields and electric currents associated with a solar flare

The high-resolution vector magnetograms obtained with the solar telescope magnetograph of the Beijing Astronomical Observatory of the active region AR 4862 on 7 October, 1987, close before and after a solar flare, were used to calculate the electric current densities in the region. Then the relations between the flare and the magnetic fields as well as the electric currents were studied. The results are: (i) the transverse magnetic fields, and hence the longitudinal electric currents in the region before and after the flare, are evidently different, while the longitudinal magnetic fields remain unchanged; (ii) this confirms the result obtained previously that the flare kernels coincide with the peaks of longitudinal electric density in active regions; (iii) the close relation between the flare kernels and the electric currents indicates that the variations of the transverse magnetic fields and the longitudinal electric currents arise not from the general global evolution of the active region, but from the flare. These results tend to the conclusion that the triggering of a solar flare might be related with the plasma instability caused by the surplus longitudinal electric currents at some local regions in the solar atmosphere.