Solar interior differential rotation and meridional flow play important roles in dynamo models. In this review, I briefly review results in interior rotational profiles and zonal flows obtained from helioseismology studies. Due to the new developments in recent years in interior meridional flow studies, this review focuses more on results on meridional flow. I describe new developments in the shallower poleward meridional flow, and the temporal evolution of these flows. Then I introduce a newly identified center-to-limb variation effect in helioseismology studies, and present recent results in the search of equatorward meridional flows. I also discuss how these results will effect the dynamo models.

The helicity is important to present the basic topological configuration of magnetic field in solar atmosphere. The distribution of magnetic helicity in solar atmosphere is presented by means of the observational (vector) magnetograms. As the kinetic helicity in the solar subatmosphere can be inferred from the velocity field based on the technique of the helioseismology and used to compare with the magnetic helicity in the solar atmosphere, the observational helicities provide the important chance for the confirmation on the generation of magnetic fields in the subatmosphere and solar dynamo models also. In this paper, we present the observational magnetic and kinetic helicity in solar active regions and corresponding questions, except the relationship with solar eruptive phenomena.

Sunspot 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.

We point out the difficulties in carrying out direct numerical simulation of the solar dynamo problem and argue that kinematic mean-field models are our best theoretical tools at present for explaining various aspects of the solar cycle in detail. The most promising kinematic mean-field model is the flux transport dynamo model, in which the toroidal field is produced by differential rotation in the tachocline, the poloidal field is produced by the Babcock–Leighton mechanism at the solar surface and the meridional circulation plays a crucial role. Depending on whether the diffusivity is high or low, either the diffusivity or the meridional circulation provides the main transport mechanism for the poloidal field to reach the bottom of the convection zone from the top. We point out that the high-diffusivity flux transport dynamo model is consistent with various aspects of observational data. The irregularities of the solar cycle are primarily produced by fluctuations in the Babcock–Leighton mechanism and in the meridional circulation. We summarize recent work on the fluctuations of meridional circulation in the flux transport dynamo, leading to explanations of such things as the Waldmeier effect.

The sunspot number data during the past 400 years indicates that both the profile and the amplitude of the solar cycle have large variations. Some precursors of the solar cycle were identified aiming to predict the solar cycle. The polar field and the geomagnetic index are two precursors which are received the most attention. The geomagnetic variations during the solar minima are potentially caused by the solar polar field by the connection of the solar open flux. The robust prediction skill of the polar field indicates that the memory of the dynamo process is less than 11 yrs based on the frame of the Babcock-Leighton flux transport dynamo. One possible reason to get the short magnetic memory is the high magnetic diffusivity in the convective zone. Our recent studies show that the radial downward pumping is another possible reason. Based upon the mechanism, we well simulate the cycle irregularities during RGO time period. This opens the possibility to set up a standard dynamo based model to predict the solar cycle. In the end, the no correlation between the polar field and the preceding cycle strength due to two nonlinearities involved in the sunspot emergence will be stressed.

Linear and nonlinear approaches are used to investigate the phase asynchrony between the polar faculae (PF) and sunspot numbers (SNs). It is found that, (1) PF show leads of 52 months relative to SNs on the average of the considered time interval; (2) the cross-wavelet transform analysis shows that they are asynchronous in both the low- and high-frequency components. These indicate that their phase relationship is not only time-dependent but also frequency-dependent.

Much of our knowledge about the solar dynamo is based on sunspot observations. It is thus desirable to extend the set of positional and morphological data of sunspots into the past. Gustav Spörer observed in Germany from Anklam (1861–1873) and Potsdam (1874–1894). He left detailed prints of sunspot groups, which we digitized and processed to mitigate artifacts left in the print by the passage of time. After careful geometrical correction, the sunspot data are now available as synoptic charts for almost 450 solar rotation periods. Individual sunspot positions can thus be precisely determined and spot areas can be accurately measured using morphological image processing techniques. These methods also allow us to determine tilt angles of active regions (Joy's law) and to assess the complexity of an active region.

The subject of our work is the review and comparison of solar activity during the last two solar minima that occurred between recent activity cycles. We use the soft X-ray global solar corona observations covering the two nine-months long time intervals in 1997/98 and 2009. Data from RF15-I multichannel photometer are used for the penultimate minimum. For the last unusually deep and prolonged solar activity minimum in 2009 the data from SphinX spectrophotometer are used. Comparison of measurements from both minima takes place in the overlapping energy range 2–15 keV. We focus on the active region formation, evolution and flaring productivity during respective minima.

We use a Babcock-Leighton-type of dynamo with the poloidal source based as closely as possible on the observations to model the solar cycle irregularities during the cycles 12-20. The nonlinearities in the poloidal field generation, i.e., the cycle dependence of the sunspot group tilt angles and the latitudes are included. The convective pumping dominates the transport of the surface poloidal field to the tachocline. Our results show that the modeled polar fields have a good correlation with the observed next cycle strength and the build-up of the toroidal flux at the tachocline is strongly correlated with the observed cycle strength as well. Both correlation coefficients are above 0.8. The success of the model indicates that they are the nonlinearities in the poloidal field generation which cause the solar cycle irregularities.

An explanation of the mystery of the extended 23rd solar cycle duration about 13 years in the frame of non-linear regime of the αΩ- dynamo model is proposed. The calculated dynamo-period of the solar cycle, T, depends (in the inverse proportion) on the intensity of the α- effect in the solar convection zone (SCZ). As well, the intensity of the α- effect in non-linear regime depends (also in the inverse proportion) on the value of toroidal magnetic field, BT (magnetic alpha-quenching). Thus, the calculated period is in direct proportion to the value of toroidal magnetic field: the stronger toroidal field BT in certain cycle, the longer dynamo-period T of this cycle. Since the toroidal field is hidden in the deep layers of the SCZ, it is necessary to know some other magnetic experimental evidence that reflects something like information about inner toroidal field. In this connection we allow for that the strong toroidal field is transported by magnetic buoyancy to the solar surface and produces here the sunspots, so they carry indirect information on BT. In this connection we took into account up-to-date observed data on the essential increase of the averaged annual module of the magnetic field of the large-scale sunspots, Bsp, in the 23rd cycle; and then we made calculation of the alpha-quenching which depends on these referred data. It is important to know only relative variations of magnetic index Bsp for calculation of the dynamo-period variation. Our estimations showed that the average solar period, which is about 11 years, must increase by a factor of 1,2; so the calculated 23rd cycle dynamo-period would be about 13 years.

The dependence of the solar cycle duration, T, on the 3 years averaged module of the large-scale sunspots magnetic fields (30-60 arcsec), Bsp index, was investigated on the base of about 10,000 visual observations conducted during last eight (16-23) cycles. It was found that the duration T of the investigated cycles linearly depends on the index Bsp of the magnetic fields observed during 3 years on decline phase of the solar cycle (second, third and fourth years after solar maximum Tmax). Namely, the duration of the cycles T was varied between 9,5 and 12,5 years, when the magnetic index Bsp was ranged from 2450 to 2600 G. An explanation for this dependence is proposed within the framework of non-linear αΩ- dynamo model. We found the following equation for the dependence of solar dynamo-period on magnetic index: T ≈ Bsp3/2. Therefore, the large observed index Bsp, the longer calculated period T.

The prolonged period of solar minimum between cycles 23 and 24 has invoked a great deal of interest to understand the origin of the unusually low solar activity. Even though the origin of solar activity is believed to lie in the shear layer at the base of the convection zone, the analysis of helioseismic data seem to orientate us toward the near surface. In this context, we analyze the signature of the quasi-biennial periodicity seen in the oscillation frequencies which may provide additional constraints on the solar dynamo models.

We study how the solar magnetic field evolves from antisymmetric (dipolar) to symmetric (quadrupolar) state during the course of its 11-yr cycle. We show that based on equatorial symmetries of the induction equation, flux transport solar mean field dynamo models excite mostly the antisymmetric (dipolar) family whereas a decomposition of the solar magnetic field data reveals that both families should be excited to similar amplitude levels. We propose an alternative solar dynamo solution based on North-South asymmetry of the meridional circulation to better reconcile models and observations.

We have examined solar polar fields during the solar cycles 21–23 using both ground and space based synoptic magnetograms. It has been shown that the unsigned polar fields in the latitude range (78°–90°) show a steady decline starting ~1995–1996 till the maximum of cycle 23. We also find that the long term changes in the unsigned polar fields at higher latitudes are well correlated with changes in the surface meridional flow speed that have been reported for the cycle 23.

We have used interplanetary scintillation (IPS) observations at 327 MHz spanning years 1983-2009 to study microturbulence levels in the inner heliosphere. We find that the microturbulence levels show a steady and significant drop in the entire inner heliosphere starting from around 1995. The fact that the solar polar fields have also shown a similar declining trend provides a consistent result showing the buildup to the solar minimum between the solar cycles 23 and 24, the deepest in the past 100 years, actually began more than a decade earlier.

Employing wavelet and Fourier methods, we investigate temporal variations of periodicities in the photospheric fields obtained from synoptic magnetograms of the National Solar Observatory at Kitt Peak (NSO/KP) spanning the years 1975-2009. A north-south asymmetry is noticed in the periodicities of photospheric fields in the latitude range, 45°-78°, when the data is grouped into fields prior to and after 1996. This asymmetry when coupled with the fact that both solar fields in the latitude range, 45°-78°, and the micro-turbulence levels in the inner heliosphere began declining ~ 1995-1996 suggests that active changes occurred in the underlying basic solar processes which eventually initiated, at the end of solar cycle 23, the build-up of the deepest solar minimum, in the past 100 years.

The poleward magnetic field streams on time-latitude diagram of the photospheric magnetic field of the Sun during 1975–2011 (Kitt Peak NSO, SOLIS NSO, SOHO MDI data) are modeled. We performed simulations in terms of probability density function and bipole orientation according to Joy's law and Hale's cycle. The difference between distributions of leading and trailing fluxes of bipolar sunspots defines the so-called surplus. Finally, magnetic field streams and polar field reversals are a result of meridional drift of a surplus to the poles.

An overview is given about recent developments and results of comprehensive simulations of magneto-convective processes in the near-surface layers and photosphere of the Sun. Simulations now cover a wide range of phenomena, from whole active regions, over individual sunspots and pores, magnetic flux concentrations and vortices in intergranular lanes, down to the intricate mixed-polarity structure of the magnetic field generated by small-scale dynamo action. The simulations in concert with high-resolution observations have provided breakthroughs in our understanding of the structure and dynamics of the magnetic fields in the solar photosphere.

A few years before the Hinode space telescope was launched, an investigation based on the Hanle effect in atomic and molecular lines indicated that the bulk of the quiet solar photosphere is significantly magnetized, due to the ubiquitous presence of an unresolved magnetic field with an average strength 〈B〉, ≈ 130 G. It was pointed out also that this “hidden” field must be much stronger in the intergranular regions of solar surface convection than in the granular regions, and it was suggested that this unresolved magnetic field could perhaps provide the clue for understanding how the outer solar atmosphere is energized. In fact, the ensuing magnetic energy density is so significant that the energy flux estimated using the typical value of 1 km/s for the convective velocity (thinking in rising magnetic loops) or the Alfvén speed (thinking in Alfvén waves generated by magnetic reconnection) turns out to be substantially larger than that required to balance the chromospheric energy losses. Here we present a brief review of the research that led to such conclusions, with emphasis on a new three-dimensional radiative transfer investigation aimed at determining the magnetization of the quiet Sun photosphere from the Hanle effect in the Sr I 4607 Å line and the Zeeman effect in Fe I lines.

It is often claimed that there is not only one, but two different types of solar dynamos: the one that is responsible for the appearance of sunspots and the 11-yr cycle, frequently referred to as the “global dynamo”, and a statistically time-invariant dynamo, generally referred to as the “local dynamo”, which is supposed to be responsible for the ubiquitous magnetic structuring observed at small scales. Here we examine the relative contributions of these two qualitatively different dynamos to the small-scale magnetic flux, with the following conclusion: The local dynamo does not play a significant role at any of the spatially resolved scales, nearly all the small-scale flux, including the flux revealed by Hinode, is supplied by the global dynamo. This conclusion is reached by careful determination of the Sun's noise-corrected basal magnetic flux density while making use of a flux cancellation function determined from Hinode data. The only allowed range where there may be substantial or even dominating contributions from a local dynamo seems to be the scales below about 10 km, as suggested by observations of the Hanle depolarization effect in atomic spectral lines. To determine the fraction of the Hanle depolarization that may be due to the action of a local dynamo, a synoptic program is being initiated at IRSOL (Istituto Ricerche Solari Locarno).