As an introduction to the theme of this symposium, I give a simple review of the photospheric magnetic field, the properties of the solar cycle, the way in which the magnetic field is thought to be generated by dynamo action, and finally the unusual properties of the recent solar minimum. This has awakened an interest in improving predictions of the solar cycle and in the nature of solar minima not just as gaps between maxima but as phenomena of intrinsic interest in their own right.

We summarize the fifty-year concerted effort to place the “activity” of the Sun in the context of the stars. As a working definition of solar activity in the context of stars, we adopt those globally–observable variations on time scales below thermal time scales, of ~105 yr for the convection zone. So defined, activity is dominated by magnetic–field evolution, including the 22–year Hale cycle, the typical time it takes for the quasi-periodic reversal in which the global magnetic–field takes place. This is accompanied by sunspot variations with 11 year periods, known since the time of Schwabe, as well as faster variations due to rotation of active regions and flaring. “Diagnostics and indices” are terms given to the indirect signatures of varying magnetic–fields, including the photometric (broad-band) variations associated with the sunspot cycle, and variations of the accompanying heated plasma in higher layers of stellar atmospheres seen at special optical wavelengths, and UV and X-ray wavelengths. Our attention is also focussed on the theme of the Symposium by examining evidence for deep and extended minima of stars, and placing the 70–year long solar Maunder Minimum into a stellar context.

We show that only two adjustments are necessary to harmonize the Group Sunspot Number with the Zürich Sunspot Number. The latter has been increased from the 1940s on to the present by 20% due to weighting of sunspot counts according to size of the spots and can be corrected by increasing the earlier values as well. The Group Sunspot Number before ~1885 is too low by ~50%. With these adjustments a single sunspot number series results. Of note is that there is no longer a distinct Modern Grand Maximum.

Some selected concepts of the solar activity cycle are reviewed. Cycle modulations through a stochastic α effect are being identified with limited scale separation ratios. Three-dimensional turbulence simulations with helicity and shear are compared at two different scale separation ratios. In both cases the level of fluctuations shows relatively little variation with the dynamo cycle. Prospects for a shallow origin of sunspots are discussed in terms of the negative effective magnetic pressure instability. Tilt angles of bipolar active regions are discussed as a consequence of shear rather than the Coriolis force.

Magnetic helicity fluxes in turbulently driven α2 dynamos are studied to demonstrate their ability to alleviate catastrophic quenching. A one-dimensional mean-field formalism is used to achieve magnetic Reynolds numbers of the order of 105. We study both diffusive magnetic helicity fluxes through the mid-plane as well as those resulting from the recently proposed alternate dynamic quenching formalism. By adding shear we make a parameter scan for the critical values of the shear and forcing parameters for which dynamo action occurs. For this αΩ dynamo we find that the preferred mode is antisymmetric about the mid-plane. This is also verified in 3-D direct numerical simulations.

Stellar magnetic fields are produced by a magnetohydrodynamic dynamo mechanism working in their interior – which relies on the interaction between plasma flows and magnetic fields. The Sun, being a well-observed star, offers an unique opportunity to test theoretical ideas and models of stellar magnetic field generation. Solar magnetic fields produce sunspots, whose number increases and decreases with a 11 year periodicity – giving rise to what is known as the solar cycle. Dynamo models of the solar cycle seek to understand its origin, variation and evolution with time. In this review, I summarize observations of the solar cycle and describe theoretical ideas and kinematic dynamo modeling efforts to address its origin. I end with a discussion on the future of solar cycle modeling – emphasizing the importance of a close synergy between observational data assimilation, kinematic dynamo models and full magnetohydrodynamic models of the solar interior.

The chiral symmetry breaking properties of the Tayler instability are discussed. Effective amplitude equations are determined in one case. This model has three free parameters that are determined numerically. Comparison with chiral symmetry breaking in biochemistry is made.

Recent observations revealed that small magnetic elements abundant at the solar surface move poleward with a velocity which seems to be lower than the plasma velocity U. Guerrero et al. (2011) explained this discrepancy as a consequence of diffusive spreading of the magnetic elements due to a positive radial gradient of |Uθ|. As the gradient's sign (inferred by local helioseismology) is still unclear, cases with a negative gradient are studied in this paper. Under this condition, the velocity of the magnetic tracers turns out to be larger than the plasma velocity, in disagreement with the observations. Alternative mechanisms for explaining them independently are proposed. For the turbulent magnetic pumping it is shown that it has to be unrealistically strong to reconcile the model with the observations.

Helioseismology is a very powerful tool that allows us to explore the interior of the Sun. Here we give particular emphasis to the justification for the likely location of the zone that is most sensitive to cycle-related changes. For the low degree modes we find that more than one timescale for changes in the oscillations is discovered. We also note the successive cycles have differing sensitivities to the activity. We end with a warning of the risk of being misled with short datasets such as are seen with stellar data.

The time-latitude diagram of the photospheric magnetic field of the Sun during 1975-2011 (Kitt Peak NSO, SOLIS NSO, SOHO MDI data) is analyzed using Gnevysvev's idea of impulsed structure of sunspot cycle and a flux transport concept. It is demonstrated that poleward migrations of magnetic trailing polarities are closely associated with the impulses of sunspot activity. We use a fitting procedure to reconstruct the sunspot impulses and poleward magnetic field surges. We compare our results for Cycle 22 model with the time-latitude diagram of the photospheric magnetic field of the Sun.

The stratosphere is the region where the ozone chemistry is important for the balance of energy, and radiation in the near UV plays a fundamental role in the creation and destruction of ozone. However, the radiation in this range of wavelength has not been very well modeled. One of the most important elements, according to its abundance in the solar atmosphere, that contribute to the emission and absorption of radiation in the spectral range between 1900 and 3900 Å, is neutral nickel (Ni I). In this work we improve the atomic model of this element, taking into account 490 lines over the spectrum. We solve these lines in NLTE using the Solar Radiation Physical Modeling (SRPM) program and compare the results with observation of the quiet sun spectrum.

We present preliminary reconstructions of the EUV from 26 to 34 nm from February 1997 to May 2005, covering most of solar cycle 23. The reconstruction is based on synthetic EUV spectra calculated with the spectral synthesis code Solar Modeling in 3D (SolMod3D). These spectra are weighted by the relative area coverage of the coronal features as identified from EIT images. The calculations are based on one-dimensional atmospheric structures that represent a temporal and spatial mean of the chromosphere, transition region, and corona. The employed segmentation analysis considers coronal holes, the quiet corona, and active regions identified on the solar disk. The reconstructed EUV irradiance shows a good agreement with observations taken with the CELIAS/SEM instrument onboard SOHO. Further improvement of the reconstruction including more solar features as well as the off-limb detection of activity features will be addressed in the near future.

The slow decline of solar Cycle 23 combined with the slow rise of Cycle 24 resulted in a very long period of low magnetic activity during the years 2007–2009 with sunspot number reaching the lowest level since 1913. This long solar minimum was characterized by weak polar magnetic fields, smaller polar coronal holes, and a relatively complex coronal morphology with multiple streamers extending to mid latitudes. At the same time, low latitude coronal holes remained present on the Sun until the end of 2008 modulating the solar wind at the Earth in co-rotating, fast solar wind streams. This magnetic configuration was remarkably different from the one observed during the previous two solar minima when coronal streamers were confined near the equator and the fast solar wind was mainly originating from the large coronal holes around the Sun's poles. This paper presents the evolution of the polar magnetic fields and coronal holes during the past minimum, compare it with the previous minima, and discuss the implications for the solar wind near the Earth. It also considers the minimum of Cycle 23 in an historical perspective and, in particular, compares it to the long minima at the turn of the 19th century.

The topology of the large-scale magnetic field of the Sun and its role in the development of magnetic activity were investigated using Hα charts of the Sun in the period 1887-2011. We have considered the indices characterizing the minimum activity epoch, according to the data of large-scale magnetic fields. Such indices include: dipole-octopole index, area and average latitude of the field with dominant polarity in each hemisphere and others. We studied the correlation between these indices and the amplitude of the following sunspot cycle, and the relation between the duration of the cycle of large-scale magnetic fields and the duration of the sunspot cycle.

The comparative analysis of the solar corona during the minimum epochs in activity cycles 12 to 24 shows that the large-scale magnetic field has been slow and steadily changing during the past 130 years. The reasons for the variations in the solar coronal structure and its relation with long-term variations in the geomagnetic indices, solar wind and Gleissberg cycle are discussed.

We also discuss the origin of the large-scale magnetic field. Perhaps the large-scale field leads to the generation of small-scale bipolar ephemeral regions, which in turn support the large-scale field. The existence of two dynamos: a dynamo of sunspots and a surface dynamo can explain phenomena such as long periods of sunspot minima, permanent dynamo in stars and the geomagnetic field.

Differential emission measure tomography (DEMT) makes use of extreme ultraviolet (EUV) image series to deliver two products: a) the three-dimensional (3D) reconstruction of the coronal emissivity in the instrumental bands, and b) the 3D distribution of the local differential emission measure (LDEM). The LDEM allows, in turn, construction of 3D maps of the electron density and temperature distribution. DEMT is being currently applied to the space-based EUV imagers, allowing reconstruction of the inner corona in the height range 1.00 to 1.25 R⊙. In this work we applied DEMT to different Carrington Rotations corresponding to the last two solar Cycle minima. To reconstruct the 2008 minimum we used data taken by the Extreme UltraViolet Imager (EUVI), on board the Solar TErrestrial RElations Observatory (STEREO) spacecraft, and to reconstruct the 1996 minimum we used data taken by the Extreme ultraviolet Imaging Telescope (EIT), on board the Solar and Heliospheric Observatory (SOHO). We show here comparative results, discussing the observed 3D density and temperature distributions in the context of global potential magnetic field extrapolations. We also compare the DEMT results with other observational and modeling efforts of the same periods.

On 2009 September 21, a filament eruption and the associated Coronal Mass Ejection (CME) was observed by the STEREO spacecraft. The CME originated from the southern hemisphere and showed a deflection of about 15° towards the heliospheric current sheet (HCS) during its propagation in the COR1 field-of-view (FOV). The aim of this paper is to provide a physical explanation for the strong deflection of the CME. We first use the STEREO observations in order to reconstruct the three dimensional (3D) trajectory of the CME. Starting from a magnetic configuration that closely resembles the potential field extrapolation for that date, we performed numerical magneto-hydrodynamics (MHD) simulations. By applying localized shearing motions, a CME is initiated in the simulation, showing a similar non-radial evolution, structure, and velocity as the observed event. The CME gets deflected towards the current sheet of the larger northern helmet streamer, due to an imbalance in the magnetic pressure and tension forces and finally it gets into the streamer and propagates along the heliospheric current sheet.

Magnetic clouds (MCs) are objects of extreme importance in the heliosphere. They have a major role on releasing magnetic helicity from the Sun (with crucial consequences on the solar dynamo), they are the hugest transient object in the interplanetary medium, and the main actors for the Sun-Earth coupling. The comparison between models and observations is beginning to clarify several open questions on MCs, such as their internal magnetic configuration and their interaction with the ambient solar wind. Due to the decay of the solar wind pressure with the distance to the Sun, MCs are typically in expansion. However, their detailed and local expansion properties depend on their environment plasma properties. On the other hand, while it is well known that the solar cycle determines several properties of the heliosphere, the effects of the cycle on MC properties are not so well understood. In this work we review two major properties of MCs: (i) their expansion, and (ii) the magnetic flux and helicity that they transport through the interplanetary medium. We find that the amount of magnetic flux and helicity released via MCs during the last solar minimum (years 2007-2009) was significantly lower than in the previous one (years 1995-1997). Moreover, both MC size and mean velocity are in phase with the solar cycle while the expansion rate is weakly variable and has no relationship with the cycle.

We have investigated two full solar rotations belonging to two distinct solar minima, in the frame of two coordinated observational and research campaigns. The nearly uninterrupted gathering of solar coronal data since the beginning of the SOHO era offers the exceptional possibility of comparing two solar minima for the first time, with regard to coronal transients. This study characterizes the variety of outward-travelling transients observed in the solar corona during both time intervals, from very narrow jet-like events to coronal mass ejections (CMEs). Their solar source regions and ensuing interplanetary structures were identified and characterized. Multi-wavelength images from the space missions SOHO, Yohkoh and STEREO, and ground-based observatories were studied for coronal ejecta and their solar sources, while in situ data registered by the ACE spacecraft were inspected for interplanetary CMEs and magnetic clouds. Instrumental aspects such as dissimilar resolution, cadence, and fields of view are considered in order to discern instrumentally-driven disparities from inherent differences between solar minima.

We present a three-dimensional model of rotating convection combined with a simplified model of a corona in spherical coordinates. The motions in the convection zone generate a large-scale magnetic field which is sporadically ejected into the outer layers above. Our model corona is approximately isothermal, but it includes density stratification due to gravity.

We present a study about the propagation of interplanetary shock waves driven by super magnetosonic coronal mass ejections (CMEs). The discussion focuses on a model which describes the dynamic relationship between the CME and its driven shock and the way to approximate the trajectory of shocks based on those relationships, from near the Sun to 1 AU. We apply the model to the analysis of a case study in which our calculations show quantitative and qualitative agreements with different kinds of data. We discuss the importance of solar wind and CME initial conditions on the shock wave evolution.