Computational heliophysics has shed light on the fundamental physical processes inside the Sun, such as the differential rotation, meridional circulation, and dynamo-generation of magnetic fields. However, despite the substantial advances, the current results of 3D MHD simulations are still far from reproducing helioseismic inferences and surface observations. The reason is the multi-scale nature of the solar dynamics, covering a vast range of scales, which cannot be solved with the current computational resources. In such a situation, significant progress has been achieved by the mean-field approach, based on the separation of small-scale turbulence and large-scale dynamics. The mean-field simulations can reproduce solar observations, qualitatively and quantitatively, and uncover new phenomena. However, they do not reveal the complex physics of large-scale convection, solar magnetic cycles, and the magnetic self-organization that causes sunspots and solar eruptions. Thus, developing a synergy of these approaches seems to be a necessary but very challenging task.

Properties of helioseismic acoustic oscillations (p modes) are modified by flows and magnetic fields in the solar interior, with frequencies, amplitudes and damping rates all varying systematically through the solar cycle. Crucially, now, we have a long enough baseline of helioseismic data to compare of the different activity cycles. We review recent efforts along these lines, from the impact of near-surface magnetic fields on p-mode frequencies to the evolution of the torsional oscillation and meridional circulation. We show that each activity cycle for which we have helioseismic data is slightly different in terms of the relationship between p mode frequencies and atmospheric proxies of activity, and in terms of the rotation and meridional circulation flows. However, many challenges remain, crucially including our ability to constrain flows and magnetic fields in the deep solar interior.

Solar magnetic fields are believed to originate from the base of convection zone. However, it has been difficult to obtain convincing observational evidence of the magnetic fields in the deep convection zone. The goal of this study is to investigate whether solar meridional flows can be used to detect the magnetic-field effects. Meridional flows are axisymmetric flows on the meridional plane. Our result shows that the flow pattern in the entire convection zone changes significantly from solar minimum to maximum. The changes all centered around active latitudes, suggesting that the magnetic fields are responsible for the changes. The results indicate that the meridional flow can be used to detect the effects of magnetic field in the deep convection zone.

The results have been published in the Astrophysical Journal (lc2018).

We analyze Sun-as-a-star observations spanning over solar cycles 22 – 24 from the ground-based network BiSON and solar cycles 23 – 24 collected by the space-based VIRGO and GOLF instruments on board the SoHO satellite. Using simultaneous observations from all three instruments, our analysis suggests that the structural and magnetic changes responsible for modifying the frequencies remained comparable between cycle 23 and cycle 24 but differ from cycle 22. Thus we infer that the magnetic layer of the Sun has become thinner since the beginning of cycle 23 and continues during the current cycle.

Using continuous observations for 22 years from ground-based network GONG and space-borne instruments MDI onboard SoHO and HMI onboard SDO, we report both global and local properties of the convection zone and their variations with time.

The Solar Orbiter is the next solar physics mission of the European Space Agency, ESA, in collaboration with NASA, with a launch planned in 2018. The spacecraft is designed to approach the Sun to within 0.28 AU at perihelion of a highly eccentric orbit. The proximity with the Sun will also allow its observation at uniformly high resolution at EUV and visible wavelengths. Such observations are central for learning more about the magnetic coupling of the solar atmosphere. At a later phase in the mission the spacecraft will leave the ecliptic and study the enigmatic poles of the Sun from a heliographic latitude of up to 33○.

A central instrument of Solar Orbiter} is the Polarimetric and Helioseismic Imager, SO/PHI. It will do full Stokes imaging in the Landé g = 2.5 Fe I 617.3 nm line. It is composed of two telescopes, a full-disk telescope and a high-resolution telescope, that will allow observations at a resolution as high as 200 km on the solar surface. SO/PHI will also be the first solar polarimeter to leave the Sun-Earth line, opening up new possibilities, such as stereoscopic polarimetry (besides stereoscopic imaging of the photosphere and stereoscopic helioseismology). Finally, SO/PHI will have a unique view of the solar poles, allowing not just more precise and exact measurements of the polar field than possible so far, but also enabling us to follow the dynamics of individual magnetic features at high latitudes and to determine solar surface and sub-surface flows right up to the poles.

In this paper an introduction to the science goals and the capabilities of SO/PHI will be given, as well as a brief overview of the instrument and of the current status of its development.

Selected events of the scientific biography of Wojtek Dziembowski are briefly described, and several related photos are presented. The full version of the presentation is available at the IAU Symposium 301 webpage.

I present a personal view of Wojtek Dziembowski's scientific career, derived mainly from my direct interactions with Wojtek. Necessarily this presentation is biased towards the earlier days, partly because we interacted more then, and partly because the presentation after mine is by a local admirer who has been much more involved than I with Wojtek's later work.

We discuss the potential of asteroseismic inversion to study the internal dynamics of solar-type stars and to reconstruct the evolution of the internal rotation from the main sequence to the red-giant phase. In particular, we consider the use of gravity and mixed modes and the application of different inversion methods.

Over more than twenty years, Wojtek Dziembowski and I collaborated on nearly fifty papers, which were concentrated in helioseismology through the 1980s and 1990s, but extended early into the new century. In this review, I discuss the most significant results of this collaboration and some of the underlying sociology that contributed to the intensity and longevity of our collaboration. Our work began with placing limits on the Sun's buried magnetic field and ended with extracting from the solar-cycle dependent oscillation frequency changes the roles (and net result) of competing dynamical drivers of changes in the solar diameter.

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.

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 Sun is a plasma laboratory for astrophysics, which allows us to investigate many important phenomena in turbulent magnetized plasma in detail. Solar Dynamics Observatory (SDO) launched in February 2010 provides unique information about plasma processes from the interior to the corona. The primary processes of magnetic field generation and formation of magnetic structures are hidden beneath the visible surface. Helioseismic diagnostics, based on observations and analysis of solar oscillations and waves, give insights into the physical processes in the solar interior and mechanisms of solar magnetic activity. In addition, simultaneous high-resolution multi-wavelength observations of the solar corona provide opportunity to investigate in unprecedented detail the coronal dynamics and links to the interior processes. These capabilities are illustrated by initial results on the large-scale dynamics of the Sun, the subsurface structure and dynamics of a sunspot and observations of a X-class solar flare.

The magnetohydrodynamic (MHD) sausage tube waves are excited in the magnetic flux tubes by p-mode forcing. These tube waves thus carry energy away from the p-mode cavity which results in the deficit of incident p-mode energy. We calculate the loss of incident p-mode energy as a damping rate of f- and p-modes. We calculate the damping rates of f- and p-modes by a model Sun consisting of an ensemble of many thin magnetic flux tubes with varying plasma properties and distributions. Each magnetic flux tube is modelled as axisymmetric, vertically oriented and untwisted. We find that the magnitude and the form of the damping rates are sensitive to the plasma-β of the tubes and the upper boundary condition used.

Numerical computations of wave propagation through sunspot-like magnetic field structures are critical to developing and testing methods to deduce the subsurface structure of sunspots and active regions. We show that helioseismic analysis applied to the MHD sunspot simulations of Rempel and collaborators, as well as to translation-invariant models of umbral-like fields, yield wave travel-time measurements in qualitative agreement with those obtained in real sunspots. However, standard inversion methods applied to these data fail to reproduce the true wave-speed structure beneath the surface of the model. Inversion methods which incorporate direct effects of the magnetic field, including mode conversion, may be required.

We study the temporal variation of subsurface flows associated with active regions within 16 Mm of the solar surface. We have analyzed the subsurface flows of nearly 1000 active and quiet regions applying ring-diagram analysis to Global Oscillation Network Group (GONG) Dopplergram data. We find that newly emerging active regions are characterized by enhanced upflows and fast zonal flows in the near-surface layers, as expected for a flux tube rising from deeper layers of the convection zone. The subsurface flows associated with strong active regions are highly twisted, as indicated by their large vorticity and helicity values. The dipolar pattern exhibited by the zonal and meridional vorticity component leads to the interpretation that these subsurface flows resemble vortex rings, when measured on the spatial scales of the standard ring-diagram analysis.

We discuss recent progress in the helioseismic probing of the subsurface structure of solar magnetic regions. To simulate the interaction of helioseismic waves with magnetic fields and thermal perturbations we use a simple model that is translation invariant in the horizontal directions, has a realistic stratification in the vertical direction, and has physically consistent boundary conditions for the waves at the upper and lower boundaries of the computational domain. Using this model we generate synthetic helioseismic data and subsequently measure time-distance travel times. We evaluate a model for the wave-speed perturbation below sunspots that replaces the sound speed in a non-magnetic model by the fast-mode speed from a magnetic model; our results indicate that this approach is unlikely to be useful in modeling wave-speed perturbations in sunspots. We develop and test an inversion algorithm for inferring the sound-speed perturbation in magnetic regions. We show that this algorithm retrieves the correct sound-speed perturbation only when the sensitivity kernels employed account for the effects of the magnetic field on the waves and the subsurface structure.

In this paper, we compare components of the horizontal flow below the solar surface in and around regions consisting of rotating and non-rotating sunspots. Our analysis suggests that there is a significant variation in both components of the horizontal flow at the beginning of sunspot rotation as compared to the non-rotating sunspot. The flows in surrounding areas are in most cases relatively small. However, there is a significant influence of the motion on flows in an area closest to the sunspot rotation.

Sunspot regions often form complexes of activity that may live for several solar rotations, and represent a major component of the Sun's magnetic activity. It had been suggested that the close appearance of active regions in space and time might be related to common subsurface roots, or “nests” of activity. EUV images show that the active regions are magnetically connected in the corona, but subsurface connections have not been established. We investigate the subsurface structure and dynamics of a large complex of activity, NOAA 10987-10989, observed during the SOHO/MDI Dynamics run in March-April 2008, which was a part of the Whole Heliospheric Interval (WHI) campaign. The active regions in this complex appeared in a narrow latitudinal range, probably representing a subsurface toroidal flux tube. We use the MDI full-disk Dopplergrams to measure perturbations of travel times of acoustic waves traveling to various depths by using time-distance helioseismology, and obtain sound-speed and flow maps by inversion of the travel times. The subsurface flow maps show an interesting dynamics of decaying active regions with persistent shearing flows, which may be important for driving the flaring and CME activity, observed during the WHI campaign. Our analyses, including the seismic sound-speed inversion results and the distribution of deep-focus travel-time anomalies, gave indications of diverging roots of the magnetic structures, as could be expected from Ω-loop structures. However, no clear connection in the depth range of 0-48 Mm among the three active regions in this complex of activity was detected.

The large-scale dynamics of the solar convection zone have been inferred using both global and local helioseismology applied to data from the Global Oscillation Network Group (GONG) and the Michelson Doppler Imager (MDI) on board SOHO. The global analysis has revealed temporal variations of the “torsional oscillation” zonal flow as a function of depth, which may be related to the properties of the solar cycle. The horizontal flow field as a function of heliographic position and depth can be derived from ring diagrams, and shows near-surface meridional flows that change over the activity cycle. Time-distance techniques can be used to infer the deep meridional flow, which is important for flux-transport dynamo models. Temporal variations of the vorticity can be used to investigate the production of flare activity. This paper summarizes the state of our knowledge in these areas.