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.

Prediction of solar activity cycles is challenging because physical processes inside the Sun involve a broad range of multiscale dynamics that no model can reproduce and because the available observations are highly limited and cover mostly surface layers. Helioseismology makes it possible to probe solar dynamics in the convective zone, but variations in differential rotation and meridional circulation are currently available for only two solar activity cycles. It has been demonstrated that sunspot observations, which cover over 400 years, can be used to calibrate the Parker-Kleeorin-Ruzmaikin dynamo model, and that the Ensemble Kalman Filter (EnKF) method can be used to link the modeled magnetic fields to sunspot observations and make reliable predictions of a following activity cycle. However, for more accurate predictions, it is necessary to use actual observations of the solar magnetic fields, which are available only for the last four solar cycles. In this paper I briefly discuss the influence of the limited number of available observations on the accuracy of EnKF estimates of solar cycle parameters, the criteria to evaluate the predictions, and application of synoptic magnetograms to the prediction of solar activity.

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.

The observed convective flows on the photosphere (e.g., supergranulation, granulation) play a key role in the Babcock-Leighton (BL) process to generate large scale polar fields from sunspots fields. In most surface flux transport (SFT) and BL dynamo models, the dispersal and migration of surface fields is modeled as an effective turbulent diffusion. We present the first kinematic 3D FT/BL model to explicitly incorporate realistic convective flows based on solar observations. The results obtained are generally in good agreement with the observed surface flux evolution and with non-convective models that have a turbulent diffusivity on the order of 3 × 1012 cm2 s−1 (300 km2 s−1). However, we find that the use of a turbulent diffusivity underestimates the dynamo efficiency, producing weaker mean fields and shorter 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 meridional circulation of the Sun is observationally found to vary with the solar cycle, becoming slower during the solar maxima. We explain this by constructing a theoretical model in which the equation of the meridional circulation (the φ component of the vorticity equation) is coupled with the equations of the flux transport dynamo model. We find that the Lorentz force of the dynamo-generated magnetic fields can slow down the meridional circulation during the solar maxima in broad conformity with the observations.

We analyze the flux emergence rate of solar active regions (ARs). Numerical simulations by other authors suggest that the flux emergence rate depends on the AR’s twist. To prove this statement observationally, we make a comparison of the flux emergence rate and twist of 215 emerging ARs. Our results confirm that the correlation exists: the higher the twist the higher the flux emergence rate of an AR. We suppose that the difference in the twist can be caused by chaotic influence of the convective plasma motions on the lifting magnetic flux tube.

The origin of magnetic cycles in the Sun and other cool stars is one of the great theoretical challenge in stellar astrophysics that still resists our understanding. Ab-initio numerical simulations are today required to explore the extreme turbulent regime in which stars operate and sustain their large-scale, cyclic magnetic field. We report in this work on recent progresses made with high performance numerical simulations of global turbulent convective envelopes. We rapidly review previous prominent results from numerical simulations, and present for the first time a series of turbulent, global simulations producing regular magnetic cycles whose period varies systematically with the convective envelope parameters (rotation rate, convective luminosity). We find that the fundamentally non-linear character of the dynamo simulated in this work leads the magnetic cycle period to be inversely proportional to the Rossby number. These results promote an original interpretation of stellar magnetic cycles, and could help reconcile the cyclic behaviour of the Sun and other solar-type stars.

Low mass, main sequence stars like our Sun exhibit a wide variety of rotational and magnetic states. Observational and theoretical advances have led to a renewed emphasis on understanding the rotational and magnetic evolution of sun-like stars has become a pressing problem in stellar physics. We use global 3D convection and convective dynamo simulations in rotating spherical shells and with realistic stellar stratification to explore the behavior of “middle-aged” stars. We show that for stars with slightly less rotational influence than our Sun a transition occurs from solar-like (fast equator, slow poles) to anti-solar (slow equator, fast poles) differential rotation. We investigate this transition using two different treatments for the upper boundary of our simulations and we hypothesize that this transition from solar-like to anti-solar differential rotation may be responsible for observations of anomalously rapid rotation for stars older than our Sun.

Convection is one of the fundamental mechanisms to transport energy, e.g., in planetology, oceanography, as well as in astrophysics where stellar structure is customarily described by the mixing-length theory, which makes use of the mixing-length scale parameter to express the convective flux, velocity, and temperature gradients of the convective elements and stellar medium. The mixing-length scale is taken to be proportional to the local pressure scale height of the star, and the proportionality factor (the mixing-length parameter) must be determined by comparing the stellar models to some calibrator, usually the Sun. No strong arguments exist to claim that the mixing-length parameter is the same in all stars and all evolutionary phases. Because of this, all stellar models in the literature are hampered by this basic uncertainty. In a recent paper (Pasetto et al. 2014) we presented the first fully analytical scale-free theory of convection that does not require the mixing-length parameter. Our self-consistent analytical formulation of convection determines all the properties of convection as a function of the physical behaviour of the convective elements themselves and the surrounding medium (be it a star, an ocean, or a primordial planet). The new theory of convection is formulated starting from a conventional solution of the Navier-Stokes/Euler equations, i.e. the Bernoulli equation for a perfect fluid, but expressed in a non-inertial reference frame co-moving with the convective elements. In our formalism, the motion of convective cells inside convective-unstable layers is fully determined by a new system of equations for convection in a non-local and time dependent formalism. We obtained an analytical, non-local, time-dependent solution for the convective energy transport that does not depend on any free parameter. The predictions of the new theory in astrophysical environment are compared with those from the standard mixing-length paradigm in stars with exceptional results for atmosphere models of the Sun and all the stars in the Hertzsprung-Russell diagram.

Los Alamos National Laboratory has calculated a new generation of radiative opacities (OPLIB data using the ATOMIC code) for elements with atomic number Z = 1-30 with improved physics input, updated atomic data, and finer temperature grid to replace the Los Alamos LEDCOP opacities released in the year 2000. We calculate the evolution of standard solar models including these new opacities, and compare with models evolved using the Lawrence Livermore National Laboratory OPAL opacities (Iglesias & Rogers 1996). We use the solar abundance mixture of Asplund et al. 2009. The Los Alamos ATOMIC opacities (Colgan et al. 2013a, 2013b, 2015) have steeper opacity derivatives than those of OPAL for temperatures and densities of the solar interior radiative zone. We compare the calculated nonadiabatic solar oscillation frequencies and solar interior sound speed to observed frequencies and helioseismic inferences. The calculated sound-speed profiles are similar for models evolved using either the updated Iben evolution code (see Guzik & Mussack 2010), or the MESA evolution code (Paxton et al. 2015). The LANL ATOMIC opacities partially mitigate the ‘solar abundance problem’.

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.

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 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.

We briefly review our current understanding of how the solar differential rotation and meridional circulation are maintained, which has important implications for understanding cyclic magnetic activity in the Sun and stars.

We summarise the motivations and main results of the joint discussion “3D Views of the Cycling Sun in Stellar Context”, and give credit to contributed talks and poster presentations, as due to the limited number of pages, this proceedings could only include contributions from the keynote speakers.

We investigate the relations between tachocline-based dynamos and the surface flux transport mechanisms in stars with outer convection zones. Using our combined models of flux generation and transport, we demonstrate the importance of the buoyant rise of magnetic flux, which physically determines the emergence latitudes and tilt angles of bipolar magnetic regions. The combined effects of the dynamo strength, flux rise, and surface transport lead to various cyclic and non-cyclic time series of total unsigned surface magnetic flux.

Convection is simulated numerically based on two-dimensional Boussinesq equations for a fluid layer with a specially chosen stratification such that the convective instability is much stronger in a thin subsurface sublayer than in the remaining part of the layer. The developing convective flow has a small-scale component superposed onto a basic large-scale roll flow.

Magnetic helicity is a physical quantity that describes field topology. It is also a conserved quantity as Berger in 1984 demonstrated that the total magnetic helicity is still conserved in the corona even when there is a fast magnetic reconnection. It is generally believed that solar magnetic fields, together with their helicity, are created in the convection zone by various dynamo processes. These fields and helicity are transported into the corona through solar photosphere and finally released into the interplanetary space via various processes such as coronal mass ejections (CMEs) and solar winds. Here I will give a brief review on our recent works, first on helicity observations on the photosphere and how to understand these observations via dynamo models. Mostly, I will talk about what are the possible consequences of magnetic helicity accumulation in the corona, namely, the formation of magnetic flux ropes, CMEs taking place as an unavoidable product of coronal evolution, and flux emergences as a trigger of CMEs. Finally, I will address on in what a form magnetic field in the interplanetary space would accommodate a large amount of magnetic helicity that solar dynamo processes have been continuously producing.