Helioseismology has discovered a thin layer beneath the solar surface where the rotation rate increases rapidly with depth. The normalized rotational shear in the upper 10 Mm of the layer is constant with latitude. Differential rotation theory explains such a rotational state by a radial-type anisotropy of the near-surface convection and a short correlation time of convective turbulence compared to the rotation period. The shear layer is the main driver of the global meridional circulation.

The canonical undestanding of stellar convection has recently been put under doubt due to helioseismic results and global 3D convection simulations. This “convective conundrum” is manifested by much higher velocity amplitudes in simulations at large scales in comparison to helioseismic results, and the difficulty in reproducing the solar differential rotation and dynamo with global 3D simulations. Here some aspects of this conundrum are discussed from the viewpoint of hydrodynamic Cartesian 3D simulations targeted at testing the rotational influence and surface forcing on deep convection. More specifically, the dominant scale of convection and the depths of the convection zone and the weakly subadiabatic – yet convecting – Deardorff zone are discussed in detail.

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.

The dynamo mechanism, responsible for the solar magnetic activity, is still an open problem in astrophysics. Different theories proposed to explain such phenomena have failed in reproducing the observational properties of the solar magnetism. Thus, ab-initio computational modeling of the convective dynamo in a spherical shell turns out as the best alternative to tackle this problem. In this work we review the efforts performed in global simulations over the past decades. Regarding the development and sustain of mean-flows, as well as mean magnetic field, we discuss the points of agreement and divergence between the different modeling strategies. Special attention is given to the implicit large-eddy simulations performed with the EULAG-MHD code.

Solar oblateness has been the subject of several studies dating back to the nineteenth century. Despite difficulties, both theoretical and observational, tangible results have been achieved. However, variability of the solar oblateness with time is still poorly known. How the solar shape evolves with the solar cycle has been a challenging problem. Analysis of the helioseismic data, which are the most accurate measure of the solar structure up to now, leads to the determination of asphericity coefficients which have been found to change with time. We show here that by inverting even coefficients of f-mode oscillation frequency splitting to obtain the oblateness magnitude and its temporal dependence can be inferred. It is found that the oblateness variations lag the solar activity cycles by about 3 years. A major change occurred between solar cycles 23 and 24 is that the oblateness was greater in cycle 24 despite the lower solar activity level. Such results may help to better understand the near-subsurface layers as they strongly impacts the internal dynamics of the Sun and may induce instabilities driving the transport of angular momentum.

Solar rotation is still one of the unresolved concern of solar physics. We performed time series analysis on the bins formed on equally separated latitude regions on the soft X-ray images. These images are observed with the X-ray telescope (XRT) on board the Hinode satellite. The flux modulation method traces the passage of X-ray feature over the solar disc and statistical analysis of the time series data of the SXR images (one per day) for the period extends from year 2015 to 2017 gives the coronal rotation period as a function of latitude. The investigation provided quite systematic information of the solar rotation and its variability.

The longitudinal distribution of solar active regions shows non-homogeneous spatial behaviour, which is often referred to as Active Longitude (AL). Evidence for a significant statistical relationships between the AL and the longitudinal distribution of flare and coronal mass ejections (CME) occurrences is found in Gyenge et al. 2017 (ApJ, 838, 18). The present work forecasts the spatial position of AL, hence the most flare/CME capable active regions are also predictable. Our forecast method applies Autoregressive Integrated Moving Average model for the next 2 years time period. We estimated the dates when the solar flare/CME-capable longitudinal belts face towards Earth.

The evolution of rotational velocity and magnetic activity with age follows approximately a t−1/2 relation, the famous Skumanich law. Using a large sample of about 80 solar twins with precise ages, we show departures from this law. We found a steep drop in rotational velocity and activity in the first 2-3 Gyr and afterwards there seems to be a shallow decrease. Our inferred rotational periods suggest that the Sun will continue to slow down, validating thus the use of gyrochronology beyond solar age. The Sun displays normal rotational velocity and activity when compared to solar twins of solar age. We also show that stars with exceedingly high stellar activity for their age are spectroscopic binaries that also exhibit enhanced rotational velocities and chemical signatures of mass transfer.

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.

Differential rotation and meridional flow are key ingredients in flux transport dynamo models of the solar activity cycle. As the subsurface flow pattern is not sufficiently constrained by observations, it is a major source of uncertainty in solar and stellar dynamo models. We discuss the current mean field theory of stellar differential rotation and meridional flows and its predicitons for the Sun and stars on the lower main sequence.

We report on turbulent dynamo simulations in a spherical wedge with an outer coronal layer. We apply a two-layer model where the lower layer represents the convection zone and the upper layer the solar corona. This setup is used to study the coronal influence on the dynamo action beneath the surface. Increasing the radial coronal extent gradually to three times the solar radius and changing the magnetic Reynolds number, we find that dynamo action benefits from the additional coronal extent in terms of higher magnetic energy in the saturated stage. The flux of magnetic helicity can play an important role in this context.

We present evidence to show that changes in the Sun's equatorial rotation rate are synchronized with changes in its orbital motion about the barycentre of the Solar System. We propose that this synchronization is indicative of a spin–orbit coupling mechanism operating between the Jovian planets and the Sun. However, we are unable to suggest a plausible underlying physical cause for the coupling. Some researchers have proposed that it is the period of the meridional flow in the convective zone of the Sun that controls both the duration and strength of the Solar cycle. We postulate that the overall period of the meridional flow is set by the level of disruption to the flow that is caused by changes in Sun's equatorial rotation speed. Based on our claim that changes in the Sun's equatorial rotation rate are synchronized with changes in the Sun's orbital motion about the barycentre, we propose that the mean period for the Sun's meridional flow is set by a Synodic resonance between the flow period (∼22.3 yr), the overall 178.7-yr repetition period for the solar orbital motion, and the 19.86-yr synodic period of Jupiter and Saturn.

We review some of the currently used techniques to detect stellar magnetic fields on cool stars. Emphasis is put on spectropolarimetry with high-resolution spectrographs and its related data de-noising techniques and multi-line inverse modeling. Detections and results from Zeeman splittings and broadenings are briefly mentioned. We discuss some of our most recent Zeeman Doppler Imaging (ZDI) results and present a comparison of ZDI maps of the K-type WTTS V410 Tauri and the planet-hosting F8 star HD 179949 with results from other groups.

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.

The interplay between stellar rotation and turbulent flows is a major ingredient for vertical angular momentum transport in stellar convection zone. Combined with the centrifugal force and the buoyancy force due to pole-equator temperature gradients one can expect a large-scale flow structure that is usually referred to as differential rotation and meridional flows. I review such observations for stars other than the Sun, mostly for stars significantly more active, and ask the question whether such observations can constrain the dynamo process.

Meridional flow results from slight deviations from the thermal wind balance. The deviations are relatively large in the boundary layers near the top and bottom of the convection zone. Accordingly, the meridional flow attains its largest velocities at the boundaries and decreases inside the convection zone. The thickness of the boundary layers, where meridional flow is concentrated, decreases with rotation rate, so that an advection-dominated regime of dynamos is not probable in rapidly rotating stars. Angular momentum transport by convection and by the meridional flow produce differential rotation. The convective fluxes of angular momentum point radially inward in the case of slow rotation but change their direction to equatorward and parallel to the rotation axis as the rotation rate increases. The differential rotation of main-sequence dwarfs is predicted to vary mildly with rotation rate but increase strongly with stellar surface temperature. The significance of differential rotation for dynamos has the opposite tendency to increase with spectral type.

We present results of convective turbulent dynamo simulations including a coronal layer in a spherical wedge. We find an equatorward migration of the radial and azimuthal fields similar to the behavior of sunspots during the solar cycle. The migration of the field coexist with a spoke-like differential rotation and anti-solar (clockwise) meridional circulation. Even though the migration extends over the whole convection zone, the mechanism causing this is not yet fully understood.

The observed uniform rotation of the Sun's radiative interior can be explained by the presence of a global-scale interior magnetic field, provided that the field remains confined below the convection zone. In high latitudes, such magnetic confinement is possible by means of persistent downwelling, driven by the convection zone's turbulent stresses.