Time–distance helioseismology uses solar surface Doppler observations to measure areas that are not directly observable, such as solar interior, far side, and sunquake sources. In this work, we briefly review recent advancements in time–distance helioseismology, focusing on meridional circulation measurements, far-side imaging, and sunquakes. Solar deep meridional flows are crucial for understanding the dynamics of the solar interior, but precise measurements of these flows are challenging. This review explores recent developments in this area, particularly highlighting new findings related to systematic effects that have long challenged meridional circulation determination. We also review recent progress in solar far-side imaging, which is useful in improving space weather forecasting. Recent developments in far-side imaging using time–distance techniques and Deep Learning are introduced. Additionally, we review a new approach in sunquake reconstruction by incorporating observation-based Green’s functions constructed by time–distance helioseismology.

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.

The Sun’s meridional circulation is a crucial component for understanding the Sun’s dynamo and its interior dynamics. However, the determination of meridional circulation is affected by a systematic center-to-limb (CtoL) effect, which introduces systematic errors 5–10 times stronger than the meridional-flow-induced travel-time shifts in deep-flow measurements. Recently, it was found that the CtoL effect has a significant acoustic-frequency dependence, while flow-induced travel-time shifts show little frequency dependence (Chen & Zhao 2018). This discovery forms the basis for designing a new method to remove the CtoL effect. We therefore propose a frequency-dependent approach to measure the CtoL effect and the flow-induced signals in the Fourier domain. In this work, we present this new method and compare time–distance measurements in different frequency bands with those obtained by previous time-domain methods. The results demonstrate consistency with conventional time-domain fitting methods in the dominant frequency range, promising the potential for conducting meridional flow inversion across a broader frequency spectrum.

Our understanding of solar convection is incomplete. A crucial gap is the unknown superadiabaticity in the solar convection zone, δ = ▽–▽ad. Global modes of oscillations in the inertial frequency range are sensitive to δ and serve as a novel tool to explore solar convection. Here, we address the forward problem where the superadiabaticity δ(r) varies with radius. We solve the 2.5D eigenvalue problem, considering the linearized equations for momentum, mass and energy conservation with respect to a realistic solar model. We find that the frequency and eigenfunction of the m = 1 high-latitude mode are influenced by δ in the lower convection zone. Our prescribed setup suggests that the superadiabaticity in the lower half of the convection zone is below 2.4×10-7 to reach a qualitative agreement with the observed eigenfunction.

We investigate the evolution of subsurface flows during the emergence and the active phase of sunspot regions using the time–distance helioseismology analysis of the full-disk Dopplergrams from the Helioseismic and Magnetic Imager (HMI) onboard the Solar Dynamics Observatory (SDO). We present an analysis of emerging active regions of various types, including delta-type active regions and regions with the reverse polarity order (‘anti-Hale active regions’). The results reveal strong vortical and shearing flows during the emergence of magnetic flux, as well as the process of formation of large-scale converging flow patterns around developing active regions, predominantly in the top 6 Mm deep layers of the convection zone. Our analysis revealed a significant correlation between the flow divergence and helicity in the active regions with their flaring activity, indicating that measuring characteristics of subsurface flows can contribute to flare forecasting.

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.