The inherent stochastic and nonlinear nature of the solar dynamo makes the strength of the solar cycles vary in a wide range, making it difficult to predict the strength of an upcoming solar cycle. Recently, our work has shown that by using the observed correlation of the polar field rise rate with the peak of polar field at cycle minimum and amplitude of following cycle, an early prediction can be made. In a follow-up study, we perform SFT simulations to explore the robustness of this correlation against variation of meridional flow speed, and against stochastic fluctuations of BMR tilt properties that give rise to anti-Joy and anti-Hale type anomalous BMRs. The results suggest that the observed correlation is a robust feature of the solar cycle and can be utilized for a reliable prediction of peak strength of a cycle at least 2 to 3 years earlier than the minimum.

Statistical study of 3047 active regions (ARs) from 1996 to 2021 was performed using the catalog of the magneto-morphological classes (MMC) of ARs CrAO. According to the magneto-morphological classification of ARs proposed earlier, all ARs, except for unipolar spots, were sorted out between two categories: regular (bipolar groups obeying the Hale’s polarity law, the Joy’s law, etc.) and irregular ARs (all the rest). We analyzed the number and fluxes of ARs depending on their location in different (relative to the equator) hemispheres. We found that the trends for fluxes are more pronounced. For ARs of both MMC types, they demonstrate signs of both a multi-peak and double-peak structure. Some peaks coincide with the main maxima of the cycle. The second main maximum is mainly formed by the irregular ARs in the S-hemisphere. This might be due to the interaction of the dipole and quadrupole components of the global magnetic field.

We correlate the annual Wolf numbers W and their time derivatives Wʹ by shifting time fragments of W and Wʹ relative to each other. The most significant (up to 0.874) correlation is with 3 years shifts for fragments covering 14 years. For longer and shorter periods, the correlation coefficients 0.771–0.855 with 2–3 years shift. The most significant 9 years shift corresponds to -0.852/-0.824 anti-correlation coefficient for 14/11 years period. The other periods are less significant. To evaluate predictive estimates, we use the times series fragments of W shifted back into the past. A forecast can be made using the leading graphs based upon the derived calibration factor. Test calculations show that the most effective is the calibration factor calculated for changing the phase of the cycle. The best linear pairwise correlation coefficient of the approximation is 0.94.

The study’s focus on the modulation of geomagnetism by low latitude solar magnetically activity, including coronal mass ejections (CMEs), solar flares, and solar energetic particles (SEPs). It mentions the Babcock–Leighton (B-L) dynamo model used to predict sunspot numbers in Solar Cycle 25 (SC25) and highlights the challenges in understanding aspects such as the regeneration of the poloidal field and the occurrence of magnetic regions, active longitudes, and coronal holes. The abstract introduces the study’s concentration on the activity of polar regions using chromosphere jets activity proxies and other parameters like polar faculae density and cool ejection events. It also mentions the observation of chromospheric prolateness during the minimum solar activity periods.

The Sun and solar-type stars exhibit irregular cyclic variations in their magnetic activity over long time scales. To understand this irregularity, we employed the flux transport dynamo models to investigate the behavior of one solar mass star at various rotation rates. To achieve this, we have utilized a mean-field hydrodynamic model to specify differential rotation and meridional circulation, and we have incorporated stochastic fluctuations in the Babcock–Leighton source of the poloidal field to capture inherent fluctuations in the stellar convection. Our simulations successfully demonstrated consistency with the observational data, revealing that rapidly rotating stars exhibit highly irregular cycles with strong magnetic fields and no Maunder-like grand minima. On the other hand, slow rotators produce smoother cycles with weaker magnetic fields, long-term amplitude modulation, and occasional extended grand minima. We observed that the frequency and duration of grand minima increase with the decreasing rotation rate. These results can be understood as the tendency of a less supercritical dynamo in slow rotators to be more prone to produce extended grand minima. We further explore the possible existence of the dynamo in the subcritical regime in a Babcock–Leighton-type framework and in the presence of a small-scale dynamo.

The fast rotating solar analogs show a decrease of the dynamo period with an increase of the rotation rate for the moderate stellar rotation periods in the range between 10 and 25 days. Simultaneously, observations indicate two branches: the “in-active” branch stars shows short dynamo cycles and the active branch stars show the relatively long magnetic cycles. We suggest that this phenomenon can be produced by effect of the doubling frequency of the dynamo waves, which is due to excitation of the second harmonic. It is generated because of the nonlinear B2 effects in the large-scale dynamo.

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.

During the last decade, our understanding of stellar physics and evolution has undergone a tremendous revolution thanks to asteroseismology. Space missions such as CoRoT, Kepler, K2, and TESS have already been observing millions of stars providing high-precision photometric data. With these data, it is possible to study the convection of stars through the convective background in the power spectrum density of the light curves. The properties of the convective background or granulation has been shown to be correlated to the surface gravity of the stars. In addition, when we have enough resolution (so long enough observations) and a high signal-to-noise ratio (SNR), the individual modes can be characterized in particular to study the internal rotational splittings and magnetic field of stars. Finally, the surface magnetic activity also impacts the amplitude and hence detection of the acoustic modes. This effect can be seen as a double-edged sword. Indeed, modes can be studied to look for magnetic activity changes. However, this also means that for stars too magnetically active, modes can be suppressed, preventing us from detecting them.

In this talk, I will present some highlights on what asteroseismology has allowed us to better understand the convection, rotation, and magnetism of solar-like stars while opening doors to many more questions.

The Sun’s global inertial modes are very sensitive to the solar differential rotation and to properties of the deep solar convection zone which are currently poorly constrained. These properties include the superadiabatic temperature gradient, the latitudinal entropy gradient, and the turbulent viscosity. The inertial modes also play a key role in controlling the Sun’s large-scale structure and dynamics, in particular the solar differential rotation. This paper summarizes recent observations and advances in the (linear and nonlinear) modeling of the solar inertial modes.

The newly discovered inertial modes in the Sun offer the opportunity to probe the solar convective zone down to the tachocline. While linear analysis predicts the frequencies and eigenfunctions of the modes, it gives no information about their excitation or their amplitudes. We present here a theoretical formalism for the stochastic excitation of the solar inertial modes by turbulent convection. The amplitudes predicted by our model are in complete agreement with observations, thus supporting the assumption that they are stochastically excited. Our work also uncovers a qualitative transition in the shape of the inertial mode spectrum, between m ≲ 5 where the modes are clearly resolved in frequency, and m ≳ 5 where the modes overlap. This complicates the interpretation of the high-m data, and suggests that a model for the whole shape of the power spectrum is necessary to exploit the full seismic potential of solar inertial modes.

We use nearly two decades of helioseismic data obtained from the GONG (2002–2020) and HMI (2010–2020) ring-diagram pipelines to examine the temporal variations of the properties of individual equatorial Rossby modes with azimuthal orders in the range 6 ≤ m ≤ 10. We find that the mode parameters obtained from GONG and HMI are consistent during the data overlapping period of 2010–2020. The power and the frequency of each mode exhibit significant temporal variations over the full observing period. Using the GONG data during solar cycles 23 and 24, we find that the mode power averaged over 6 ≤ m ≤ 10 shows a positive correlation with the sunspot number (0.42), while the averaged frequency shift is anti-correlated (–0.91). The anti-correlation between the average mode power and frequency shift is –0.44.

We study the m = 1 high-latitude inertial mode and its contribution to the latitudinal transport of the Sun’s angular momentum. Ring-diagram helioseismology applied to 5° tiles is used to obtain the horizontal flows near the surface of the Sun. Using 10 years of data from SDO/HMI, we report on the horizontal eigenfunction and Reynolds stress $\[{Q_{\theta \phi }} = \langle {u'_\theta }{u'_\phi }\rangle \]$ for the m = 1 high-latitude inertial mode (frequency –86.3 nHz, critical latitudes ±58°). We find that Qθφ takes significant values above the critical latitude and is positive (negative) in the northern (southern) hemisphere, implying equatorward transport of angular momentum. The Qθφ peaks above latitude 70° with a value of 38 m2/s2.

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.

Magnetic fields are important physics in stellar evolutionary theory, which seriously affects the stellar structure and evolutionary statues. The small-scale magnetic fields in the photosphere are ubiquitous, and float on the stellar surface, which usually couple with the acoustic waves, affecting the propagation of the acoustic waves. Considering the effect of the magnetic fields in the stellar photosphere on the oscillation frequencies, we calculate the asteroseismology for solar-like star KIC 11295426 and KIC 10963065. We obtain the stellar fundamental parameters, especially the strength of small-scale magnetic fields in the stellar photosphere. We find that the small-scale magnetic fields in the stellar photosphere may obviously improve the agreement between the observations and the theoretical models for two stars. The magnetic strength for KIC 11295426 and KIC 10963065 from asteroseismology are in agreement with the stellar period-activity relation.

As is well known, low-mass stars constitute the most abundant class of stars in our galaxy. In stars less massive than the Sun, the density within stellar interiors increases as the stellar mass decreases. Therefore, for low-mass stars, the significance of electrostatic effects in stellar interiors cannot be neglected, as these interactions can alter the properties of matter.

In our study, we focus on exploring the outer layers of stars less massive than the Sun. We have computed a range of stellar models, ranging from 0.4 to 0.9 solar masses, to investigate the effects of two physical processes on the acoustic oscillations in the envelopes of these stars: partial ionization of chemical elements and electrostatic interactions between particles in the outer layers. In addition to partial ionization, we demonstrate that Coulomb effects also influence the acoustic oscillation spectrum. Our investigation reveals the following findings:

1. Coulomb effects can indeed influence the acoustic oscillations in low-mass stars.

2. The model with a mass of inline1 serves as a transition point. For models less massive than inline1, their acoustic spectrum is more affected by electrostatic interactions, whereas models more massive than inline1 have their acoustic spectrum more impacted by partial ionization processes.

Our work unveils the promising possibilities that future discoveries related to the detection of solar-like oscillations in stars less massive than the Sun could offer in terms of understanding the connections between the internal structure of low-mass stars and their observable characteristics.

The solar dynamo is a physical process of magnetic field generation due to conversion of kinetic energy of plasma flows into magnetic energy. However, in the mean-field dynamo theory, one needs to segregate scales and consider separately large-scale dynamo and small-scale dynamo. The large-scale dynamo produces the large-scale mean field and unavoidable fluctuations of the mean field. Both are cycle-dependent. The small-scale dynamo is supposed to produce only the small-scale field, and this field is cycle-independent. There is no sharp boundary between the intervals of the large-scale and small-scale dynamos. An unavoidable presence of a smooth transition implies that there is a region where the properties of the large-scale global dynamo and fluctuations inherent to small-scale dynamo co-exist on some intermediate scales. Recent achievements in observations of the small-scale dynamo operation on the smallest observable scales and on the intermediate scales of typical active regions are discussed in the review.

In this article, the physical processes occurring in the convective layer and the photosphere of the Sun and their connection to the formation of active regions (ARs) and the development of the corresponding magnetic field are explored. Specifically, we test the magnetic flux emergence hypothesis and based on the line-of-sight magnetic field and Doppler shift data obtained from the Global Oscillation Network Group (GONG) observations. The study encompasses the analysis of 24 ARs observed during the period from 2011 to 2022. We find a strong correlation between the magnetic flux and the imbalance of radial velocity fluxes. The results indicate that the magnetic flux emergence hypothesis cannot fully explain the evolution of ARs during their early stages of development.

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.

We present analysis of the evolution of subsurface flows in and around active regions with peculiar magnetic configurations and compare their characteristics with the normal active regions. We also study the zonal and meridional components of subsurface flows separately in different polarity regions separately to better understand their role in flux migration. We use the techniques of local correlation tracking and ring diagrams for computing surface and subsurface flows, respectively. Our study manifests an evidence that the meridional component of the flows near anti-Hale active regions is predominantly equatorward which disagrees with the poleward flow pattern seen in pro-Hale active regions. We also find clockwise or anti-clockwise flows surrounding the anti-Joy active regions depending on their locations in the Southern or Northern hemispheres, respectively.

As a relatively active region, ephemeral region (ER) exhibits highly complex pattern of magnetic flux emergence. We aim to study detailed secondary flux emergences (SFEs) which we define as bipoles that their locations close to ERs and finally coalesce with ERs after a period. We study the SFEs during the whole process from emergence to decay of 5 ERs observed by the Helioseismic and Magnetic Imager (HMI) aboard Solar Dynamics Observatory (SDO). We find that the maximum unsigned magnetic flux for each of the ERs is around 1020 Mx. All ERs have tens of SFEs with an average emerging magnetic flux of approximately 5×1018 Mx. The frequency of normalized magnetic flux for all the SFEs follows a power law distribution with an index of -2.08. The majority of SFEs occur between the positive and negative polarities of ER, and their growth time is concentrated within one hour. The magnetic axis of SFEs also exhibits a random characteristic. We suggest that the relationship between SFEs and ERs can be understood by regarding the photospheric magnetic field observations as cross-sections of an emerging magnetic structure. Tracking the ERs’ evolution, we propose that the flux emergences are partially emerged Ω-loops, and that the SFEs in ERs may be sequent emergences from the bundle of flux tube of ERs.