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The Global Oscillations at Low Frequencies instrument aboard the Solar and Heliospheric Observatory has provided over two decades of continuous, high-precision data, enabling detailed measurements of the Sun's oscillation frequencies. These oscillations, analyzed through Doppler velocity shifts, offer invaluable insights into the Sun's internal structure and dynamics using the methods of helioseismology. This methodology has been extended beyond the Sun to the study of other stars, leveraging data from various space missions. Notably, NASA's Kepler mission, in operation from 2009 until 2018, observed over 500,000 stars, analyzing brightness variations over time and generating a vast database for asteroseismic studies. This investigation focuses on the solar-type star KIC 6106415, comparing its oscillation frequencies with those derived from GOLF data. By analyzing frequency patterns and mode lifetimes, we explore the similarities and differences in internal structures, stellar evolution, and magnetic activity cycles between KIC 6106415 and the Sun. Our analysis reveals that KIC 6106415 exhibits starspot numbers similar to the Sun, peaking at an estimated 175, which is consistent with its faster rotation rate. The data suggest that KIC 6106415 may have shorter magnetic activity cycles than the Sun, reinforcing the established link between stellar rotation and magnetic field generation in solar-type stars., Comment: 12 pages, 14 figures

The nonlinear coupling between stellar convection and rotation is of great interest because it relates to understanding both stellar evolution and activity. We investigated the influence of rotation and the Coriolis force on the dynamics and thermodynamic structure of an F-type main-sequence star with a shallow outer convection zone. We performed a series of 3D radiative hydrodynamic simulations of a 1.47Msun star for different rotation rates (periods of rotation 1 and 14 days) and with computational domains placed at latitudes of 0degrees (equator), 30degrees, and 60degrees. Because the star has a relatively shallow convection zone (28.5 Mm thick or about 2.81% R*), we model its dynamics from the upper layers of the radiative zone, the whole convection zone, and the low atmosphere. The simulation results show a weak shift of the ionization zones to the photosphere and a decrease of the stellar radius by about 29 km at the equator and about 58 km at higher latitudes in the presence of rotation with a period of 1 day. The models presented reveal the formation of radial differential rotation, meridional flows, latitude-dependent roll-like structures of convection, a tachocline, the presence of a gravity-darkening effect, and others. In this paper, we primarily discuss the properties of the outer convection zone for different rotation rates. Detailed analysis of the properties of the tachocline, the overshoot layer, and small-scale turbulence will be discussed in follow-on papers., Comment: 19 pages, 14 figures, 1 table. Submitted to ApJ

Solar oblateness has been the subject of several studies dating back to the nineteenth century. Despite diffculties, 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 coeffcients which have been found to change with time. We show here that by inverting even coeffcients 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., Comment: 6 pages

The discovery of the solar activity cycle was linked from the outset to the observation of the temporal variability of sunspots, which we know to be the result of complex processes associated with the dynamics of inner layers. Numerous recent studies have highlighted changes in the Sun's Near-Surface Shear Layer (NSSL), pointing to the role of the leptocline, a shallow and sharp rotational shear layer in the top around 8 Mm. The leptocline, mainly characterized by a strong radial rotational gradient at middle latitudes and self-organized meridional flows, is the cradle of numerous phenomena: opacity, superadiabaticity, and turbulent pressure changes; the hydrogen and helium ionization processes; a sharp decrease in the sound speed; and, probably, variations of the seismic radius associated with a nonmonotonic expansion of subsurface layers with depth. In addition, the leptocline may play a key role in forming the magnetic butterfly diagram. Such results are a starting point for further systematic investigations of the structure and dynamics of this layer, which will lead to a better understanding of solar activity., Comment: 10 pages

Convection, differential rotation, and meridional circulation of solar plasma are studied based on helioseismic data covering the period from May 2010 to August 2024, significantly prolonged compared to that previously considered. Depth variation in the spatial spectrum of convective motions indicates a superposition of differently scaled flows. The giant-cell-scale component of the velocity field demonstrates a tendency to form meridionally elongated (possibly bananashaped) structures. The integrated spectral power of the flows is anticorrelated with the solar-activity level in the near-surface layers and positively correlates with it in deeper layers. An extended 22-year cycle of zonal flows ("torsional oscillations" of the Sun) and variations of the meridional flows are traced. A secondary meridional flow observed at the epoch of the maximum of Solar Cycle 24 to be directed equatorward in the subsurface layers is clearly manifest in Cycle 25., Comment: To be published in Astronomicheskii Zhurnal (Russian version) and Astronomy Reports (English version)

Between 2017 and 2024, the Helioseismic and Magnetic Imager (HMI) onboard the Solar Dynamics Observatory has observed numerous white-light solar flares (WLFs). HMI spectro-polarimetric observations of certain WLFs, in particular the X9.3 flare of September 6, 2017, reveal one or more locations within the umbra or along the umbra/penumbra boundary of the flaring active region where the Fe I 6173 {\AA} line briefly goes into full emission, indicating significant heating of the photosphere and lower chromosphere. For five flares featuring Fe I 6173 {\AA} line-core emission, we perform spectro-polarimetric analysis using HMI 90-second-cadence Stokes data. Line-core emission is observed to last for a single 90 s frame and is either concurrent with or followed by an increase in the line continuum intensity lasting one to two frames (90 s - 180 s). This is followed by a smooth decay to pre-flare conditions over the next three to twenty minutes. Additionally, permanent changes to the Stokes Q, U, and/or V profiles were observed, indicating long-lasting non-transient changes to the photospheric magnetic field. These emissions coincided with local maxima in hard X-ray emission observed by the Konus instrument onboard the Wind spacecraft, as well as local maxima in the time derivative of soft X-ray emission observed by GOES satellites. Comparison of the Fe I 6173 {\AA} line profile synthesis for the ad-hoc heating of the initial empirical VAL-S umbra model and quiescent Sun (VAL-C-like) model indicates that the Fe I 6173 {\AA} line emission in the white-light flare kernels could be explained by the strong heating of initially cool photospheric regions.

We developed Long Short-Term Memory (LSTM) models to predict the formation of active regions (ARs) on the solar surface. Using the Doppler shift velocity, the continuum intensity, and the magnetic field observations from the Solar Dynamics Observatory (SDO) Helioseismic and Magnetic Imager (HMI), we have created time-series datasets of acoustic power and magnetic flux, which are used to train LSTM models on predicting continuum intensity, 12 hours in advance. These novel machine learning (ML) models are able to capture variations of the acoustic power density associated with upcoming magnetic flux emergence and continuum intensity decrease. Testing of the models' performance was done on data for 5 ARs, unseen from the models during training. Model 8, the best performing model trained, was able to make a successful prediction of emergence for all testing active regions in an experimental setting and three of them in an operational. The model predicted the emergence of AR11726, AR13165, and AR13179 respectively 10, 29, and 5 hours in advance, and variations of this model achieved average RMSE values of 0.11 for both active and quiet areas on the solar disc. This work sets the foundations for ML-aided prediction of solar ARs., Comment: 20 pages, 8 figures, 5 tables, under review at the AAS Astrophysical Journal

Prediction of the Solar Energetic Particle (SEP) events garner increasing interest as space missions extend beyond Earth's protective magnetosphere. These events, which are, in most cases, products of magnetic reconnection-driven processes during solar flares or fast coronal-mass-ejection-driven shock waves, pose significant radiation hazards to aviation, space-based electronics, and particularly, space exploration. In this work, we utilize the recently developed dataset that combines the Solar Dynamics Observatory/Helioseismic and Magnetic Imager's (SDO/HMI) Space weather HMI Active Region Patches (SHARP) and the Solar and Heliospheric Observatory/Michelson Doppler Imager's (SoHO/MDI) Space Weather MDI Active Region Patches (SMARP). We employ a suite of machine learning strategies, including Support Vector Machines (SVM) and regression models, to evaluate the predictive potential of this new data product for a forecast of post-solar flare SEP events. Our study indicates that despite the augmented volume of data, the prediction accuracy reaches 0.7 +- 0.1, which aligns with but does not exceed these published benchmarks. A linear SVM model with training and testing configurations that mimic an operational setting (positive-negative imbalance) reveals a slight increase (+ 0.04 +- 0.05) in the accuracy of a 14-hour SEP forecast compared to previous studies. This outcome emphasizes the imperative for more sophisticated, physics-informed models to better understand the underlying processes leading to SEP events., Comment: Article submitted and is under revision to the AAS Astrophysical Journal

Solar differential rotation exhibits a prominent feature: its cyclic variations over the solar cycle, referred to as zonal flows or torsional oscillations, are observed throughout the convection zone. Given the challenge of measuring magnetic fields in subsurface layers, understanding deep torsional oscillations becomes pivotal in deciphering the underlying solar dynamo mechanism. In this study, we address the critical question of identifying specific signatures within helioseismic frequency-splitting data associated with the torsional oscillations. To achieve this, a comprehensive forward modeling approach is employed to simulate the helioseismic data for a dynamo model that, to some extent, reproduces solar-cycle variations of magnetic fields and flows. We provide a comprehensive derivation of the forward modeling process utilizing generalized spherical harmonics, as it involves intricate algebraic computations. All estimated frequency-splitting coefficients from the model display an 11-year periodicity. Using the simulated splitting coefficients and realistic noise, we show that it is possible to identify the dynamo wave signal present in the solar zonal flow from the tachocline to the solar surface. By analyzing observed data, we find similar dynamo wave patterns in the observational data from MDI, HMI, and GONG. This validates the earlier detection of dynamo waves and holds potential implications for the solar dynamo theory models., Comment: 22 pages, 10 Figures, submitted to ApJ

To create early warning capabilities for upcoming Space Weather disturbances, we have selected a dataset of 61 emerging active regions, which allows us to identify characteristic features in the evolution of acoustic power density to predict continuum intensity emergence. For our study, we have utilized Doppler shift and continuum intensity observations from the Helioseismic and Magnetic Imager (HMI) onboard the Solar Dynamics Observatory (SDO). The local tracking of 30.66 x 30.66-degree patches in the vicinity of active regions allowed us to trace the evolution of active regions starting from the pre-emergence state. We have developed a machine learning model to capture the acoustic power flux density variations associated with upcoming magnetic flux emergence. The trained Long Short-Term Memory (LSTM) model is able to predict 5 hours ahead whether, in a given area of the solar surface, continuum intensity values will decrease. The performed study allows us to investigate the potential of the machine learning approach to predict the emergence of active regions using acoustic power maps as input., Comment: 9 pages, 4 figures, IAU Symposium 365 Proceedings

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., Comment: 21 pages, 8 figures, 5 ancillary mp4 files of subsurface flows for active regions 11158, 12673, 12882, 13006, and 13179; to appear in Dynamics of Solar and Stellar Convection Zones and Atmospheres, Proc. IAU Symp. 365, 2024

Solar flare prediction studies have been recently conducted with the use of Space-Weather MDI (Michelson Doppler Imager onboard Solar and Heliospheric Observatory) Active Region Patches (SMARP) and Space-Weather HMI (Helioseismic and Magnetic Imager onboard Solar Dynamics Observatory) Active Region Patches (SHARP), which are two currently available data products containing magnetic field characteristics of solar active regions. The present work is an effort to combine them into one data product, and perform some initial statistical analyses in order to further expand their application in space weather forecasting. The combined data are derived by filtering, rescaling, and merging the SMARP with SHARP parameters, which can then be spatially reduced to create uniform multivariate time series. The resulting combined MDI-HMI dataset currently spans the period between April 4, 1996, and December 13, 2022, and may be extended to a more recent date. This provides an opportunity to correlate and compare it with other space weather time series, such as the daily solar flare index or the statistical properties of the soft X-ray flux measured by the Geostationary Operational Environmental Satellites (GOES). Time-lagged cross-correlation indicates that a relationship may exist, where some magnetic field properties of active regions lead the flare index in time. Applying the rolling window technique makes it possible to see how this leader-follower dynamic varies with time. Preliminary results indicate that areas of high correlation generally correspond to increased flare activity during the peak solar cycle.

The first significant sunquake event of Solar Cycle 25 was observed during the X1.5 flare of May 10, 2022, by the Helioseismic and Magnetic Imager (HMI) onboard the Solar Dynamics Observatory. We perform a detailed spectro-polarimetric analysis of the sunquake photospheric sources, using the Stokes profiles of the FeI 6173A line, reconstructed from the HMI linear and circular polarized filtergrams. The results show fast variations of the continuum emission with rapid growth and slower decay lasting 3-4 min, coinciding in time with the hard X-ray impulses observed by the Konus instrument onboard the Wind spacecraft. The variations in the line core appeared slightly ahead of the variations in the line wings, showing that the heating started in the higher atmospheric layers and propagated downward. The most significant feature of the line profile variations is the transient emission in the line core in three of the four sources, indicating intense, impulsive heating in the lower chromosphere and photosphere. In addition, the observed variations of the Stokes profiles reflect transient and permanent changes in the magnetic field strength and geometry in the sunquake sources. Comparison with the radiative hydrodynamics models shows that the physical processes in the impulsive flare phase are substantially more complex than those predicted by proton and electron beam flare models currently presented in the literature., Comment: 15 pages, 12 figures, accepted for publication in ApJ, for associated mpeg file, see https://spaceweather.com/images2022/12may22/Sunquake_X1.5_flare_051022_1.mp4

SDO/HMI observations reveal a class of solar flares with substantial energy and momentum impacts in the photosphere, concurrent with white-light emission and helioseismic responses, known as sunquakes. Previous radiative hydrodynamic modeling has demonstrated the challenges of explaining sunquakes in the framework of the standard flare model of `electron beam' heating. One of the possibilities to explain the sunquakes and other signatures of the photospheric impact is to consider additional heating mechanisms involved in solar flares, for example, via flare-accelerated protons. In this work, we analyze a set of single-loop Fokker-Planck and radiative hydrodynamics RADYN+FP simulations where the atmosphere is heated by non-thermal power-law-distributed proton beams which can penetrate deeper than the electron beams into the low atmospheric layers. Using the output of the RADYN models, we calculate synthetic Fe I 6173 A line Stokes profiles and from those the line-of-sight (LOS) observables of the SDO/HMI instrument, as well as the 3D helioseismic response and compare them with the corresponding observational characteristics. These initial results show that the models with proton beam heating can produce the enhancement of the HMI continuum observable and explain qualitatively generation of sunquakes. The continuum observable enhancement is evident in all models but is more prominent in ones with $E_{c}\geq$500 keV. In contrast, the models with $E_{c}\leq$100 keV provide a stronger sunquake-like helioseismic impact according to the 3D acoustic modeling, suggesting that low-energy (deka- and hecto-keV) protons have an important role in the generation of sunquakes., Comment: 22 pages, 11 figures, 2 tables

We study the toroidal magnetic flux budget of the axisymmetric part of a 3D mean-field dynamo model of Solar Cycles 23 and 24. The model simulates the global solar dynamo that includes effects of the formation and evolution of bipolar magnetic regions emerging on the solar surface. Our analysis shows that the hemispheric magnitude of the net axisymmetric toroidal magnetic field in the bulk of the convection zone is partly defined by the surface parameters of the differential rotation and the axisymmetric radial magnetic field. The contribution of the rotational radial shear to the net axisymmetric toroidal field production has the same magnitude and it goes nearly sin-phase with the effect of the latitudinal differential rotation. For our model, the effect of the radial shear to the net axisymmetric toroidal magnetic field is determined mostly by the near equatorial regions that are slightly above and below the bottom of the convection zone. Also, we find that the toroidal field generation rate depends strongly on the latitudinal profile of the axisymmetric radial magnetic field near the poles. We find that the magnitude of the axisymmetric toroidal flux generation rate in the 3D dynamo model is by about 10 percent higher than in the axisymmetric 2D mean-field dynamo model, due to the bipolar active regions., Comment: 16 pages, 7 figures

The application of machine learning and deep learning, including the wide use of non-ensemble, conventional neural networks (CoNN), for predicting various phenomena has become very popular in recent years thanks to the efficiencies and the abilities of these techniques to find relationships in data without human intervention. However, certain CoNN setups may not work on some datasets, especially if the parameters passed to it, including model parameters and hyperparameters, are arguably arbitrary in nature and need to continuously be updated with the need to retrain the model. This concern can be partially alleviated by employing committees of neural networks that are identical in terms of input features and architectures, initialized randomly, and "vote" on the decisions made by the committees as a whole. Yet, it is possible for the committee members to "agree" on identical sets of weights and biases for all nodes and edges. Members of these committees also cannot be expanded to accommodate new features and entire committees must therefore be retrained in order to do so. We propose the Random Hivemind (RH) approach, which helps to alleviate this concern by having multiple neural network estimators make decisions based on random permutations of features and prescribing a method to determine the weight of the decision of each individual estimator. The effectiveness of RH is demonstrated through experimentation in the predictions of hazardous Solar Energetic Particle (SEP) events by comparing it to that of using both CoNNs and the aforementioned setup of committees. Our results demonstrate that RH, while having a comparable or better performance than the CoNN and a Committee-based approach, demonstrates a lesser score spread for the individual experiments, and shows promising results with respect to capturing almost every single flare instance leading to SEPs., Comment: 14 pages, 6 figures, 2 tables

The flux of energetic particles originating from the Sun fluctuates during the solar cycles. It depends on the number and properties of Active Regions (ARs) present in a single day and associated solar activities, such as solar flares and coronal mass ejections (CMEs). Observational records of the Space Weather Prediction Center (SWPC NOAA) enable the creation of time-indexed databases containing information about ARs and particle flux enhancements, most widely known as Solar Energetic Particle events (SEPs). In this work, we utilize the data available for Solar Cycles 21-24, and the initial phase of Cycle 25 to perform a statistical analysis of the correlation between SEPs and properties of ARs inferred from the McIntosh and Hale classifications. We find that the complexity of the magnetic field, longitudinal location, area, and penumbra type of the largest sunspot of ARs are most correlated with the production of SEPs. It is found that most SEPs ($\approx$60\%, or 108 out of 181 considered events) were generated from an AR classified with the 'k' McIntosh subclass as the second component, and these ARs are more likely to produce SEPs if they fall in a Hale class containing $\delta$ component. The resulting database containing information about SEP events and ARs is publicly available and can be used for the development of Machine Learning (ML) models to predict the occurrence of SEPs., Comment: 27 pages, 7 figures, 1 table

Solar Energetic Particle (SEP) events and their major subclass, Solar Proton Events (SPEs), can have unfavorable consequences on numerous aspects of life and technology, making them one of the most harmful effects of solar activity. Garnering knowledge preceding such events by studying operational data flows is essential for their forecasting. Considering only Solar Cycle (SC) 24 in our previous study, Sadykov et al. 2021, we found that it may be sufficient to utilize only proton and soft X-ray (SXR) parameters for SPE forecasts. Here, we report a catalog recording $\geq$ 10 MeV $\geq$ 10 particle flux unit SPEs with their properties, spanning SCs 22-24, using NOAA's Geostationary Operational Environmental Satellite flux data. We report an additional catalog of daily proton and SXR flux statistics for this period, employing it to test the application of machine learning (ML) on the prediction of SPEs using a Support Vector Machine (SVM) and eXtreme Gradient Boosting (XGBoost). We explore the effects of training models with data from one and two SCs, evaluating how transferable a model can be across different time periods. XGBoost proved to be more accurate than SVMs for almost every test considered, while outperforming operational SWPC NOAA predictions and a persistence forecast. Interestingly, training done with SC 24 produces weaker TSS and HSS2, even when paired with SC 22 or SC 23, indicating transferability issues. This work contributes towards validating forecasts using long-spanning data -- an understudied area in SEP research that should be considered to verify the cross-cycle robustness of ML-driven forecasts.

We investigate deviations in the mean phase travel time of acoustic waves preceding the emergence of 46 large active regions observed by the Helioseismic and Magnetic Imager (HMI). In our investigation, we consider two different procedures for obtaining the mean phase travel time, by minimizing the difference between cross-correlations and a reference, as well as the Gabor wavelet fitting procedure. We cross-correlate the time series of mean phase travel time deviations with the surface magnetic field and determine the peak correlation time lag. We also compute the perturbation index--the area integrated mean phase travel time deviations exceeding quiet sun thresholds--and compare the time of peak perturbation index with the correlation time lag. We find that the lag times derived from the difference minimization procedure precede the flux emergence for 36 of the 46 active regions, and that this lag time has a noticeable correlation with the maximum flux rate. However, only 28 of the active regions have peak perturbation index times in the range of 24 to 48 hours prior to the flux emergence. Additionally, we examine the relationship between properties of the emerged active regions and the strength of helioseismic signals prior to their emergence.

We model the physical parameters of Solar Cycles 23 and 24 using a nonlinear dynamical mean-field dynamo model that includes the formation and evolution of bipolar magnetic regions (BMR). The Parker-type dynamo model consists of a complete MHD system in the mean-field formulation: the 3D magnetic induction equation, and 2D momentum and energy equations in the anelastic approximation. The initialization of BMR is modeled in the framework of Parker's magnetic buoyancy instability. It defines the depths of BMR injections, which are typically located at the edge of the global dynamo waves. The distribution with longitude and latitude and the size of the initial BMR perturbations are taken from the NOAA database of active regions. The tilt of the perturbations is modeled by random function, and the mean tilt is modeled as a near-surface helicity (alpha-effect) term. The data-driven models are compared with the models calculated for random longitudinal and latitudinal distributions of the initial perturbation. The modeling results are compared with various observed characteristics of the solar cycles, including the magnetic butterfly diagram, the polar magnetic and basal magnetic fluxes, and the probability distributions of the BMR flux on the surface. Our results show that BMR can play a substantial role in the dynamo processes, and affect the strength of the solar cycle. However, the data-driven model shows that the BMR effect alone cannot explain the weak Cycle 24. This weak cycle and the prolonged preceding minimum of magnetic activity were probably caused by a decrease of the turbulent helicity in the bulk of the convection zone during the decaying phase of Cycle 23., Comment: 18 pages, 10 figures, accepted in ApJ

Recent work published by Lindsey et al find evidence for a deep and compact seismic source for the sunquake associated with the 2011 July 30 M9.3 flare, as well as seismic emission extending up to 10 mHz. We examine the sunquake independently, and a possible wavefront is found in the 8 mHz band, though no wavefront is easily discernible in the 10 mHz band. Additionally, we perform numerical simulations of seismic excitation modeled with the reported parameters and changes in the power spectra with increasing depth of the excitation source are examined. It is found that the peak frequency decreases for increasing depths, but a shallow minimum is indicated between z=0 and z=-840 km. Analysis of the suspected wavefront of the M9.3 sunquake finds that the power spectrum of the reported seismic emission is close to that of background oscillations, though with a peak frequency noticeably lower than the background peak. Additionally, it is found that the amplitude of the source estimated by Lindsey et al is too low to produce the observed wavefront.

Simulating deep solar convection and its coupled mean-field motions is a formidable challenge where few observational results constrain models that suffer from the non-physical influence of the grid resolution. We present hydrodynamic global Implicit Large-Eddy simulations (ILES) of deep solar convection performed with the EULAG-MHD code, and explore the effects of grid resolution on the properties of rotating and non-rotating convection. The results, based on low-order moments and turbulent spectra reveal that convergence could be achieved in non-rotating simulations provided sufficient resolution in the radial direction. The flow is highly anisotropic, with the energy contained in horizontal divergent motions exceeding by more than three orders of magnitude their radial counterpart. By contrast, in rotating simulations the largest energy is in the toroidal part of the horizontal motions. As the grid resolution increases, the turbulent correlations change in such a way that a solar-like differential rotation, obtained in the simulation with the coarser grid, transitions to the anti-solar differential rotation. The reason for this change is the contribution of the effective viscosity to the balance of the forces driving large-scale flows. As the effective viscosity decreases, the angular momentum balance improves, yet the force balance in the meridional direction lessens, favoring a strong meridional flow that advects angular momentum towards the poles. The results suggest that obtaining the correct distribution of angular momentum may not be a mere issue of numerical resolution. Accounting for additional physics, such as magnetism or the near-surface shear layer, may be necessary in simulating the solar interior., Comment: 23 pages, 16 figures, submitted to ApJ

Spectral analysis of the spatial structure of solar subphotospheric convection is carried out for subsurface flow maps constructed using the time--distance helioseismological technique. The source data are obtained from the Helioseismic and Magnetic Imager (HMI) onboard Solar Dynamics Observatory (SDO) from 2010 May to 2020 September. A spherical-harmonic transform is applied to the horizontal-velocity-divergence field at depths from 0 to 19~Mm. The range of flow scales is fairly broad in shallow layers and narrows as the depth increases. The horizontal flow scales rapidly increase with depth, from supergranulation to giant-cell values, and indicate the existence of large-scale convective motions in the near-surface shear layer. The results can naturally be interpreted in terms of a superposition of differently scaled flows localized in different depth intervals. There is some tendency toward the emergence of meridionally elongated (banana-shaped) convection structures in the deep layers. The total power of convective flows is anticorrelated with the sunspot-number variation over the solar activity cycle in shallow subsurface layers and positively correlated at larger depths, which is suggestive of the depth redistribution of the convective-flow energy due to the action of magnetic fields., Comment: 13 pages, 10 figures. arXiv admin note: text overlap with arXiv:2201.00638

Global hydrodynamic simulations of internal solar dynamics have focused on replicating the conditions for solar-like differential rotation and meridional circulation using the results of helioseismic inversions as a constraint. Inferences of meridional circulation, however, have provided controversial results showing the possibility of one, two, or multiple cells along the radius. To resolve this controversy and develop a more robust understanding of global flow regimes in the solar interior, we apply a "forward-modeling" approach to the analysis of helioseismic signatures of meridional circulation profiles obtained from numerical simulations. We employ the global acoustic modeling code GALE to simulate the propagation of acoustic waves through regimes of mean mass flows generated by global hydrodynamic and magnetohydrodynamic models: EULAG, the Pencil Code, and the Rayleigh code. These models are used to create synthetic dopplergram data products, used as inputs for local time-distance helioseismology techniques. Helioseismic travel-time signals from solutions obtained through global numerical simulations are compared directly with inferences from solar observations, in order to set additional constraints on global model parameters in a direct way. We show that even though these models are able to replicate solar-like differential rotation, the resulting rotationally-constrained convection develops a multi-cell global meridional circulation profile that is measurably inconsistent with local time-distance inferences of solar observations. However, we find that the development of rotationally-unconstrained convection close to the model surface is able to maintain solar-like differential rotation, while having a significant impact on the helioseismic travel-time signal, replicating solar observations within one standard deviation of the error due to noise., Comment: 13 pages, 7 figures

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., Comment: 20 pages, 11 figures, submitted for publication in Proceedings of IAU Symposium 362 "Predictive Power of Computational Astrophysics as a Discovery Tool"

Solar and Heliosphere physics are areas of remarkable data-driven discoveries. Recent advances in high-cadence, high-resolution multiwavelength observations, growing amounts of data from realistic modeling, and operational needs for uninterrupted science-quality data coverage generate the demand for a solar metadata standardization and overall healthy data infrastructure. This white paper is prepared as an effort of the working group "Uniform Semantics and Syntax of Solar Observations and Events" created within the "Towards Integration of Heliophysics Data, Modeling, and Analysis Tools" EarthCube Research Coordination Network (@HDMIEC RCN), with primary objectives to discuss current advances and identify future needs for the solar research cyberinfrastructure. The white paper summarizes presentations and discussions held during the special working group session at the EarthCube Annual Meeting on June 19th, 2020, as well as community contribution gathered during a series of preceding workshops and subsequent RCN working group sessions. The authors provide examples of the current standing of the solar research cyberinfrastructure, and describe the problems related to current data handling approaches. The list of the top-level recommendations agreed by the authors of the current white paper is presented at the beginning of the paper., Comment: White Paper

A time-distance measurement technique is derived to isolate phase travel time anisotropy caused by subsurface horizontal magnetic fields, and a method which uses the measured anisotropy to estimate the field's orientation is also derived. A simulation of acoustic waves propagating in a uniform, inclined magnetic field with solar background structure is used to verify the derived technique. Then, the procedure is applied to a numerical simulation of a sunspot, for which the subsurface state is known, to provide context for the results obtained from the study of several sunspots observed by the Helioseismic and Magnetic Imager. Significant anisotropies are detected, on the order of one minute, and the subsurface field's azimuth is estimated and compared with the azimuth of the surface magnetic field. In all cases, the subsurface azimuth is found to be well-aligned with that of the surface, and the results from the numerical simulation are used to interpret features in the detected travel time anisotropy.

Understanding effects driven by rotation in the solar convection zone is essential for many problems related to solar activity, such as the formation of differential rotation, meridional circulation, and others. We analyze realistic 3D radiative hydrodynamics simulations of solar subsurface dynamics in the presence of rotation in a local domain 80 Mm wide and 25 Mm deep, located at 30 degrees latitude. The simulation results reveal the development of a shallow 10-Mm deep substructure of the Near-Surface Shear Layer (NSSL), characterized by a strong radial rotational gradient and self-organized meridional flows. This shallow layer ("leptocline") is located in the hydrogen ionization zone associated with enhanced anisotropic overshooting-type flows into a less unstable layer between the H and HeII ionization zones. We discuss current observational evidence of the presence of the leptocline and show that the radial variations of the differential rotation and meridional flow profiles obtained from the simulations in this layer qualitatively agree with helioseismic observations., Comment: 11 pages, 8 figures, submitted to MNRAS

The Sun shrinks during solar maximum and regrows during solar minimum by a few kilometers. Here, we observe, for the first time, that the solar radius variation shows planetary relationship. This suggests that some remote planetary links must exist, even though this is unexpected within known physics. Therefore, we speculate about its cause, which is the driving idea behind this investigation. Namely, it must be some generic as yet invisible streaming matter from the dark Universe. The associated energy change is massive although it extends from months to several years. The impact by the tentative invisible massive matter accumulates with time, triggering slowly the underlying processes. This study shows that the sun size response is as short as a few months. Then, the solar system is the target and the antenna of still unidentified external impact, assuming to be from the dark sector., Comment: 15 pages, 6 Figures, published in Symmetry 2022, 14, 325

Large-eddy simulations (LES) and implicit LES (ILES) are wise and affordable alternatives to the unfeasible direct numerical simulations (DNS) of turbulent flows at high Reynolds numbers (Re). However, for systems with few observational constraints, it is a formidable challenge to determine if these strategies adequately capture the physics of the system. Here we address this problem by analyzing numerical convergence of ILES of turbulent convection in 2D, with resolutions between $64^2$ and $2048^2$ grid points, along with the estimation of their effective viscosities, resulting in effective Reynolds numbers between $1$ and $\sim10^4$. The thermodynamic structure of our model resembles the solar interior, including a fraction of the radiative zone and the convection zone. In the convective layer, the ILES solutions converge for the simulations with $\ge 512^2$ grid points, as evidenced by the integral properties of the flow and its power spectra. Most importantly, we found that even a resolution of $128^2$ grid points, Re$\sim10$, is sufficient to capture the dynamics of the large scales accurately. This is a consequence of the ILES method allowing that the energy contained in these scales is the same in simulations with low and high resolution. Special attention is needed in regions with a small density scale height driving the formation of fine structures unresolved by the numerical grid. In the stable layer we found the excitation of internal gravity waves, yet high resolution is needed to capture their development and interaction., Comment: 15 pages, 9 figures, accepted for publication in The Astrophysical Journal

We analyze spectral properties of solar convection in the range of depths from 0 to 19~Mm using subsurface flow maps obtained by the time-distance heiioseismology analysis of solar-oscillation data from the Helioseismic and Magnetic Imager (HMI) onboard Solar Dynamics Observatory (SDO) from May 2010 to September 2020. The results reveal a rapid increase of the horizontal flow scales with the depth, from supergranulation to giant-cell scales, and support the evidence of large-scale convection, previously detected by tracking the motion of supergranular cells on the surface. The total power of convective flows correlates with the solar activity cycle. During the solar maximum, the total power decreases in shallow subsurface layers and increases in the deeper layers., Comment: 8 pages, 5 figures

Solar Energetic Particle events (SEPs) are among the most dangerous transient phenomena of solar activity. As hazardous radiation, SEPs may affect the health of astronauts in outer space and adversely impact current and future space exploration. In this paper, we consider the problem of daily prediction of Solar Proton Events (SPEs) based on the characteristics of the magnetic fields in solar Active Regions (ARs), preceding soft X-ray and proton fluxes, and statistics of solar radio bursts. The machine learning (ML) algorithm uses an artificial neural network of custom architecture designed for whole-Sun input. The predictions of the ML model are compared with the SWPC NOAA operational forecasts of SPEs. Our preliminary results indicate that 1) for the AR-based predictions, it is necessary to take into account ARs at the western limb and on the far side of the Sun; 2) characteristics of the preceding proton flux represent the most valuable input for prediction; 3) daily median characteristics of ARs and the counts of type II, III, and IV radio bursts may be excluded from the forecast without performance loss; and 4) ML-based forecasts outperform SWPC NOAA forecasts in situations in which missing SPE events is very undesirable. The introduced approach indicates the possibility of developing robust "all-clear" SPE forecasts by employing machine learning methods., Comment: 22 pages, 8 figures, 4 tables

Coronal holes are the observational manifestation of the solar magnetic field open to the heliosphere and are of pivotal importance for our understanding of the origin and acceleration of the solar wind. Observations from space missions such as the Solar Dynamics Observatory now allow us to study coronal holes in unprecedented detail. Instrumental effects and other factors, however, pose a challenge to automatically detect coronal holes in solar imagery. The science community addresses these challenges with different detection schemes. Until now, little attention has been paid to assessing the disagreement between these schemes. In this COSPAR ISWAT initiative, we present a comparison of nine automated detection schemes widely-applied in solar and space science. We study, specifically, a prevailing coronal hole observed by the Atmospheric Imaging Assembly instrument on 2018 May 30. Our results indicate that the choice of detection scheme has a significant effect on the location of the coronal hole boundary. Physical properties in coronal holes such as the area, mean intensity, and mean magnetic field strength vary by a factor of up to 4.5 between the maximum and minimum values. We conclude that our findings are relevant for coronal hole research from the past decade, and are therefore of interest to the solar and space research community., Comment: Accepted for publication in The Astrophysical Journal. (Received January 20, 2021; Accepted March 25, 2021)

In this study we extract the deep features and investigate the compression of the Mg II k spectral line profiles observed in quiet Sun regions by NASA's IRIS satellite. The data set of line profiles used for the analysis was obtained on April 20th, 2020, at the center of the solar disc, and contains almost 300,000 individual Mg II k line profiles after data cleaning. The data are separated into train and test subsets. The train subset was used to train the autoencoder of the varying embedding layer size. The early stopping criterion was implemented on the test subset to prevent the model from overfitting. Our results indicate that it is possible to compress the spectral line profiles more than 27 times (which corresponds to the reduction of the data dimensionality from 110 to 4) while having a 4 DN average reconstruction error, which is comparable to the variations in the line continuum. The mean squared error and the reconstruction error of even statistical moments sharply decrease when the dimensionality of the embedding layer increases from 1 to 4 and almost stop decreasing for higher numbers. The observed occasional improvements in training for values higher than 4 indicate that a better compact embedding may potentially be obtained if other training strategies and longer training times are used. The features learned for the critical four-dimensional case can be interpreted. In particular, three of these four features mainly control the line width, line asymmetry, and line dip formation respectively. The presented results are the first attempt to obtain a compact embedding for spectroscopic line profiles and confirm the value of this approach, in particular for feature extraction, data compression, and denoising., Comment: 6 pages, 3 figures, submitted to CBMI 2021 (Special session: Mining and indexing multimedia data for remote sensing of the environment and our changing planet)

Using a 3D global solver of the linearized Euler equations, we model acoustic oscillations over background velocity flow fields of single-cell meridional circulation with deep and shallow return flows as well as double-cell meridional circulation with strong and weak reversals. The velocities are generated using a mean-field hydrodynamic and dynamo model -- moving through the regimes with minimal parameter changes; counter-rotation near the base of the tachocline is induced by sign inversion of the non-diffusive action of turbulent Reynolds stresses ($\Lambda$-effect) due to the radial inhomogeneity of the Coriolis number. By mimicking the stochastic excitation of resonant modes in the convective interior, we simulate realization noise present in solar observations. Using deep-focusing to analyze differences in travel-time signatures between the four regimes, as well as comparing to solar observations, we show that current helioseismology techniques may offer important insights about the location and strength of the return flow, however, that it may not currently be possible to definitively distinguish between profiles of single-cell or double-cell meridional circulation.

The results of determinations of the azimuthal and meridional velocities by time-distance helioseismology from Helioseismic and Magnetic Imager (HMI) onboard Solar Dynamics Observatory (SDO) from May 2010 to September 2020 at latitudes from -60{\deg} to +60{\deg} and depths to about 19 Mm below the photosphere are used to analyze spatiotemporal variations of the solar differential rotation and meridional circulation. The pattern of torsional oscillations, or latitudinal belts of alternating `fast' and `slow' zonal flows migrating from high latitudes towards the equator, is found to extend in the time--latitude diagrams over the whole time interval. The oscillation period is comparable with a doubled solar-activity-cycle and can be described as an extended solar cycle. The zonal-velocity variations are related to the solar-activity level, the local-velocity increases corresponding to the sunspot-number increases and being localized at latitudes where the strongest magnetic fields are recorded. The dramatic growth of the zonal velocities in 2018 appears to be a precursor of the beginning of activity Cycle 25. The strong symmetrization of the zonal-velocity field by 2020 can be considered another precursor. The general pattern of poleward meridional flows is modulated by latitudinal variations that are similar to the extended-solar-cycle behavior of the zonal flows. During the activity maximum, these variations are superposed with a higher harmonic corresponding to meridional flows converging to the spot-formation latitudes. Our results indicate that variations of both the zonal and meridional flows exhibit the extended solar-cycle behavior, which is an intrinsic feature of the solar dynamo., Comment: 9 pages, 5 figures

The next decade will be an exciting period for solar astrophysics, as new ground- and space-based instrumentation will provide unprecedented observations of the solar atmosphere and heliosphere. The synergy between modeling effort and comprehensive analysis of observations is crucial for the understanding of the physical processes behind the observed phenomena. However, the unprecedented wealth of data on one hand, and the complexity of the physical phenomena on the other, require the development of new approaches in both data analysis and numerical modeling. In this white paper, we summarize recent numerical achievements to reproduce structure, dynamics, and observed phenomena from the photosphere to the low corona and outline challenges we expect to face for the interpretation of future observations.

A time-distance helioseismic technique, similar to the one used by Ilonidis et al (2011), is applied to two independent numerical models of subsurface sound-speed perturbations to determine the spatial resolution and accuracy of phase travel time shift measurements. The technique is also used to examine pre-emergence signatures of several active regions observed by the Michelson Doppler Imager (MDI) and the Helioseismic Magnetic Imager (HMI). In the context of similar measurements of quiet sun regions, three of the five studied active regions show strong phase travel time shifts several hours prior to emergence. These results form the basis of a discussion of noise in the derived phase travel time maps and possible criteria to distinguish between true and false positive detection of emerging flux.

We present a 3-dimensional (3D) numerical solver of the linearized compressible Euler equations (GALE -- Global Acoustic Linearized Euler), used to model acoustic oscillations throughout the solar interior. The governing equations are solved in conservation form on a fully global spherical mesh ($0 \le \phi \le 2\pi$, $0 \le \theta \le \pi$, $0 \le r \le R_{\odot}$) over a background state generated by the standard Solar Model S. We implement an efficient pseudo-spectral computational method to calculate the contribution of the compressible material derivative dyad to internal velocity perturbations, computing oscillations over arbitrary 3D background velocity fields. This model offers a foundation for a "forward-modeling" approach, using helioseismology techniques to explore various regimes of internal mass flows. We demonstrate the efficacy of the numerical method presented in this paper by reproducing observed solar power spectra, showing rotational splitting due to differential rotation, and applying local helioseismology techniques to measure travel times created by a simple model of single-cell meridional circulation.

We analyze the evolution of shock waves in high-resolution 3D radiative MHD simulations of the quiet Sun and their synthetic emission characteristics. The simulations model the dynamics of a 12.8x12.8x15.2 Mm quiet-Sun region (including a 5.2 Mm layer of the upper convection zone and a 10 Mm atmosphere from the photosphere to corona) with an initially uniform vertical magnetic field of 10 G, naturally driven by convective flows. We synthesize the Mg II and C II spectral lines observed by the IRIS satellite and EUV emission observed by the SDO/AIA telescope. Synthetic observations are obtained using the RH1.5D radiative transfer code and temperature response functions at both the numerical and instrumental resolutions. We found that the Doppler velocity jumps of the C II 1334.5 A IRIS line and a relative enhancement of the emission in the 335 A SDO/AIA channel are the best proxies for the enthalpy deposited by shock waves into the corona (with Kendall's $\tau$ correlation coefficients of 0.59 and 0.38, respectively). The synthetic emission of the lines and extreme ultraviolet passbands are correlated with each other during the shock wave propagation. All studied shocks are mostly hydrodynamic (i.e., the magnetic energy carried by horizontal fields is $\leq{}$2.6% of the enthalpy for all events) and have Mach numbers > 1.0-1.2 in the low corona. The study reveals the possibility of diagnosing energy transport by shock waves into the solar corona, as well as their other properties, by using IRIS and SDO/AIA sensing observations., Comment: 31 pages, 8 figures, 2 tables

The authors of this white paper met on 16-17 January 2020 at the New Jersey Institute of Technology, Newark, NJ, for a 2-day workshop that brought together a group of heliophysicists, data providers, expert modelers, and computer/data scientists. Their objective was to discuss critical developments and prospects of the application of machine and/or deep learning techniques for data analysis, modeling and forecasting in Heliophysics, and to shape a strategy for further developments in the field. The workshop combined a set of plenary sessions featuring invited introductory talks interleaved with a set of open discussion sessions. The outcome of the discussion is encapsulated in this white paper that also features a top-level list of recommendations agreed by participants., Comment: Workshop Report

Identification of solar coronal holes (CHs) provides information both for operational space weather forecasting and long-term investigation of solar activity. Source data for the first problem are typically most recent solar disk observations, while for the second problem it is convenient to consider solar synoptic maps. Motivated by the idea that the concept of CHs should be similar for both cases we investigate universal models that can learn a CHs segmentation in disk images and reproduce the same segmentation in synoptic maps. We demonstrate that Convolutional Neural Networks (CNN) trained on daily disk images provide an accurate CHs segmentation in synoptic maps and their pole-centric projections. Using this approach we construct a catalog of synoptic maps for the period of 2010-20 based on SDO/AIA observations in the 193 Angstrom wavelength. The obtained CHs synoptic maps are compared with magnetic synoptic maps in the time-latitude and time-longitude diagrams. The initial results demonstrate that while in some cases the CHs are associated with magnetic flux transport events there are other mechanisms contributing to the CHs formation and evolution. To stimulate further investigations the catalog of synoptic maps is published in open access.

Using a nonlinear mean-field solar dynamo model, we study relationships between the amplitude of the `extended' mode of migrating zonal flows (`torsional oscillations') and magnetic cycles, and investigate whether properties the torsional oscillations in subsurface layers and in the deep convection zone can provide information about the future solar cycles. We consider two types of dynamo models: models with regular variations of the alpha-effect, and models with stochastic fluctuations, simulating `long'- and 'short-memory' types of magnetic activity variations. It is found that torsional oscillation parameters, such the zonal acceleration, show a considerable correlation with the magnitude of the subsequent cycles with a time lag of 11-20 yr. The sign of the correlation and the time-lag parameters can depend on the depth and latitude of the torsional oscillations as well as on the properties of long-term (`centennial') variations of the dynamo cycles. The strongest correlations are found for the zonal acceleration at high latitudes at the base of the convection zone. The model results demonstrate that helioseismic observations of the torsional oscillations can be useful for advanced prediction of the solar cycles, one-two sunspot cycles ahead., Comment: 14 pages, 11 figures

The Kepler Asteroseismic Legacy Project provided frequencies, separation ratios, error estimates, and covariance matrices for 66 Kepler main sequence targets. Most of the previous analysis of these data was focused on fitting standard stellar models. We present results of direct asteroseismic inversions using the method of optimally localized averages (OLA), which effectively eliminates the surface effects and attempts to resolve the stellar core structure. The inversions are presented for various structure properties, including the density stratification and sound speed. The results show that the mixed modes observed in post-main sequence F-type stars allow us to resolve the stellar core structure and reveal significant deviations from the evolutionary models obtained by the grid-fitting procedure to match the observed oscillation frequencies., Comment: 9 pages, 5 figures