Helioseismic Data Research Articles

Case Studies on Pre-eruptive X-class Flares using R-value in the Lower Solar Atmosphere

The R-value is a measure of the strength of photospheric magnetic polarity inversion lines in active regions (ARs). This work investigates the possibility of a relation between R-value variations and the occurrence of X-class flares in ARs, not in the solar photosphere, as usual, but above it in regions closer to where flares occur. The modus operandi is to extrapolate the Solar Dynamic Observatory’s Helioseismic and Magnetic Imager magnetogram data up to a height of 3.24 Mm above the photosphere and then compute the R-value based on the extrapolated magnetic field. Recent studies have shown that certain flare-predictive parameters such as the horizontal gradient of the vertical magnetic field and magnetic helicity may improve flare prediction lead times significantly if studied at a specific height range above the photosphere, called the optimal height range (OHR). Here, we define the OHR as a collection of heights where a sudden but sustained increase in R-value is found. For the eight case studies discussed in this paper, our results indicate that it is possible for OHRs to exist in the low solar atmosphere (between 0.36 and 3.24 Mm), where R-value spikes occur 48–68 hr before the first X-class flare of an emerging AR. The temporal evolution of R-value before the first X-class flare for an emerging AR is also found to be distinct from that of nonflaring ARs. For X-class flares associated with nonemerging ARs, an OHR could not be found.

Helioseismic Properties of Dynamo Waves in the Variation of Solar Differential Rotation

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 yr 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 the Michelson Doppler Imager, Helioseismic Magnetic Imager, and Global Oscillation Network Group. This validates the earlier detection of dynamo waves and holds potential implications for the solar dynamo theory models.

In-depth analysis of solar models with high-metallicity abundances and updated opacity tables

Context. As a result of the high-quality constraints available for the Sun, we are able to carry out detailed combined analyses using neutrino, spectroscopic, and helioseismic observations. These studies lay the ground for future improvements of the key physical components of solar and stellar models because ingredients such as the equation of state, the radiative opacities, or the prescriptions for macroscopic transport processes of chemicals are then used to study other stars in the Universe. Aims. We study the existing degeneracies in solar models using the recent high-metallicity spectroscopic abundances by comparing them to helioseismic and neutrino data and discuss the effect on their properties of changes in the micro and macro physical ingredients. Methods. We carried out a detailed study of solar models computed with a high-metallicity composition from the literature based on averaged 3D models that were claimed to resolve the solar modelling problem. We compared these models to helioseismic and neutrino constraints. Results. The properties of the solar models are significantly affected by the use of the recent OPLIB opacity tables and the inclusion of macroscopic transport. The properties of the standard solar models computed using the OPAL opacities are similar to those for which the OP opacities were used. We show that a modification of the temperature gradient just below the base of the convective zone is required to remove the discrepancies in solar models, particularly in the presence of macroscopic mixing. This can be simulated by a localised increase in the opacity of a few percent. Conclusions. We conclude that the existing degeneracies and issues in solar modelling are not removed by using an increase in the solar metallicity, in contradiction to what has been suggested in the recent literature. Therefore, standard solar models cannot be used as an argument for a high-metallicity composition. While further work is required to improve solar models, we note that direct helioseismic inversions indicate a low metallicity in the convective envelope, in agreement with spectroscopic analyses based on full 3D models.

A SART-Based Iterative Inversion Methodology to Infer the Solar Rotation Rate from Global Helioseismic Data

A SART-Based Iterative Inversion Methodology to Infer the Solar Rotation Rate from Global Helioseismic Data

Asphericity of the Base of the Solar Convection Zone

We have used solar oscillation frequencies and frequency splittings obtained over solar cycles 23 and 24 to investigate whether the base of the solar convection zone shows any departure from spherical symmetry. We used the even-order splitting coefficients, a 2–a 8, and estimated the contributions from each one separately. The average asphericity over the two solar cycles was determined using frequencies and splittings obtained with a 9216-day time series. We find that evidence of asphericity is, at best, marginal: the a 2 component is consistent with no asphericity, the a 4 and a 6 components yield results at a level a little greater than 1σ, while the a 8 component shows a signature below 1σ. The combined results indicate that the time average of the departure from the spherically symmetric position of the base of the convection zone is ≲0.0001R ⊙. We have also used helioseismic data obtained from time series of lengths of 360, 576, 1152, and 2304 days in order to examine the consistency of the results and evaluate whether there is any time variation. We find that the evidence for time variation is statistically marginal in all cases, except for the a 6 component, for which tests consistently yield p-values of less than 0.05.

Helioseismic determination of the solar metal mass fraction

Context. The metal mass fraction of the Sun Z is a key constraint in solar modelling, but its value is still under debate. The standard solar chemical composition of the late 2000s has the ratio of metals to hydrogen as Z/X = 0.0181, and there was a small increase to 0.0187 in 2021, as inferred from 3D non-LTE spectroscopy. However, more recent work on a horizontally and temporally averaged ⟨3D⟩ model claim Z/X = 0.0225, which is consistent with the high values based on 1D LTE spectroscopy from 25 years ago. Aims. We aim to determine a precise and robust value of the solar metal mass fraction from helioseismic inversions, thus providing independent constraints from spectroscopic methods. Methods. We devised a detailed seismic reconstruction technique of the solar envelope, combining multiple inversions and equations of state in order to accurately and precisely determine the metal mass fraction value. Results. We show that a low value of the solar metal mass fraction corresponding to Z/X = 0.0187 is favoured by helioseismic constraints and that a higher metal mass fraction corresponding to Z/X = 0.0225 is strongly rejected by helioseismic data. Conclusions. We conclude that direct measurement of the metal mass fraction in the solar envelope favours a low metallicity, in line with the 3D non-LTE spectroscopic determination of 2021. A high metal mass fraction, as measured using a ⟨3D⟩ model in 2022, is disfavoured by helioseismology for all modern equations of state used to model the solar convective envelope.

Inferring the Solar Meridional Circulation Flow Profile by Applying Bayesian Methods to Time–Distance Helioseismology

Mapping the large-scale subsurface plasma flow profile within the Sun has been attempted using various methods for several decades. One such flow in particular is the meridional circulation, for which numerous studies have been published. However, such studies often show disagreement in structure. In an effort to constrain the flow profile from the data, a Bayesian Markov chain Monte Carlo framework has been developed to take advantage of the advances in computing power that allow for the efficient exploration of high-dimensional parameter spaces. This study utilizes helioseismic travel-time difference data covering a span of 21 years and a parameterized model of the meridional circulation to find the most likely flow profiles. Tests were carried out on artificial data to determine the ability of this method to recover expected solar-like flow profiles, as well as a few extreme cases. We find that this method is capable of recovering the input flows of both single- and double-cell flow structures. Some inversion results indicate potential differences in meridional circulation between the two solar cycles in terms of both magnitude and morphology, in particular in the mid-convection zone. Of these, the most likely solutions show that solar cycle 23 has a large single-celled profile, while cycle 24 shows weaker flows in general and hints toward a double-celled structure.

Analysis of Magnetic Nonpotentiality in the Flaring Active Region NOAA 12887

Solar flares are explosive events resulting from the release of stored magnetic energy in active regions. In this study, the Spaceweather Helioseismic and Magnetic Imager Active Region Patch (SHARP) data is utilized to extract nonpotential magnetic parameters of the NOAA 12887 active region, which produced an X1.0 class flare in October 2021. The analysis revealed that the electric current became non-neutral and unstable before the X-class flare due to an increase in the shear angle, exceeding 90 degrees through a collision of positive and negative polarities. We also assessed the magnetic nonpotentiality parameters, including free energy, vertical current, current helicity, and current neutrality. At the beginning, the parameters exhibited elevated values, reflecting the complex nature of the active region. Subsequently, it became even more complex following the collision event. Flare Ribbons and filaments were also observed by the AIA/SDO 1600 Å and 304Å images on this phase. However, the overall complexity decreased over time, with temporary increases after the collision event and subsequent flares. The development of new complex areas outside the collision zone had a lesser impact on the parameter values. The current neutrality value increased after the collision, implying an increasingly unstable region, but sharply decreased after the X-class flare, indicating a return to a more stable state for the active region.

A Dataset for Exploring Stellar Activity in Astrometric Measurements from SDO Images of the Sun

We present a data set for investigating the impact of stellar activity on astrometric measurements using NASA’s Solar Dynamics Observatory (SDO) images of the Sun. The sensitivity of astrometry for detecting exoplanets is limited by stellar activity (e.g., starspots), which causes the measured “center of flux” of the star to deviate from the true, geometric, center, producing false positive detections. We analyze Helioseismic and Magnetic Imager continuum image data obtained from SDO between 2015 July and 2022 December to examine this “astrometric jitter” phenomenon for the Sun. We employ data processing procedures to clean the images and compute the time series of the sunspot-induced shift between the center of flux and the geometric center. The resulting time series show quasiperiodic variations up to 0.05% of the Sun’s radius at its rotation period.

Evolution of coronal magnetic field parameters during X5.4 solar flare

The coronal magnetic field over NOAA Active Region 11,429 during a X5.4 solar flare on 7 March 2012 is modeled using optimization based Non-Linear Force-Free Field extrapolation. Specifically, 3D magnetic fields were modeled for 11 timesteps using the 12-min cadence Solar Dynamics Observatory (SDO) Helioseismic and Magnetic Imager photospheric vector magnetic field data, spanning a time period of 1 hour before through 1 hour after the start of the flare. Using the modeled coronal magnetic field data, seven different magnetic field parameters were calculated for 3 separate regions: areas with surface |Bz|≥ 300 G, areas of flare brightening seen in SDO Atmospheric Imaging Assembly imagery, and areas with surface |B| ≥ 1000 G and high twist. Time series of the magnetic field parameters were analyzed to investigate the evolution of the coronal field during the solar flare event and discern pre-eruptive signatures. The data shows that areas with |B| ≥ 1000 G and |Tw|≥ 1.5 align well with areas of initial flare brightening during the pre-flare phase and at the beginning of the eruptive phase of the flare, suggesting that measurements of the photospheric magnetic field strength and twist can be used to predict the flare location within an active region if triggered. Additionally, the evolution of seven investigated magnetic field parameters indicated a destabilizing magnetic field structure that could likely erupt.

Precision and systematic errors in global helioseismology mode fitting and inversions: Leveraging some 25 years of nearly uninterrupted observations

We have on hand some 25 years of nearly uninterrupted high-quality and high-cadence global helioseismic data. The Global Oscillations Network Group (GONG) project has been producing science quality data since 1995, the Michelson Doppler Imager (MDI) started in 1996, and the Helioseismic and Magnetic Imager (HMI) took over in 2010. Fundamental new constraints have been imposed by helioseismic inferences, yet global helioseismology data processing seems somewhat frozen in time for some of its methodologies. I review and discuss some specific aspects of global helioseismology data analysis, with an emphasis on the issues and challenges presented by mode fitting and inversion techniques. I compare and contrast results derived by different fitting methods, whether using different techniques, different lengths of time series, or different fitting parameters, like leakage matrices or the inclusion or omission of the mode profile asymmetry, leading to our current best handle on the residual systematic errors.

The Nonpotentiality of Steady-state Coronal Magnetic Field Derived with Time-relaxation Magnetohydrodynamics Simulations Using Helioseismic and Magnetic Imager Three-component Magnetic Field Data

The steady states of the coronal magnetic field obtained with the magnetohydrodynamic (MHD) time-relaxation simulation model are examined. Our electric-field-driven model can introduce the three components of the solar surface magnetic field data maps as the boundary values of an MHD simulation, without violating the divergence-free condition of the magnetic field. The magnetic field in the simulated steady-state solar corona exhibits substantial nonpotentiality in the closed-field streamers. A few choices are allowed in our model, such as the criteria for determining whether or not the horizontal components at the weak-field region are included. The initial magnetic field configuration can be arbitrarily determined. In this work, we examined the differences between the steady states obtained with the information on the horizontal components and with several choices of the simulation setting, and compared the new steady states with those obtained without using the horizontal magnetic field components. We found that nonpotential magnetic structures in the derived steady states well correspond to the observed solar filament structures during a selected period of Carrington Rotation 2106. The difference in the steady state with different boundary treatments is found to be large. The difference caused by the initial magnetic configuration is found to be small.

Characterizing the Umbral Magnetic Knots of δ-Sunspots

Delta (δ) spots are active regions (ARs) in which positive and negative umbrae share a penumbra. They are known to be the source of strong flares. We introduce a new quantity, the degree of δ (Doδ), to measure the fraction of umbral flux participating in the δ-configuration and to isolate the dynamics of the magnetic knot, i.e., adjacent umbrae in the δ-configuration. Using Helioseismic and Magnetic Imager data, we analyze 19 δ-spots and 11 β-spots in detail, as well as 120 δ-spots in less detail. We find that δ-regions are not in a δ-configuration for the entire time but spend 55% of their observed time as δ-spots with an average, maximum Doδ of 72%. Compared to β-spots, δ-spots have 2.6× the maximum umbral flux, 1.9× the flux emergence rate, 2.6× the rotation, and 72× the flare energy. On average, the magnetic knots rotate 17° day−1, while the β-spots rotate 2° day−1. Approximately 72% of the magnetic knots present anti-Hale or anti-Joy tilts, contrasting starkly with only 9% of the β-spots. A positive correlation exists between ϕ Doδ and the flare energy emitted by that region. The δ-spots obey the hemispheric current helicity rule 64% of the time. A total of 84% of the δ-spots are formed by single flux emergence events, and 58% have a quadrupolar magnetic configuration. The δ-spot characteristics are consistent with the formation mechanism signatures as follows: 42% with the kink instability or Sigma effect, 32% with multisegment buoyancy, 16% with collisions, and two ARs that are unclassified but consistent with a rising O-ring.

Solar-cycle variation of quiet-Sun magnetism and surface gravity oscillation mode

Context. The origins of quiet-Sun magnetism (QS) is still under debate and investigating the solar cycle variation observationally in greater detail can provide clues on how to resolve the ensuing controversies. Aims. We investigate the solar cycle variation of the most magnetically quiet regions and their surface gravity oscillation (f-) mode-integrated energy, Ef. Methods. We used 12 years of Helioseismic and Magnetic Imager (HMI) data and applied a stringent selection criteria based on spatial and temporal quietness to avoid any influence from active regions (ARs). We developed an automated high-throughput pipeline to go through all available magnetogram data and to compute the value of Ef for the selected quiet regions. Results. We observed a clear solar cycle dependence of the magnetic field strength in the most quiet regions containing several supergranular cells. For patch sizes smaller than a supergranular cell, no significant cycle dependence was detected. The Ef at the supergranular scale is not constant over time. During the late ascending phase of Cycle 24 (SC24, 2011-2012), it is roughly constant, but starts diminishing in 2013, as the maximum of SC24 is approached. This trend continues until mid-2017, when hints of strengthening at higher southern latitudes are seen. Slow strengthening continues, stronger at higher latitudes than at the equatorial regions, but Ef never returns to the values seen in 2011-2012. In addition, the strengthening trend continues past the solar minimum, to the years when SC25 is already clearly ascending. Hence, the Ef behavior is not in phase with the solar cycle. Conclusions. The dependence of Ef on the solar cycle at supergranular scales is indicative of the fluctuating magnetic field being replenished by tangling from the large-scale magnetic field – and not solely due to the action of a fluctuation dynamo process in the surface regions. The absence of variations on smaller scales might be an effect of the limited spatial resolution and magnetic sensitivity of HMI. The anticorrelation of Ef with the solar cycle in gross terms is expected, but the phase shift of several years indicates a connection to the large-scale poloidal magnetic field component rather than the toroidal one. Calibrating AR signals with the QS Ef does not reveal significant enhancement of the f-mode prior to AR emergence.

The effect of spatial sampling on magnetic field modeling and helicity computation

Context. Nonlinear force-free (NLFF) modeling is regularly used to indirectly infer the 3D geometry of the coronal magnetic field, which is not otherwise accessible on a regular basis by means of direct measurements. Aims. We study the effect of binning in time-series NLFF modeling of individual active regions (ARs) in order to quantify the effect of a different underlying spatial sampling on the quality of modeling as well as on the derived physical parameters. Methods. We apply an optimization method to sequences of Solar Dynamics Observatory (SDO) Helioseismic and Magnetic Imager (HMI) vector magnetogram data at three different plate scales for three solar active regions to obtain nine NLFF model time series. From the NLFF models, we deduce active-region magnetic fluxes, electric currents, magnetic energies, and relative helicities, and analyze those with respect to the underlying spatial sampling. We calculate various metrics to quantify the quality of the derived NLFF models and apply a Helmholtz decomposition to characterize solenoidal errors. Results. At a given spatial sampling, the quality of NLFF modeling is different for different ARs, and the quality varies along the individual model time series. For a given AR, modeling at a certain spatial sampling is not necessarily of superior quality compared to that performed with a different plate scale. Generally, the NLFF model quality tends to be higher for larger pixel sizes with the solenoidal quality being the ultimate cause for systematic variations in model-deduced physical quantities. Conclusions. Optimization-based modeling using SDO/HMI vector data binned to larger pixel sizes yields variations in magnetic energy and helicity estimates of ≲30% on overall, given that concise checks ensure the physical plausibility and high solenoidal quality of the tested model. Spatial-sampling-induced differences are relatively small compared to those arising from other sources of uncertainty, including the effects of applying different data calibration methods, those of using vector data from different instruments, or those arising from application of different NLFF methods to identical input data.

Changes in the Near-surface Shear Layer of the Sun

Abstract We use helioseismic data obtained over two solar cycles to determine whether there are changes in the near-surface shear layer (NSSL). We examine this by determining the radial gradient of the solar rotation rate. The radial gradient itself shows a solar-cycle dependence, and the changes are more pronounced in the active latitudes than at adjoining higher latitudes; results at the highest latitudes (≳70°) are unreliable. The pattern changes with depth, even within the NSSL. We find that the near-surface shear layer is deeper at lower latitudes than at high latitudes and that the extent of the layer also shows a small solar-cycle-related change.

Long-term evolution of magnetic fields in flaring Active Region NOAA 12673

During the lifetime of AR 12673, its magnetic field evolved drastically and produced numerous large flares. In this study, using full maps of the Sun observed by the Solar Dynamics Observatory and the Solar Terrestrial Relations Observatory, we identified that AR 12673 emerged in decayed AR 12665, which had survived for two solar rotations. Although both ARs emerged at the same location, they possessed different characteristics and different flare productivities. Therefore, it is important to study the long-term magnetic evolution of both ARs to identify the distinguishing characteristics of an AR that can produce large solar flares. We used the Space-weather Helioseismic and Magnetic Imager Active Region Patch data to investigate the evolution of the photospheric magnetic field and other physical properties of the recurring ARs during five Carrington rotations. All these investigated parameters dynamically evolved through a series of solar rotations. We compared the long-term evolution of AR 12665 and AR 12673 to understand the differences in their flare-producing properties. We also studied the relation of the long-term evolution of these ARs with the presence of active longitude. We found that the magnetic flux and complexity of AR 12673 developed much faster than those of AR 12665. Our results confirmed that a strong emerging flux that emerged in the pre-existing AR near the active longitude created a very strong and complex AR that produced large flares.

Multiple CNN Variants and Ensemble Learning for Sunspot Group Classification by Magnetic Type

Abstract A solar active region is a source of disturbance for the Sun–terrestrial space environment and usually causes extreme space weather, such as geomagnetic storms. The main indicator of an active region is sunspots. Certain types of sunspots are related to extreme space weather caused by eruptive events such as coronal mass ejections or solar flares. Thus, the automatic classification of sunspot groups is helpful to predict solar activity quickly and accurately. This paper completed the automatic classification of a sunspot group data set based on the Mount Wilson classification scheme, which contains continuum and magnetogram images provided by the Solar Dynamics Observatory’s Helioseismic and Magnetic Imager SHARP data from 2010 May 1 to 2017 December 12. After applying some data preprocessing steps such as image cropping and data standardization, the features of magnetic type in the data are more obvious, and the amount of data is increased. The processed data are spliced into two frames of single-channel data for the neural network to perform 3D convolution operations. This paper constructs a variety of convolutional neural networks with different structures and numbers of layers, selects 10 models as representatives, and chooses XGBoost, which is commonly used in ensemble-learning algorithms, to fuse the results of independent classification models. We found that XGBoost is an effective way to fuse models, which is proved by the relatively balanced high scores in the three magnetic types. The accuracy of the ensemble model is above 92%. The F1 scores of the magnetic types of Alpha, Beta, and Beta-x reached 0.95, 0.91, and 0.82 respectively.

Evidence of Solar-cycle-related Structural Changes in the Solar Convection Zone

Abstract While it has been relatively easy to determine solar-cycle related changes in solar dynamics, determining changes in structure in the deeper layers of the Sun has proved to be difficult. By using helioseismic data obtained over two solar cycles, and sacrificing resolution in favor of lower uncertainties, we show that there are significant changes in the solar convection zone, and perhaps even below it. Using Michelson Doppler Imager (MDI) data, we find a relative squared sound-speed difference of (2.56 ± 0.71) × 10−5 at the convection-zone base between the maximum of solar Cycle 23 and the minimum between Cycles 23 and 24. The squared sound-speed difference for the maximum of Cycle 24 obtained with Helioseismic and Magnetic Imager (HMI) data is (1.95 ± 0.69) × 10−5. Global Oscillation Network Group (GONG) data support these results. We also find that the sound speed in the solar convection zone decreases compared to the sound speed in the layers below it as the Sun becomes more active. We find evidence of changes in the radial derivative of the sound-speed difference between the solar minimum and other epochs at the base of the convection zone, implying possible small changes in the position of the convection-zone base; however, the results are too noisy to make any definitive estimates of the change.

Detection of Rossby modes with even azimuthal orders using helioseismic normal-mode coupling

Context. Retrograde Rossby waves, measured to have significant amplitudes in the Sun, likely have notable implications for various solar phenomena. Aims. Rossby waves create small-amplitude, very-low frequency motions, on the order of the rotation rate and lower, which in turn shift the resonant frequencies and eigenfunctions of the acoustic modes of the Sun. The detection of even azimuthal orders Rossby modes using mode coupling presents additional challenges and prior work therefore only focused on odd orders. Here, we successfully extend the methodology to measure even azimuthal orders as well. Methods. We analyze 4 and 8 years of Helioseismic and Magnetic Imager (HMI) data and consider coupling between different-degree acoustic modes (of separations 1 and 3 in the harmonic degree). The technique uses couplings between different frequency bins to capture the temporal variability of the Rossby modes. Results. We observe significant power close to the theoretical dispersion relation for sectoral Rossby modes, where the azimuthal order is the same as the harmonic degree, s = |t|. Our results are consistent with prior measurements of Rossby modes with azimuthal orders over the range t = 4 to 16 with maximum power occurring at mode t = 8. The amplitudes of these modes vary from 1 to 2 m s−1. We place an upper bound of 0.2 m s−1 on the sectoral t = 2 mode, which we do not detect in our measurements. Conclusions. This effort adds credence to the mode-coupling methodology in helioseismology.