Time-distance Helioseismology Research Articles

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.

Constraining Global Solar Models through Helioseismic Analysis

Global hydrodynamic simulations of internal solar dynamics have focused on replicating the conditions for solar-like (equator rotating faster than the poles) 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 help address 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 multicell 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.

Analysis of Time–Distance Helioseismology for Detection of Emerging Active Regions

Abstract A time–distance helioseismic technique, similar to the one used by Ilonidis et al., 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 and the Helioseismic Magnetic Imager. 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.

Helioseismological determination of the subsurface spatial spectrum of solar convection: Demonstration using numerical simulations

Context. Understanding convection is important in stellar physics, for example, when it is an input in stellar evolution models. Helioseismic estimates of convective flow amplitudes in deeper regions of the solar interior disagree by orders of magnitude among themselves and with simulations. Aims. We aim to assess the validity of an existing upper limit of solar convective flow amplitudes at a depth of 0.96 solar radii obtained using time-distance helioseismology and several simplifying assumptions. Methods. We generated synthetic observations for convective flow fields from a magnetohydrodynamic simulation (MURaM) using travel-time sensitivity functions and a noise model. We compared the estimates of the flow amplitude with the actual value of the flow. Results. For the scales of interest (ℓ < 100), we find that the current procedure for obtaining an upper limit gives the correct order of magnitude of the flow for the given flow fields. We also show that this estimate is not an upper limit in a strict sense because it underestimates the flow amplitude at the largest scales by a factor of about two because the scale dependence of the signal-to-noise ratio has to be taken into account. After correcting for this and after taking the dependence of the measurements on direction in Fourier space into account, we show that the obtained estimate is indeed an upper limit. Conclusions. We conclude that time-distance helioseismology is able to correctly estimate the order of magnitude (or an upper limit) of solar convective flows in the deeper interior when the vertical correlation function of the different flow components is known and the scale dependence of the signal-to-noise ratio is taken into account. We suggest that future work should include information from different target depths to better separate the effect of near-surface flows from those at greater depths. In addition, the measurements are sensitive to all three flow directions, which should be taken into account.

Evolution of Subsurface Zonal and Meridional Flows in Solar Cycle 24 from Helioseismological Data

Abstract The results of determinations of the azimuthal and meridional velocities by time–distance helioseismology from Helioseismic and Magnetic Imager on board Solar Dynamics Observatory from 2010 May to 2020 September at latitudes and Stonyhurst longitudes from − 60° to + 60° 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 toward 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 Solar 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 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.

Plasma flows and sound-speed perturbations in the average supergranule

Context. Supergranules create a peak in the spatial spectrum of photospheric velocity features. Even though they have some properties of convection cells, their origin is still being debated in the literature. The time–distance helioseismology constitutes a method that is suitable for investigating the deep structure of supergranules. Aims. Our aim is to construct the model of the flows in the average supergranular cell using fully consistent time–distance inverse methodology. Methods. We used the Multi-Channel Subtractive Optimally Localised Averaging inversion method with regularisation of the cross-talk. We combined the difference and the mean travel-time averaging geometries. We applied this methodology to travel-time maps averaged over more than 104 individual supergranular cells. These cells were detected automatically in travel-time maps computed for 64 quiet days around the disc centre. The ensemble averaging method allows us to significantly improve the signal-to-noise ratio and to obtain a clear picture of the flows in the average supergranule. Results. We found near-surface divergent horizontal flows which quickly and monotonously weakened with depth; they became particularly weak at the depth of about 7 Mm, where they even apparently switched sign. The amplitude of the ‘reversed’ flow was comparable to the background flows. The inverted vertical flows and sound-speed perturbations were spoiled by unknown systematic errors. To learn about the vertical component, we integrated the continuity equation from the surface. The derived estimates of the vertical flow depicted a sub-surface increase from about 5 m s−1 at the surface to about 35 m s−1 at the depth of about 3 Mm followed by a monotonous decrease to greater depths. The vertical flow remained positive (an upflow) and became indistinguishable from the background at the depth of about 15 Mm. We further detected a systematic flow in the longitudinal direction. The course of this systematic flow with depth agrees well with the model of the solar rotation in the sub-surface layers.

Probabilistic Inversions for Time–Distance Helioseismology

Time-distance helioseismology is a set of powerful tools to study features below the Sun's surface. Inverse methods are needed to interpret time-distance measurements, with many examples in the literature. However, techniques that utilize a more statistical approach to inferences, and broadly used in the astronomical community, are less-commonly found in helioseismology. This article aims to introduce a potentially powerful inversion scheme based on Bayesian probability theory and Monte Carlo sampling that is suitable for local helioseismology. We describe the probabilistic method and how it is conceptually different from standard inversions used in local helioseismology. Several example calculations are carried out to compare and contrast the setup of the problems and the results that are obtained. The examples focus on two important phenomena studied with helioseismology: meridional circulation and supergranulation. Numerical models are used to compute synthetic observations, providing the added benefit of knowing the solution against which the results can be tested. For demonstration purposes, the problems are formulated in two and three dimensions, using both ray- and Born-theoretical approaches. The results seem to indicate that the probabilistic inversions not only find a better solution with much more realistic estimation of the uncertainties, but they also provide a broader view of the range of solutions possible for any given model, making the interpretation of the inversion more quantitative in nature. Unlike the progress being made in fundamental measurement schemes in local helioseismology that image the far side of the Sun, or have detected signatures of global Rossby waves, among many others, inversions of those measurements have had significantly less success. Such statistical methods may help overcome some of these barriers to move the field forward.

Evolution of photospheric flows under an erupting filament in the quiet-Sun region

Context. We studied the dynamics of the solar atmosphere in the region of a large quiet-Sun filament, which erupted on 21 October 2010. The filament eruption started at its northern end and disappeared from the Hα line-core filtergrams line within a few hours. The very fast motions of the northern leg were recorded in ultraviolet light by the Atmospheric Imaging Assembly (AIA) imager. Aims. We aim to study a wide range of available datasets describing the dynamics of the solar atmosphere for five days around the filament eruption. This interval covers three days of the filament evolution, one day before the filament growth and one day after the eruption. We search for possible triggers that lead to the eruption of the filament. Methods. The surface velocity field in the region of the filament were measured by means of time–distance helioseismology and coherent structure tracking. The apparent velocities in the higher atmosphere were estimated by tracking the features in the 30.4 nm AIA observations. To capture the evolution of the magnetic field, we extrapolated the photospheric line-of-sight magnetograms and also computed the decay index of the magnetic field. Results. We found that photospheric velocity fields showed some peculiarities. Before the filament activation, we observed a temporal increase of the converging flows towards the filament’s spine. In addition, the mean squared velocity increased temporarily before the activation and peaked just before it, followed by a steep decrease. We further see an increase in the average shear of the zonal flow component in the filament’s region, followed by a steep decrease. The photospheric line-of-sight magnetic field shows a persistent increase of induction eastward from the filament spine. The decay index of the magnetic field at heights around 10 Mm shows a value larger than critical one at the connecting point of the northern filament end. The value of the decay index increases monotonically there until the filament activation. Then, it decreased sharply.

Characterizing the spatial pattern of solar supergranulation using the bispectrum

Context. The spatial power spectrum of supergranulation does not fully characterize the underlying physics of turbulent convection. For example, it does not describe the non-Gaussianity in the horizontal flow divergence. Aims. Our aim is to statistically characterize the spatial pattern of solar supergranulation beyond the power spectrum. The next-order statistic is the bispectrum. It measures correlations of three Fourier components and is related to the nonlinearities in the underlying physics. It also characterizes how a skewness in the dataset is generated by the coupling of three Fourier components. Methods. We estimated the bispectrum of supergranular horizontal surface divergence maps that were obtained using local correlation tracking (LCT) and time-distance helioseismology (TD) from one year of data from the helioseismic and magnetic imager on-board the solar dynamics observatory starting in May 2010. Results. We find significantly nonzero and consistent estimates for the bispectrum using LCT and TD. The strongest nonlinearity is present when the three coupling wave vectors are at the supergranular scale. These are the same wave vectors that are present in regular hexagons, which have been used in analytical studies of solar convection. At these Fourier components, the bispectrum is positive, consistent with the positive skewness in the data and consistent with supergranules preferentially consisting of outflows surrounded by a network of inflows. We use the bispectral estimates to generate synthetic divergence maps that are very similar to the data. This is done by a model that consists of a Gaussian term and a weaker quadratic nonlinear component. Using this method, we estimate the fraction of the variance in the divergence maps from the nonlinear component to be of the order of 4–6%. Conclusions. We propose that bispectral analysis is useful for understanding the dynamics of solar turbulent convection, for example for comparing observations and numerical models of supergranular flows. This analysis may also be useful to generate synthetic flow fields.

Investigation of Surface Effects of Simple Flux Tubes Using Numerical Simulations

Abstract We use the SPARC code for MHD simulations with monolithic flux tubes of varying subsurface topology. Our studies involve the interactions of waves caused by a single source with subsurface magnetic fields. Mode conversion causing acoustic power to trickle downwards along the flux tube has been described before and can be visualized in our simulations. We show that this downward propagation causes the flux tube to act as an isolated source, creating a characteristic surface wave field. Measuring this wave field at the surface reveals subsurface properties of the magnetic field topology. Using time–distance helioseismology, we demonstrate how to detect such a flux tube signal based on a group travel time delay of Δt = 282.6 s due to the wave packet spending time subsurface as a slow mode wave. Although the amplitude is small and generally superimposed by the full wave field, it can be detected if assumptions about Δt are made. We demonstrate this for a simulation with solar-like sources. This kind of study has the potential to reveal subsurface information of sunspots based on the analysis of a surface signal.

A Time–Distance Helioseismology Method for Quasi-Linear Geometries

Helioseismology is the study of the solar interior, through which we extract flow and wave-speed information from Doppler velocity observations at the surface. Local helioseismology involves the study of small regions on the solar disk and is used to create a detailed picture of the interior in that particular region. Perturbations in the flow and wave-speed results indicate, e.g. magnetic-flux or temperature variations. There are multiple methods used in local-helioseismic research, but all current local-helioseismic techniques assume a point-source perturbation. For this study, we develop a new time–distance (TD) helioseismic methodology that can exploit the quasi-linear geometry of an elongated feature, allowing us to i) improve the signal-to-noise ratio of the TD results, and ii) greatly decrease the number of calculations required and therefore the computing time of the TD analysis. Ultimately, the new method will allow us to investigate solar features with magnetic-field configurations previously unexplored. We validate our new technique using a simple $f$-mode wave simulation, comparing results of point-source and linear perturbations. Results indicate that local-helioseismic analysis is dependent on the geometry of the system and can be improved by taking the magnetic-field configuration into account.

Time-distance helioseismology of solar Rossby waves

Context. Solar Rossby waves (r modes) have recently been discovered in the near-surface horizontal flow field using the techniques of granulation-tracking and ring-diagram analysis applied to six years of SDO/HMI data. Aims. Here we apply time-distance helioseismology to the combined SOHO/MDI and SDO/HMI data sets, which cover 21 years of observations from May 1996 to April 2017. The goal of this study is to provide an independent confirmation over two solar cycles and in deeper layers of the Sun. Methods. We have measured south-north helioseismic travel times along the equator, which are sensitive to subsurface north-south flows. To reduce noise, the travel times were averaged over travel distances from 6° to 30°; the mean distance corresponds to a p-mode lower turning point of 0.91 R⊙. The 21-year time series of travel-time measurements was split into three seven-year subsets and transformed to obtain power spectra in a corotating frame. Results. The power spectra all show peaks near the frequencies of the classical sectoral Rossby waves for azimuthal wavenumbers in the range 3 ≤ m ≤ 15. The mode frequencies and linewidths of the modes with m ≤ 9 are consistent with a previous study whereas modes with m ≥ 10 are shifted toward less negative frequencies by 10–20 nHz. While most of these modes have e-folding lifetimes on the order of a few months, the longest lived mode, m = 3, has an e-folding lifetime of more than one year. For each mode, the rms velocity at the equator is in the range of 1–3 m s−1, with the largest values for m ∼ 10. No evidence for the m = 2 sectoral mode is found in the power spectrum, implying that the rms velocity of this mode is below ∼0.5 m s−1. Conclusions. This work confirms the existence of equatorial global Rossby waves in the solar interior over the past two solar cycles and shows that time-distance helioseismology is a promising technique to study them deep in the convection zone.

Combined helioseismic inversions for 3D vector flows and sound-speed perturbations

Context. Time–distance helioseismology is the method of the study of the propagation of waves through the solar interior via the travel times of those waves. The travel times of wave packets contain information about the conditions in the interior integrated along the propagation path of the wave. The travel times are sensitive to perturbations of a variety of quantities. The usual task is to invert for the vector of plasma flows or the sound–speed perturbations separately. The separate inversions may be polluted by systematic bias, for instance, originating in the leakage of vector flows into the sound–speed perturbations and vice versa (called a cross-talk). Information about the cross-talk is necessary for a proper interpretation of results. Aims. We introduce an improved methodology of the time-distance helioseismology which allows us to invert for a full 3D vector of plasma flows and the sound–speed perturbations at once. Using this methodology one can also derive the mean value of the vertical component of plasma flows and the cross-talk between the plasma flows and the sound–speed perturbations. Methods. We used the Subtractive Optimally Localised Averaging method with a minimisation of the cross-talk as a tool for inverse modelling. In the forward model, we use Born approximation travel-time sensitivity kernels with the Model S as a background. The methodology was validated using forward-modelled travel times with both mean and difference point-to-annulus averaging geometries applied to a snapshot of fully self-consistent simulation of the convection. Results. We tested the methodology on synthetic data. We demonstrate that we are able to recover flows and sound–speed perturbations in the near-surface layers. We have taken the advantage of the sensitivity of our methodology to entire vertical velocity, and not only to its variations as in other available methodologies. The cross-talk from both the vertical flow component and the sound–speed perturbation has only a negligible effect for inversions for the horizontal flow components. Furthermore, this cross-talk can be minimised if needed. The inversions for the vertical component of the vector flows or for the sound–speed perturbations are affected by the cross-talk from the horizontal components, which needs to be minimised in order to provide valid results. It seems that there is a nearly constant cross-talk between the vertical component of the vector flows and the sound–speed perturbations.

Detection of Rossby Waves in the Sun using Normal-mode Coupling

Abstract Rossby waves play a fundamental role in angular momentum processes in rotating fluids. In addition to the potential to shed light on physical mechanisms operating in the solar convection zone, the recent detection of Rossby waves in the Sun also serves as a means of comparison between different helioseismic methods. Time–distance helioseismology, ring-diagram analysis, and other techniques have all proven successful in recovering the Rossby-wave dispersion relation from analyses of Helioseismic and Magnetic Imager data (HMI). In this article, we demonstrate that analyses of two years of HMI global-mode-oscillation data using the technique of normal-mode coupling also show signatures of Rossby waves. In addition to providing an independent means of inferring Rossby waves, this detection lends credence to the methodology of mode coupling and encourages a more complete exploration of its possibilities.

Signal and noise in helioseismic holography

Context. Helioseismic holography is an imaging technique used to study heterogeneities and flows in the solar interior from observations of solar oscillations at the surface. Holographic images contain noise due to the stochastic nature of solar oscillations. Aims. We aim to provide a theoretical framework for modeling signal and noise in Porter–Bojarski helioseismic holography. Methods. The wave equation may be recast into a Helmholtz-like equation, so as to connect with the acoustics literature and define the holography Green’s function in a meaningful way. Sources of wave excitation are assumed to be stationary, horizontally homogeneous, and spatially uncorrelated. Using the first Born approximation we calculated holographic images in the presence of perturbations in sound-speed, density, flows, and source covariance, as well as the noise level as a function of position. This work is a direct extension of the methods used in time-distance helioseismology to model signal and noise. Results. To illustrate the theory, we compute the holographic image intensity numerically for a buried sound-speed perturbation at different depths in the solar interior. The reference Green’s function is obtained for a spherically-symmetric solar model using a finite-element solver in the frequency domain. Below the pupil area on the surface, we find that the spatial resolution of the holographic image intensity is very close to half the local wavelength. For a sound-speed perturbation of size comparable to the local spatial resolution, the signal-to-noise ratio is approximately constant with depth. Averaging the image intensity over a number N of frequencies above 3 mHz increases the signal-to-noise ratio by a factor nearly equal to the square root of N. This may not be the case at lower frequencies, where large variations in the holographic signal are due to the contributions from the long-lived modes of oscillation.

Solar meridional circulation from twenty-one years of SOHO/MDI and SDO/HMI observations

Context. The solar meridional flow is an essential ingredient in flux-transport dynamo models. However, no consensus on its subsurface structure has been reached.Aims. We merge the data sets from SOHO/MDI and SDO/HMI with the aim of achieving a greater precision on helioseismic measurements of the subsurface meridional flow.Methods. The south-north travel-time differences are measured by applying time-distance helioseismology to the MDI and HMI medium-degree Dopplergrams covering May 1996–April 2017. Our data analysis corrects for several sources of systematic effects:P-angle error, surface magnetic field effects, and center-to-limb variations. For HMI data, we used theP-angle correction provided by the HMI team based on the Venus and Mercury transits. For MDI data, we used aP-angle correction estimated from the correlation of MDI and HMI data during the period of overlap. The center-to-limb effect is estimated from the east-west travel-time differences and is different for MDI and HMI observations. An interpretation of the travel-time measurements is obtained using a forward-modeling approach in the ray approximation.Results. In the latitude range 20°–35°, the travel-time differences are similar in the southern hemisphere for cycles 23 and 24. However, they differ in the northern hemisphere between cycles 23 and 24. Except for cycle 24’s northern hemisphere, the measurements favor a single-cell meridional circulation model where the poleward flows persist down to ∼0.8R⊙, accompanied by local inflows toward the activity belts in the near-surface layers. Cycle 24’s northern hemisphere is anomalous: travel-time differences are significantly smaller when travel distances are greater than 20°. This asymmetry between northern and southern hemispheres during cycle 24 was not present in previous measurements, which assumed a differentP-angle error correction where south-north travel-time differences are shifted to zero at the equator for all travel distances. In our measurements, the travel-time differences at the equator are zero for travel distances less than ∼30°, but they do not vanish for larger travel distances. This equatorial offset for large travel distances need not be interpreted as a deep cross-equator flow; it could be due to the presence of asymmetrical local flows at the surface near the end points of the acoustic ray paths.Conclusions. The combined MDI and HMI helioseismic measurements presented here contain a wealth of information about the subsurface structure and the temporal evolution of the meridional circulation over 21 years. To infer the deep meridional flow, it will be necessary to model the contribution from the complex time-varying flows in the near-surface layers.

Evolution and wave-like properties of the average solar supergranule

Context. Solar supergranulation presents us with many mysteries. For example, previous studies in spectral space have found that supergranulation has wave-like properties. Aims. Here we study, in real space, the wave-like evolution of the average supergranule over a range of spatial scales (from 10 to 80 Mm). We complement this by characterizing the evolution of the associated network magnetic field. Methods. We used one year of data from the Helioseismic and Magnetic Imager (HMI) onboard the Solar Dynamics Observatory to measure horizontal near-surface flows near the solar equator by applying time-distance helioseismology (TD) on Dopplergrams and granulation tracking (LCT) on intensity images. The average supergranule outflow (or inflow) was constructed by averaging over 10 000 individual outflows (or inflows). The contemporaneous evolution of the magnetic field was studied with HMI line-of-sight observations. Results. We confirm and extend previous measurements of the supergranular wave dispersion relation to angular wavenumbers in the range 50 < kR⊙ < 270. We find a plateau for kR⊙ > 120. In real space, larger supergranules undergo oscillations with longer periods and lifetimes than smaller cells. We find excellent agreement between TD and LCT and obtain wave properties that are independent of the tracking rate. The observed network magnetic field follows the oscillations of the supergranular flows with a six-hour time lag. This behavior can be explained by computing the motions of corks carried by the supergranular flows. Conclusions. Signatures of supergranular waves in surface horizontal flows near the solar equator can be observed in real space. These oscillatory flows control the evolution of the network magnetic field, in particular they explain the recently discovered east-west anisotropy of the magnetic field around the average supergranule. Background flow measurements that we obtain from Doppler frequency shifts do not favor shallow models of supergranulation.

Effect of Magnetic Field Strength on Solar Differential Rotation and Meridional Circulation

Abstract We studied the solar surface flows (differential rotation and meridional circulation) using a magnetic element feature tracking technique by which the surface velocity is obtained using magnetic field data. We used the line-of-sight magnetograms obtained by the Helioseismic and Magnetic Imager on board the Solar Dynamics Observatory from 2010 May 01 to 2017 August 16 (Carrington rotations 2096 to 2193) and tracked the magnetic element features every hour. Using our method, we estimated the differential rotation velocity profile. We found rotation velocities of ∼30 and −170 m s−1 at latitudes of 0° and 60° in the Carrington rotation frame, respectively. Our results are consistent with previous results obtained by other methods, such as direct Doppler, time-distance helioseismology, or cross-correlation analyses. We also estimated the meridional circulation velocity profile and found that it peaked at ∼12 m s−1 at a latitude of 45°, which is also consistent with previous results. The dependence of the surface flow velocity on the magnetic field strength was also studied. In our analysis, the magnetic elements with stronger and weaker magnetic fields largely represent the characteristics of the active region remnants and solar magnetic networks, respectively. We found that magnetic elements with a strong (weak) magnetic field show a faster (slower) rotation speed. On the other hand, magnetic elements with a strong (weak) magnetic field show slower (faster) meridional circulation velocity. These results might be related to the Sun’s internal dynamics.

Observational Evidence of Shallow Origins for the Magnetic Fields of Solar Cycles

Observational evidence for the origin of active region magnetic fields has been sought from published information on extended solar cycles, statistical distributions of active regions and ephemeral regions, helioseismology results, positional relationships to supergranules, and fine-scale magnetic structure of active regions and their sunspots during their growth. Statistical distributions of areas of ephemeral and active regions blend together to reveal a single power law. The shape of the size distribution in latitude of all active regions is independent of time during the solar cycle, yielding further evidence that active regions of all sizes belong to the same population. Elementary bipoles, identified also by other names, appear to be the building blocks of active regions; sunspots form from elementary bipoles and are therefore deduced to develop from the photosphere downward, consistent with helioseismic detection of downflows to 3-4 Mm below sunspots as well as long-observed downflows from chromospheric/coronal arch filaments into sunspots from their earliest appearance. Time-distance helioseismology has been effective in revealing flows related to sunspots to depths of 20 Mm. Ring diagram analysis shows a statistically significant preference for upflows to precede major active region emergence and downflows after flux emergence but both are often observed together or sometimes not detected. From deep-focus helioseismic techniques for seeking magnetic flux below the photosphere prior major active regions, there is evidence of acoustic travel-time perturbation signatures rising in the limited range of depths of 42-75 Mm but these have not been verified or found at more shallow depths by helioseismic holographic techniques. The development of active regions from clusters of elementary bipoles appears to be the same irrespective of how much flux an active region eventually develops. This property would be consistent with the magnetic fields of large active regions being generated in the same way and close the same depth as small active regions in a shallow zone below the photosphere. All evidence considered together, understanding the origins of the magnetic fields of solar cycles boils down to learning how and where elementary bipoles are generated beneath the photosphere.

Probing sunspots with two-skip time–distance helioseismology

Context.Previous helioseismology of sunspots has been sensitive to both the structural and magnetic aspects of sunspot structure.Aims.We aim to develop a technique that is insensitive to the magnetic component so the two aspects can be more readily separated.Methods.We study waves reflected almost vertically from the underside of a sunspot. Time–distance helioseismology was used to measure travel times for the waves. Ray theory and a detailed sunspot model were used to calculate travel times for comparison.Results.It is shown that these large distance waves are insensitive to the magnetic field in the sunspot. The largest travel time differences for any solar phenomena are observed.Conclusions.With sufficient modeling effort, these should lead to better understanding of sunspot structure.