Recent Developments in Local Helioseismology

Local helioseismology is providing new views of subphotospheric flows from supergranulation to global-scale meridional circulation and for studying structures and dynamics in the quiet Sun and active regions. In this short review we focus on recent developments, and in particular on a number of current issues, including the sensitivity of different measures of travel time and testing the forward modelling used in local helioseismology. We discuss observational and theoretical concerns regarding the adequacy of current analyses of waves in sunspots and active regions, and we report on recent progress in the use of numerical simulations to test local helioseismic methods.     

Can variable meridional flows lead to false exoplanet detections?

The search for habitable exoplanets centers on planets with Earth-like conditions around late type stars. Radial velocity searches for these planets require precisions of 1 m/s and better. That is now being achieved. At these precisions stellar surface motions might lead to false detections. Of particular interest are variable meridional flows on stellar surfaces. I review the available observations of solar surface meridional flows using both Doppler shift and local helioseismology techniques. Interpretation in terms of Doppler shifts in integrated starlight leads to estimates of the likelihood of false detections. It is unlikely that these false detections occur in the habitability zones of exoplanets. (© 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Effects of Foreshortening on Shallow Sub-surface Flows Observed with Local Helioseismology

From the results given in a recent paper by Zaatri et al. (2006, Solar Phys. 236, 227) it is clear that foreshortening effects play a major role in estimating the magnitude and direction of meridional and other flows in the shallow solar sub-surface layers using local helioseismology. Using a different algorithm to account for these effects I arrive at a significantly different estimate for the meridional flows.     

Configurations of dynamo waves in a two-layer medium and the 11-year solar cycle

The behavior of dynamo waves in a two-layer medium is investigated in terms of the Parker dynamo model. The solar cycle duration is shown to depend on the ratio of turbulent diffusivities in the layers. Meridional circulation has been incorporated into the Parker system. An increase in the intensity of meridional flows is shown to decelerate the propagation of dynamo waves. The minimum of solar magnetic activity can occur not only in the case of intense meridional circulation in both layers but also when a difference in physical characteristics arises between the layers and the meridional flows are moderate.     

Helioseismology and the solar cycle: Past, present and future

A major goal of helioseismology is to understand the mechanism of the solar cycle. In this paper, some results of helioseismic observations relevant to the cycle are briefly reviewed, the current state-of-the-art is discussed, and near-term future directions are sketched out. Topics covered include the internal rotation rate; activity-related parameter variations; the tachocline; far-side imaging; the torsional oscillation; and meridional flows.     

Subsurface Meridional Circulation in the Active Belts

Temporal variations of the subsurface meridional flow with the solar cycle have been reported by several authors. The measurements are typically averaged over periods of time during which surface magnetic activity existed in the regions where the velocities are calculated. The present work examines the possible contamination of these measurements due to the extra velocity fields associated with active regions plus the uncertainties in the data obtained where strong magnetic fields are present. We perform a systematic analysis of more than five years of GONG data and compare meridional flows obtained by ring-diagram analysis before and after removing the areas of strong magnetic field. The overall trend of increased amplitude of the meridional flow towards solar minimum remains after removal of large areas associated with surface activity. We also find residual circulation toward the active belts that persists even after the removal of the surface magnetic activity, suggesting the existence of a global pattern or longitudinally-located organized flows.     

Formation of polar starspots through meridional circulation

To explain the observed intermingling of polarities in the magnetic field distributions of rapidly rotating stars, surface magnetic flux transport models demand the presence of fast meridional flows.We combine simulations of the pre-eruptive and post-eruptive magnetic flux transport in cool stars to investigate the influence of a fast meridional circulation on the latitudinal eruption pattern of magnetic flux tubes and on the polar magnetic field properties. Magnetic flux tubes rising through the convection zone experience an enhanced latitude-dependent poleward deflection through meridional flows, which renders the wings of stellar butterfly diagrams convex. The larger amount of magnetic flux emerging at higher latitudes supports the intermingling of opposite polarities of polar magnetic fields and yields magnetic flux densities in the polar regions about 20% higher than in the case disregarding the pre-eruptive deflection. Taking the pre-eruptive evolution of magnetic flux into account therefore eases the need for the fast meridional flows predicted by previous investigations. (© 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Large-Scale Zonal Flows Near the Solar Surface

Migrating bands of weak, zonal flow, associated with the activity bands in the solar cycle, have been observed at the solar surface for some time. More recently, these flows have been probed deep within the convection zone using global helioseismology and examined in more detail close to the surface with the techniques of local helioseismology. We compare the near-surface results from global and local helioseismology using data from the Michelson Doppler Imager and the Global Oscillation Network Group with surface Doppler velocity measurements from the Mount Wilson 150-foot tower and find that the results are in reasonable agreement, with some explicable differences in detail. All of the data sets show zones of faster rotation approaching the equator from mid-latitudes during the solar cycle, with a variation at any given location that can be approximately, but not completely, described by a single sinusoid and an amplitude that does not drop off steeply below the surface.     

Comparison of Large-Scale Flows on the Sun Measured by Time-Distance Helioseismology and Local Correlation Tracking

We present a direct comparison between two different techniques: time-distance helioseismology and a local correlation tracking method for measuring mass flows in the solar photosphere and in a near-surface layer. We applied both methods to the same dataset (MDI high-cadence Dopplergrams covering almost the entire Carrington rotation 1974) and compared the results. We found that, after necessary corrections, the vector flow fields obtained by these techniques are very similar. The median difference between directions of corresponding vectors is 24°, and the correlation coefficients of the results for mean zonal and meridional flows are 0.98 and 0.88, respectively. The largest discrepancies are found in areas of small velocities where the inaccuracies of the computed vectors play a significant role. The good agreement of these two methods increases confidence in the reliability of large-scale synoptic maps obtained by them.     

Coherence of Coronal Mass Ejections in Near-Earth Space

Time–distance helioseismology is a set of powerful tools to study localized features below the Sun’s surface. Inverse methods are needed to robustly interpret time–distance measurements, with many examples in the literature. However, techniques that utilize a more statistical approach to inferences, and that are 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 first 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 that are currently outstanding issues in 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. The probabilistic inversions are also easy to set up for a broad range of problems, and they can take advantage of software that is publicly available. 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.

     

Origin of the torsional oscillation pattern of solar rotation

A model is presented that explains the `torsional oscillation' pattern of deviations in the solar rotation rate as a geostrophic flow. The flow is driven by temperature variations near the surface due to the enhanced emission of radiation by the small-scale magnetic field. The model explains the sign of the flow, its amplitude and the fact that the maxima occur near the boundaries of the main activity belts. The amplitude of the flow decreases with depth from its maximum at the surface but penetrates over much of the depth of the convection zone, in agreement with the data from helioseismology. It predicts that the flow is axisymmetric only on average, and in reality consists of a superposition of circulations around areas of enhanced magnetic activity. It must be accompanied by a meridional flow component, which declines more rapidly with depth.     

The impact of meridional circulation on stellar butterfly diagrams and polar caps

Observations of rapidly rotating solar-like stars show a significant mixture of opposite-polarity magnetic fields within their polar regions. To explain these observations, models describing the surface transport of magnetic flux demand the presence of fast meridional flows. Here, we link subsurface and surface magnetic flux transport simulations to investigate (i) the impact of meridional circulations with peak velocities of  ≤125 m s⁻¹  on the latitudinal eruption pattern of magnetic flux tubes and (ii) the influence of the resulting butterfly diagrams on polar magnetic field properties. Prior to their eruption, magnetic flux tubes with low field strengths and initial cross-sections below  ∼300 km  experience an enhanced poleward deflection through meridional flows (assumed to be polewards at the top of the convection zone and equatorwards at the bottom). In particular, flux tubes which originate between low and intermediate latitudes within the convective overshoot region are strongly affected. This latitude-dependent poleward deflection of erupting magnetic flux renders the wings of stellar butterfly diagrams distinctively convex. The subsequent evolution of the surface magnetic field shows that the increased number of newly emerging bipoles at higher latitudes promotes the intermingling of opposite polarities of polar magnetic fields. The associated magnetic flux densities are about 20 per cent higher than in the case disregarding the pre-eruptive deflection, which eases the necessity for fast meridional flows predicted by previous investigations. In order to reproduce the observed polar field properties, the rate of the meridional circulation has to be of the order of 100 m s⁻¹, and the latitudinal range from which magnetic flux tubes originate at the base of the convective zone (≲50°) must be larger than in the solar case (≲35°).     

Local Helioseismology of Sunspots: Current Status and Perspectives

Mechanisms of the formation and stability of sunspots are among the longest-standing and intriguing puzzles of solar physics and astrophysics. Sunspots are controlled by subsurface dynamics, hidden from direct observations. Recently, substantial progress in our understanding of the physics of the turbulent magnetized plasma in strong-field regions has been made by using numerical simulations and local helioseismology. Both the simulations and helioseismic measurements are extremely challenging, but it is becoming clear that the key to understanding the enigma of sunspots is a synergy between models and observations. Recent observations and radiative MHD numerical models have provided a convincing explanation for the Evershed flows in sunspot penumbrae. Also, they lead to the understanding of sunspots as self-organized magnetic structures in the turbulent plasma of the upper convection zone, which are maintained by a large-scale dynamics. Local helioseismic diagnostics of sunspots still have many uncertainties, some of which are discussed in this review. However, there have been significant achievements in resolving these uncertainties, verifying the basic results by new high-resolution observations, testing the helioseismic techniques by numerical simulations, and comparing results obtained by different methods. For instance, a recent analysis of helioseismology data from the Hinode space mission has successfully resolved several uncertainties and concerns (such as the inclined-field and phase-speed filtering effects) that might affect the inferences of the subsurface wave-speed structure of sunspots and the flow pattern. It is becoming clear that for the understanding of the phenomenon of sunspots it is important to further improve the helioseismology methods and investigate the whole life cycle of active regions, from magnetic flux emergence to dissipation. The Solar Dynamics Observatory mission has started to provide data for such investigations.     

Predicting solar ‘climate’ by assimilating magnetic data into a flux-transport dynamo

Observational and theoretical knowledge about global-scale solar dynamo ingredients have reached the stage that it is possible to calibrate a flux-transport dynamo for the Sun by adjusting only a few tunable parameters. The important ingredients in this class of model are differential rotation (Omega-effect), helical turbulence (alpha-effect), meridional circulation and turbulent diffusion. The meridional circulation works as a conveyor belt and governs the dynamo cycle period. Meridional circulation and magnetic diffusivity together govern the memory of the Sun's past magnetic fields. After describing the physical processes involved in a flux-transport dynamo, we will show that a predictive tool can be built from it to predict mean solar cycle features by assimilating magnetic field data from previous cycles. We will discuss the theoretical and observational connections among various predictors, such as dynamo-generated toroidal flux integral, cross-equatorial flux, polar fields and geomagnetic indices. (© 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Time-Distance Helioseismology with f Modes as a Method for Measurement of Near-Surface Flows

Travel times measured for the f mode have been used to study flows near the solar surface in conjunction with simultaneous measurements of the magnetic field. Previous flow measurements of Doppler surface rotation, small magnetic feature rotation, supergranular pattern rotation, and surface meridional circulation have been confirmed. In addition, the flow in supergranules due to Coriolis forces has been measured. The spatial and temporal power spectra for a six-day observing sequence have been measured.     

Quenching of Meridional Circulation in Flux Transport Dynamo Models

Guided by the recent observational result that the meridional circulation of the Sun becomes weaker at the time of the sunspot maximum, we have included a parametric quenching of the meridional circulation in solar dynamo models such that the meridional circulation becomes weaker when the magnetic field at the base of the convection zone is stronger. We find that a flux transport solar dynamo tends to become unstable on including this quenching of meridional circulation if the diffusivity in the convection zone is less than about 2×10¹¹ cm² s⁻¹. The quenching of α, however, has a stabilizing effect and it is possible to stabilize a dynamo with low diffusivity with sufficiently strong α-quenching. For dynamo models with high diffusivity, the quenching of meridional circulation does not produce a large effect and the dynamo remains stable. We present a solar-like solution from a dynamo model with diffusivity 2.8×10¹² cm² s⁻¹ in which the quenching of meridional circulation makes the meridional circulation vary periodically with solar cycle as observed and does not have any other significant effect on the dynamo.     

Imaging bright-spots in the accretion flow near the black hole horizon of Sgr A*

Solar active regions are distinguished by their strong magnetic fields. Modern local helioseismology seeks to probe them by observing waves which emerge at the solar surface having passed through their interiors. We address the question of how an acoustic wave from below is partially converted to magnetic waves as it passes through a vertical magnetic field layer where the sound and Alfvén speeds coincide (the equipartition level), and find that (i) there is no associated reflection at this depth, either acoustic or magnetic, only transmission and conversion to an ongoing magnetic wave; and (ii) conversion in active regions is likely to be strong, though not total, at frequencies typically used in local helioseismology, with lower frequencies less strongly converted. A simple analytical formula is presented for the acoustic-to-magnetic conversion coefficient.     

A model of solar differential rotation

An axisymmetric model for the Sun's differential rotation based upon a mechanism for angular momentum transport by compressible convection is developed. Convective heat transport is also considered. The model is simplified by the neglect of meridional circulation and radiative heat transport but is otherwise a self-consistent one because no adjustable parameters are used and the effective transport coefficients are expressed explicitly in terms of superadiabaticity of stratification rather than assigned externally. The model predictions agree satisfactorily with the observed rotation of the photosphere and with helioseismology data. The dependence of the rotation law, produced by the model, on rotation rate of a Sun-like star is discussed.     

Latest Results Found with Ring-Diagram Analysis

Ring-diagram analysis is a helioseismic tool useful for studying the near-surface layers of the Sun. It has been employed to study near-surface shear, meridional circulation, flows around sunspots, and thermal structure beneath active regions. We review recent results obtained using ring-diagram analysis, state some of the more important outstanding difficulties in the technique, and point out several extensions to the technique that are just now beginning to bear fruit.     

Solar dynamo models with α ‐effect and turbulent pumping from local 3D convection calculations

Results from kinematic solar dynamo models employing α ‐effect and turbulent pumping from local convection calculations are presented. We estimate the magnitude of these effects to be around 2–3 m s^–1, having scaled the local quantities with the convective velocity at the bottom of the convection zone from a solar mixing‐length model. Rotation profile of the Sun as obtained from helioseismology is applied in the models; we also investigate the effects of the observed surface shear layer on the dynamo solutions. With these choices of the small‐ and large‐scale velocity fields, we obtain estimate of the ratio of the two induction effects, C _α /C _Ω ≈ 10^–3, which we keep fixed in all models. We also include a one‐cell meridional circulation pattern having a magnitude of 10–20 m s^–1 near the surface and 1–2 m s^–1 at the bottom of the convection zone. The model essentially represents a distributed turbulent dynamo, as the α ‐effect is nonzero throughout the convection zone, although it concentrates near the bottom of the convection zone obtaining a maximum around 30° of latitude. Turbulent pumping of the mean fields is predominantly down‐ and equatorward. The anisotropies in the turbulent diffusivity are neglected apart from the fact that the diffusivity is significantly reduced in the overshoot region. We find that, when all these effects are included in the model, it is possible to correctly reproduce many features of the solar activity cycle, namely the correct equatorward migration at low latitudes and the polar branch at high latitudes, and the observed negative sign of B _r B _ϕ . Although the activity clearly shifts towards the equator in comparison to previous models due to the combined action of the α ‐effect peaking at midlatitudes, meridional circulation and latitudinal pumping, most of the activity still occurs at too high latitudes (between 5° … 60°). Other problems include the relatively narrow parameter space within which the preferred solution is dipolar (A0), and the somewhat too short cycle lengths of the solar‐type solutions. The role of the surface shear layer is found to be important only in the case where the α ‐effect has an appreciable magnitude near the surface. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)