Dynamics and Structure of Supergranulation

In this paper we investigate the temporal evolution and geometric properties of solar supergranular features. For this purpose we apply an automatic feature-tracking algorithm to a 6-day time series of 18 near-surface flowmaps containing 548 target objects. Lifetimes are calculated by measuring the time elapsing between the birth and death of each target. Using an exponential fit on the lifetime distribution of single supergranules we derived a mean lifetime of 22 hours. Based on the application of segmentation numerical procedures, we estimated characteristic geometric parameters such as area distributions of supergranular cells. We also derive the relationship between measured lifetime and the area of the supergranules.     

Structure Properties of Supergranulation and Granulation

We investigate spatial dislocation ordering of the solar structures associated with supergranulation and granulation scales. The supergranular and granular structures are automatically segmented from time-distance divergence maps and from broad-band images, respectively. The spatial dislocation ordering analysis is accomplished by applying the statistical method of Pair Correlation Function, g ₂(r), to segmented features in the solar fields. We compare the computed g ₂(r) functions obtained from both single and persistent, i.e., time-averaged, fields associated with supergranulation and granulation. We conclude that supergranulation and granulation patterns present a different topological order both in single and persistent fields. The analysis carried out on single fields suggests that the granulation behaves as an essentially random distribution of soft plasma features with a very broad distribution in size, while supergranulation behaves as a random distribution of close packed, coherent stiff features with a rather defined mean size.     

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.     

Phase Jumps in Local Helioseismology

Helioseismic rays trapped in a nonmagnetic acoustic cavity suffer a +90° phase jump at their lower (Lamb) turning point and −90° at the upper (acoustic cutoff) reflection point. That the two cancel allows helioseismologists to effectively assume that phase is locally continuous along a ray path joining two surface points. However, in strong surface magnetic field, as found in sunspots, it is shown – for an isothermal model with uniform magnetic field – that the phase jump for fast magnetoacoustic rays that penetrate the acoustic/Alfvénic equipartition level (c=a) is around −120°. Moreover, there are further negative phase jumps on the upgoing and downgoing legs at c=a that add to the net phase change. Neglecting these effects can lead to a misinterpretation of helioseismic data in terms of travel-time shifts.     

On the Fractal Structure of Solar Supergranulation

We employ fractal analysis to study the complexity of supergranulation structure using the Solar and Heliospheric Observatory (SOHO) dopplergrams. Our data consists of 200 visually selected supergranular cells, for which we find a broad, slightly asymmetric dispersion in the size distribution, with the most probable size around 31.9 Mm. From the area–perimeter relation, we deduce a fractal dimension D of about 1.25. This is consistent with that for isobars, and suggests a possible turbulent origin of supergranulation. By relating this to the variances of kinetic energy, temperature and pressure, it is concluded that the supergranular network is close to being isobaric and that it has a possible turbulent origin.     

Multichannel Three-Dimensional SOLA Inversion for Local Helioseismology

Inversions for local helioseismology are an important and necessary step for obtaining three-dimensional maps of various physical quantities in the solar interior. Frequently, the full inverse problems that one would like to solve prove intractable because of computational constraints. Due to the enormous seismic data sets that already exist and those forthcoming, this is a problem that needs to be addressed. To this end, we present a very efficient linear inversion algorithm for local helioseismology. It is based on a subtractive optimally localized averaging (SOLA) scheme in the Fourier domain, utilizing the horizontal-translation invariance of the sensitivity kernels. In Fourier space the problem decouples into many small problems, one for each horizontal wave vector. This multichannel SOLA method is demonstrated for an example problem in time–distance helioseismology that is small enough to be solved both in real and Fourier space. We find that both approaches are successful in solving the inverse problem. However, the multichannel SOLA algorithm is much faster and can easily be parallelized.     

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.     

Constructing and Characterising Solar Structure Models for Computational Helioseismology

In local helioseismology, numerical simulations of wave propagation are useful to model the interaction of solar waves with perturbations to a background solar model. However, the solution to the linearised equations of motion include convective modes that can swamp the helioseismic waves that we are interested in. In this article, we construct background solar models that are stable against convection, by modifying the vertical pressure gradient of Model S (Christensen-Dalsgaard et al., 1996, Science 272, 1286) relinquishing hydrostatic equilibrium. However, the stabilisation affects the eigenmodes that we wish to remain as close to Model S as possible. In a bid to recover the Model S eigenmodes, we choose to make additional corrections to the sound speed of Model S before stabilisation. No stabilised model can be perfectly solar-like, so we present three stabilised models with slightly different eigenmodes. The models are appropriate to study the f and p ₁ to p ₄ modes with spherical harmonic degrees in the range from 400 to 900. Background model CSM has a modified pressure gradient for stabilisation and has eigenfrequencies within 2% of Model S. Model CSM_A has an additional 10% increase in sound speed in the top 1 Mm resulting in eigenfrequencies within 2% of Model S and eigenfunctions that are, in comparison with CSM, closest to those of Model S. Model CSM_B has a 3% decrease in sound speed in the top 5 Mm resulting in eigenfrequencies within 1% of Model S and eigenfunctions that are only marginally adversely affected. These models are useful to study the interaction of solar waves with embedded three-dimensional heterogeneities, such as convective flows and model sunspots. We have also calculated the response of the stabilised models to excitation by random near-surface sources, using simulations of the propagation of linear waves. We find that the simulated power spectra of wave motion are in good agreement with an observed SOHO/MDI power spectrum. Overall, our convectively stabilised background models provide a good basis for quantitative numerical local helioseismology. The models are available for download from http://www.mps.mpg.de/projects/seismo/NA4/ .     

What We Have Learned from Helioseismology

The Sun's global oscillations, which are studied both in spatially unresolved ("Sun-as-a-star") and resolved observations of the solar disk, have enabled helioseismology to probe in detail the solar interior. I review first what is learned from the unresolved measurements, since this gives an idea of what we may in the not too distant future be able to learn about the interiors of other stars undergoing solar-type oscillations. I then look at the main results from resolved observations, which have begun to reveal the structure and dynamics of the interior of a star in exquisite detail. This revised version was published online in July 2006 with corrections to the Cover Date.     

A Full-Sun Magnetic Index from Helioseismology Inferences

Solar magnetic indices are used to model the solar irradiance and ultimately to forecast it. However, the observation of such indices is generally limited to the Earth-facing hemisphere of the Sun. Seismic maps of the far side of the Sun have proven their capability to locate and track medium–large active regions at the non-visible hemisphere. We present here the possibility of using the average signal from these seismic far-side maps, combined with similarly calculated near-side maps, as a proxy to the full-Sun magnetic activity.     

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.     

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.     

Helioseismology and the solar interior dynamics

The inversion of helioseismic modes leads to the sound velocity inside the Sun with a precision of about 0.1 per cent. Comparisoons of solar models with the “seismic sun” represent powerful tools to test the physics: depth of the convection zone, equation of state, opacities, element diffusion processes and mixing inside the radiative zone. We now have evidence that microscopic diffusion (element segregation) does occur below the convection zone, leading to a mild helium depletion in the solar outer layers. Meanwhile this process must be slowed down by some macroscopic effect, presumably rotation-induced mixing. The same mixing is also responsible for the observed lithium depletion. On the other hand, the observations of beryllium and helium 3 impose specific constraints on the depth of this mildly mixed zone. Helioseismology also gives information on the internal solar rotation: while differential rotation exists in the convection zone, solid rotation prevails in the radiative zone, and the transition layer (the so-called “tachocline”) is very small. These effects are discussed, together with the astrophysical constraints on the solar neutrino fluxes.     

Structure and Evolution of White Dwarfs and their Interaction with the Local Interstellar Medium

The development of far-UV astronomy has been particularly important for the study of hot white dwarf stars. A significant fraction of their emergent flux appears in the far-UV and traces of elements heavier than hydrogen or helium are, in general, only detected in this waveband or at shorter wavelengths that are also only accessible from space. Although white dwarfs have been studied in the far-UV throughout the past ∼25 years, since the launch of IUE, only a few tens of objects have been studied in great detail and a much larger sample is required to gain a detailed understanding of the evolution of hot white dwarfs and the physical processes that determine their appearance. We review here the current knowledge regarding hot white dwarfs and outline what work needs to be carried out by future far-UV observatories.     

Tri-Phonic Helioseismology: Comparison of Solar p Modes Observed by the Helioseismology Instruments Aboard SOHO

The three helioseismology instruments aboard SOHO observe solar p modes in velocity (GOLF and MDI) and in intensity (VIRGO and MDI). Time series of two months duration are compared and confirm that the instruments indeed observe the same Sun to a high degree of precision. Power spectra of 108 days are compared showing systematic differences between mode frequencies measured in intensity and in velocity. Data coverage exceeds 97% for all the instruments during this interval. The weighted mean differences (V-I) are −0.1 μHz for l=0, and −0.16 μHz for l=1. The source of this systematic difference may be due to an asymmetry effect that is stronger for modes seen in intensity. Wavelet analysis is also used to compare the shape of the forcing functions. In these data sets nearly all of the variations in mode amplitude are of solar origin. Some implications for structure inversions are discussed.     

The Quest to Understand Supergranulation and Large-Scale Convection in the Sun

Surface granulation of the Sun is primarily a consequence of thermal transport in the outer 1 % of the radius. Its typical scale of about 1?–?2 Mm?is set by the balance between convection, free-streaming radiation, and the strong density stratification in the surface layers. The physics of granulation is well understood, as demonstrated by the close agreement between numerical simulation, theory, and observation. Superimposed on the energetic granular structure comprising high-speed flows, are larger-scale long-lived flow systems (≈?300 m?s^?1) called supergranules. Supergranulation has a typical scale of 24?–?36 Mm. It is not clear if supergranulation results from the interaction of granules or is causally linked to deep convection or a consequence of magneto–convection. Other outstanding questions remain: how deep are supergranules? How do they participate in global dynamics of the Sun? Further challenges are posed by our lack of insight into the dynamics of larger scales in the deep convection region. Recent helioseismic constraints have suggested that convective-velocity amplitudes on large scales may be overestimated by an order of magnitude or more, implying that Reynolds stresses associated with large-scale convection, thought to play a significant role in the sustenance of differential rotation and meridional circulation, might be two orders of magnitude weaker than theory and computation predict. While basic understanding on the nature of convection on global scales and the maintenance of global circulations is incomplete, progress is imminent, given substantial improvements in computation, theory, and helioseismic inferences.     

Perspectives in Global Helioseismology and the Road Ahead

We review the impact of global helioseismology on key questions concerning the internal structure and dynamics of the Sun and consider the exciting challenges the field faces as it enters a fourth decade of science exploitation. We do so with an eye on the past, looking at the perspectives global helioseismology offered in its earlier phases, in particular the mid-to-late 1970s and the 1980s. We look at how modern, higher quality, longer datasets coupled with new developments in analysis have altered, refined, and changed some of those perspectives and opened others that were not previously available for study. We finish by discussing outstanding challenges and questions for the field.     

Effects of Polar-Angle Errors in Imaged Helioseismology

Differences between the solar rotation axis and that of a spherical-harmonic decomposition of imaged helioseismic data cause power from each mode to be erroneously resolved into other nearby modes with the same spherical harmonic degree l, but somewhat different values of the azimuthal order m. In the long-term average, this leakage artificially broadens the line width of each mode, decreases the peak power, and produces an asymmetrical line profile that pulls the line centroid toward the m = 0 frequency. The magnitude of these effects depends on the values of l, m, and the error angle. Angular difference of a few tenths of a degree at intermediate ls (50–150) can produce line broadening of up to 20%, apparent peak-power reductions of up to 10%, and line centroid errors of up to a few nanoHertz.