Helioseismology: Observational methods and requirements

IL NUOVO CIMENTO VOL. 105 B, N. 8-9 Agosto-Settembre 1990

Helioseismology: Observational Methods and Requirements (*)(**).

D. RICCI and P. ROSATI Dipartimento di Fisica, Universitd di Roma I ,,La Sapienza,, P.le A. Moro 2, 00185 Roma, Italia

(ricevuto ii 15 Gennaio 1990)

S u m m a r y . - - The basic method of helioseismology, i.e. the study of the internal structure and dynamics of the Sun using observations of its surface oscillations, is briefly reviewed. A sampling of some recent accomplishment of helioseismology and its scientific goals is presented, focussing on observational and instrumental requirements. Results and recent improvements related to the instrumental technique being developed in Rome are indicated. Experiments are in progress addressing the measurement of l = 1 rotational frequency splitting and solarlike oscillations on other stars.

PACS 96.60.Ly - Oscillations and waves. PACS 95.55.Ev - Solar instruments. PACS 95.75.Mn - Image processing. PACS 95.85.Kr - Visible (3900 + 7500)/~.

1. - I n t r o d u c t i o n .

In the last 20 years, the s tudy of solar oscillations have rapidly evolved into a new branch of solar physies known as helioseismology.

Observations of the solar photosphere show a complicated velocity pattern, detec- table as Doppler shifts of the spectral lines or associated intensi ty fluctuations. We now know that it is the result of the interference between about 107 resonant modes of oscillation which penetrate at different levels inside the Sun, thus probing directly various aspects of its internal s tructure and dynamics. This information, in some respects, is analogous to what we obtain from seismological studies of the Earth .

1"1. Nature o f solar oscillations. - Solar oscillations were discovered in 1960 by Leighton, Noyes and Simon [1, 2] who found a small-scale velocity pat tern (1% of Ro) oscillating with periods near 5 minutes and amplitude of about 1 km/s. They did not

(*) Presented at the Second Italian-Korean Meeting on Relativistic Astrophysics held at the University of Rome and in Limone Piemonte in July 1989. (**) To speed up publication, proofs were not sent to the authors and were supervised by the Scientific Committee.

67 - I1 Nuovo C~mento B. 1 0 0 9

1010 D. RICCI and P. ROSATI

realize the actual nature of oscillations that for a long time were regarded as local phenomena triggered by below convective motions.

Approximately ten years later, Ulrich[3, 4], and independently Leibacher and Stein [5] proposed that these oscillations are the superposition of coherent acoustic internal modes. They are essentially pressure waves (p-modes) which may undergo reflection where appropriate conditions are fulfilled and can thus be confined within a cavity.

The upper turning point of a p-mode, which is just beneath the photosphere, is due to the rapid decrease in the density, thus, the surface layers act as a reflecting boundary, provided that the frequency is less than a critical value which is determined by the vertical scale of density (re ~ 5.5 mHz for the Sun). If v > Vc the p-mode does not undergo reflection at the surface.

On the other hand, downward propagating waves are refracted back upward, since temperature, and consequently sound speed, increase with depth, causing deeper parts of the wave fronts to travel more quickly. If the horizontal wavelength is shorter, that is the horizontal wave number (Kh) is larger, the wave will be refracted more quickly and the cavity within which it is confined is shallower.

For each value of Kh there is a foundamental acoustic frequency and a sequence of overtones which are identified by the radial order n increasing with increasing frequency. Following this model Ulrich shows how the frequencies were expected to depend on n and Kh. The theoretical spatial-temporal power spectrum of oscillations is shown in fig. 1.

o so 06 i

"~ 3.0

2.0 03

O2 1.0

I 0 ~ , i L i l l l i l l , i l K , i

0 5 10 15 20 25 b 0 5 10 15 20 25

Fig. 1. - ~-l diagram of theoretical eigenfrequencies of p and g modes [Christensen-Dalsgaard, 1982]. a) acoustic modes, b) gravity modes.

In 1975 Deubner [6], making measurements lasting several hours in an equatorial strip and performing Fourier trasforms in longitude and time, obtained a Kh-~ diagram confirming the Ulrich theory. The diagram in fig. 2 shows how the cavity responds more strongly to a number of discrete values of frequency vn for each value of Kh according to the law

~n ~ ~/(2n + 3) Kh,

HELIOSEISMOLOGY: OBSERVATIONAL METHODS AND REQUIREMENTS 1011

Fig 2. - K~,-~,) & a g r a m computed using da ta ob ta ined wi th the magne to -op t i ca l f i l ter a t Mt Wilson in 1985.

p-modes have periods between 3minutes and I hour with a peak amphtude of the single modes of ~ 20 cm/s around 5minutes.

A few years later more accurate observations gave cleaner Kh-o) dmgrams thereby permitting the determination of the initial solar helium abundance and of the sound speed with depth (down to 0.7Ro). These were the first scientific inferences of methods of helioseismology.

1"2. Classi f icat ion of n o ~ n a l modes - The spatial structure of any normal mode is naturally represented in spherical coordinates (r, -3, ~) as a product of a radial function V,~(r), describing the radial structure of the mode with n nodes, and a spherical harmonic Y~,~(~, ?) describing the velocity pattern at the surface. In fact the radial component of the velocity of a mode can be expressed as

~' (mz oJ~ t) . Vr(r, "~, ~?, t) = P~(~ ) P l (COS o$) COS , -

The degree l determines the horizontal scale of the mode, since )~h = (2=Ro)/~r / + 1); the azimuthal order m characterizes the orientation of the mode.

If the Sun were perfectly spherically symmetric the frequency should be independent of m. Any departure from spherical symmetry, due to rotation or a magnetic field, for instance, breaks the degeneracy of ~ on m.

The sensitivity of the measurements to modes of a given l is determined by the spatial resolution of observations. In order to detect high-degree modes, high spatial resolution is needed. On the other hand, in integrated sun-light observations, the sensitivity is limited to oscillations with 1 ~< 4. In such a case, in fact, one detects only


an average of velocity signals over the entire solar disk and the contribution of high C- modes is averaged at zero.

Besides p-modes, that is acoustic waves which originate from pressure gradients, another kind of waves is theoretically predicted. In a gravitationally stratified and compressible medium, such as the Sun, the action of gravity gives rise to buoyancy that manifests itself either as convection, where the gas is unstably stratified, or <<gravity waves~,, called g-modes, where the stratification is locally stable. The propagation of g-modes is thereby possible below the convection zone. They are trapped in regions where their frequency is less than the local buoyancy frequency and all share an upper reflection point near the base of the convection zone.

The periods of g-modes are between 40minutes to several hours long, their amplitude at the surface is very small ( - minis) because of the strong damping in the convection zone. Nevertheless, there is some evidence that g-modes of low degree have been detected at the surface. The modes, being confined in the core of the Sun, approach the centre more closely than the p-modes of low l do, thereby providing a more powerful probe of the innermost regions.

2. - Sc i en t i f i c objec t ives o f h e l i o s e i s m o l o g y .

The aim of this section is to summarize the scientific goals of helioseismology and how they might be attained showing the relationship between measured quantities and derived solar properties.

As to the frequency distribution with varying n and l, for p-modes the characteristic frequency depends on the travel time between the turning points within the cavity. This is controlled by the behaviour of the sound speed with depth, which in turn measures the stratification of density, temperature and pressure with depth. So that, the v~z distribution allows us to determine the density and temperature profile inside the Sun and to estimate the depth of the convection zone. The comparison between the observed Kh-co diagram of p-modes and the theoretical one also permits us to estimate the initial helium abundance.

~ for g-modes is determined by buoyancy frequency with depth, which, in turn, measures the chemical composition of deeper layers. Thus mixing hypothesis of the core may be tested.

Direct probing of the core may be able to resolve the solar-neutrino problem. In particular, whether the explanation is in the context of theories of stellar structure and evolution or in the framework of particle physics (WIMP's, MSW effect, v magnetic moment and so on). Crucial issues are involved, such as the existence of neutrino masses and leptonic mixing.

Measurements of frequency fine structure, i.e. frequency splitting of modes with different m, address one of the most important issue which can be investigated only with the methods of helioseismology: the rotation rate of solar interior as a function of depth and latitude.

Although there are nonhelioseismology observations concerning the internal solar rotation, they provide only hints.

Measurements of the oblatness of the Sun are not very sensitive, but they seem to exclude a core rotating faster than the double of the surface velocity. In 1970 Dicke proposed that a rapidly rotating core would create a quadrupole moment J2 of the Sun gravitational field sufficient to have a significance influence on the perihelion precession of Mercury, thereby challenging a classical test of general relativity [7, 8].


Observations of visible features, such as Sun spots, magnetic-field patterns and supergranulation can probe the internal rotation with difficulty, since the depth relative to these phenomena is roughly known.

In spite of that, frequencies of oscillation modes of a rotating Sun are clearly modified compared with a nonrotating Sun. The frequency splitting depends on a suitable average of the rotation rate of the cavity within which the mode is confined. Modes with different 1 and m sample a wide range of cavities in radius and latitude, thus, the rotation profile with depth and latitude can be determined by measuring, respectively, the 1 and m dependence of the frequency splitting. Some complications come from other factors, such as a strong magnetic field in the inner regions, which can slightly alter the structure of frequencies in m.

The knowledge of differential rotation with radius and latitude allows us to determine the structure of the convection zone and the coupling between rotation and convection, so providing vital input to solar dynamo models. The angular-velocity distribution can also be used to test theories of transport and evolution of the angular momentum in stars.

What excites the modes is yet an unresolved issue. A higher frequency resolution is needed to measure width and amplitude of peaks in the power spectra related to excitation and damping of single modes.

2"1. Some accomplishments of helioseismology. - Considerable important information has already been obtained through the use of the helioseismological technique. The first achievement was the confLrmation of the basic correctness of the solar internal temperature and density profiles as predicted by standard solar models. The general agreement is a strong verification of the stellar interior theory, although clear differences between observed oscillation eigenfrequencies and those of standard models show that some simplifying assumptions that underlie these models are to be left out.

One major uncertainty in standard interior models was removed by using oscillation frequencies to determine the depth of the convection zone. It turned out deeper (0.28R| than previously believed.

The present-day structure inferred from the Kh-~ diagrams, together with the results of standard evolution models, suggests that the initial helium abundance was about 25% by mass (Y~-0.25), in general agreement with current theories of primordial nucleosyntesis [9].

As to interior dynamics, the rotational profile in the Sun interior has been preliminarly estimated by splitting data of high- and intermediate-I modes [10, 11].

Independent measurements are in essential agreement on the fact that the differential rotation within the convection zone differs slightly from the observed rotation of the surface. The rotation rate of the core is not well probed by p-mode oscillations with the exception of low I p-mode, whose frequency splitting has not yet been clearly detected. Low l g-modes offer the best way of probing the rotation of the innermost regions. Preliminary results seem to indicate a rapidly rotating core [12].

3. - Observat iona l goa l s and r e q u i r e m e n t s .

The observational goal of helioseismology is to measure as many frequencies and amplitudes as possible with high accuracy as a function of time.


Until now we know several thousands of p-modes with 1 up to -1000 and 2 ~< v ~< 5 mHz, with uncertainties as low as one part in 104.

The main observational goal in the future is to measure very high-/p-modes up to l = l ~ -~ 3000, which is the smallest horizontal scale of oscillation and low-frequency, low-amplitude oscillations, e.g., low-/and low-n p-modes with periods up to - 1 hour,. and g-modes with periods of the order of several hours.

Another important goal is the measurement of the frequency splitting of low-/p- modes and g-modes.

In order to meet these requirements, the observations must be carried out with high spatial resolution on the full disk, so as to cover a wide range in l, m with maximum resolution in 1 and m, and for a long period with high sensitivity and stability. A minimum duration is set by the need to solve individual modes of oscillation that share the same degree l and the radial order n. The frequency separation of such modes is set by the rotation frequency of the Sun which, for the surface and most of the interior, is of the order of 0.4 ~Hz. This implies a minimum duration of order 5.106 s ~ 2 months.

An important task is to achieve a 100% duty cycle, that is continuous observations without periodic gaps. Brief interruptions do not seriously degrade the quality of data because good technique exist to fill brief data gaps. However, if the duty cycle falls below - 50%, it is practically impossible to recover low amplitude signals adequately because of the presence of a great number of side lobes introduced by day/night observing cycle. This implies that observations are to be made from South Pole or with a network of stations placed at different longitude (Global Oscillations Network Group project), or, alternatively, from space in an appropriate orbit. The Solar and Heliospheric Observatory (SOHO) space mission, planned for 1995, offers the opportunity of making uninterrupted high-resolution observations unaffected by seeing, without diurnal effects producing noise at harmonics of a day that obscure low- frequency oscillations.

In order to reach the largest possible signal-to-noise ratio, besides reducing any observational temporal modulation, one has to minimize the solar background nonoscillatory velocity signal (solar velocity noise) compared with the oscillatory signal. This can be accomplished selecting opportunely the solar absorption line which should be relatively insensitive to temperature changes and magnetic field. In addition, complex and incoherent velocity patterns in the Sun atmosphere can be source of noise for Doppler measurements. The magnitude of this effect depends strongly on height and can be reduced by using a spectrum line formed in a narrow height range, at intermediate heights, above the photosphere, far from convective motions, and below the cromosphere.

Also good seeing and trasparency conditions during long data runs are required. Spatial variations in atmospheric transmission combined with solar velocity gradients cause spurious velocity signals, particularly in integrated-disk Doppler measurements. Moreover, since the Doppler signal is usually derived from differences of images obtained at different times, temporal trasparency fluctuations, as well as atmospheric image distortion, reduce the S/N ratio if this temporal lag is too long.

3"1. I n s t r u m e n t a l requ irements . - Several kinds of spectrometric techniques have been used for solar-oscillation observations. The main characteristic of a Doppler analyser that one requires is the imaging capability, e.g., the entire image must be

H E L I O S E I S M O L O G Y : O B S E R V A T I O N A L M E T H O D S AND R E Q U I R E M E N T S 1015

observed simultaneously without any kind of image scanning. This makes grating spectrographs unsuitable, even if they were used for early works.

The oscillatory signal of single modes has amplitude less than - 0 . 1 m/s but it is buried in large bias velocity signals of several km/s, due to solar rotation, supergranulation, Earth rotation and orbital velocity. So that, one requires both high sensitivity and good linearity over a large dynamic range. High-sensitivity instruments usually have not a linear Doppler response over an adequate dynamic range. In such a case, some type of real-time calibration technique is required to reduce the signal distortion of nonlinearity. Moreover, long-term stability is also required in very long observing runs for detecting low-frequency and low-amplitude oscillations.

4. - R e s u l t s w i t h t h e M a g n e t o - O p t i c a l F i l t e r .

a) Resolved disk. The most widely used spectrometers for imaging observations are narrow-band filters of various kinds: the birifrangent filter[13], the Fabry-Perot [14] and the Magneto-Optical Filter (MOF)[15].

The MOF has been developed in Rome by Cacciani since 1970. In the last years it has proved a good compromise among the requirements mentioned above.

The working principle is shown in fig. 3: alkali metal vapour is produced within a small cell, pervaded by a magnetic field and placed among two crossed polarizers. The magnetic field is able to change, through the ordinary Zeeman effect and the so-called Macaluso-Corbino effect (similar to the Faraday effect), the polarization state of the incoming light in very narrow spectral bands, simmetrically placed around the central wavelength. Thus, only the light in these bandpasses can pass through, while all the continuum is suppressed. The two bandpasses are simmetrically tunable in the wings of the solar absorption lines simply varying the temperature of the vapour. An electro- optical modulator and a second cell allow the MOF to alternatly sample the red and the

90 ~

P,

Zeemoun

No, vo~pour 0 o

j"t 1 ,;

Fig. 3. - MOF working principle.

~'~ +z+5~ ,

I


blue wing of the solar spectrum line. Spatially resolved images of the Sun are obtained in both positions, thereby, the Doppler shift of the solar line relative to the central wavelength can be deduced by the difference of intensity in the line wings properly normalized. By separating in polarization the incoming light, the images can be processed to build up simultaneously a map of the velocity field and the longitudinal magnetic field (see fig. 4)[16].

A main characteristic of the MOF is its spectral stability, due to the existence of an absolute wavelength reference intrinsically stable, the central wavelength. This is ideal for a dopplergraph and is not shared by other narrow-band filters which need an external wavelength reference. In addition, its high spectral resolution, with bandpasses as narrow as 25 mA, ensures high sensitivity to Doppler shifts. This limits

1.o , , , , I . . . . I �84 ' ' ' I . . . . ' ~ . . Na D, s o l a r / . : f : ' ~ / ' - _ ~ X \ absorption line f ~ / / " :

0.8

6 if+ \ 0.6 ~ / / ( / /

0.4 MOF blue bandpass ~ /i I /MOF red bandpass \

o . . . . i , , , , Z , J l , , , . . . . - - 0 . 5 0 0 5

(A)

~)

Fig. 4. - a) Method of velocity and magnetic-field measurement. R/B = image taken in the red/blue wing of the solar Na D lines. + / - = image taken in right/left-handed circularly polarized light, b) A single dopplergram thereby obtained with the MOF at Mt. Wilson is also shown.


linearity and dynamic range at least as long as two samples are made across the line profile. Nevertheless, it is possible to arrange a two-channel MOF, with maximum quantum efficiency, able to sample the spectrum line at four different wavelengths, thereby improving the linear response.

A limitation of the MOF is that it is not tunable, its use being limited to a few lines, such as sodium and potassium, for which the fabrication of the cell is technologically possible. This does not allow to minimize the effect of solar noise by better choice of spectrum lines, but it is the price one has to pay in order to have spectral stability. Fortunately, available lines are quite suitable for Doppler measurements.

The spectral stability of the MOF has been theoretically investigated developing a model, in full agreement with experimental high-resolution spectral scans [17], which has better made its thermal behaviour clear. The radiation transfer through the MOF has been computed taking into account the temperature and vapour density distribution inside the cell and the magnetic-field inhomogeneity. The latter involves the computation of the hyperfine structure of the Zeeman pattern at whatever magnetic-field strength.

The result, experimentally confirmed, is that the r.m.s, noise velocity signal is a few cm/s at level of the experimental thermal stability. In fig. 5 the MOF theoretical transmission profile, tunable across the solar sodium spectrum line, is shown.

~ sobo, r No. D 2 bine

f

230.~C

Fig. 5. - Theoretical MOF transmission profiles tunable across the solar Na D2 spectrum line varying sodium vapour temperature.


b) Integrated disk. No-resolution techniques have intrinsic capability of detecting small-amplitude oscillations of low degree. They are currently the only practical means of examining oscillations with l <~ 3, the only p-modes probing Sun's central regions, not accessible with spatially resolved methods.

So far, the best data have been obtained with resonant scattering spectrometers[18], specially by the Birmingham group[19] using a two-station network (Tenerife-Hawaii). These detectors use sunlight scattered by a metal vapour within a magnetic field to sample selectively solar spectrum lines. They are characterized by relative simplicity, high sensitivity and stability. The MOF can also be arranged to make integrated-disk measurements[20]. Besides sharing the above-mentioned advantages, it provides a high photon flux which makes it a potentially useful technique for studies of solarlike oscillations on other stars [21].

A power spectrum of a 10 days observing run, obtained at JPL (Cal., USA) with the MOF during the 1989 summer season, is shown in fig. 6. Equally spaced frequencies of

i i I i i i i I i i i i i i i i i i i i i i i

I I I I I .

/l, 3 4. 5 6 7 8

f r ' e o l uency ( m H z )

Fig. 6. - Power spectrum from 10 days with day-night interruptions. Data have been obtained using a MOF during the 1989 summer season at JPL (Cal., USA).

modes with 1 ~< 3 are visible, even if the presence of a great number of side lobes, due to the diurnal modulation in the data string, increases the effective noise leading to confusion between modes with different degrees. The largest amplitude of a single mode is - 15 cm/s. Fur ther analysis may be found in ref. [22]. From an astrophysical point of view, an important task is the measurement of the frequency splitting of low-/ p-modes, which contains information about the rotation of the very core of the Sun. Neverthless, it is hard to identify the individual l, m modes in power spectra of integrated-disk observations. Problems arise from the overlapping of spectral features of different 1 states and side lobes. In addition, the finite lifetime of the modes


broadens the spectral profile of each one introducing a fine structure with a scale not so different from the rotational splitting.

A minimum of image resolution is required to separate prograde and retrograde modes thereby unambiguously measuring the rotational splitting. An experiment has been proposed [22] able to measure the l = 1 frequency splitting, the lowest, as well as the deepest, p-mode that can provide rotational splitting data. A two-channel set-up of the M0F can be arranged in order to obtain the desired image resolution, without any noisy physical masking technique over the solar image. Tests and numerical simulations are in progress to study the feasibility of such an experiment.

5. - C o n c l u s i o n s .

Solar oscillations, extensively studied in the last decade, have been proved to be the most powerful diagnostic tool for investigating stellar interiors. Some results of helioseismology may go beyond the physics of the Sun and similar stars and may contribute to broader issues (particle physics and cosmology).

The MOF which is being developed in Rome, both experimentally and theoretically, has proved a good-imaging dopplergraph. With the MOF data obtained at Mt. Wilson the rotational profile has preliminarily been estimated through the outer half of the star [10].

Nonimaging measurements show a low noise level. An experiment is being developed addressing the measurement of the frequency splitting of l = 1, m = --- 1 p-modes bringing information about the rotation of the innermost layers.

Routine observations will also establish whether the M0F sensitivity and stability is suitable to detect solarlike stellar oscillations, whose detection is the next challenge for the future.

R E F E R E N C E S

[1] R. [2] R. [3] R. [4] R. [5] J. [6] F. [7] R. [8] R. [9] J.

B. LEIGHTON, R. W. NOYES and G. W. SIMON: Astrophys. J., 135, 474 (1962). B. LEIGHTON: Proceedings of the IAU Syrup., 12, 321 (1960). K. ULRICH: Astrophys. J., 162, 993 (1970). K. ULRICH, F. L. DEUBNER and E. J. RHODES: Astron. Astrophys., 72, 177 (1979).

W. LEIBACHER and R. F. STEIN: Astrophys. J. Lett., 7, 191 (1971). L. DEUBNER: Astron. Astrophys., 44, 371 (1975). H. DICKE: Annu. Rev. Astron. Astrophys., 8, 297 (1970). H. DICKE: Sol. Phys., 78, 3 (1982).

CHRISTENSEN-DALGSDAARD and D. O. GOUGH: Nature (London), 288, 544 (1980). [10] E. J. RHODES, A. CACCIANI, S. KORZENNIK, S. TOMCZYK, R. K. ULRICH and M. F.

WOODDARD: to be published in Astrophys. J. (March 10, 1989). [11] T. M. BROWN: Nature (London), 317, 591 (1986). [12] P. L. PALLI~ and T. ROCA CORTES: in Advance in Helio- and Asteroseismology (D.

Reidel, Dordrecht, 1988), p. 79. [13] K. G. LIBBRECHT: Nature (London), 319 753 (1986). [14] D. M. RUST, R. KUNSKI and R. COHEN: John8 Hopkins APL Tech. Digest, 7, 209 (1986). [15] A. CACCIANI and M. FOFI: Sol. Phys., 59, 179 (1978). [16] A. CACCIANI, D. RICCI, P. ROSATI, E. J. RHODES, E. SMITH, S. TOMCZYK and R. K.

ULRICH: Proceedings of the Symposium ,,Seismology of the Sun and Sun-like Stars,,, Tenerife, Spain, ESA, SP-286, 185 (1988).


[17] A. CACCIANI, D. RICCI and P. ROSATI: to be submitted to Appl. Opt. [18] J. R. BROOKES, G. R. ISAAK and H. B. VAN DER RAAY: Mon. No$. R. Astron. Soc., 185, 1

(1978). [19] A. CLAVIERE, G. R. ISAAK, C. P. MC LEOD, H. B. VAN DER RAAY, P. L. PALLI~ and T.

ROCA CORTES: Mere. Soc. Astron. It., 55, 63 (1984). [20] A. CACCIANI, R. MARQUEDANT, E. SMITH, D. RICCI and P. ROSATI: Proceedings of the

Symposium ,,Seismology of the Sun and Sun-like Stars,,, Tenerife, Spain, ESA, SP-286, 181 (1988).

[21] F. X. SCHMIDER, E. FOSSAT, G. GREC and B. GELLY: Proceedings of the Symposium ,,Seismology of the Sun and Sun-like Stars,~, Tenerife, Spain, ESA, SP-286, 605 (1988).

[22] A. CACCIANI, E. PAVERANI, D. RICCI, P. ROSATI, R. MARQUEDANT, E. SMITH and S. TOlgCZYK: Oji International Seminar on ,,Progress of Seismology of the Sun and Stars~, Hakon, Japan, Proceedings in Lecture Notes in Physics, edited by Y. OSAK! and H. SHIBAHASttI.

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Helioseismology: Observational methods and requirements