How does helioseismology work

Three images are taken in every modulation cycle in order to determine the phase, the amplitude and the brightness at each pixel. The captures are intergrated over 60 seconds and the result is digitally stored on tape. The container harbors the complete electronic assembly, a computer for data recording and all the instruments.

Hence the observatory can be operated autonomously at remote locations by two computers and a accurate clock. Usually, there is a snapshot of doppler velocity, line strength, continuum intensity and Zeeman splitting in every minute — day and night.

In the nightime the instrumental parameters and the weather conditions are recorded only. As soon as the program detects that the Sun has risen, the instrument coverage is removed automatically. Then the instrument is pointed close to the Sun and a guiding sensor gives precise positioning orders. As soon as there is in daytime enough sunlight, a calibration sequence is called.

The observations are carried out until sunset. Afterwards the instrument stows itself again autonomously. The instrument can be run for one week without human intervention.

Then, the only need is to change the tapes or to do maintenance if necessary. Observations with an observatory in space from a suitable orbit avoid interruptions by the day and night cycle. SOHO was launchend in The scientific operation was started in from an orbit around the first Lagrange point between Earth and Sun. Because of a technical defect in it seemed that SOHO was lost. But skillful actions brought SOHO back.

SOHO harbors three instruments for helioseismic data recording. But up to now g modes could not be found doubtlessly.

These are used to record in every minute the observations of the Doppler velocity over the whole solar surface with a spatial resolution of 2 arcseconds. This corresponds to simultaneous and independent velocity measurements at different places. Especially, studies of solar oscillations and important details about the solar interior became possible with these two instruments MDI and GONG. Recently a further instrument was added on Tenerife to form a network of two sites.

This network does not record resolved images of the solar surface, but averages the solar oscillations over the whole solar disc.

Conclusions about the structuring of the solar interior are drawn by means of inversions. The principle of inversion methods is simple. The paths of every two scillation modes with different radial degree n or harmonic degree l differ from each other. As these modes have different frequencies, the integrated sound speed on their paths must be different, too.

This can knowledge is used in turn for the seismic investigation of the Sun. The relation between frequency and sound speed is know, but the sound speed can not be measured directly, but only the frequencies. In order to determine the sound speed, this integral relation is inverted. This is a well-know mathematical and often difficult problem. Therefore, helioseismologists spend a lot of time on the development of effective mathematical techniques and computer software for the inversion of the oscillation frequencies.

Based on the frequency difference between two modes, the sound speed can be determined in that region in the Sun that was passed by only one of the modes. For a detailed map of the physical properties of the solar interior, many mode frequencies must be measured.

Afterwards, a careful analysis of the different wavepaths throught the solar interior must be performed. Aa a result, the sound speed in every region of the Sun is determined.

The investigation of modes with different order m allows studies of properties of the Sun that depend on latitude. Especially, this is important for the determination of the rotation rate in the solar interior.

The seismic determination of the internal structure of the Sun shows that the theoretical calculations and simulations are in well agreement with the real Sun. There are only small differences in the sound speed profile of less than 0. This is a remarkable result, as it shows the great possiblities of modern physics that lead to the present substantiated state of knowledge about such a complex object as the Sun.

Starting from the inverted sound speed, the central temperature of the Sun can be determined to be This result was available directly after the first observation campaign with SOHO in Newer experiments at the Sudbury Neutrino Observatory lead to overall approvement of this result in Up to that date, there was still speculation, that the reason for the too low rate of measured neutrinos, which are set free during under high tempertature during the fusion processes in the solar core, might be a lower central temperature of the Sun.

Now, it became clear, that neutrinos are able to change their characteristics which makes them undetectable for the earlier neutrino detectors. Also starting from the inverted sound speed, the depth of the convection zone can be determined with great precision. Sarbani Basu and H. Antia found that the ratio of depth of the convection zone and solar radius is given by 0. The solar radius is determined from the frequencies of the f-modes.

Being acoustic waves, the p modes can not be used for the determination of the solar radius as their frequency depend on the sound speed additionally. Observations of the solar surface reveal a non-uniform rotation. The equator needs 25 days whereas regions at the poles need approximately 30 days for one full revolution.

This result is in principle not very amazing, because in contrast to the Earth the Sun is a gasball. Hence, there is no reason for assuming that the Sun would rotate as a solid body.

However, the origin of the observed solar differential rotation is not completely understood. The question, how the differential rotation profil at the surface continues in the solar body was answered by inverting the p-mode frequencies.

The upper figure shows the solar rotation in a cross section view, determined on the basis of GONG data. The colors represent the rotation period blue slow, red fast. A welcome sign of this inversion result is the agreement of the rotation rate near the surface with earlier observations of, e.

The rotation rate is almost constant on all latitudes from the surface down to a depth marked by the dotted circle. In this region there are only minor variations in the differential rotation. The dotted circle marks the lower boundary of the convection zone.

There, energy is transported by gas motions. The whole convection zone therefore rotates very similar as the surface. The transition to a constant rotation rate at the bottom of the convection zone seems to be very sharp. The details and reason for this transition are still topics of current research. Moreover as can be seen from this figure, only less is known about the rotation in the central regions of the Sun.

The next years will reveal more details about the central rotation on the basis of new observations and improved data analysis methods. Consulting data from various years and comparing those, amazing results are detected. The solar differential rotation changes with time. A good discussion of the helioseismic results may be found in the review by Christensen-Dalsgaard The sound speed in a solar model that is closely in agreement with the helioseismic data is illustrated in figure 3.

Square of the adiabatic sound speed c inside a model of the present Sun, as a function of fractional radius r. The general increase in sound speed with depth reflects the increase in temperature from the surface to the centre of the Sun. The gradient of the temperature, and hence of the sound speed, is related to the physics by which heat is transported from the centre to the surface.

In the bulk of the Sun, that transport is by radiation; but in the outer envelope the transport is by convection. A break in the second derivative of the sound speed near a radius of 0. Beneath the convection zone, the gradients of temperature and sound speed are influenced by the opacity of the material to radiation: it has thus been possible to use the seismically determined sound speed to find errors in the theoretical estimates of the opacity, which is one of the main microphysical inputs for modelling the interiors of stars.

There is some evidence from remaining discrepancies between the sound speed in the Sun and in solar models of partial mixing of material beneath the convection zone and in the outer part of the energy-generating core at a radius of about 0. Helioseismology has thus been able to constrain tightly any proposed astrophysical solution of the solar neutrino problem.

The recent results from the Sudbury Neutrino Observatory and Super-Kamiokande experiments have provided evidence for neutrino oscillations and give a neutrino production rate in the Sun that is consistent with standard models and with helioseismology Ahmad et al.

This variation depends on the equation of state of the material and on the abundances of the elements: it has been used to determine that the fractional helium abundance by mass in the convection zone, which is poorly determined from surface spectroscopic observations, is 0. Kosovichev et al. This is significantly lower than the value of 0. The deficiency of helium in the present Sun's convection zone is understood to arise from gravitational settling of helium and heavier elements out of the convection zone and into the radiative interior over the 4.

This inference is confirmed by an associated modification to the sound speed profile beneath the convection zone Christensen-Dalsgaard et al. A major deduction of global-mode helioseismology has been the rotation as a function of position through much of the solar interior e.

Schou et al. The rotation inferred from one such inversion is illustrated in figure 4. In the convection zone the rotation varies principally with latitude and rather little with depth: at low solar latitudes the rotation is fastest, with a rotation period of about 25 days; while at high latitudes the rotation periods in the convection zone are in excess of 30 days.

These rates are consistent with deductions of the surface rotation from spectroscopic observations and from measurements of motions of magnetic features such as sunspots. The finding is at variance with early hydrodynamical models that indicated the rotation in the convection zone would vary principally with distance from the rotation axis.

At low- and mid-latitudes there is a near-surface layer of rotational shear: this may account for the different rotational speeds at which small and large surface magnetic features move. Near the base of the convection zone the latitudinally differential rotation makes a transition to latitudinally independent rotation. This gives rise to a layer of rotational shear at low and high latitudes, which is called the tachocline Spiegel and Zahn It is widely believed that the tachocline is where the Sun's large-scale magnetic field is generated by dynamo action, leading to the year solar cycle of sunspots and the large-scale dipole field see discussion by Bushby and Mason, pages 4.

Crucial to the tachocline's possible role in the dynamo are its location and depth. Following initial estimates of these by Kosovichev b , various investigators have made detailed studies.

Charbonneau et al. They also found some indication that the tachocline may be prolate. The rotation rate inside the Sun inferred from MDI data. The rotation axis is up the y -axis, the solar equator is along the x -axis.

Contour spacings are 10 nHz; contours at nHz, nHz and nHz are thicker. The obscured region indicates where a localized solution has not been possible with these data.

Deeper still the rotation appears to be consistent with solid-body rotation. In the core there is some hint of a slower rotation Chaplin et al. These are illustrated in figure 5. Helioseismology has shown that these flows extend at least one third of the way through the convection zone and possibly the deep convection zone and high latitudes are also involved Howe et al.

There are also reported weak variations in the rotation rate, with periodicities around 1. However, the causal connection between all these time-varying flows and the solar dynamo and activity cycle is as yet uncertain see Bushby and Mason, this issue pages 4. The temporal evolution of the zonal flows inferred from inversions of data from MDI, after subtraction of an average rotation rate.

The plot is symmetric around the equator, because global rotational inversion only senses the symmetrical component of the rotation rate. Courtesy S V Vorontsov. Analysis of the Sun's global mode frequencies has provided an unprecedented view of the interior of a star, but the approach has limitations.

In particular, the frequencies sense only a longitudinal average of the internal structure. To make more localized inferences, various local helioseismic techniques have been devised. One technique is ring analysis. The wave motions are analysed as a function of frequency and the two horizontal components of the wavenumber in localized patches. The method is called ring analysis because the mode power lies on rings in the horizontal wavenumber plane when viewed at fixed frequency. By performing inversions for the depth dependence under each tile, maps with horizontal resolution similar to the size of the tiles can be obtained of structures and flows in the outer few per cent of the solar interior.

As well as the zonal flows, the meridional i. The analyses have revealed complex and changing flow patterns within the shear layer near the top of the convection zone: these flows, which have been termed solar subsurface weather e. Toomre , exhibit temporal variations on timescales of days to years Haber et al. Two examples of flow maps are shown in figure 6. The large-scale patterns show strikingly different character as magnetic activity intensifies.

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