The end of the millennium marks the beginning of the third phase of helioseismology. The first phase was the establishment of the initial astronomical inferences, such as estimates of the depth of the solar convection zone and the protosolar helium abundance, obtained by comparing the seismic properties of theoretical solar models with the first wave of helioseismic data acquired using instruments that had not been designed for the purpose. The second phase was the determination of the spherically symmetric component of the hydrostatic stratification throughout most of the solar interior, and the angular velocity, using inverse methods to analyse the frequencies of normal modes estimated from data obtained most recently from purpose-built networks of ground-based observatories and from space. We have reached the point beyond which further pursuit of the now-well-tried methods to improve the inferences will be apparently slow. The next era will be characterized by painstaking attention to detail, to extract a new level of precision necessary to isolate subtle properties of the sun for asking more sophisticated questions. We are already seeing the normal-mode representation of helioseismic waves being complemented by other representations that may be more suitable for investigating inhomogeneity and time variability particularly of the sun's surface layers. The outcome will enable us to address more accurately issues concerning global dynamics, the equation of state and the chemical composition, and also the properties of convection and the seat of solar activity.

Over the past few years the quality and quantity of basic helioseismic data have increased dramatically as instruments such as MDI on the SOHO spacecraft and the GONG network have become operational. The data from these new instruments have led to a significant increase in our ability to make inferences about the solar interior, and resulted in a long series of often surprising and spectacular discoveries. In this review I describe some of the most recent results and what progress we may be able to make in the near future with improved analysis methods and with a better understanding of solar oscillations and the instruments used to observe them.

Acoustic modes are well-suited probes to check the internal stellar structure and bring interesting constraints on turbulence regions, mixing in stellar interiors and magnetic fields. The SOHO satellite, through the helioseismic instruments GOLF, MDI and VIRGO, has significantly improved the knowledge of these modes owing to an excellent duty cycle (greater than 90%) and the capability to detect very low amplitude modes, down to 3 mm/s. Five years of the SOHO misson guarantee an accurate view of the solar interior, weakly dependent on the turbulent surface, from the energy-generating core to the surface.

The recent results allow us to verify some of the theoretical assumptions of stellar modelling. The tachocline layers, located in a narrow region at the base of the convection zone, support an hydro (or magnetohydro) dynamical instability which induces mixing and results in 7Li depletion in accordance with photospheric observations. On the contrary, central mixing is not favoured by the present observations. Nuclear reaction rates of the pp chain are now constrained by the behaviour of the sound speed and density. Döppler velocity measurements appear as an excellent technique to follow in real time the temporal evolution of the luminosity produced in the core. Some puzzling questions about dynamical effects in stellar plasmas can now start to be addressed for the first time. The theoretical neutrino emissions can be now directly deduced from our helioseismic vision of the energy-generating core.

Nowadays, helioseismology provides a dynamical vision of the external half of the Sun (20% in mass), as a result of the extraction of the sound speed, density, rotation profiles and of the time evolution of velocity measurements. Below, the classical static vision of the nuclear region persists because of the poor spatial resolution offered by acoustic modes (±6% in radius, 10% in mass) and the long integration time (several years). Gravity modes will be extremely useful to improve the spatial resolution in the radiative region. The extended observations with the SOHO satellite may be extremely useful to detect some of these modes.

Helioseismic measurements with the MDI instrument aboard SOHO, and complementary measurements from the GONG network, are revealing changes deep within the Sun as the solar cycle progresses. We present results based on recent data from both experiments, including variations in the rotation rate deep inside the convection zone.

In our previous work (Takata & Shibahashi 1998), we constructed a solar model called the seismic solar model, which has the consistent profile of sound speed as well as the consistent depth of the convection zone with helioseismology. The profile of the heavy element abundance, however, had to be assumed to be constant for feasibility. Here we try to constrain the distribution of the heavy element abundance as well by the solar oscillation frequencies, adopting all of the basic equations which govern the solar structure.

Solar model with moderate enrichment of heavy elements in the convective envelope is investigated using the up-to-date input physics. It is found that metal enriched model can result in adequate depth of the convection zone and appropriate surface helium abundance, and the agreement between the calculated and observed p-mode frequencies are also improved. The sound speed of our model is worse than SSM and DSM in deep interior, but is better in the base of convection zone.

Asteroseismology, the study of stellar interiors on the basis of observations of multi-mode stellar oscillations, extends over a large part of the Hertzsprung-Russell diagram. The recently discovered EC14026 stars promise information about the properties of stars on the horizontal branch. Solar-like oscillations excited stochastically by convection have been tentatively identified in a few cases. Promising examples are giant stars, where the expected amplitudes may make ground-based observations of the oscillations relatively straightforward. Major advances can be expected from the upcoming asteroseismic space projects under development or study, including the Eddington mission adopted by ESA as a ‘reserve mission’ in the recent round of selections.

From considerations of kinetic energy input from turbulent convection into g-mode pulsation, we show that g-mode pulsation may obtain enough energy from the turbulence to overcome damping in the stellar interior. The development of thick convective envelope in the stellar models requires a small value of the convection parameter α = 1.2 to ensure the low mass limit of the γ Dor stars' instability strip to be in agreement with the observations.

The relative variation of the solar irradiance depends strongly on the wavelength band, with the shortest wavelengths exhibiting the largest variations over the solar cycle. This means that not only the total irradiance varies with solar activity but also the shape of the solar spectrum. These measured effects have been successfully modelled. The models indicate that more than 90% of the total and spectral irradiance variations over the solar cycle are due to the magnetic field at the solar surface. The solar spectral irradiance variations play an important part in constraining the models, since they can directly distinguish between changes in the solar effective temperature and changes produced by variations of solar surface magnetic flux. They also help to determine what fraction of the total solar radiative input to Earth is absorbed by the Earth's atmosphere.

The variability of several dozen stars similar to the Sun in mass, age, and average activity has been monitored regularly in chromospheric Ca II HK emission for over three decades, and photometrically for over fifteen years. Larger samples have been observed less comprehensively. Analogous solar time series exist. A comparison of solar variability with its stellar analogs indicates that the Sun's current behavior is not unusual among sunlike stars. Both solar models and stellar measurements suggest that a true luminosity variation underlies the cyclic total irradiance changes observed on the Sun.

The metrological qualities render the modified CCD solar astrolabe a very reliable instrument for the difficult conditions of solar diameter measurements. At O.N. an average value of 959”.04 ± 0”.01 is found, for λ = 563.5nm, and an effective bandpass of 168nm. To improve the signal to noise ratio, the images are treated for flat field. This includes distortions brought about by the COHU 4710 camera, the astrolabe optics, and by the system of filters that cut down the incoming solar light. The extensive series observed (over 12000 independent measures) is examined, using a CLEAN periodogram algorithm. The outcome shows periods reconcilable with the solar activity and geometry of observation.

The pulsation properties of the rapidly oscillating Ap (roAp) stars are briefly presented. The combined effect of a strong magnetic field and rotation on pulsations is also discussed.

We consider the theoretical prediction of the power spectrum of oscillations of Procyon A, a bright subgiant star which shows solar like pulsations, comparing models computed by taking into account overshoot from the convective core, as well as diffusion of helium and heavy elements.

The IRIS network has accumulated low-l p-modes data since July, 1989, i.e. one complete solar cycle. Since the last publication of a frequency table (Gelly et al. 1997) the IRIS data bank was not only filled with new data, but also has been supplemented with data from other helioseismology instruments, through cooperative programs. The results of a new estimations of frequencies and splitting obtained from IRIS++ data (Gelly et al. 1998) for period 1989-1996, as well as their variation along the solar magnetic activity cycle are presented.

Is the Solar Radius a constant? Ground experiments show evidence of possible variations in the visual solar semi diameter that are correlated with the solar activity. Those measurements are limited by the Earth's atmospheric turbulance. It is importance to accurately determine the solar radius variations because of their implication for stellar structure and possible relation to the terrestrial climate. Here we report on data from a space experiment (MDI-SOHO) used to detect solar diameter fluctuations. We stabilish a superior limit for changes in the solar radius.

The long-term changes of the VIRGO radiometers have been re-analyzed in detail in order to resolve the puzzle of the early increase of the total solar irradiance (TSI) as observed by VIRGO. The exposure dependent changes can be described by a model which is based on a combination of an early increase of the sensitivity and a degradation with time which is modulated by the dose of solar UV radiation each detector receives. After correcting for the exposure-dependent behaviour both operational radiometers show an increase of their sensitivity which depends only on the time they are switched-on. After removing this increase the VIRGO TSI remains more or less constant during the minimum period of solar activity and reaches the solar maximum at levels comparable to the ones of former maxima.

The solar limb is potentially a sharp spatial reference with which we can detect the effects of solar oscillations (both pression and gravitation modes), the quadrupole moment -and higher moments if any-, the true shape of the helioid (the oblateness at the first order), and changes in the solar radius. It is shown in this paper, that the accurate determination of the successive differential gravitational moments are useful to probe the solar interior. We emphasize the main reasons, mainly the accurate determination of the planetary orbits and the adjustement of the Eddington-Robertson coefficient of the PPN gravitational theory. Moreover, both the shape and the radius measurements of the Sun help to determine the solar luminosity, as empirical models of total irradiance (solely based on magnetic effects) can not explain all aspects of irradiance changes. A complete theory is still pending. The space mission Picard, currently scheduled by the end of 2004 and currently under a manufacturing process, will lead to validate our differential theory.

We discuss a generalization of a mixing-length formalism for convection in the presence of a mean flow, and present the convective fluxes for convective cells with the geometry of rolls and of hexagons.

On the base of turbulent dynamo model with allowance for newer helioseismic measurements of the Sun's inner rotation it is shown that the physical conditions in deep layers of the solar convection zone in near-pole domain are favourable for exciting of quadrupole mode of poloidal magnetic field near maximum phase of 23-rd solar cycle