Convection consists of rising hot and descending cool parcels of gas. In order to assess the effect of such an in homogeneity on acoustic waves a simple model has been proposed by Zhugzhda and Stix (1994). The model consists of a sequence of alternating vertical layers with temperatures T1 and T2 and upward and downward velocities V1 and V2. At the interfaces between the layers the horizontal component of the velocity and the pressure are continuous. This model allows to determine the phase velocity of a vertically propagating acoustic wave. The main result is that, with increasing frequency, this phase velocity approaches the sound speed of the cooler layers. The reason of such a behavior is that the horizontal structure of the wave is oscillatory in the cool layers, but exponential (evanescent) in the hot layers, so that there is a certain amount of wave trapping in the cool layers. An analogous effect of trapping in a horizontal layer has been described by Kahn (1961) for the temperature minimum of the solar atmosphere.

The inverse problem of finding the structure of the solar interior from the observed frequencies can be written as

where, δωi is the difference in frequency of the ith mode between the solar data and the reference model, f1 and f2 are an appropriate pair of model parameters (e.g. sound speed squared c2, and density ρ), Ei is the mode kinetic energy, K(1) and K(2) are known functions of the reference model, and F(ω) is the unknown function added to account for uncertainties associated with the physics of the surface layers.

The equation of state of astrophysical plasmas is, for a wide range of stars, nearly ideal with only small non-ideal Coulomb corrections. Calculating the equation of state of an ionizing plasma from a ground state ion, ideal gas model is easy, whereas, fundamental methods to include the small Coulomb corrections are difficult. Attempts to include excited bound states are also complicated by many-body effects that weaken and broaden these states. Nevertheless, the high quality of current observations, particularly seismic data, dictates that the best possible models should be used. The equation of state used in the OPAL opacity tables is based on many-body quantum statistical methods (Rogers, 1994; 1986; 1981) and is suitable for the modeling of seismic data. Extensive tables of the OPAL equation of state are now available. These tables cover the temperature range 5 × 10−3 to 1 × 108 K, the density range 10-14 to 105 g/cm3, the hydrogen mass fraction (X) range 0.0 to 0.8, and the metallicity (Z) range 0.0 to 0.04.

The last few years have seen rapid progress in solar interior modeling, and standard solar models (SSM) now predict a p-mode oscillation spectrum which agrees, within the estimated uncertainties in the physical input, with the observed oscillation spectrum of the Sun (Guenther et al., 1992a, 1992b; Guzik & Cox, 1993). This is the result of a number of improvements in the input physics, most notably the advances in opacities for the solar interior (Rogers & Iglesias, 1994) and the low temperature regions of the Sun (Kurucz, 1991). The agreement between the observed solar p-mode frequencies and the frequencies predicted by the SSM is not yet perfect, however, and understanding these discrepancies has become a focus of our research.

The data taken by the Birmingham Solar Oscillation Network (BISON) forms an interesting link between the twin themes of this session: solar and stellar seismology. Like stellar astronomers, we view the Sun as a star without spatial resolution. There are clearly disadvantages in this, in that we lose information about oscillations which vary rapidly across the Sun. But we are not limited to just the simple radial mode which has l=0; because of Doppler imaging we see modes with a range of l from 0 to 4. Unlike stellar astronomers, our star is near to us and the photon flux is high enough that we need not be limited by photon shot noise. We detect the modes by measuring the integrated surface velocity of the Sun. With long integration times, and for the coherent modes, the smallest amplitudes that we can measure are between 1 and 0.1 cm s−1.

The design of the LOI instrument was an original idea of Andersen et al. (1988). It consists of a Ritchey-Chrétien telescope (f=1300 mm) imaging the Sun through an 5-nm passband interference filter at 500 nm. The image is projected on a photodiode array detector built to our specifications (Appourchaux et al., 1992). The detector is made out of 12 scientific pixels and of 4 guiding pixels. The shape of the scientific pixels are trimmed to detect low degree modes for l < 7 (Appourchaux and Andersen, 1990). The guiding pixels are 4 quadrants of an annulus with an inner and outer radius of 0.95 and 1.05 solar radius, respectively.

We have observed evidence for p-mode oscillations in the G0 IV star η Boo (V = 2.68). This represents the first clear evidence of solar-like oscillations in a star other than the Sun. We used a new technique in which we measure fluctuations in the temperature of the star via their effect on the equivalent width of the Balmer lines. The observations were obtained over six nights with the 2.5 m Nordic Optical Telescope on La Palma and consist of 13000 low-dispersion spectra. The upper part of Fig. 1 shows the power spectrum of the equivalent-width measurements (the inset shows the window function).

Among the A stars there is a subclass of peculiar stars, the Ap stars, which show strongly enhanced spectral lines of the Fe peak, rare earth and lanthanide elements. These stars have global surface magnetic fields several orders of magnitude larger than that of the Sun, 0.3 to 30 kGauss is the measured range. For stars with the strongest magnetic fields, the spectral lines are split by the Zeeman Effect and the surface magnetic field strength can be measured. Generally, though, the magnetic fields are not strong enough for the magnetic splitting to exceed other sources of line broadening. In these cases residual polarization differences between the red and blue wings of the spectral lines give a measure of the effective magnetic field strength - the integral of the longitudinal component of the global magnetic field over the visible hemisphere, weighted by limb-darkening. In the Ap stars the effective magnetic field strengths vary with rotation. This is well understood in terms of the oblique rotator model in which the magnetic axis is oblique to the rotation axis, so that the magnetic field is seen from varying aspect with rotation.

Perhaps the hardest scientific problems to solve are those most scientists believe have already been solved, but which have not. Any model we make of an astronomical process is doomed to be incomplete at some level; the “broad-brush” picture of stellar structure and evolution is often accepted as a solved problem, but in fact many discrepancies exist between our models and the observations.

For example, the “standard solar model” fails to predict the observed neutrino flux from the Sun, and its insistence that the Sun’s luminosity increased by 30% over geological time is not in accord with the evidence. White dwarf stars were thought to be stable against pulsation because the models did not pulsate, and it took a long time to improve them to the point where they did, and could then begin to match our observations of pulsating white dwarfs. For several years their outer hydrogen layers were thought to be extremely thin because models with thicker layers did not pulsate; once the zoning problem was found and solved in the models they could begin to match observations better. These past difficulties illustrate a common danger: it is very easy to confuse our models with the observed reality they try to mimic, and to assume they match better than they do. In what follows I will try to keep the observations and our models of them separate.

Several δ Scuti stars (A/F stars) have been observed during multi-site campaigns of observations and have been found to be multiperiodic pulsators. They are thus good candidates for asteroseismology from ground based observations. Observations provide the position of the star in the H-R diagram and some frequencies (about 5 for the STEPHI campaigns). Comparisons with models should then allow to identify the oscillation modes of the star and then give information on the unknown parameters of the star (mass, age, chemical composition). However the situation is complicated, since stellar models are based on a physical description of the stellar material, which is not well known in many respects. In particular A/F stars have convective cores, the extent of which depends on the amount of overshooting considered and on the description of this process.

High-resolution, time-resolved spectroscopy in both optical and UV wavebands has shown that the outer layers of luminous OB stars vary on time scales of hours-days. Spectroscopic monitoring with the IUE satellite provides evidence that the stellar winds of luminous, hot stars are not smooth and steady, but are frequently disrupted by the presence of time-dependent structures. In addition, variability is often present in optical photospheric line profiles; these variations are likely due to the influence of photospheric velocity fields, especially those from one or more modes of nonradial pulsation (NRP). The process (or processes) responsible for the formation of time-dependent wind structure is (are) not known. Issues concerning potential connections between NRPs, variations at the base of the outflow, and the development of wind structure pose some of the greatest challenges to our understanding of mass-loss via radiatively driven stellar winds.

Study of the dust in circumstellar disks around young stars is currently an extremely active area in astronomy. There is little doubt that accretion disks are a natural part of protostellar evolution. Much recent observational and theoretical work is giving us a clearer picture of the physical conditions in dust disks and their evolutionary progression. IRAS observations revealed that many main-sequence stars, such as p Pictoris, have circumstellar disks. But whether these disks are related to planetary formation is not yet understood.

A portion of the dust in disks around young stars ultimately may be incorporated into planetary systems. Thus, study of the dust in our own solar system complements the remote sensing of protostellar regions and aids in reconstructing the evolutionary history of the dust. Since comets formed in the cold outer regions of the solar nebula, they may contain intact interstellar grains. As the comets lose material during passage through the warm inner solar system, some of these grains will be released into interplanetary space. Technical advances now allow analysis of individual micrometer or smaller grains in interplanetary dust particles and primitive meteorite samples. Isotopic anomalies and patterns of crystal growth in these particles are yielding tantalizing clues about the interstellar material incorporated into these solar system samples.

The content of my oral contribution has been reduced here to a guide to the recent litterature on the subject.

The effective temperature of a star can be obtained directly by measuring the total flux received on earth from it, and its angular diameter. In principle interferometrie methods could determine both the limb-darkening law of the stellar disk and the angular diameter of the disk. In practice, in order to obtain a decent accuracy on the angular diameter, interferometrie methods have so far borrowed the limb-darkening law from stellar atmosphere theory, in order to concentrate all the observational information on a single parameter. The total number of stellar diameters and effective temperatures obtained by this basic method remains very small (about 30 stars) and concerns exclusively giant or subgiant stars. The reader is invited to look at the following references and those therein (Di Benedetto 1993, Mozurkewich et al. 1991, Alonso et al. 1994). Smalley and Dworetsky (A&A in press) have reinvestigated the old Code et al. (1976) calibration with more recent spatial UV data, for B, A, and F stars, and have found no significant changes. The accuracy of the basic method is at the best of the order of 1.5 %, and there is a deep need for more data, and for doubling the current accuracy. Actually there is a strong effort for developping interferometry both from the ground (ESO VLTI, USNO astrometric interferometer) andfrom space (OSI project, Colavita et al. 1993; GAIA project at ESA). So there is hope for a not to far future.

The Hertzprung-Russel (HR) diagram luminosity calibration relies basically on three kinds of data: trigonometric parallaxes, kinematical data (proper motions and radial velocities) and cluster distances obtained by the zero-age main sequence fitting procedure. The most fundamental method to calculate the absolute magnitude is the use of trigonometric parallaxes, but up to now, accurate data only exist for stars contained in a small volume around the sun. Individual absolute magnitudes are obtained using trigonometric parallaxes or photometric and spectroscopic calibrations. In these calibrations the accuracy on the absolute magnitude determination ranges from ±0.m2 in the main sequence to ±0m5 in the giant branch. On the other hand, trigonometric parallaxes, kinematical data or cluster distances have been used to make statistical calibrations of the absolute magnitude. The standard error on the mean absolute magnitude calibrations ranges from ±0m3 to ±0m6 on the mean sequence, from ±0m5 to ±0m7 on thegiant branch and is of about 1m for supergiants.

Future improvements in the absolute magnitude determination will depend on the improvement of the basic data from the ground and space. A brief overview of the new available data is presented. In particular, the analysis of the first 30 months data of the Hipparcos mission (H30) (from the 37 months data of the whole mission) allows to perform a statistical evaluation of the improvements expected in the luminosity determination.

This section title is identical to that of the first paper where the broadening of absorption lines in response to stellar rotation was discussed: Abney (1877).

More accurate measurements now reveal also the details of stellar line shapes, making it possible to segregate the signatures of rotational and other broadening mechanisms: e.g. Gray (1992) and Smith & Gray (1976). To determine the rotation, fits can be made to line profiles (e.g. Anders et al., 1993), to their Fourier transforms (e.g. Dravins et al. 1990;Smith & Gray 1976), or to extended spectral regions (e.g. Kurucz et al. 1977).

This review, however, concerns issues for [single-epoch] spectroscopic observations only, no temporal aspect will be discussed.

What is observed is a rotationally broadened profile, the accuracy begins to get limited by the incomplete physical understanding of stellarline profiles and of the nature of stellar rotation. In order to disentangle the rotational broadening from other effects, one needs to know the ‘intrinsic’ (i.e. rotationally unbroadened) profile of the non-rotating star. How does this profile change with latitude and longitude across the stellar disk? What effects besides rotation are broadening the lines? What about mass loss, radial pulsation, non-radial oscillations, magnetic fields, spots, etc.? And the star might not even rotate as a rigid body, but perhaps differentially with respect to latitude and/or atmospheric height. All this has to be deduced from the often blended lines in complex spectra.

I will compute representative spectra for all spectral types for which my model calculations (Kurucz 1992; 1993a; 1994a) are valid. High-resolution zero-rotation fluxes and intensities will be distributed on CD-ROMS together with programs (Kurucz 1993B) for broadening the spectra to arbitrary rotation velocities, macroturbulent velocities, and instrumental profiles, and for transmitting the spectrum through an atmosphere.

Since the line data are still not well determined, I actually have to make two calculations, one with only the lines with good wavelengths to preserve wavelength detail, and one with all lines, including predicted, to preserve the energy distribution for photometric calibration. In the first case the spectrum is usable as a radial velocity, abundance, or classification template. Even though the line list is incomplete, its signal-to-noise can be higher than that of observed spectra for cross-correlating.

The models are plane parallel, LTE, in hydrostatic equilibrium, and have no triatomic opacities. Therefore, M stars and supergiants cannot be computed realisticly. The abundances available now are scaled-solar and alpha-enhanced scaled-solar. Individual abundances can be changed for the spectrum calculation. My new model atmosphere program, ATLAS 12 (Kurucz 1993c), which does not yet work, will allow arbitrary abundances.

I have made test calculations for Arcturus, the sun, Vega, Sirius, and a17000K B. star. Figure 1 shows the effect of resolution on the appearance of the spectrum. Figure 2 shows the effect of rotation. The spectrum for Arcturus is displayed in Kurucz (1994b) with the molecular bands labelled.

Observed hydrogen line profiles are an enormously important source of diagnostic information about virtually all kinds of astronomical bodies. Therefore, it is important to understand the hydrogen line formation in sufficient detail to be able to achieve a high degree of reliability by analyzing observed hydrogen line profiles.

Calculation of the predicted hydrogen line profiles involves two basic ingredients, (i) intrinsic line profiles, or line broadening - ”atomic physics” part, and (ii) the radiative transfer problem - ”astrophysics” part. There is not enough space to discuss here the current status of the astrophysical part of the problem. Fortunately, this topic is covered by many reviews. There are two major problems here, (a) departures from local thermodynamic equilibrium (LTE) - the so-called non-LTE description (e.g. Mihalas 1978; Hubeny et al. 1994); and (b) departures from complete frequency redistribution (Cooper et al. 1989; Hubeny and Lites 1994).

Frequently, the atmospheres of stars of spectral types B to F, on which the attention is particularly focussed in this Joint Discussion, are characterized by non-standard physical conditions: non-solar abundance patterns, surface in homogeneities, strong magnetic fields. The most extreme anomalies are found in the chemically peculiar (CP) stars but more moderate departures from standard atmospheres are observed in many stars in the considered temperature range. This can affect the derivation of fundamental stellar parameters in a number of ways, some of which will be presented in this contribution. The emphasis is set on those physical processes which are specific to CP stars. Due to lack of space, this review is necessarily incomplete: a selection of recent results of interest will be pointed out and some directions of investigation will be suggested.

CP stars have an anomalous continuous energy distribution. Fitting this distribution by standard model atmospheres can only be achieved using models corresponding to different effective temperatures to represent different spectral ranges (e.g., Leone & Catalano 1991). This is obviously not physically meaningful: the effective temperature characterizes the total flux of a star, thus is unique. “Realistic” models must incorporate the anomalous elemental abundances. Such models are presently being developed by Kurucz (ATLAS12) and by the Vienna group (Weiss 1994, private communication). The latter is adapted from Muthsam’s (1979) code. One important result obtained by Muthsam is that the relation T(τ) appears steeper in magnetic Ap stars than in normal stars. This view recently received support from observations of rapid oscillations (Matthews et al. 1990). But even such realistic models may not represent satisfactorily CP star atmospheres, as some potentially important opacity sources may still be unknown. For instance, the broad continuum depressions observed in many magnetic CP stars have not been fully explained yet.

Stellar models are the means by which we describe and understand the distribution of stars in the HR diagram. A stellar model is, in principle, completely specified by the three fundamental parameters mass, chemical composition, and age. Comparing the properties of models and real stars with the same parameters will tell us if our recipe for constructing stellar models is realistic. Unfortunately, the only star for which all three are known independently of stellar models is the Sun. For stars of other masses and ages we must devise observational tests in which at least one fundamental parameter is unknown. Two such popular test objects are double-lined eclipsing binaries and star clusters.

In suitable eclipsing binaries we can determine both masses and chemical composition; the absolute age is unknown, but the same for both stars. Since evolution depends most sensitively on the mass, eclipsing binaries provide a very direct test of the models, but only for two points on a single isochrone. In star clusters, neither ages nor individual masses are known, but the detailed shape and population of a well-observed cluster sequence in the HR diagram provide a number of additional probes into the models.

The fitting of isochrones over star-cluster colour-magnitude diagrams is a favourite test of stellar evolution models because it seems to be the easiest and most evident one: the star distribution in the colour-magnitude diagram represents a constant age locus, provided the clusters are old enough and the internal age dispersion is negligible. The ratios of evolved to main-sequence stars in open clusters, or of population along the red giant branch in globular clusters, could provide valuable tests, but it is difficult to estimate these ratios with small enough uncertainties. Furthermore the detailed surface chemical composition (element abundances and isotope ratios) is not known for many cluster stars and model predictions cannot be tested in various environments.

Tests have been mostly devoted to the main sequence and the long debate between canonical precepts and core overshooting is still active. St others (1991) has argued that the use of the new opacities (Rogers & Iglesias 1992) reduces the necessity of adding overshooting to the models. Castellani et al (1992) computed extensive grids of models with canonical precepts. However, recent papers (Carraro et al. 1993; Meynet et al. 1993; Demarque et al. 1994) show that a moderate core overshooting (about 0.2 Hp) is still necessary. Basically, cluster observations call for more massive cores, whatever process is at work. An excellent review of the various ingredients included in models (equation of state, nuclear rates, opacities, convection) and the effects of their changes has been presented by Vandenberg (1991).