We extend the second-order asymptotic description developed by Tassoul (1980, 1990) to the forth order, taking into account both gravity perturbations and realistic (non-polytropic) structure of the stellar envelope. We examine the accuracy of the asymptotic description by the direct computations for a solar model.

The subseismic approximation for low-frequency modes in the Earth is used in an asymptotic treatment of low-frequency g-modes belonging to low-degree spherical harmonics in a non-rotating star.

Accurate measurement of the frequencies of low-degree acoustic oscillations of sun-like stars is imminent. We report on our first calculations with proxy data, aimed at assessing the kind of physical information that is likely to be acquired from seismic analysis and the precision with which the frequencies must be measured in order to obtain that information. The results will have an important bearing on future observing strategies, for the duration of observation should be determined primarily by the precision required of the frequency measurements. Our inversions are of eigenfrequencies of modes of an evolved main-sequence star of mass 1.1M⊙. The modes are of degree 0, 1 and 2, with frequencies in the range 1-3 mHz. Thus, by analogy with solar oscillations, they are modes that one should expect to observe in stars similar to the sun. Figure Ia depicts an idealized spectrum of stellar acoustic oscillations as one might expect from intensity variations such as those that could be measured from the proposed ESA spacecraft PRISMA. We report on the extent to which we have found it possible to determine the mass and radius of the stars, and on the seismic evidence for evolution having taken place in the core.

Stars more massive than about 1.2M⊙ are characterised by a convective core, which induces at its frontier a rapid variation of the sound speed and of the Brunt-Väissälä frequency, close to a discontinuity. We present preliminary results about the search of the signature this core could have on the p-mode spectra. For a set of frequencies of three stars of 1, 1.5 and 2 M⊙, we study in particular the small frequency separation Δν0,2, ~ νn,l, νn-1,l+2 for high order and low degree oscillation modes, which is particularly sensitive to the interior of stars. We underline characteristic behaviours of the 1.5 and 2 M⊙ stars, through the comparison between computed frequencies and their approximation obtained by asymptotic and polynomial fittings, and also through second order quantities relatively to the frequencies.

We consider here two Delta Scuti stars GX Pegasi and V650 Tauri, which show very close masses and evolution stages as infered from photometrical calibration. The se two stars have been observed by the STEPHI team (Michel et al. 1990, Belmonte et al. this procedings) and they appear to be multiperiodic pulsators. For both these stars, an identification of the observed frequencies is proposed, from comparison with adiabatic eigenfrequencies computed for well suited stellar mode ls. This interpretation reveals very different pulsational behaviors despite the sta rs are expected to present very similar internal structures. We report here a first step toward constraining models by improving the fit between the observed and the calculated eigenfrequencies. The effect of overshooting and of the recent enhancement of the opacities are i nvestigated.

The addition of seismic parameters to stellar-model calibrations substantially increases the constraints one can place on the properties of stars. We present some preliminary calculations to assess the accuracy with which certain stellar parameters can be inferred. For simplicity we use just two of the three most basic seismic parameters characterizing the low-degree p modes that might be measured from intensity variations by instruments such as photometers planned for the ESA spacecraft PRISMA. We ascertain the accuracy of a calibration of an isolated star and of a cluster of N solar-type stars.

Pulsation frequency separations, combined with other observations, can constrain the structural parameters of Sun-like stars. As an example, we treat a hypothetical visual binary system resembling α Cen.

It is important for understanding stellar evolution to constrain observationally how overshoot occurs for stellar conditions. Simplified models of the dynamics (eg. Zahn 1991) indicate that overshoot results in a slightly subadiabatic region beyond the convectively unstable layers, followed by an almost discontinuous transition to radiative stratification. Abrupt changes such as this contribute with a characteristic periodic signal to the frequencies ωn,l, of modes of low degree l (Gough 1990). This signature may therefore be detectable for distant stars. Here we show that the signal is sensitive to the “severity” of the overshoot and, of practical importance for the solar case, how it may be extracted from modes of higher degree. Finally we apply our method to solar data.

To analyze the applicability of the method, we consider four stellar models, Z1 — Z4, with solar mass, radius (R) and luminosity; of these, Z2 and Z4 have overshoot. The bases of the nearly adiabatically stratified region in the models are at radii rd/R = .729, .713, .713 and .700 respectively.

The low frequency NRP oscillations are considered in the case of differential rotation. Partial differential equations for adiabatic oscillations are reduced to a system of ordinary equations by means of a truncated spherical-harmonic expansion. The numerical method for solving the system is described. The final model also includes line profile variations (lpv) and posttheoretical mass (pth) calculations for the complete determinations of the physical, chemical, rotational and seismological properties of the stars.

Recently, one of the rapidly oscillating Ap stars, HR 3831, has been found to have an equally split frequency septuplet, though its oscillation seems to be essentially an axisymmetric dipole mode with respect to the magnetic axis which is oblique to the rotation axis (Kurtz et al. 1992; Kurtz 1992). In order to explain this fine structure, we investigate oscillations of rotating magnetic stars by taking account of the perturbations due to the magnetic fields and the rotation. We show that the magnetic field on axisymmetric dipole modes distorts the dipole oscillation pattern to have axisymmetric octapole components so that the frequency pattern becomes a septuplet rather than a triplet, and that the additional effect of the rotation leads the frequency pattern to be asymmetric. The formula allows us to get information about the magnetic fields, the rotation, and the geometrical configuration of the star from the oscillation data.

Rotating stars are normally presumed to rotate about a unique axis. Would it be possible to determine whether or not that presumption is correct? This is a natural question to raise, particularly after the suggestion by T. Bai & P. Sturrock that the core of the sun rotates about an axis that is inclined to the axis of rotation of the envelope.

A variation with radius of the direction of the rotation axis would modify the form of rotational splitting of oscillation eigenfrequencies. But so too does a variation with depth and latitude in the magnitude of the angular velocity. One type of variation can mimic the other, and so frequency information alone cannot differentiate between them. What is different, however, is the structure of the eigenfunctions. Therefore, in principle, one might hope to untangle the two phenomena using information about both the frequencies and the amplitudes of the oscillations.

We consider a simple model of a star which is divided into two regions, each of which is rotating about a different fixed axis. We enquire whether there are any circumstances under which it might be possible to determine seismologically the separate orientations of the axes.

Rotational splitting Δω(n,l,m) of the eigenfrequencies of a star rotating with angular velocity Ω(r, θ) about a unique axis can be represented as a weighted integral of Ω over r and θ, (r, θ, φ) being spherical polar coordinates about the axis of rotation. For high-frequency acoustic modes, Δω/m collapses essentially to a function of ω — ω /(l+1/2) and M = m/(l + 1/2) alone, and the weighting kernel K(r,θ) becomes asymptotically degenerate, each factor being of essentially Abel type. Therefore, formally, the splitting integral can be inverted, once a procedure has been found for extending Δω over the domain of (ω, M) such that the turning points (rt,ωt), given by (c(rt)/rt, sinωt) = (ω, M) where c is sound speed, span the star. Obtaining that representation is the most difficult stage of the inversion. We report on a procedure that treats the inverted two-dimensional Abel integral as a repeated double integral, representing the data successively along a set of parallel lines M =constant. The method is illustrated by an inversion of artificial data which is compared with the angular velocity from which those data were computed.

The cool extended atmospheres of late type giants are sites where dust formation takes place. Radiation pressure on the dust grains is an important force for driving the slow but massive winds observed in such objects. Existing calculations of dust driven stellar winds (e.g. Bowen 1988, Fleischer et al. 1991) suffer from the fact that they include approximations at various levels for different parts of the problem like the hydrodynamics or the dust formation. Furthermore they do not include time-dependent radiative transfer.

In order to overcome these insufficiencies we plan to calculate self-consistent models of dust driven winds with a full description of both the radiation hydrodynamics and the time-dependent dust formation. As a first step, however, we concentrate our investigations on the self-consistent description of the radiation hydrodynamics adopting only a simple description of the dust opacities.

It is possible to show that cool giants with very large photospheric scale heights do not perfectly reflect pulsational waves at the photosphere. This means that for these stars the classical formulation of pulsation in which the outer boundary for the resonance cavity is assumed to be perfectly reflecting is not valid. This can have significant consequences for the eigenfrequencies of the pulsation of Long Period Variables such as Mira type variables as well as for the stability of their pulsation.

Energy is transported from the central regions of a star to its surface. Generally this transport is in certain layers carried on by convective motions. Because of the structure, which these motions have due to the influence of the overall rotation, the star becomes electromagnetically unstable, i.e. a large magnetic field grows from small seed fields as a result of the dynamo process. The internal structure, especially the symmetries of a star, will be, at least to some extend, reflected by the spatial structure and the time behaviour of the excited magnetic field. In this sense observations of the magnetic field on a surface of a star and the related activity phenomena can provide insight in the internal structure of the star, since characteristic parameters like thickness of the convection zone, mixing length, turnover time, profile of the differential rotation, etc. strongly influence the dynamo process.

The actual magnetic field of a star is a product of a nonlinear process. Models elaborated on the kinematical (i.e. linear) level provide insight in the excitation conditions and the linear field modes. The marginal mode, i.e. the mode which is easiest to excite, reflects properties of the nonlinear solution in case the system operates not far from the margin to the dynamo unstable region. Here the solutions show symmetries with respect to the axis of rotation and the equatorial plane, properties which are, for example, to a large extend fulfilled for the solar average magnetic field. For systems operating far from this margin irregular or even chaotic behaviour has to be expected. From observations there is a strong indication that these theoretical possibilities find their realizations within the sample of late-type stars.

Non-radiatively heated outer atmospheres are common among stars on the cool side of the HR diagram. These atmospheres resemble that of the Sun in which the bulk of the heating is associated with magnetic fields. Consequently it is assumed that other cool stars also generate and maintain an internal magnetic field through a dynamo action. This field gives rise to a wide spectrum of phenomena in the stellar atmosphere. The dynamo process that sustains the field thrives on the interaction of rotation and turbulent convection. In this review I formulate a set of propositions outlining our present knowledge of this interaction as distilled from stellar observations. In doing so, I outline the effects of stellar evolution on rotation rate, discuss some of the proposed “dividing lines” in the HR-diagram, and comment on the possible role of the convective turnover time in dynamo efficiency and on dynamo activity for extremely slowly and rapidly rotating stars.

The vast variety of solar-like phenomena on other late-type stars, so-called activity tracers, provide an important tool for studying the structure of active stellar atmospheres and their connection to the stellar interior via strong magnetic fields. These “chromospherically active” stars include single and binary stars as well as pre- and post-main sequence objects and have rapid rotation and deep convective layers in common. They serve as astrophysical laboratories to study the vast phenomenology of activity tracers: starspots, plages, flares, prominences, which might be seen as enhanced analogs of solar activity and could be spatially resolved due to rotationally modulated indicators. In this paper we review the current observational material and discuss its impact on our knowledge of “active” atmospheres, especially in the context of stellar rotation.

It is by now well known that most main sequence stars continuously lose mass as a consequence of the winds they emit. In addition to affecting the thermal and dynamical state of the stellar atmosphere, such mass loss can also induce changes in the interiors of stars. In the present review, we consider a few of the ways in which sustained, wind-like mass loss can alter the physical state of main sequence stellar interiors by examining the differences in internal structure, composition, and rotation between mass-losing and conservatively evolving stars.

Dynamo theory needs to be guided and tested by observations. However, solar observations alone cannot provide sufficient tests of the dynamo models, and constraints obtained from stellar observations are still few, indirect, and poorly related to the properties of dynamos.

This review discusses which parameters must be observed on stars other than the Sun to usefully guide the theoretical efforts and test the resulting models. We show that most of these observables, which characterize the stellar activity phenomena, are accessible only from space, and that space-based experiments are one of the best took to trigger progress in the field of solar and stellar activity in the next few decades.

We present preliminary observational evidences on the variation of the activity level in late type stars, during the evolutionary phases on the main sequence and beyond. We have selected a sample of 51 stars (Fig. 1), lying mostly along evolutionary tracks between 1.3 and 1.7 solar masses, which have been observed in soft X-rays with the Einstein Observatory, and in UV with IUE (Maggio et al. 1990; Haisch et al.1990). Two ROSAT targets, and four new IUE observations are also included.

We find that the radiative emission from the outer atmospheres of stars with M > 1.6M⊙ seems to behave differently than for stars with lower mass.

On the main sequence, the X-ray luminosity of most stars with B-V < 0.42 (spectral type F3) is relatively low, at Lx ~ 3 × 1028erg s-1 (Fig. 2). In the early evolutionary phases beyond the main sequence, the X-ray luminosity of the higher mass stars tend to increase sistematically up to ~ 1030erg s-1, while the lower mass stars show an initial moderate increase followed by a drop, at B-V ~ 0.6, below our sensitivity threshold.