A detailed frequency analysis on ELODIE observations of the Blazhko star RR Lyrae (Chadid et al., 1999) clearly revealed the importance of non-linear effects upon the radial fundamental mode (with frequency fP), and a multiplet structure with a separation equal to the Blazhko frequency (f/B) around the main frequency and its harmonics. These results provided strong evidence for the presence of non-radial modes in the star. The identification of these non-radial modes is the following step in our work.

An analysis of new and old photometry of the RR Lyrae star XZ Cyg indicates that both its primary period and its Blazhko period have undergone significant changes.

During the study of the factors governing the modal amplitudes of the double-mode radial pulsators, it has been found that the R21 Fourier parameter deduced from the light curves is in a relationship with the ratio of the modal amplitudes, for beat Cepheids and RR Lyrae variables, as well. The form of this relation gives a natural explanation for the fact that double-mode pulsators with slightly excited second modes do not exist.

Nonlinear convective pulsation models representative of SMC Cepheids pulsating in the second overtone mode are presented. Model predictions are compared with observations and implications are derived for second overtone selection criteria. The role of overtone Cepheids as distance indicators is finally investigated and the derived distance scale is at odds with the so called short distance scale.

We present the results of several numerical experiments aimed at testing the dependence of theoretical observables predicted by Cepheid hydrodynamical models on the equation of state (EOS). We focus our attention on nonlinear and time-dependent Cepheid convective models at solar chemical composition. We find that current predictions for both the blue and red edge of the instability strip present a mild dependence on the EOS. The same outcome applies to the morphology of the lightcurves.

We present a Spectroscopic study of two long period Cepheids: X Cyg and SV Vul, together with the prototype of the class.

The new tomographic technique devised by Alvarez et al. (2000) to explore the velocity field across the atmosphere of long-period variable stars (LPVs) is applied to the Mira variable Z Oph. The method cross-correlates the optical spectrum with numerical masks constructed from synthetic spectra and probing layers of increasing depths. This technique reveals that the line doubling often observed in LPVs around maximum light is the signature of the shock wave propagating in the atmosphere of these pulsating stars.

Models for hydrogen deficient stars are presented for different L/M-ratios and temperatures typical for RCB and HdC. Initially, we searched for unstable pulsation modes and identified their character using a simple linear code based on matrix methods. In a second step, we employed our fully-implicit Radiation-Hydro-Dynamics code to obtain amplitudes, radial velocities and lightcurves. For small L/M-ratios, nonlinear periods are close to the linear ones. Cooler models show strong shock-waves, which are suggested to play a key role in the dust formation of RCB stars which will be our ultimate goal.

We report new non-linear pulsation models for low-mass high-luminosity helium stars. These are compared with the observed periods of radially pulsating extreme helium stars.

Hydrogen-deficient early-type stars have an extremely high surface helium abundance (> 98% by number) and have represented a considerable challenge to stellar evolution theory. Recent work supports the view that they are the product of a merger between two white dwarfs.

All very luminous stars (log L/M > 4) are believed to pulsate, but at effective temperatures around 20 000 K, helium stars with lower luminosities (log-L/M < 3) are also known to pulsate due to iron-group bump instability. The two known cases are V652 Her and BX Cir. Their observed periods are in good agreement with linear theory. Recently high-resolution Spectroscopic observations were used to measure the stellar dimensions and radial velocity curves with high precision.

A hydrodynamic code including recent OPAL opacity data has been used to construct non-linear models of the pulsations of these two stars. The results impose additional constraints on those stellar dimensions, including mass, which remain poorly determined by observation.

We present a summary of a new time-dependent Spectroscopic analysis of the pulsating helium star V652 Her. The instantaneous properties of the star (effective temperature, surface gravity, radial displacement, etc.) are evaluated throughout the pulsation cycle. The data are used to establish measurements of the mean stellar radius and mass more accurately than hitherto. The first direct evidence of a supersonic shock at minimum radius is also obtained.

The most convincing evidence to date of solar-type oscillations in other stars comes from recent observations of β Hydri (Bedding et al., 2001) and α Cen A (Bouchy & Carrier, 2001). It is the current belief that the convection dynamics in the outer layers of sun-like stars is the source for driving the intrinsically stable modes to the observed amplitudes. Comparing such observations with theoretical models will help us improve our understanding of the interaction between convection and pulsation.

In this contribution I review the mechanisms responsible for mode damping in stars with convective envelopes, and the basic mechanism of stochastic driving by turbulent convection. The application of a stochastic excitation formalism to the Sun is discussed and compared with recent measurements and numerical simulations. Amplitude predictions for models of Procyon, α Cen A and β Hydri are compared with observations.

The Kuhfuß theory of convection is derived from the exact hydrodynamic equations by means of anelastic approximation and diffusion approximation. In the local and time-independent limit the result is identical to the MLT case. In the more general case the theory includes overshooting and convective mixing as well as time-dependence. We present test calculations in a simple box model and first steps toward the implementation in a stellar code.

Convection is one of the most problematic components of almost every model of a pulsating star. RR Lyrae stars, in particular, have a narrow convection zone at the outer layers, and a model without convection cannot get the red edge of the instability strip (see for example Kollath et al., 2000).

In recent years, the common approach is to use non-local time-dependent extensions to the Mixing Length Theory of convection (Bono et al., 1997; Feuchtinger, 1999). These models have many free parameters that need to be calibrated. In this paper we report on a preliminary work in which a different approach is used: 2D hydro simulations similar to the red giant model in Asida (2000). This approach was used by Deupree (1975, 1977) but we used a much better numerical resolution and focused on comparison with MLT results.

We have made a clear detection of p-mode oscillations in the G2V star α Cen A with the CORALIE spectrograph. The power spectrum clearly shows several identifiable peaks between 1.8 and 2.9 mHz. A preliminary astrophysical interpretation of these p-modes is presented.

Velocity measurements of the G2 subgiant β Hyi with both UCLES and CORALIE show a clear excess of power centred at 1.0 mHz. In the UCLES data we find evidence for a short-lived, high-amplitude oscillation event. If confirmed as a feature of subgiants, such ‘starquakes’ would make it harder to measure accurate mode frequencies and perform asteroseismology.

The spectrograph CORALIE reaches the radial velocity precision needed for an asteroseismological program on bright solar-like stars. We present here two results obtained with this instrument on the stars Procyon and β Hydri. A third campaign, on α Cen A, is presented independently in these proceedings by Carrier et al.

Kjeldsen et al. (1995) detected excess power in the GO subgiant η Boo from measurements of Balmer-line equivalent widths. The excess was at the expected level, and these authors were able to extract frequency separations and individual frequencies which agreed well with theoretical models (Christensen-Dalsgaard et al., 1995; Guenther & Demarque, 1996). A more detailed discussion of theoretical models for η Bootis was given by Di Mauro & Christensen-Dalsgaard (2001).

Kjeldsen et al. (1995) estimated the average amplitude of the strongest modes to be 7 times solar, corresponding to 1.6 m/s in velocity. 13 individual oscillation modes were identified consistent with a large frequency separation of 40.3 μHz. We note, however, that a search for velocity oscillations in this star by Brown et al. (1997) failed to detect a signal, setting limits at a level below that expected on the basis of the Kjeldsen et al. result.

In this paper we report further observations made in 1998. We observed this star in Balmer-line equivalent width with the 2.5-m Nordic Optical Telescope and in velocity with the 24-inch Lick CAT.

The spectrograph EMILIE (Bouchy et al., 1999; Bouchy, 1999; Bouchy et al., 2000) coupled to the Absolute Astronomical Accelerometer (AAA, Connes, 1985; Schmitt, 1997) and implemented at the 152-cm Coudé telescope of the Observatoire de Haute Provence is dedicated to high-precision Doppler measurements. The AAA method uses a sliding reference spectrum constrained to track the stellar lines and to use the spectrograph as a null-checking device. The goal of AAA is to eliminate the calibration of the spectrograph as well as the displacement of the spectra across the CCD pixels due to the earth motion (and suspected to introduce a systematic error in the RV measurement). Here we report seismological results obtained with AAA on the Sun and the bright stars Procyon and ζ Her A that are expected to present solar-like oscillations.

Observations of solar-like oscillation frequencies allow us to constrain the theory of structure and evolution of stars with an outer convective zone. Recent improvements in radial velocity measurements have led to p-mode detection on Procyon (Martic et al., 1999) and β Hydri (Bedding et al., 2001; Carrier et al., 2001a). Very recently, characterization of the p-modes of α Cen A has been made with the spectrograph CORALIE mounted on the 1.2-m Swiss telescope at the ESO La Silla Observatory (Bouchy & Carrier, 2001, Carrier et al., these proceedings). The power of the radial velocity technique promises the development of ground-based search for solar-like oscillations on a large sample of stars especially with the future spectrograph HARPS.