Asteroseismology provides us with a unique opportunity to improve our understanding of stellar structure and evolution. Recent developments, including the first systematic studies of solar-like pulsators, have boosted the impact of this field of research within astrophysics and have led to a significant increase in the size of the research community. In the present paper we start by reviewing the basic observational and theoretical properties of classical and solar-like pulsators and present results from some of the most recent and outstanding studies of these stars. We centre our review on those classes of pulsators for which interferometric studies are expected to provide a significant input. We discuss current limitations to asteroseismic studies, including difficulties in mode identification and in the accurate determination of global parameters of pulsating stars, and, after a brief review of those aspects of interferometry that are most relevant in this context, anticipate how interferometric observations may contribute to overcome these limitations. Moreover, we present results of recent pilot studies of pulsating stars involving both asteroseismic and interferometric constraints and look into the future, summarizing ongoing efforts concerning the development of future instruments and satellite missions which are expected to have an impact in this field of research.

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Asteroseismology and interferometry

Context. The term macroturbulent broadening is commonly used to refer to a certain type of non-rotational broadening affecting the spectral line profiles of O- and B-type stars. It has been proposed to be a spectroscopic signature of the presence of stellar oscillations;however, we still lack a definitive confirmation of this hypothesis. Aims. We aim to provide new empirical clues about macroturbulent spectral line broadening in O- and B-type stars to evaluate its physical origin. Methods. We used high-resolution spectra of 430 stars with spectral types in the range O4 - B9 (all luminosity classes) compiled in the framework of the IACOB project. We characterized the line broadening of adequate diagnostic metal lines using a combined Fourier transform and goodness-of-fit technique. We performed a quantitative spectroscopic analysis of the whole sample using automatic tools coupled with a huge grid of fast wind models to determine their effective temperatures and gravities. We also incorporated quantitative information about line asymmetries into our observational description of the characteristics of the line profiles, and performed a comparison of the shape and type of line-profile variability found in a small sample of O stars and B supergiants with still undefined pulsational properties and B main-sequence stars with variable line profiles owing to a well-identified type of stellar oscillations or to the presence of spots in the stellar surface. Results. We present a homogeneous and statistically significant overview of the (single snapshot) line-broadening properties of stars in the whole O and B star domain. We find empirical evidence of the existence of various types of non-rotational broadening agents acting in the realm of massive stars. Even though all these additional sources of line-broadening could be quoted and quantified as a macroturbulent broadening from a practical point of view, their physical origin can be different. Contrarily to the early-to late-B dwarfs and giants, which present a mixture of cases in terms of line-profile shape and variability, the whole O- type and B supergiant domain (or, roughly speaking, stars with M-ZAMS greater than or similar to 15 M-circle dot) is fully dominated by stars with a remarkable non-rotational broadening component and very similar profiles (including type of variability). We provide some examples illustrating how this observational dataset can be used to evaluate scenarios aimed at explaining the existence of sources of non-rotational broadening in massive stars.

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The IACOB project: III. New observational clues to understand macroturbulent broadening in massive O- and B-type stars ?

We present an investigation of the magnetic field geometries and inhomogeneous distribution of chemical elements in the atmospheres of peculiar A and B stars. Our study combines high-quality spectroscopic and spectropolarimetric stellar observations with the development and application of novel techniques for theoretical interpretation of the shapes and variability of stellar line profiles. In particular, we extend the method of Doppler imaging to the analysis of spectra in the four Stokes parameters, making it possible to derive detailed and reliable stellar magnetic maps simultaneously with the imaging chemical inhomogeneities.The magnetic Doppler imaging is applied to study of magnetic topologies and distributions of chemical elements in the peculiar stars α2 CVn and 53 Cam. We found that the magnetic field geometry of 53 Cam is considerably more complex than a low-order multipolar topology, commonly assumed for magnetic A and B stars. Our Doppler imaging analysis also led to a discovery and study of spots of enhanced mercury abundance in the atmosphere of α And, a star where the presence of a global magnetic field is unlikely.The ESO 3.6-m telescope is used to collect unique, very high spectral- and time-resolution observations of rapidly oscillating peculiar A (roAp) stars and to reveal line profile variations due to stellar pulsations. We present a detailed characterization of the spectroscopic pulsational behaviour and demonstrate a remarkable diversity of pulsations in different spectral lines. The outstanding variability of the lines of rare-earth elements is used to study propagation of pulsation waves through the stellar atmospheres and identify pulsation modes. This analysis led to a discovery of a non-axisymmetric character of pulsations in roAp stars.Our study of chemical stratification in the atmosphere of the roAp star γ Equ provides a compelling evidence for significant variation of the chemical composition with depth. We find a combined effect of extreme chemical anomalies and a growth of pulsation amplitude in the outermost atmospheric layers to be the most likely origin of the high-amplitude pulsational variations of the lines of rare-earth elements.Observations of cool magnetic CP stars are obtained with the ESO Very Large Telescope and are used for empirical investigation of the anomalies in the atmospheric temperature structure. We show that the core-wing anomaly of the hydrogen Balmer lines observed in some cool CP stars can be attributed to a hot layer at an intermediate atmospheric depth.

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Time-resolved spectroscopy of the roAp star gamma Equ

We present the results of a spectroscopic monitoring campaign of the OB-star companions to the eclipsing X-ray pulsars SMC X−1, LMC X−4 and Cen X−3. High-resolution optical spectra obtained with UVES on the ESO Very Large Telescopeare used to determine the radial-velocity orbit of the OB (super)giants with high precision. The excellent quality of the spectra provides th e opportunity to measure the radial-velocity curve based on individual lines, and to study the effect of possible distortions of the line profiles due to e.g. X-ray heating on the derived radial-velocity amplitude. Several spectral lines show intrinsic variations with or bital phase. The magnitude of these variations depends on line strength, and thus provides a criterion to select lines that do not suffer from distortions. The undistorted lines show a larger radial-velocity amplit ude than the distorted lines, consistent with model predict ions. Application of our line-selection criteria results in a mean radial-vel ocity amplitude Kopt of 20.2±1.1, 35.1±1.5, and 27.5±2.3 km s −1 (1σ errors), for the OB companion to SMC X−1, LMC X−4 and Cen X−3, respectively. Adding information on the projected rotational velocity of the OB companion (derived from our spectra), the duration of X-ray eclipse and orbital parameters of the X-ray pulsar (obtained from literature), we arrive at a neutron star mass of 1.06 +0.11 −0.10 , 1.25 +0.11 −0.10 and 1.34 +0.16 −0.14 M⊙ for SMC X−1, LMC X−4 and Cen X−3, respectively. The mass of SMC X−1 is near the minimum mass (∼1 M⊙) expected for a neutron star produced in a supernova. We discuss the implications of the measured mass distribution on the neutron-star formation mechanism, in relation to the evolutionary history of the massive binaries.

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Determination of the mass of the neutron star in SMC X-1, LMC X-4, and Cen X-3 with VLT/UVES

V 2052 Oph is a β Cep star with v sini ∼ 60 km s −1 . The behavior of its stellar wind was studied in the ultraviolet wavelength region with the IUE satellite. It revealed periodic variations in the equivalent widths (EW) of the resonance lines of wind-sensitive ions with a period of 3.638833 d, which is identified as the rotational period. These variations are typical of magnetic stars. Therefore time-resolved circular spectropolarimetric observations were obtained with the Musicos ´ spectropolarimeter at the 2-m Telescope Bernard Lyot (TBL) to search for a magnetic field in the star. Stokes V patterns were observed, the inclination and magnetic angles were derived and a value was determined for the polar magnetic field (250 ± 190 G) using an oblique rotator dipole model. The spectroscopic information was used to search for periodicity in line-profile variations (lpv), radial velocity and minimum intensity curves. Multiperiodicity was found, corresponding to radial (f1 = 7.15 c d −1 ) and non-radial (f2 = 6.82 c d −1 , l = 3 or 4) pulsation modes. The rotation period is also detected in rotationally modulated observables because of the magnetic poles passing through the observer's line of sight. We determined the stellar parameters of the star, which was found to be chemically peculiar, in particular He-enriched. This makes V 2052 Oph the first magnetic He-strong early B star with known pulsational properties.

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Rotation, pulsations and magnetic field in V 2052 Ophiuchi: A new He-strong star

We present a useful formulation of the surface-velocity field of a rotating, adiabatically pulsating star, which accounts for the effects of the Coriolis force. We use this model to investigate the observable spectroscopic characteristics of non-radial pulsations. We calculate time series of absorption line profiles in a carefully chosen domain of parameter space. Only mono-periodic spheroidal modes are investigated; atmospheric changes due to the pulsation are neglected. The line-profile variations, as well as their behavior inferred from two well-defined diagnostics, are presented in two-dimensional parameter grids. We show that the intensity variations in time series of theoretical spectra, at each position in the line profile, cannot be described by a single sinusoid: at least one harmonic sinusoid needs to be included. Across the line profile the relative amplitudes and phases of these sinusoids vary independently. The blue-to-red phase difference found at the main pulsation frequency turns out to be an indicator of the degree , rather than the azimuthal order ; the phase difference of the variations with the first harmonic frequency is an indicator of . Hence, the evaluation of the variability at the harmonic frequency can improve the results derived from an analysis of observed line profiles. We find, that if line-profile variations at the line center dominate over the variations in the line wings, this does not give conclusive information on the ratio of the horizontal to the vertical pulsational surface motions. Tesseral modes, when observed at not too high inclinations, are as much capable of producing considerable line-profile variations as sectoral modes. We find that, within the limits of our model, the effects of rotation on the appearance of the line-profile variations are important for low-degree sectoral modes, and for the sub-class of the tesseral modes with an even number.

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E Ruymaekers

Papers

Line-profile variations due to adiabatic non-radial pulsations in rotating stars. I. Observable characteristics of spheroidal modes