The Astronomy and Astrophysics Review (2011) DOI 10.1007/s00159-007-0007-0 REVIEWARTICLE M. S. Cunha · C. Aerts · J. Christensen-Dalsgaard · A. Baglin · L. Bigot · T. M. Brown · C. Catala · O. L. Creevey · A. Domiciano de Souza · P. Eggenberger · P. J. V. Garcia · F. Grundahl · P. Kervella · D. W. Kurtz · P. Mathias · A. Miglio · M. J. P. F. G. Monteiro · G. Perrin · F. P. Pijpers · D. Pourbaix · A. Quirrenbach · K. Rousselet-Perraut · T. C. Teixeira · F. Thevenin´ · M. J. Thompson Asteroseismology and interferometry Received: 17 August 2007 c Springer-Verlag 2007 Abstract 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 ba- sic 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 stud- ies are expected to provide a significant input. We discuss current limitations to asteroseismic studies, including difficulties in mode identification and in the accu- rate 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 M. S. Cunha (B) · T. C. Teixeira · P. J. V. Garcia Centro de Astrof´ısica da Universidade do Porto, Rua das Estrelas, 4150-762 Porto, Portugal [email protected] · C. Aerts Instituut voor Sterrenkunde, Katholieke Universiteit Leuven, Celestijnenlaan 200 D, 3001 Leu- ven, Belgium · C. Aerts Afdeling Sterrenkunde, Radboud University Nijmegen, PO Box 9010, 6500 GL Nijmegen, The Netherlands · J. Christensen-Dalsgaard · F. Grundahl Institut for Fysik og Astronomi, Aarhus Universitet, Aarhus, Denmark · A. Baglin · C. Catala · P. Kervella · G. Perrin LESIA, UMR CNRS 8109, Observatoire de Paris, Paris, France · P. Mathias Observatoire de la Coteˆ d’Azur, UMR 6203, BP 4229, 06304 Nice Cedex 4, France · L. Bigot · F. Thevenin´ · P. Mathias Observatoire de la Coteˆ d’Azur, UMR 6202, BP 4229, 06304 Nice Cedex 4, France · T. M. Brown Las Cumbres Observatory Inc., Goleta, CA 93117, USA · O. L. Creevey High Altitude Observatory, National Center for Atmospheric Research, Boulder, CO 80301, USA · O. L. Creevey 2 M. S. Cunha et al. 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, sum- marizing ongoing efforts concerning the development of future instruments and satellite missions which are expected to have an impact in this field of research. Keywords Stars: variables: general · , Stars: interiors · , Techniques: interfero- metric 1 Introduction 1.1 Historical perspective Periodic variable stars have been known to exist since the seventeenth century, when Jan Fokkens Holwarda realized that the magnitude of Mira, a variable star discovered almost a century earlier by David Fabricius, varied periodically with a period of 11 months (Hoffleit 1997). The periodic variability observed by Hol- warda is intrinsic to Mira and results from consecutive contractions and expan- sions of its surface, associated with waves that propagate within its interior. Stars which owe their variability to this phenomenon are known as pulsating (variable) stars. Despite the early discovery by Holwarda, the understanding that some variable stars owe their variability to intrinsic pulsations came almost three centuries later, following a suggestion by Shapley (1914) driven by the difficulties with recon- ciling the observed variability with the hypothesis of binarity. At about the same time, pulsating stars started being systematically used as tools for astrophysics research following the discovery of the Period-Luminosity relation by Henrietta Leavitt (Leavitt 1908; Pickering 1912). Classical pulsating stars have since been Instituto de Astrofsica de Canarias, Tenerife 38200, Spain · A. Domiciano de Souza Max-Planck-Institut fur¨ Radioastronomie, Auf dem Hugel¨ 69, 53121 Bonn, Germany · P. Eggen- berger Observatoire de Geneve,` 51 chemin des Maillettes, 1290 Sauverny, Switzerland · P. Eggen- berger · A. Miglio Institut d’Astrophysique et de Geophysique´ de l’Universite´ de Liege` Allee´ du 6 Aout,ˆ 17, 4000 Liege,` Belgium · P. J. V. Garcia Departamento de Engenharia F´ısica, Faculdade de Engenharia, Universidade do Porto, Rua Dr. Roberto Frias, 4200-465 Porto, Portugal · D. W. Kurtz Centre for Astrophysics, University of Central Lancashire, Preston PR1 2HE, UK · M. J. P. F. G. Monteiro Centro de Astrof´ısica e Departamento de Matematica´ Aplicada da Faculdade de Ciencias,ˆ Uni- versidade do Porto, Porto, Portugal · F. P. Pijpers Space and Atmospheric Physics Group, Imperial College London, Exhibition Road, London SW7 2AZ, UK · D. Pourbaix F.R.S-FNRS, Institut d’Astronomie et d’Astrophysique, Universite´ Libre de Bruxelles, 1050 Brussels, Belgium · A. Quirrenbach Zentrum fur¨ Astronomie der Universitat¨ Heidelberg, Landessternwarte Konigstuhl,¨ 69117 Hei- delberg, Germany · K. Rousselet-Perraut Laboratoire d’Astrophysique de l’Observatoire de Grenoble, BP 53, 38041 Grenoble Cedex 9, France · M. J. Thompson School of Mathematics and Statistics, University of Sheffield, Hounsfield Road, Sheffield S3 7RH, UK Asteroseismology and interferometry 3 Fig. 1 Hertzsprung-Russell diagram showing different classes of pulsating stars. Some of these are named after a particular member of the class. Others are acronyms, standing, respectively, for: rapidly oscillating Ap (roAp); Slowly Pulsating B (SPB); subdwarf B variables (sdBV). The group labelled GW Vir includes what has formerly been known as the PNNV stars (for Planetary Nebulae Nuclei Variables), and the variable hot DO white dwarfs (DOV); the DBV and DAV stars are variable DB (helium-rich) and DA (hydrogen-rich) white dwarfs. The parallel long-dashed lines indicate the Cepheid instability strip used as “standard candles” of the Universe and, still today, are of fundamental importance for the determination of astrophysical distances. During the decades that followed the discovery by Henrietta Leavitt, the the- oretical studies of classical pulsating stars were directed towards the mathemati- cal description of the pulsations and the understanding of the mechanism behind their excitation (e.g. Zhevakin 1963, and references therein). In the early 1960s, the discovery and interpretation of solar oscillations (Leighton et al. 1962; Fra- zier (1968); Ulrich (1970)) opened a new era in the study of pulsating stars. So- lar oscillations have been shown to be amazing tools to “look” inside the Sun and image its structure and dynamics. The study of solar oscillations fostered the development of an entire new field of research—known as Helioseismology (e.g. Gough 1977a; Duvall 1982; Duvall et al. 1984; Christensen-Dalsgaard et al. 1985)—which has proved extremely successful in probing the physics of the solar interior (see Christensen-Dalsgaard 2002, for a recent review on helioseismology). Following the success of helioseismology, attempts to use intrinsic oscillations of stars other than the Sun to learn about their internal structure and dynamics have led to the development of Asteroseismology. However, the road-map to success of asteroseismology proved much harder, as a result of the limitations brought about by our incapacity to resolve distant stars, and also by the limited number of oscillation frequencies observed in most of them. In fact, even though many different classes of pulsating stars are presently known—most of these are shown in Fig. 1—not all classes of pulsators are suitable for asteroseismic studies (cf. Sect. 1.4). The twenty-first century has brought important new developments to astero- seismology. With highly precise spectrometers such as CORALIE and HARPS (at ESO-La Silla), UCLES (at AAT), and UVES (at ESO-Paranal) fully operational, it was finally possible to make clear detections of solar-like oscillations in stars other than the Sun (see Bedding and Kjeldsen 2007, for a recent review), thus confirming earlier evidence, found by different authors with different observing techniques and instruments, of excess power in the oscillation spectra of some of these stars (e.g. Brown et al. 1991; Schou and Buzasi 2001). Our understanding of the Sun and solar oscillations, as well as the tools developed in the context of helioseismology, make us confident that the detection of solar-like pulsations in stars other than the Sun will lead to major developments in our understanding of stellar structure, dynamics and evolution. 1.2 Stellar modelling and the ultimate goal of asteroseismology Broadly speaking, “classical” stellar observables, such as the effective tempera- ture, gravity and metallicity, are insensitive to the details of the internal structure 4 M. S. Cunha et al. of stars, and do not provide sufficient constraints for the determination of the basic stellar parameters, not to mention the calibration of parameters commonly used in stellar modelling. Pulsation frequencies, on the other hand, are very sensitive to the details of the internal structure of stars. Each individual frequency probes