Communications in Asteroseismology

Volume 145 June, 2004

Proceedings of the JENAM Minisymposium Budapest, 29-30 August, 2003 Edited by Zoltan Kollath & Gerald Handler

Editor: Michel Breger, Turk¨ enschanzstraße 17, A - 1180 Wien, Austria Layout and Production: Wolfgang Zima Editorial Board: Gerald Handler, Don Kurtz, Jaymie Matthews, Ennio Poretti Publication Board: Victoria Antoci http://www.deltascuti.net

British Library Cataloguing in Publication data. A Catalogue record for this book is available from the British Library. All rights reserved ISBN 3-7001-3291-3 ISSN 1021-2043 Copyright °c 2004 by Austrian Academy of Sciences Vienna Contents

Preface 5 Identification of modes in main-sequence pulsators by means of multi-color photometry by J. Daszynsk´ a-Daszkiewicz, W.A. Dziembowski, A.A. Pamyatnykh 6 Influence of the convective flux perturbation on stellar oscillations: application to δ Scuti and γ Doradus stars by A. Grigahcène, M-A. Dupret, R. Garrido, M. Gabriel and R. Scuflaire 9 Testing the internal physics of white dwarfs from their pulsational properties by J. Isern, E. Garc´ıa–Berro, A.H. Córsico, O.G. Benvenuto and L.G. Althaus 12 The Blazhko Effect: Facts, Figures and Future work by K. Kolenberg 15 Numerical modelling of the RR Lyrae instability strip by R. Szabó 20 UBV I Time-series Photometry of the Old LMC Globular Cluster Reticulum by V. Ripepi, M. Monelli, M. Dall’Ora et al. 23 Long-term photometric study of LBVs in M33 by A. Zharova and O. Sholukhova 26 Cepheids in binary systems – new candidates in the Magellanic Clouds by L. Szabados 27 A continuous population of variable stars up to about 1.5 mag above the horizontal branch? by L. Baldacci, G. Clementini, E.V. Held, M. Marconi, L. Rizzi 30 The core/envelope asymmetry in p-mode pulsating stars by A. Miglio and E. Antonello 35 Mapping non-radial pulsation using surface imaging techniques by S.V. Berdyugina, H. Korhonen, J.H. Telting, C. Schrijvers 38 High Amplitude δ Sct-type variables by E. Rodr´ıguez 40 Pulsational behaviour of the HADS RY Lep by E. Rodr´ıguez, C.D. Laney, P.J. Amado, M.J. López-González and M. Joner 46 SZ Lyn: New pulsational and orbital elements based on old and recent photometric observations by K.D. Gazeas, P.G. Niarchos, K.A. Boutsia 47 Short–Period Variables in ASAS Photometry by J. Molenda–Zak˙ owicz 48 Asteroseismology of Procyon: Preliminary results from SARG by R.U. Claudi, A. Bonanno, R. Ventura et al. 51 The use of Petersen diagrams and period ratios in investigating the pulsational content of stars in the classical Instability Strip by E. Poretti and M. Beltrame 53 4

Period–radius relation for semiregular and Mira stars by K. Szatmáry 58 Relevant issues in the study of Pre-Main Sequence δ Scuti stars by M. Marconi, V. Ripepi, F. Palla and A. Ruoppo 59 Pulsating stars in open clusters by T. Arentoft, L.M Freyhammer, M.Y Bouzid, C. Sterken and S. Frandsen 65 A Variable Star Survey of the Open Cluster NGC 2126 by A. Gáspár, L. L. Kiss, A. Derekas et al. 68 Amplitude and frequency variability of pulsating stars by G. Handler 69 New observational results on pulsating B stars by A. Pigulski 72 Radial Velocity variations of the roAp-star HD122970: new results by A. Gamarova, A.P. Hatzes and D. Mkrtichian 77 Pulsation and Binarity in RZ Cas by E. Rodr´ıguez, J.M. Garc´ıa, D.E. Mkrtichian et al. 78 AB Cas revisited by E. Rodr´ıguez, P.J. Amado, J.M. Garc´ıa, V. Costa and M.J. López-González 81 A few concluding remarks by A. Baglin 82 Comm. in Asteroseismology Vol. 145, 2004

Preface

Asteroseismology is a young branch of stellar astrophysics in two ways: firstly, the methods to sound stellar interiors have only recently - and are still being - developed and secondly, many researchers in this field are young people. The 12th JENAM conference has been organised with some main aims being the interaction between young and experienced scientists, and to increase the possibilities for young astronomers to find employment. In this spirit, a job market for these people was also offered for the first time. Consequently, it was only logical that a two-day asteroseismology mini-workshop, focusing on the impact of such studies on aspects of stellar evolution, was also held during the JENAM meeting in Budapest. Moreover, given the focus on communication and contents of the workshop there is no journal other than Communications in Asteroseismology more appropriate for publishing its proceedings. In the following, you will find a summary of the presentations given at this workshop, with reviews by several selected world specialists in asteroseismology and stellar evolution, but also by young researchers, supplemented by a number of poster presentations, all of which will give you a broad overview of the recent status of research and highly interesting outlooks into the future. The scientific organising committee of the ’Asteroseismology and Stellar Evolution’ minisymposium consisted of the following people:

Gerald Handler (Vienna/Austria) Hans Kjeldsen (Aarhus/Denmark) Zoltán Kolláth (Budapest, Hungary, convenor) Margit Paparó (Budapest/Hungary) Ennio Poretti (Merate/Italy) Chris Sterken (Brussels/Belgium)

The minisymposium was sponsored by the organizers of JENAM 2003: European Astro- nomical Society, Konkoly Observatory, Roland Eötvös Physical Society and Eötvös Loránd University.

The Editors Comm. in Asteroseismology Vol. 145, 2004

Identiﬁcation of modes in main-sequence pulsators by means of multi-color photometry

J. Daszynsk´ a-Daszkiewicz1,2, W.A. Dziembowski3,4, A.A. Pamyatnykh4,5,6

1 Instituut voor Sterrenkunde, Celestijnenlaan 200B, 3001 Leuven, Belgium 2 Astronomical Institute of the WrocÃlaw University, ul. Kopernika 11, 51-622 WrocÃlaw, Poland 3 Warsaw University Observatory, Al. Ujazdowskie 4, 00-478 Warsaw, Poland 4 Copernicus Astronomical Center, ul. Bartycka 18, 00-716 Warsaw, Poland 5 Institute of Astronomy, Russian Academy of Science, Pyatnitskaya Str. 48, 109017 Moscow, Russia 6 Institute of Astronomy, University of Vienna, Turk¨ enschanzstr. 17, A-1180, Vienna, Austria

Abstract

We discuss two problems connected with the application of the method of photometric amplitudes and phases for mode identification. The first one concerns the effect of rotational mode coupling in β Cep models. The second one deals with the strong dependence of the photometric observables on convection in δ Scuti stars.

Introduction

Oscillation spectra of main-sequence pulsators, like β Cep and δ Sct stars, only seldom exhibit equidistant patters, which are typical, for example, in white dwarfs. Therefore, it is diﬃcult to identify oscillation modes from frequency spectra alone. The most popular method of mode identiﬁcation is based on multicolor photometry (Balona & Stobie 1979, Watson 1988). We address here two problems concerning this method which have been discussed in details in two of our recent papers (Daszynsk´ a-Daszkiewicz et al. 2002, 2003).

Photometric amplitudes and phases in rotating β Cep models

If effects of rotation are negligible, the photometric diagnostic diagrams (amplitude ratio vs. phase difference) are independent of the inclination angle, i, and of the azimuthal order, m, and they may reveal the spherical harmonic degree, `. For β Cep star models, oscillation modes are located in the diagnostic diagrams in very well separated regions of different values of `. With the results of linear nonadiabatic theory these diagrams have been successfully applied to many stars (Cugier et al. 1994). However amongst β Cep stars we meet quite often fast rotators. The most important effect of moderate rotation is mode coupling. It occurs if the frequency difference between modes j and k is of the order of the angular velocity of rotation, ωj − ωk ∼ Ω, and if the spherical harmonic indices satisfy the relations: `j = `k §2 and mj = mk. For eigenfunctions of coupled modes one has to consider superpositions of all modes satisfying the conditions mentioned above. The complex amplitude of the monochromatic flux variation for a coupled mode is expressed as

Aλ(i) = akAλ,k(i) Xk J. Daszynsk´ a-Daszkiewicz, W.A. Dziembowski, A.A. Pamyatnykh 7

" " 2.5 '=0 2.5 '=2

0 0 2.0 2.0 y A / u

A a = 0.85 a = 0.53 1.5 11 12 1.5 a = 0.58 a = -0.82 1 1 21 22 3 3 2 2 1.0 4 1.0 4

0.5 0.5 -0.2 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 -0.2 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 ϕ - ϕ [rad] ϕ ϕ [rad] u y u - y

Figure 1: Two mode coupling between ` = 0, p1 and ` = 2, g1 with the dimensionless frequency distant ∆σ = 0.003, in the model at log Teff = 4.374 and Vrot = 100 km/s. Arrows point the polar direction.

where ak are solutions of the degenerate perturbation theory for slowly rotating stars (Soufi et al. 1998). These quantities describe contributions of kth- spherical harmonic to the coupled mode. Aλ,k is the complex amplitude for single-` mode. Now the amplitude ratios and phase differences become both i and m dependent. In Fig.1 we give an example of coupling between a close ` = 0 and 2 pair at an equatorial velocity of about 100 km/s. Open circles mark positions of single ` modes in the diagram based on u and y Strömgren passbands. In the left panel, we see the nominal ` = 0 mode. It is indeed dominated by the ` = 0 component, but there is a considerable ` = 2 component. Small dots are equally spaced in cos i, therefore their density reflects the probability of the situation. In the right panel we see the behavior of the nominal ` = 2 mode. As one can see, both modes can lie in various parts of the diagnostic diagrams. It may happen that both modes can be identified as an ` = 1 or ` = 0 doublet. We can find also positions where single-` modes never appear.

Constraints on convection from multi-color photometry of δ Sct stars

In δ Scuti star models, the photometric amplitudes and phases exhibit a strong dependence on convection. Calculations of these observables make use of the complex parameter f, which gives the ratio of the radiative flux perturbation to the radial displacement in the photosphere. This parameter is obtained with the linear nonadiabatic theory, and is very sensitive to convection, whose treatment still remains rather uncertain. The strong sensitivity of calculated mode positions in the diagnostic diagrams to treatment of convection is not necessarily bad news. Having data from more than two passbands we may try to determine simultaneously ` and f. If we succeed, the f-value inferred from the data can yield a valuable constraint on models of stellar convection. We (Daszynsk´ a-Daszkiewicz et al. 2003) proposed the method based on χ2 minimization assuming trial values of `. We regard the ` degree and the associated complex f value as the solution if it corresponds to χ2 minimum which is much deeper than at other values of `. As the next step, we generalized this method to the case of modes coupled by rotation, and we extended it by adding the radial velocity measurements. Additionally, in the case of a radial mode our method allows to refine the stellar global parameters, by fitting them to reproduce the exact value of the observed frequency. Up to now we applied this method to four stars: 8 Identification of modes in main-sequence pulsators by means of multi-color photometry

32 n=4 6 2.00 n=3 α=1.6 n=5 30 3.2 Mo 28 α=1.0 5 26 1.95 24 α=0.0 L 4 3.1 Mo 1 og χ2 l 22 fI 1.90 20

α=2.5 3 n=3, M=2.94, logT =3.884 18 eff n=4, M=3.10, logT =3.879 3.0 M eff o 2 16 2 1.85 14 M=3.10, logTeff=3.884 M=2.92, logT =3.884 3 eff 12 1 M=3.10, logTeff=3.864 2.9 M 10 M=2.93, logTeff=3.864 1.80 o 8 0 0 1 2 3 4 5 6 3.92 3.90 3.88 3.86 3.84 3.82 -25 -20 -15 -10 f -5 0 5 10 logTeff R

Figure 2: Left panel: χ2 as a function of ` for four models of 20 CVn. Middle panel: The HR diagram with the observational error box for 20 CVn and with lines of the constant periods for n = 3, 4, 5. Only models along these lines are allowed. Right panel: comparison of empirical values of the f parameter with theoretical ones calculated for four values of the MLT parameter, α.

1. β Cas, an example with a possibly coupled mode, 2. 20 CVn, an example with tuning of stellar parameters (see example in Fig. 2), 3. AB Cas, an example with large uncertainties in stellar parameters, 4. 1 Mon, an example of combining photometry and spectroscopy.

Conclusion

Fast rotators occur quite often among β Cephei stars. Rotation complicates usage of photometric diagnostic diagrams for mode identification. It causes that there are more candidates for mode identification from multi-color photometry, because modes with higher ` may ac- quire large low degree components. Moreover coupled modes are aspect- and m-dependent. Therefore the mode identification in fast rotating stars may be done only simultaneously with determination of stellar parameters and the inclination of rotational axis. Application of multi-color photometry of δ Scuti stars goes beyond the identification of the spherical harmonic degree, `. We proposed a new method of extracting the nonadiabatic parameter, f, from such data (Daszynsk´ a-Daszkiewicz et al. 2003). The method yields constraints on stellar convection. Determination of ` is an independent goal. It can be done without a priori knowledge of f. Moreover, if the observed mode is radial we are able to diminish significantly the uncertainty of stellar parameters. Finally, we proposed for the first time a way how to combine photometry and spectroscopy for mode identification, adding radial velocity data to our method.

Acknowledgments. The work was supported by the Polish KBN grant No. 5 P03D 012 20. J. D-D. gratefully thanks the Instituut voor Sterrenkunde in Leuven for ﬁnancial support for the JENAM 2003 conference. References Balona L. A., Stobie R.S., 1979, MNRAS, 189, 649 Cugier H., Dziembowski W. A., Pamyatnykh A. A., 1994, A&A, 291, 143 Daszynsk´ a-Daszkiewicz J., Dziembowski W. A., Pamyatnykh A. A., Goupil M-J., 2002, A&A 392, 151 Daszynsk´ a-Daszkiewicz J., Dziembowski W. A., Pamyatnykh A. A., 2003, A&A 407, 999 Souﬁ F., Goupil M-J., Dziembowski W. A., 1998, A&A 334, 911 Watson R. D. 1988, Ap&SS 140, 255 Comm. in Asteroseismology Vol. 145, 2004

Inﬂuence of the convective ﬂux perturbation on stellar oscillations: application to δ Scuti and γ Doradus stars

A. Grigahc`ene1, M-A. Dupret1, R. Garrido1, M. Gabriel2 and R. Scuﬂaire2

1Instituto de Astrof´ısica de Andaluc´ıa-CSIC, Apartado 3004, 18080 Granada, Spain 2Institut d’Astrophysique et de Géophysique de l’Université de Liège, Belgium

Abstract

We present a theory of convection-oscillation interaction. In our nonradial nonadiabatic pulsation code, the variation of the convective flux (radial and transversal components) is taken into account, following the theory of M. Gabriel, within the mixing length approach. We explore the influence of the convective flux variation on mode stability near the red-edge of the δ Scuti instability strip and the excitation mechanisms of γ Doradus stars.

Introduction

The determination of theoretical instability strips is of great interest in the study of pulsating stars, because their confrontation with observations enables us to test our knowledge of stellar interiors and our understanding of the driving mechanisms of these stars. Using the time- dependent convection theory of Gabriel (1974, 1996, 1998, 2000), we study the inﬂuence of the convective ﬂux perturbation on stellar oscillations. We present instability strips for δ Scuti and γ Doradus stars.

Results

We have implemented the perturbation of the convective ﬂux in the linear non-adiabatic code MAD (Dupret et al. 2002). In order to determine the theoretical instability strips, a large number of evolutionary tracks were computed, with masses ranging from 1.4 to 2.2 M¯, and with diﬀerent values of the MLT parameter α. Then, we studied the stability of the modes in the appropriate frequency range.

δ Scuti instability strip Contrary to the calculations with frozen convection, with our time-dependent convection treatment we are able to reproduce the red edge of the δ Scuti instability strip, for radial as well as for non-radial modes. In the left panel of Fig. 1, we present the theoretical instability strip obtained for radial modes, for models with the solar calibrated value α = 1.8. Each curve corresponds to the blue or red edge of a mode of given radial order n. Labels permit to identify the modes (e.g. p4R for the red edge of the p4 mode). As the radial order of the modes increases, the blue and red edges are displaced towards higher Teff . The points correspond to the position of observed δ Scuti stars, as taken from the catalogue of Rodriguez et al. (2000), using the calibrations of Moon & Dworetsky (1985). 10 Influence of the convective flux perturbation on stellar oscillations

δ Scuti Instability Strip, α=1.8, l=0 δ Scuti Instability Strip, α=1.8, l=2

1.6 2.2 M0 1.6 2.2 M0

2.0 M0 2.0 M0 1.4 1.4

) 1.8 M ) 1.8 M

0 0 0 0 1.2 1.2

1.6 M 1.6 M 0 P 0 Log(L/L 1.0 P Log(L/L 1.0 4B 4B g3B f P1B B 1.4 M0 0.8 1.4 M0 0.8 g P 3R P4R 4R 0.6 P1R 0.6 fR 3.98 3.94 3.90 3.86 3.82 3.78 3.98 3.94 3.90 3.86 3.82 3.78 Log(Teff) Log(Teff)

Figure 1: Left panel: Blue and red edges of the δ Scuti theoretical instability strip for models with α = 1.8 and radial modes from p1 to p4. Right panel: Blue and red edges of the δ Scuti theoretical instability strip for models with α = 1.8 and ` = 2 modes from g3 to p4. The points correspond to observations.

In the right panel of Fig. 1, we present the theoretical instability strip obtained for ` = 2 modes, for models with α = 1.8.

γ Doradus instability strip The driving of the high-order gravity modes of γ Doradus stars can also be explained by our time-dependent convection models. In the left panel of Fig. 2, we show the periods of all the unstable ` = 1 gravity modes obtained for models of 1.6 M¯ with α = 2, as a function of the effective temperature. Each cross corresponds to an unstable mode. As can be seen, the periods of those modes correspond to the typical observed periods of γ Doradus stars. Moreover, we see in the bottom of this figure that our models have also unstable p-modes, typical of δ Scuti stars. In the right panel of Fig. 2, we show the theoretical instability strips of γ Doradus ` = 1 modes obtained for three families of models with different values of the MLT parameter α: 1, 1.5 and 2. In this case, we give global instability strips and not individual ones for each mode. For any model inside the instability strip, at least one unstable high order g-mode is found; outside it all the g-modes are found to be stable. The small circles correspond to the observed positions of bona fide γ Doradus stars from the catalogue of Handler (2002); their effective temperatures are taken from Kaye et al. (1999) who used the calibrations of Villa (1998). As for δ Scuti stars, we see that the theoretical predictions are very sensitive to α. In agreement with Guzik et al. (2000), we find that the depth of the convective envelope plays the major role in the driving of γ Doradus g-modes. This explains the high sensitivity of our results to α.

Conclusion

Including the perturbation of the convective flux, following Gabriel’s theory, we obtained theoretical instability strip of δ Scuti and γ Doradus stars. For δ Scuti stars, we succeed to reproduce both the blue and red edges, for radial as well as for non-radial modes. The location of the theoretical red edge appears to be very sensitive to the value of the MLT parameter α. With the solar calibrated value α = 1.8, a good agreement with observations is found. We A. Grigahcène, M-A. Dupret, R. Garrido, M. Gabriel and R. Scuflaire 11

3.0 γ Dor Instability Strips: α=1, 1.5, 2; l=1 1.5 M=1.6 M0 2.0 M0 2.5 α=2 1.4 α l=1 1.3 =2 1.8 M 2.0 0 1.2 α

) =1.5 0 1.1 1.5 1.6 M0 1.0 P (days) α=1 1.0 Log(L/L 0.9 1.4 M 0.8 0

0.5 0.7

0.6 0.0 7400 7200 7000 6800 6600 6400 3.90 3.88 3.86 3.84 3.82 3.80 3.78 3.76 3.74 Teff (K) Log(Teff)

Figure 2: Left panel: Periods (in days) of all the unstable ` = 1 gravity modes obtained for models of 1.6 M¯ with α = 2, as a function of the effective temperature. Each cross corresponds to a given g-mode. Right panel: γ Doradus theoretical instability strips for ` = 1 modes, for three families of models with different values of α: 1, 1.5 and 2. The small circles correspond to observations of bona fide γ Doradus stars. obtained also theoretical instability strips for the γ Doradus g-modes. As for δ Scuti stars, the theoretical instability strips of γ Doradus stars are very sensitive to the value of the MLT parameter α. We obtain good agreement with observations for models with α = 2. Finally, for some models, we found a mixture of unstable p- and g-modes, therefore predicting objects able to show simultaneous γ Doradus and δ Scuti pulsational behaviour.

Acknowledgments. MAD acknowledges support through a European Community Marie Curie Fellowship. AG and RG acknowledge ﬁnancial support from the program ESP2001- 4528-PE. References Dupret, M.-A., De Ridder, J., Neuforge, C., et al. 2002, A&A, 385, 563 Gabriel, M., Scuﬂaire, R., Noels, A. 1974, Bul. Ac. Roy. Belgique, Classe des Sciences 60, 866 Gabriel, M. 1996, Bull. Astron. Soc. of India, 24, 233 Gabriel, M. 1998, In: SOHO 6/GONG 98 Workshop, Boston, Massachusetts, p. 863 Gabriel, M. 2000, A&A, 353, 399 Guzik, J. A., Kaye, A. B., Bradley, P. A., et al. 2000, ApJ, 542, L57 Handler, G. 2002, http://www.astro.univie.ac.at/∼dsn/gerald/gdorlist.html Kaye, A. B., Handler, G., Krisciunas, K., et al. 1999, PASP, 111, 840 Moon, T. T., & Dworetsky, M. M. 1985, MNRAS, 217, 305 Rodriguez, E., Lopez-Gonzalez, M. J., Lopez de Coca, P. 2000, A&As, 144, 469 Villa, P. 1998, M.Sc. thesis, Univ. Vienna Comm. in Asteroseismology Vol. 145, 2004

Testing the internal physics of white dwarfs from their pulsational properties

J. Isern1,2, E. Garc´ıa–Berro1,3, A.H. C´orsico1,2, O.G. Benvenuto4, L.G. Althaus1,3

1 Institut d’Estudis Espacials de Catalunya, E. NEXUS, c/Gran Capità 2–4, 08034 Barcelona, Spain 2 Institut de Ciències de l’Espai (CSIC), Edifici Nexus, c/Gran Capità 2–4, 08034 Barcelona, Spain 3 Departament de F´ısica Aplicada (UPC), Escola Politècnica Superior de Castelldefels, 08860 Castelldefels, Spain 4 Facultad de Ciencias Astronómicas y Geof´ısicas, Universidad Nacional de La Plata, Paseo del Bosque S/N,(1900) La Plata, Argentina

Abstract

White dwarfs are well studied objects. The relative simplicity of their physics allows to obtain very detailed models which can be ultimately compared with their observed properties. Among white dwarfs there is a speciﬁc class of stars, known as ZZ-Ceti objects, which have a hydrogen-rich envelope and show periodic variations in their light curves. The rate of change of the period is closely related to the star’s cooling timescale, which can be accurately computed. In this paper we study the pulsational properties of G117-B15A and we use the observed rate of change of the period to impose constraints on the axion emissivity. This upper bound turns out to be 4 cos2 β meV. Although there are still several observational and theoretical uncertainties, we conclude that G117-B15A is a very promising stellar object to set up constraints on particle physics.

Introduction

Astrophysical arguments and observations have become a well known tool to obtain empirical information or constraints on existing or hypothetical elementary particles. One of the most important reasons for this is that the dense environment of stars is potentially a powerful source of low-mass weakly interacting particles. Since these particles subsequently escape from the star this mechanism constitutes a sink of energy that ultimately modifies the stellar lifetimes, thus allowing a comparison with the observed lifetimes. This is particularly useful since, as it is well known, the different non-standard theories leave open the possibility that several exotic particles (like axions or gravitons) could exist. Moreover, for several of these particles there are not yet laboratory experiments in the relevant mass range that could eventually impose tight constraints on their existence. Among other weakly interacting massive particles, axions are the most promising candidates for non-baryonic dark matter and, therefore, a great deal of attention has been paid to them. There are two types of axion models, the KVSZ model and the DFSZ model. The first one couples to hadrons and photons whereas the second one also couples to charged leptons. The coupling strength depends on the specific implementation of the Peccei-Quinn mechanism through dimensionless coupling constants that are related to the mass. Both models do not set any constraint on the mass of the axion which must be obtained from experimental tests. J. Isern et al. 13

One way to constrain the mass of the DFSZ axion is the following (Isern et al. 1992, 1993): the observed rate of change of the pulsational period P˙obs and the rate of change of the period given by the models P˙mod when axion emission is considered are related through the following expression:

L + Lax P˙ phot = obs (1) Lphot P˙mod since the axion luminosity is proportional to the mass of the axion, it is possible to obtain it if P˙mod is known.

Characteristics of G117-B15A

G117-B15A is a typical DA (hydrogen-rich) white dwarf star whose variability was first discovered by McGraw & Robinson (1976). Since then on, it has been monitored almost continuously. Its mass and effective temperature have been spectroscopically estimated to be 0.59 M¯ and 11,620 K, respectively (Bergeron et al. 1995). Regarding the variability of this star, its observed periods are (Kepler et al. 1982) 215.2, 271 and 304.4 s together with harmonics and linear combinations of the quoted periods. Of particular interest for this work is the fact that for the 215.2 s mode it has been possible to find its rate of change, P˙ . The first published value of P˙ (Kepler et al. 1991) was calculated using all the data obtained from 1975 to 1990 and was P˙ = (12.0 § 3.5) × 10−15s s−1, much larger than the theoretical predictions. Very recently, with a much longer time interval of acquired data, Kepler et al. (2000) re-determined P˙ finding a significantly lower value of P˙ = (2.3 § 1.4) × 10−15s s−1. We have looked for a model that matches the three observed modes as good as possible. After having such a fiducial model, the computation of the theoretical P˙ for different values of the axion mass is rather straightforward (Córsico et al. 2001). Our results clearly indicate that the mass of G117-B15A should be very close to 0.55 M¯ and that the hydrogen mass −4 fraction present in the star should also be close to MH/M? = 10 . In fact, the value we derive for the mass of G117-B15A is nicely bracketed by the independent spectroscopic determinations of Bergeron et al. (1995), who obtained 0.59 M¯, and Koester & Allard (2000), who obtained 0.53 M¯. The model that provides the best fit to the observations (M? = 0.55 M¯, l = 1, k = 2, 3, 4 and log MH/M? = −4.0) will be hereafter referred to as the fiducial model. The rate of change of the period for this model is P˙ = 3.9 × 10−15s s−1. After examining all the possible uncertainties a few words are necessary to justify the discrepancy between this value and the measured rate of change of the period of the 215.2 s mode, P˙ = (2.3 § 1.4) × 10−15s s−1, and its computed value for the fiducial model. First, the theoretical uncertainties can account for a spread of about §1 × 10−15s s−1. Second, the proper motion and parallax (Pajdosz 1995, Kepler et al. 2000) contribute as much as P˙ = (9.2 § 0.5) × 10−16s s−1. We thus conclude that taking into account all these uncertainties our preferred model could be safely considered as satisfactory and that our value for P˙ is fully consistent with the observed rate of change of the period.

The eﬀects of enhanced cooling due to axion emission

Now, we turn our attention to compute the effects of axion emission on the evolutionary timescale of G117-B15A and its effect on the expected value of P˙ for the l = 1, k = 2 mode (Córsico et al. 2001). In order to do this in a self-consistent way we have run an additional set of cooling sequences with different axion masses (and considered the pulsational characteristics in the relevant effective temperature range) for our fiducial model, starting from the same initial conditions used for the models computed without axion emission. We have found that, even considering a wide range for the mass of the axion, the period of 14 Testing the internal physics of white dwarfs from their pulsational properties the l = 1, k = 2, 3, and 4 modes show a very small variation for the whole considered interval. This is indeed a very fortunate situation that allowed us to employ the procedure of identifying first the structure of the fiducial model without considering axion emission and then to incorporate the axion emissivity. This would have not been the case should we have had to identify a white dwarf structure for each value of the axion mass. In such a case we would have had no fiducial model, thus complicating our analysis enormously. In sharp contrast with the small variation of the computed values of the periods of all the modes with the axion emissivity found previously, the value of P˙ for the three identified modes is extremely sensitive. Therefore, we can compute the value of P˙ of the l = 1, k = 2 mode of the fiducial model at Teff = 11, 620 K as a function of the mass of the axion. Now we can look for an upper limit to the axion mass by imposing that the value of P˙ should be lower than the observed value plus two times the standard deviation, that is, lower than 5.1 × 10−15s s−1. A close inspection of the data shows that for this to be the case, the axion mass must be lower than 3.97 cos2 β meV, where cos2 β is a free parameter in the theory of axions. This is the main result of the present work.

Conclusions

We have used this ZZ Ceti star to put constraints on the mass of the axion. Since G117-B15A is the most stable optical clock yet known, with a rate of period change of the 215.2 s mode of P˙ = (2.3 § 1.4) × 10−15s s−1, the cooling timescale of this white dwarf is well constrained (Kepler et al. 2000). This fact has allowed us to set up tight constraints on any additional cooling mechanism diﬀerent to the standard ones. In particular we have obtained an upper bound to the mass of the axion which is ' 4 cos2 β meV at the 95% conﬁdence level. This upper limit is a factor of 2.5 smaller than the previously existing limits. From the the above analysis it seems clear that in order to have more stringent upper limits to the mass of axions, we should have a smaller uncertainty in the observed value of P˙ , since the uncertainties in the models of white dwarf stars are clearly of lower relevance in this context. To this regard it is important to realize that at the 1σ level the stability of the dominant period of G117-B15A seems to rule out the existence of the DFSZ axion, provided that our current knowledge of the origin, structure and evolution of white dwarf stars turns out to be correct. Thus, clearly more observations are required but these observations are on their way.

Acknowledgments. This work has been supported by the MCyT grants AYA04094–C03– 01 and 02, and by the CIRIT References Bergeron, P., Wesemael, F., Lamontagne, R., Fontaine, G., Saﬀer, R. A., Allard, N. F., 1995, ApJ, 449, 258 C´orsico, A. H., Benvenuto, O. G., Altahus, L. G., Isern, J., Garc´ıa–Berro, E. 2001, New Astron., 6, 197 Isern, J., Hernanz, M., Garc´ıa–Berro, E., 1992, ApJ, 392, L23 Isern, J., Hernanz, M., Garc´ıa–Berro, E., 1993, in White Dwarfs: Advances in Observations and Theory, Ed.: M. A. Barstow (Dordrecht: Kluwer Academic Publishers), 139 Kepler, S. O., Robinson, E. L., Nather, R. E., McGraw, J. T., 1982, ApJ, 254, 676 Kepler, S. O., et al., 1991, ApJ, 378, L45 Kepler, S. O., Mukadam, A., Winget, D. E., Nather, R. E., Metcalfe, T. S., Reed, M. D., Kawaler, S. D., Bradley, P. A., 2000, ApJ, 534, L185 Koester, D., Allard, N. F., 2000, Baltic Astron., 9, 119 McGraw, J. T., Robinson, E. L., 1976, ApJ, 205, L155 Pajdosz, G., 1995, A&A 295, L17 Comm. in Asteroseismology Vol. 145, 2004

The Blazhko Eﬀect: Facts, Figures and Future work

K. Kolenberg

1 Institut fur¨ Astronomie, Turk¨ enschanzstrasse 17, 1180 Vienna, Austria

Abstract

Almost a century after its discovery, the phenomenon of amplitude and/or phase modulation (Blazhko effect), observed in a large percentage of the RR Lyrae stars, still lacks widely acceptable theoretical understanding. Recent attempts to theoretically explain the Blazhko effect have focused on two alternatives: the magnetic models and the resonance models, both involving the presence of nonradial pulsation components. In the course of the past decades, large photometric data bases have yielded important statistics on the phenomenology of the Blazhko effect, which impose additional constraints upon the applicability of the models. On the other hand, the new approach of studying the Blazhko effect through line profile analysis, can provide essential information on the nature of the pulsation components responsible for the modulation. The answer to this century-old question will definitely clarify similar phenomena observed in other types of pulsating stars.

Introduction: RR Lyrae stars and the Blazhko eﬀect

Since their discovery at the end of the 19th century, the RR Lyrae stars have contributed to almost every branch of modern astronomy. These pulsating stars have mean periods of about half a day, and show brightness variations of about 1 magnitude. Traditionally, RR Lyrae stars are thought to represent the simplest type of pulsation, namely radial pulsation. They oscillate in the radial fundamental mode (Bailey type RRab), the radial first overtone (Bailey type RRc), and both of these radial modes simultaneously (RRd). However, additional cycles occur in many RR Lyrae stars. The most intriguing subclass of RR Lyrae stars consists of the stars showing the Blazhko effect. These stars have light curves that are modulated on timescales of tens to hundreds of days. Blazhko (1907) was the first to report this phenomenon in RW Dra. The estimated incidence rate of Blazhko variables among the Galactic RRab stars is about 20-30% (Szeidl 1988; Moskalik & Poretti 2003). In the LMC this rate is considerably lower (about 12%; Alcock et al. 2003). RRc stars show the Blazhko effect even less frequently (less than 5%). Characteristic for the phenomenon is the periodic variation of the brightness and times of maximum light of Blazhko stars over the secondary period (Figure 1a). Past and present observational studies of the Blazhko effect

The Blazhko eﬀect has been the frequent subject of photographic and photometric studies, e.g., the systematic investigations carried out at Konkoly Observatory in Budapest, Hungary (Szeidl & Kollath 2000, and references therein). Traditionally the phenomenon was studied by means of O-C analysis. Therefore the observations were in general strongly biased towards the ascending branch and maximum phase of the primary light curve, a sampling pernicious for Fourier analyses. Nevertheless, some photometric data sets, which also include other parts 16 The Blazhko Eﬀect: Facts, Figures and Future work

Figure 1: a. Light curve changes of a Blazhko star; b. Triplet or doublet structure; c. The two prevailing models for the Blazhko effect of the light curve, allowed a rigorous frequency analysis ,e.g., Borkowski (1980), Smith et al. (1994), Kovacs (1995), Nagy (1998), Smith et al. (1999), Szeidl & Kollath (2000), Jurcsik et al. (2002a), Smith et al. (2003). For a long time the presence of the Blazhko effect in RRc stars was an open question: because of the small changes in the height of maximum of their light curves it was more difficult to detect. The controversy was resolved by the systematic studies of accurate CCD data of globular clusters and the large variable star data bases resulting from microlensing surveys (MACHO for the LMC and OGLE for the Galactic Bulge). These studies have cast a new light upon the study of RR Lyrae variability (Moskalik & Poretti 2003; Alcock et al. 2000, 2003), and yielded important statistics on the phenomenology of the Blazhko effect. The frequency spectra of light curves of RR Lyrae Blazhko stars exhibit either a doublet or an equally-spaced triplet structure, with a very small frequency separation close to the main radial pulsation component, corresponding to the frequency of the modulation (see Figure 1b). Only a small fraction of the observed triplets show non-equidistant frequency spacings. No trace of a quintuplet structure is found. The observed period ratios are 0.95-1.02. The modulation components have amplitudes of about 10-20% of the corresponding pulsation component and are also observed around the harmonics of the main frequency. If a triplet structure is observed, both side peaks appear to have unequal amplitudes, most often with the larger modulation peak at the higher frequency side of the main pulsation component. The continuous transition between the variables showing an equidistant triplet and those displaying only a close doublet suggests that both features are the result of the same phenomenon. No connection seems to exist between the pulsation and the Blazhko periods. At their largest light amplitude Blazhko stars fall approximately on the curve of amplitude versus period as defined by stars with regular light curves (Szeidl 1988). Jurcsik et al. (2002b) tackled the important question what phase of the modulation, if any, can be regarded as undistorted behaviour. From studying photometric and radial velocity amplitudes of RRab Blazhko stars, as well as their light curve shapes, they concluded that for Blazhko stars with K. Kolenberg 17 large amplitude modulation the light curves are always distorted. Period changes, too fast to be of evolutionary nature, are a common feature in RR Lyrae stars, and also occur in Blazhko stars (Smith 1995; Szeidl & Kollath 2000). Their origin is currently unknown. Coincident changes in the primary and Blazhko periods have been reported (e.g., LaCluzé et al. 2002). Some field Blazhko stars (e.g. RR Lyr, XZ Cyg, RV UMa, XZ Dra, RW Dra, Y LMi) are reported to display, besides their Blazhko cycles, also very long cycles, of the order of years. In some stars (SW And, RR Gem) the Blazhko effect ceased. Explanations for the Blazhko effect in RR Lyrae stars

Almost a century after its discovery, the physical origin of the Blazhko effect remains a mystery. Different mechanisms have been proposed to explain the phenomenon, such as resonance effects, nonadiabatic effects, magnetic effects and tidal effects in binary systems. Models for the Blazhko effect using only radial mode interactions have failed (see Kovacs 2002). The most plausible hypotheses to explain this phenomenon focus on two types of models, both involving nonradial pulsation components.

• The resonance models are based on a (nonlinear) resonance between the radial fundamental mode and a nonradial mode. In these models the dipole modes (` = 1) have the highest probability to be nonlinearly excited (Cox 1993; Van Hoolst et al. 1998). The dipole pulsation components lead to a triplet structure in the frequency spectrum of Blazhko variables. In the model proposed by Nowakowski & Dziembowski (2001), significant amplitude and phase modulation is predicted in the case of excitation of a rotationally split ` = 1, m = §1 pair. The modulation period is determined by the rotation rate (currently unknown) and the Brunt-Väisälä frequency in the deepest part of the radiative interior. Peterson et al. (1996) obtained an upper limit of 10 km/s for the projected rotational velocities of a sample of 27 RR Lyrae stars.

• The magnetic models, like the simple oblique pulsator model for roAp stars (Kurtz 1982), suppose that Blazhko stars have a magnetic field inclined to the stellar rotation axis (Cousens 1983; Shibahashi & Takata 1995). The main radial mode is deformed by the magnetic field to have an additional quadrupole component (`=2), for which the symmetry axis coincides with the magnetic axis. As the star rotates, the pulsation components change with observer aspect, causing the observed amplitude modulation. Shibahashi & Takata (1995) predict a quintuplet structure in the frequency spectrum, but also show that the quintuplet looks almost like a triplet for certain geometrical configurations. Depending on which of the side components we then observe, the Blazhko period is supposed to be equal to the rotation period or half of the rotation period. A magnetic field of order 1 kG is needed in this model for the amplitude modulation to be observable. Babcock (1958) and Romanov et al. (1994) reported a detection of a variable magnetic field in the brightest Blazhko star RR Lyrae with a strength up to 1.5 kG, but so far, these observations have not been confirmed (e.g., Preston 1967; Chadid 2001). A straightforward detection of magnetic fields in Blazhko stars is hampered by their relative faintness.

In both models the observed modulation of the light curve is a consequence of rotation and the degree of modulation is aspect-dependent. Each of the models predicts constant modulation components of equal amplitudes, in sharp contrast to the large majority of the frequency patterns observed. The question why RRc Blazhko stars have significantly lower incidence rates has not yet been addressed in the magnetic model. The resonance model does predict a lower probability for first overtone pulsators to show amplitude modulation, though still not in the degree observed. Deviations from strict amplitude/phase modulations (see e.g., 18 The Blazhko Effect: Facts, Figures and Future work

Szeidl 1988) also need to be explained. The different incidence rates in different populations, probably related to metallicity (Moskalik & Poretti 2003), have yet to be taken into account. Moreover, explanations predicting an undistorted light curve along any phase of a large amplitude modulation seem unrealistic (Jurcsik et al. 2002b). Empirical evidence suggests that RR Lyrae Blazhko stars have pulsation periods shorter than 0.66 days. This might be related to the fact that, when moving from the blue to the red edge of the instability strip, the convective transport in RR Lyrae stars becomes more efficient. Convective turbulence may play a role in driving/quenching the Blazhko effect (Bono et al. 2003). New developments in line profile analysis

Up to now most observational studies of Blazhko stars were based on photometric data. However, high-resolution line profiles offer much better diagnostics to find and identify nonradial oscillation components in pulsating stars. The pioneering work in the spectroscopic study of the Blazhko effect consisted in studying the line profile variations of RR Lyrae, by far the brightest Blazhko star (Chadid et al. 1999; Kolenberg 2002). A detailed study of the variations of the FeII line profile at 4923.921 A˚ led to a clear detection of nonradial pulsation components in the star and provided promising results concerning their identification. By means of an adapted version of the moment method, a quantitative spectroscopic identification method (Aerts 1996), the additional components were identified as non-axisymmetric nonradial dipole (` = 1) or quadrupole (` = 2) modes (Kolenberg 2002). Subsequent line profile fitting on the observed profiles confirmed these results. However, as the existing data did not provide a complete coverage of the Blazhko cycle, these results need to be checked on new data with a better spread over the Blazhko cycle. Similar high-resolution spectra of a non-Blazhko RR Lyrae star would allow us to carry out a spectroscopic comparison between Blazhko and non-Blazhko stars (see also Kolenberg et al. 2003). Long-term cycles in other types of stars

The Blazhko effect is rather uncommon among the fundamental mode Cepheids. One of the few field Cepheids known to show strong amplitude modulation is HR 7308 (Breger 1981; Burki et al. 1982). Van Hoolst & Waelkens (1995) considered the beating hypothesis for this star in a nonlinear framework and concluded that a resonance between the radial mode and a low-degree, low-order p-mode with nearly equal frequencies can produce periodic amplitude variations of the radial mode. Among multimode pulsators, amplitude and/or phase modulation is a rather common phenomenon. Recently Poretti (2003) showed that the pulsational content of the δ Scuti star V974 Oph suggests a mixture of radial and nonradial modes. The ratio f1/f2 = 0.978 is reminiscent of the Blazhko effect in RR Lyrae stars. In FG Vir Breger et al. (2004) detected a nonradial mode very close to the radial mode. Finally, the β Cephei star 16 Lac also shows a radial and a close nonradial mode leading to amplitude variations (Aerts et al. 2003; Sareyan et al. 1997). These are just some examples illustrating the widespread occurrence of amplitude and/or phase modulation, i.e. Blazhko- like behaviour. A better understanding of the phenomenon in RR Lyrae stars will definitely clarify similar phenomena in other types of pulsating stars. The Blazhko project

Despite the progress made in the past decades both in observations and modelling, the basic physical understanding of the Blazhko phenomenon is still missing. In order to join the efforts to come to a better understanding, we have set up an international collaboration centered on the Blazhko effect (the Blazhko project). The concept is to obtain sufficient high-resolution spectroscopic data of some well-selected field RR Lyrae Blazhko stars: both fundamental mode (RRab) stars and first harmonic (RRc) pulsators. Similar data sets for at least two non-modulated RR Lyrae stars (RRab and RRc) will permit a spectroscopic K. Kolenberg 19 comparison of line profile variations between Blazhko and non-Blazhko stars. Moreover, they are essential as a test for the new methods to disentangle the (supposed nonradial) pulsation components which are suspected to be responsible for the amplitude modulation. Extensive photometric data and radial velocity measurements will be obtained to supplement the high- resolution spectroscopic data and for accurate period determination. Target stars are carefully selected in both hemispheres. This new and so far untapped approach of combining high- resolution spectra, additional radial velocity data, and extensive photometry of both Blazhko and non-Blazhko stars will provide a deeper insight in the mechanism behind the phenomenon. People who are interested in actively collaborating, either from the observational side (by collaborating in a Blazhko star campaign), or from the theoretical side (by participating in the interpretation of the measurements) are welcome to contact [email protected]. Acknowledgments. KK cordially thanks the SOC for inviting this contribution, for registration and accommodation grant. The LOC is acknowledged for their hospitality and smooth organisation. KK thanks Michel Breger for his encouraging support of this project, and all the people who have expressed their interest in the Blazhko effect and thereby motivated a larger-scale tackling of the problem. References Aerts, C., 1996, A&A 314, 115 Aerts, C., Lehmann, H., Briquet, M., et al. 2003, A&A 399, 639 Alcock, C., Allsmann, R., Alves, D.R., et al., 2003, in preparation Alcock, C., Allsmann, R., Alves, D.R., et al., 2000, ApJ 542, 257 Babcock, H.W., 1958, ApJS 3, 141 Blazhko, S., 1907, Astron. Nachr. 175, 325 Bono, G., Petroni, S., Marconi, M., 2003, ASP Conf. Ser. 292, 71 Breger, M., 1981, ApJ 249, 666 Breger, M., Rodler, F., Pretorius, R., et al., 2004, A&A, in press Borkowski, K.J., 1980, Acta Astr. 30, 393 Burki, G., Mayor, M., Benz, W., 1982, A&A 109, 258 Chadid, M., Kolenberg, K., Aerts, C, Gillet, D., 1999, A&A 352, 201 Chadid, M., 2001, ASP Conf. Ser. 248, 427 Cousens, A., 1983, MNRAS 203, 1171 Cox, A.N., 1993, Proc. IAU Coll. 21, 31 Jurcsik, J., Benkö, J.M., & Szeidl, B., 2002a, A&A 396, 539 Jurcsik, J., Benkö, J.M., & Szeidl, B., 2002b, A&A 390, 133 Kolenberg, K., 2002, PhD thesis, http://www.ster.kuleuven.ac.be/pub/kolenberg phd/ Kolenberg, K., Aerts, C., Chadid, M., Gillet, D., 2003, ASP Conf. Ser. 305, 167 Kovács, G., 1995, A&A 295, 693 Kovács, G., 2002, ASP Conf. Ser. 259, 396 Kurtz, D.W., 1982, MNRAS 200, 807 LaCluyzé, A., Smith, H.A., Gil, E.-M. et al., 2002, ASP Conf. Ser. 259, 416 Moskalik, P., & Poretti, E., 2003, A&A 398, 213 Nagy, A., 1998, A&A 339, 440 Nowakowski, R.M., & Dziembowski, W.A., 2001, Acta Astron. 51, 5 Peterson, R.C., Carney, B.W., & Latham, D.W., 1996, ApJ 465, 47 Poretti, E., 2003, A&A 409, 1031 Preston, G.W., 1967, in The Magnetic and Related Stars, Baltimore Mono Book Corp., 3 Romanov, Yu.S., Udovichenko, S.N., Frolov, M.S., 1994, Bul. Spec. Astrophys. Obs. 38, 169 Sareyan, J.P., Chauville, J., Chapellier, E., Alvarez, M., 1997, A&A 321, 145 Shibahashi, H., & Takata, M., 1995, ASP Conf. Ser. 83, 42 Smith, H.A., Matthews, J.M., Lee, K.M., et al., 1994, ApJ 107, 679 Smith, H.A., 1995, RR Lyrae Stars, Cambridge Univ. Press Smith, H.A., Barnett, M., silbermann, N.A., Gay, P., 1999, AJ 118, 572 Smith, H.A., Church, J.A., Fournier, J., et al. 2003, PASP 115, 43 Szeidl, B., 1988, in Multimode Stellar Pulsations, Proc. Budapest Workshop 1987, 45 Szeidl, B., & Kolláth, Z., 2000, ASP Conf. Ser. 203, 281 Van Hoolst, T., & Waelkens, C., 1995, A&A 295, 361 Van Hoolst, T., Dziembowski, W.A., Kawaler, S.D., 1998, MNRAS 297, 536 Comm. in Asteroseismology Vol. 145, 2004

Numerical modelling of the RR Lyrae instability strip

R. Szab´o

Konkoly Observatory, Budapest, H-1525, P.O. Box. 67., Hungary

Abstract

Selected results are presented of an extensive model survey of the radial pulsation of HB stars using a turbulent convective (TC) code. The main goal of the investigation was to systematically map the possible pulsational modes in the classical instability strip. This contribution focuses on (i) the slope of the fundamental mode blue edge and (ii) double- mode RR Lyrae stars. The importance of the interplay between mode-selection eﬀects and stellar evolution is emphasized in both cases.

Introduction

Two main problems are addressed: (i) The discrepancy between the empirical and theoretical RR Lyrae fundamental (F) blue edges (Jurcsik 1997). Neither radiative nor convective models could explain the shallow slope of the blue edges of the F and O1 instability regions (Kolláth et al. 2000). It is well known from the early suggestion of van Albada & Baker (1973) that in the case of classical pulsators ’either-or-regions’ exist on the HRD. The width of this hysteresis region can be several hundred K. As stars of different parameters pass through this region, mode selection can bend the average slope of the F blue edge significantly. The main motivation was to investigate this scenario by performing a large-scale nonlinear survey of radial RR Lyrae pulsation. (ii) Benefiting from the mode selection results we carried out a comprehensive investigation of nonlinear double-mode (DM) models. Since the first claim of successful modelling of double-mode pulsation (Feuchtinger 1998), no systematic exploration of the double-mode models has been published except some limited attempts (Szabó et al. 2000). These two issues are discussed within the common framework of the connection of pulsation and evolution.

The method

In order to explore the mode selection characteristics the Florida-Budapest code (Kolláth et al. 2002) was used, which is a one-dimensional, nonlinear hydrocode including turbulent convection. Hydrogen content was set to be X = 0.75. Turbulent convection parameters were also taken from Kolláth et al. (2002). Model sequences with the following parameters were computed: M = 0.50, 0.55, 0.60, 0.65, 0.71, 0.77, 0.82, 0.87M¯, L = 40, 50, 60, 70 L¯, −4 −3 −3 and Z = 10 , 10 , 4 · 10 ; where only Teff was varied. To reduce significantly the computational cost, time-dependent amplitude equations were fitted to the sequences (Szabó et al. 2004). This allowed the interpolation of the limits of different pulsational states within a sequence. This way a large grid resulted, containing mode selection information throughout the relevant regions of the parameter space. We stress that the selection of turbulent parameters is not unique. The application of a different TC parameter set usually R. Szabó 21

Table 1: RR Lyrae fundamental blue edge slopes derived by diﬀerent methods, assuming a linear relation.

method slope (1σ) source empirical -5.40 Jurcsik 1998 convective, linear -13.34 Koll´ath et al. 2000 convective, nonlin., Dorman ev. tracks -3.91 (0.51) this paper convective, nonlin., Demarque ev. tracks -3.96 (0.25) this paper convective, nonlin., Padova ev. tracks -4.25 (0.47) this paper

causes a temperature shift in instability strip structures, but the fundamental blue edge slope is not aﬀected by this shift.

Mode selection

In the following we simply denote the union of DM and F/DM region by DMR, if not stated otherwise. (1) The following combinations of stable fixed points were present in our models: single stable fixed point: F, O1, or DM; two simultaneously stable fixed points, i.e. hysteresis regions: F/O1 and F/DM. (2) The topology of the instability strip is similar but not identical for different metallicity and luminosity values. (3) F/O1 can be seen across the whole investigated range of Z and L. (4) DMR is also present at all Z and L values, generally with a small width: 10 − 60K. At low L one can find a mostly pure DM area, while at higher luminosity F/DM appears immediately at the lower temperature side of DM. (5) DMR and F/O1 have a strong connection, both are situated between pure F and O1 regions. For fixed L and Z one can see F/O1 at low mass and DM at higher mass. The transition mass increases with increasing luminosity.

Fundamental blue edge

Combining the mode selection and evolutionary information one can construct a theoretical Teff − L diagram containing RR Lyrae stars pulsating in the fundamental or first overtone mode. Then the blue edge slope can be easily determined. To this end a synthetic horizontal branch stellar population was generated with uniform mass, metallicity and age distributions. Three HB evolutionary track sets were applied: (1) Dorman-tracks (Dorman 1992), (2) Demarque-tracks (Demarque et al. 2000) and (3) Padova-tracks (Girardi et al. 2000). For the parameter sets of each individual model star an evolutionary track and its pulsational properties were determined by interpolation of the evolutionary and pulsational grids, respectively. RRd stars could be omitted thanks to the narrow double-mode regions. The short time delay during switching from one pulsational state to another (Buchler & Kolláth 2002) could be safely ignored as well. 10 000 Monte-Carlo iterations were performed for all the three evolutionary track sets. The slopes of the linear fits are listed in Table 1. The distribution around the mean slope is well approximated by a Gaussian, standard deviations (1σ) of these distributions are listed in parenthesis. The presented method provides much better agreement between empirical and theoretical slopes than previous simulations did. No significant variations were found using different evolutionary computations. From the observational point of view the fundamental blue edge is equivalent to the envelope of the RRab stars. We emphasize that from the theoretical side F blue edge always means the blue edge of F/O1, and the O1 red edge is defined by the red edge of F/O1. Evidently, the fundamental blue edge established by this new method is also defined as the blue envelope of the fundamental pulsators, because of the combined 22 Numerical modelling of the RR Lyrae instability strip effect of mode selection and evolution. It is worth mentioning that the L,M,Z-dependence of the F/O1 edges are all important factors, and the relevance of both mode selection and evolution in blue edge modelling were confirmed by simple tests and our earlier work (Szabó et al. 2002).

Double-mode pulsation and evolution

Synthesis of existing evolutionary calculations and mode selection maps led to surprising results. The most important feature is the narrow mass range, (M = 0.745 § 0.010M¯, Z = 0.0001) where the DMR is crossed by evolutionary tracks. For Z = 0.001 the mass range is similar, but at lower mass regime (M = 0.665 § 0.010M¯). At Z = 0.004 no tracks cross the DMR. This trend is in good agreement with the results of Popielski et al. (2000), although they get somewhat higher mass and larger mass range. We emphasize again that altering the TC parameters affects instability strip structures. In this case the result may be an enlarged DM mass range, and/or increased DM mass. Petersen-diagram supports the narrow mass-range (Szabó et al. 2004). If evolution is taken into account, i.e. tracks crossing the DMR, then the possible DM region on the Petersen-diagram is approximately confined to the distribution of RRd stars. This is the first attempt to reproduce the RR Lyrae Petersen- diagram on the basis of nonlinear double-mode models. It is important to note that if only the F/DM region exists, then only redward evolution produces DM pulsation. Although we encountered this scenario we are not in the position to exclude the possibility that blueward or both blue- and redward evolution produce DM stars. A small shift in DM and F/DM positions or in evolutionary tracks may change the situation. This clearly demonstrates the delicate interplay between mode selection and evolutionary effects in determining the possible parameter range of double-mode RR Lyrae pulsation.

Acknowledgments. This work was supported by Hungarian OTKA (T-038440). References Buchler, J.R., Kolláth, Z. 2002, ApJ, 573, 324 Demarque, P., Zinn, R., Lee, Y-W., Yi, S., 2000, AJ, 119, 1398 Dorman, B. 1992, ApJS, 81, 221 Feuchtinger, M.U. 1998, A&A, 337, 29 Girardi, L., Bressan, A., Bertelli, G., Chiosi, C. 2000, A&AS, 141, 371 Jurcsik, J. 1997, Poster Vol. of the IAU Symp. No. 181. p 261 Eds.: Schmider, F. X. and Provost, J. Jurcsik, J. 1998, A&A, 333, 571 Kolláth, Z., Buchler, J. R., Feuchtinger, M. 2000, ApJ, 540, 468 Kolláth, Z., Buchler, J. R., Szabó, R., Csubry, Z. 2002, A&A, 385, 932 Kovács, G., Jurcsik, J. 1996, ApJL, 466, L17 Kovács, G., Jurcsik, J. 1997, A&A, 322, 218 Popielski, B. L., Dziembowski, W. A., Cassisi, S. 2000, Acta Astron. 50, 491 Szabó, R., Csubry, Z., Kolláth, Z., Buchler, J. R. 2000, ASP Conf. Ser., 203, 374 Szabó, R., Csubry, Z., Kolláth, Z., Buchler J. R. 2002, ASP Conf. Ser., 259, 404 Szabó, R., Kolláth, Z., Buchler, J. R. 2004, A&A submitted van Albada, T. S., Baker N. 1973, ApJ, 185, 477 Comm. in Asteroseismology Vol. 145, 2004

UBV I Time-series Photometry of the Old LMC Globular Cluster Reticulum

V. Ripepi1, M. Monelli2, M. Dall’Ora2, G. Bono2, C. Corsi2, F. Caputo2 , L. Pulone2, V. Testa2, G. Andreuzzi2, R. Buonanno2, G. Marconi3, M. Marconi1, M. Di Criscienzo1, J. Storm4, S. Degl’Innocenti5

1 INAF-Osservatorio Astronomico di Capodimonte, Via Moiariello 16, 80131 Napoli, Italy 2 INAF-Osservatorio Astronomico di Monteporzio, Via di Frascati 33, 00044 Rome, Italy 3 European Southern Observatory, 3107 Alonso de Cordova, Santiago, Chile 4 Astrophysikalisches Institut Potsdam, An der Sternwarte 16, 14482 Potsdam, Germany 5 Dipartimento di Fisica, University of Pisa, via Buonarroti 2, 56127, Pisa, Italy

Abstract

We present new UBV I CCD observations of the old LMC globular cluster RETICULUM. These data allowed us to re-determine periods and light curves and to identify 4 double mode RR Lyrae stars. A comparison with the theoretical instability strip in the MV − log P plane shows good agreement between theory and observations when an apparent distance modulus of (m − M)=18.45§0.12 mag (i.e.(m − M)0=18.39§0.12 mag) is assumed.

Introduction

GLC 0435-59 (RETICULUM) is an old globular cluster placed about 11 degrees in the north- west direction with respect to the bar of LMC. It is bound to this galaxy and is part of its halo system. RETICULUM is already known to host 32 RR Lyrae (Walker 1991), and its metallicity has been estimated by means of medium resolution spectra: [Fe/H]≈-1.71§0.1 (Suntzeﬀ et al. 1992).

Observations and data reduction

We collected UBV I data with SUSI2 at NTT (La Silla, Chile) during three different runs in 1999-2000-2001. In addition we got from the NTT archive some V I frames obtained with SUSI1 during 1995. In total we obtained about 33 phase points in UBV and around 12 in I. A few long exposures have also been taken in order to provide deep Color-Magnitude Diagrams (CMD). NTT during the these two filters with Data reduction have been performed by using the usual procedures (IRAF package), whereas the photometry has been carried out by using DAOPHOT/ALLFRAMES packages (Stetson 1987). An accurate photometric calibration has been obtained by observing several Landolt (1992) standard fields, complemented in BV I with new standard stars by Stetson (2000). In the following we shall concentrate on some results from the BV photometry only. 24 UBV I Time-series Photometry of the Old LMC Globular Cluster Reticulum

The RR Lyrae variables

In order to obtain well sampled light curves for the RR Lyrae stars, we coupled our BV data with those by Walker (1992). This operation was easy since the photometric agreement is good (< 0.02 mag in BV ). The resulting time series include about 63 epochs and span around 10 years, allowing a precise determination of the periods and, in turn, of light curves for the majority of RR Lyrae in RETICULUM. The latter were fitted with spline functions in order to derive the colors. An example of light curves in UBV I with over-imposed a spline fit to the data is shown in Fig. 1 for a fundamental (V37) and a first overtone (V36) pulsator.

Figure 1: Light curves for V36 (RRc) and V37 (RRab). The open and filled circles denote photometry from Walker (1992) and from this paper, respectively. Solid lines show a spline fit to the data. Note the use of B and V spline fits as templates to fit U and I light curves respectively (due to the lack of sampling in these bands).

An important result obtained on the basis of the present observations is the discovery of four double mode (RRd) pulsators among RETICULUM RR Lyrae stars: namely the stars V41, V72, V98 and V110. A detailed discussion of the properties of these RRd stars, as well as of the procedures quoted above, will be given in a forthcoming paper (Ripepi et al. in preparation).

Comparison with the theory of pulsation

In Figure 3 we show the comparison between the observed and predicted RR Lyrae instability strip in the MV − log P plane. This plane is interesting since it allows to estimate the V. Ripepi et al. 25

apparent distance modulus of the cluster by constraining the observed RRc distribution to match the predicted blue limit of the pulsation region, under the assumption of solar-scaled chemical composition (see Caputo 1997 and Caputo et al. 2000). This method is only slightly dependent on the uncertainties on pulsation models and, in particular, on the treatment of convection, which mainly aﬀects the red boundary of the strip (see Fig. 3). As shown in Fig. 3 the distance of RETICULUM estimated with the quoted method is (m − M)(RETICULUM)=18.45§0.12 mag, where the error includes the theoretical uncertainties and the metallicity error. Assuming a reddening of 0.02 mag (Ripepi et al. in preparation) this means (m − M)0(RETICULUM)=18.39§0.12 mag.

0.2

0.4

0.6

0.8

1 -0.6 -0.4 -0.2 0

Figure 2: RR Lyrae of RETICULUM in the MV − log P plane. The upper and lower panel show the diﬀerence in the predicted red edge of the fundamental pulsators by using a diﬀerent assumption of the mixing length parameter α in the convective treatment (see labels).

Acknowledgments. It is a pleasure to thank G. Clementini who kindly analysed the four double mode pulsators with her software GRATIS. References Caputo F. 1997, MNRAS 284, 994 Caputo F., Castellani V., Marconi M., Ripepi V. 2000, MNRAS 316, 819 Landolt A.U. 1992, AJ 104, 372 Stetson P.B. 1987, PASP 99, 191 Stetson P.B. 2000, PASP 112, 925 Suntzeﬀ N.B., Schommer R.A., Olszewski E.W., Walker A.R. 1992, AJ 104, 1743 Walker A.R. 1992, AJ 103, 1166 Comm. in Asteroseismology Vol. 145, 2004

Long-term photometric study of LBVs in M33

A. Zharova1, O. Sholukhova2 1 Sternberg Astronomical Institute, Moscow, Russia 2 Special Astrophysical Observatory of Russian Academy of Sciences The extensive plate collection of Sternberg Astronomical Institute (Moscow) was used for a study of the photometric behaviour of bright variable stars in M33. We present here LBV V268 (VarC) and the LBV-candidate Hα7. About 600 magnitude estimates were obtained for each star for 1973 - 2002. The light curves of both stars are typical for Luminous Blue Variables. V268 shows large and complex quasiperiodic variations from 2 to 3400 days. In Hα7, we found several quasi-periods from 20 to 160 days. Amplitudes of these variations depend on the state of activity of the stars. The historical light curve of V268 combined with the new data is shown in Fig.1. We see the photometric behaviour typical for LBVs. 1) The star’s magnitude varies with an amplitude of about 0.2-0.3 mag on time scales from weeks to months. 2) There were few bright states (outbursts) with amplitudes of 1-2 mag on time scales of decades. There are low and high states in the light curve and the amplitude of the variations depends on the state. In total, we found 12 periods ranging from 2 days up to 3400 days.

Figure 1: Light curve of V268. Open circles are the data of Hubble and Sandage (1953); triangles, the data of Sharov (1973); asterisks, the data of Rosino and Bianchini (1973); squares, the data of Kurtev et al. (1999); ﬁlled circles, our estimates.

Acknowledgments. This study was supported by a grant from the Programme of Support for Leading Scientiﬁc Schools of Russia No. 389-2003-2, and RFBR grant No. 03- 02-16341. O. Sholukhova has been supported by INTAS grant YSF 2002-281. The authors are grateful to S.Fabrika and N.Samus for useful remarks. References Hubble E., Sandage A., 1953, ApJ, 118, 353 Kurtev R.G., Corral L.J., Georgiev L., 1999, A&A, 349, 796 Rosino L., Bianchini A., 1973, A&A, 22, 453 Sharov A.S., 1973, Perem. Zvezdi, 19, 3 Comm. in Asteroseismology Vol. 145, 2004

Cepheids in binary systems – new candidates in the Magellanic Clouds

L. Szabados

Konkoly Observatory, Budapest, Hungary; email: [email protected]

Abstract

While in our Milky Way galaxy the majority of Cepheids is not solitary, in the Magellanic Clouds only a few binaries have been revealed in lack of systematic spectroscopic studies. A simple numerical parameter, the ratio of the radial velocity and the photometric amplitudes was studied for the Magellanic Cloud Cepheids. A large value of this amplitude ratio is a hint that the Cepheid has a companion. According to this duplicity indicator HV 834 and HV 2864 are possibly members in binary systems.

Introduction

Owing to their role as primary distance indicators, Cepheids were intensely searched for in other galaxies of the Local Group and even beyond. Up to now Cepheids were found in more than 20 external galaxies but no binary system among them has been identiﬁed beyond the Magellanic Clouds. In order to get a reliable zero point of the period-luminosity relationship, the brightness contributions of the companion(s) of Cepheids belonging to binary (or multiple) systems have to be removed before converting the apparent magnitude into absolute brightness. For this purpose Cepheids belonging to binary systems have to be identiﬁed.

Binary Cepheids in the Magellanic Clouds

The Magellanic Clouds are fundamental objects for astronomy in several respects. Classical Cepheids belonging to the Clouds are especially important because the period-luminosity relation has been traditionally calibrated by using Cepheids in these nearby galaxies. In view of the fact that the photometric effects of the companions have to be taken into account when determining the luminosities of the Cepheids, and because of the high incidence of duplicity among Galactic Cepheids, it is essential to study binarity of the Magellanic Cloud Cepheids as well. In this respect, however, our knowledge on companions to Cepheids in the neighbouring galaxies is rather incomplete. Although several thousand Cepheids have been discovered in the two Clouds, binarity has been established only in 7 cases. This is a serious deficiency because binaries among Cepheids are more frequent than solitary Cepheids (Szabados 2003b). In spite of the strong selection bias, there are about 150 known binaries among the less than a thousand Galactic Cepheids (Szabados 2003a). Three long period spectroscopic binary systems have been found from among eleven Cepheids by Imbert et al. (1985): HV 837 and HV 11157 in the SMC, and HV 883 in the LMC. The orbital elements of these binaries were determined in a subsequent paper by Imbert (1994). The fourth single lined spectroscopic binary among Magellanic Cloud Cepheids was discovered during a detailed photometric/spectroscopic study of the LMC cluster NGC 1866 (Welch et al., 1991), but the radial velocity data obtained in two 28 Cepheids in binary systems – new candidates in the Magellanic Clouds consecutive years have been insufficient to derive the orbital period (and other elements) of the system involving the Cepheid HV 12202. The extensive photometry carried out for finding microlensing events resulted in discovering 3 eclipsing binaries from among nearly 1800 MACHO Cepheids in the Magellanic Clouds (Alcock et al., 2002). Based on their location in the colour-magnitude diagram, MACHO 81.8997.87 is a Cepheid pulsating in the first overtone (Ppuls = 2.035 days, Porb = 800.5 days), MACHO 6.6454.5 (Ppuls = 4.974 days, Porb = 397.142 days) has a lower luminosity than the fundamental mode pulsators if the flux from the companion is removed properly, while the third Cepheid in an eclipsing binary system, MACHO 78.6338.24 (Ppuls = 17.686 days, Porb = 419.718 days) is a Population II Cepheid.

Ratio of radial velocity and photometric amplitudes as a hint for duplicity

The ratio of the radial velocity and photometric amplitudes (determined for the complete pulsational cycle) as a possible indicator of duplicity was first mentioned by Coulson and Caldwell (1989) but in their study this criterion was only applied to a limited sample. If there existed a normal value of the amplitude ratio AVRAD/AB for a given pulsation period, it would be expected that in the presence of a companion one observes a modified value: the photometric data result in a decreased amplitude, while the radial velocity variations of pulsational origin are not affected by the companion. Moreover, the unrecognized orbital motion superimposed on the pulsational changes results in an increased AVRAD. Therefore a larger-than-normal value of AVRAD/AB (in what follows, this amplitude ratio is referred to as AR) may indicate presence of a companion. The behaviour of the AR has been studied using the data on more than a hundred classical Cepheids in the Magellanic Clouds and the Milky Way for which reliable radial velocity and photometric data have been available (via the on-line data base compiled by D. L. Welch at the URL: http://dogwood.physics.mcmaster.ca/Cepheid/HomePage.html). The diagram showing AR against the logarithm of the pulsation period is seen in Figure 1. In this plot, circles denote fundamental pulsators, squares mean the AR values for the first overtone mode. The overtone pulsation can be readily identified if the Cepheid is either in the Magellanic Clouds (the overtone pulsators are more luminous in the colour–magnitude diagram), or pulsates in two modes simultaneously (beat Cepheid). A beat Cepheid can be characterized by two AR values, one for each excited mode. Some general conclusions can be deduced from Figure 1: - At a given pulsation period, no normal value of the AR exists. At any period there is a large spread in both photometric and radial velocity amplitudes; - The AR value is systematically larger for overtone pulsators than for the fundamental mode; - For Cepheids pulsating in the fundamental mode, the average AR is independent of the pulsation period itself. The larger AR of the overtone pulsators is a consequence of the higher frequency of the overtone as compared with the fundamental mode oscillation of the same star. From their linear pulsational model Balona and Stobie (1979) derived that

2 1/2 AVRAD /AV = 4.097R0/[P (f + 4f cos ψ + 4) ] where R0 is the average radius, ψ is the phase lag between the moments of the maximum flux and maximum radius, f is the ratio of flux variation to radius variation. Because the period ratio of the two excited modes is about 0.7 for beat Cepheids, one expects 1/0.7 times larger value of AR for the first overtone pulsation as compared with the fundamental mode oscillation (considering a given photometric band). The numerical values of the AR determined from the observational data of Galactic double-mode Cepheids are in accordance with this theoretical value. L. Szabados 29

Galaxy + SMC + LMC

60 HV 2864 HV 834 40 Amplitude ratio 20

0 0 .5 1 1.5 2 log P

Figure 1: The AR (defined in the text) as a function of the pulsation period. Circles denote AR values of fundamental mode pulsators, squares are used for denoting Cepheid oscillating in the first overtone. Binaries, marked with filled symbols, tend to have larger values of the amplitude ratio than solitary Cepheids. The two most upwardly deviating stars, HV 2864 and HV 834, are newly suspected binaries.

In order to demonstrate the eﬀect of binarity on the AR in Figure 1, Cepheids with known companions are marked with ﬁlled symbols, while empty symbols denote solitary Cepheids as well as those stars, whose companions have not been detected yet. It is seen that, in accordance with the expectation, binaries tend to have larger AR values on average than solitary Cepheids. Keeping in mind, however, the width of the interval of normal AR values, the larger-than-average value of the AR does not necessarily imply duplicity of the individual variables. There are, however, two Cepheids, HV 834 in the SMC and HV 2864 in the LMC whose extremely large amplitude ratio may well be caused by a companion star.

Acknowledgments. The author expresses his gratitude to Dr. M´aria Kun for her useful comments on the manuscript. Financial support from the Hungarian OTKA grant T34584 is acknowledged. References Alcock C., Allsman R. A., Alves, D. R., et al. (The MACHO Collaboration), 2002, ApJ 573, 338 Balona L. A., Stobie R. S., 1979, MNRAS 189, 649 Coulson I. M., Caldwell J. A. R., 1989, MNRAS 240, 285 Imbert M., 1996, A&AS 116, 497 Imbert M., Andersen J., Ardeberg A., et al., 1985, A&AS 81, 339 Szabados L., 2003a, Inf. Bull. Var. Stars, No. 5394 Szabados L., 2003b, in GAIA Spectroscopy, Science and Technology, ed. U. Munari, ASP Conf. Ser. 298 (San Francisco: ASP), p. 237 Welch D. L., Mateo M., Cot´e P., Fischer P., Madore B. F., 1991, AJ 101, 490 Comm. in Asteroseismology Vol. 145, 2004

A continuous population of variable stars up to about 1.5 mag above the horizontal branch?

L. Baldacci1, G. Clementini2, E.V. Held3, M. Marconi4 L. Rizzi3

1 Bologna University, via Ranzani 1, I-40127 Bologna 2 INAF - Bologna Observatory, via Ranzani 1 I-40127 Bologna 3 INAF - Padova Observatory, vicolo dell’Osservatorio 5 I-35122 Padova 4 INAF - Capodimonte Observatory, via Moiariello 16 I-80131 Napoli

Abstract

Increasing samples of pulsating variable stars populating the classical instability strip from the horizontal branch to a few magnitudes brighter are being found in several Local Group galaxies, irrespective of the galaxy morphological type. We will review the observational scenario focusing in particular on the Anomalous Cepheids and related objects.

Introduction

In recent years many Local Group (LG) galaxies have been surveyed looking for variable stars, however the observational scenario is rather inhomogeneous. In fact, while several of the dwarf Spheroidal (dSph) companions of the Milky Way had been studied in the early eighties, the advent of CCD detectors and wide field cameras, and the development of new powerful methods for the detection of the variables (e.g. the image subtraction techniques), have prompted for new surveys whose results, however, often are not yet published. On the other side, the study of the variable stars in the Irregular galaxies was impossible until a few years ago, except in the Magellanic Clouds. Thus recent and good quality photometric data exist only for a few of these galaxies. Moreover, the Magellanic Clouds benefited from the systematic surveys of the microlensing studies (e.g. MACHO: Alcock et al. 1996; OGLE: Udalski et al. 1997). Hence, samples for these two galaxies are much better studied and complete than for others. A number of different types of pulsating variables lie in the portion of the HR diagram brighter than the RR Lyr stars. We will briefly describe the different types here. Anomalous Cepheids (ACs) are metal poor (Z ∼ 10−4) helium burning stars about 1 mag brighter than the RR Lyr stars, showing a range in period from 0.3 d to 2 d. First observed in the Draco dSph by Baade & Swope (1961), they occur in all the known dSphs (Pritzl et al. 2002, and references therein). On the contrary they are remarkably rare in Globular Clusters (GCs) where only one confirmed AC has been found in the low density globular cluster NGC 5466 (Zinn & Dahn 1976). Zinn & Searle (1976) named these variables Anomalous Cepheids because they fail to follow the period-luminosity (P/L) relation of Classical and Population II Cepheids (P2C). Because ACs do no show a different morphology of the light curves whether they pulsate in the fundamental or in the first overtone mode, the P/L relations (Nemec et al. 1988, Nemec et al. 1994, Bono et al. 1997, Pritzl et al. 2002) are the only way to determine their pulsation mode, that, however, still remains uncertain for many of them. Theory and observations suggest that ACs are 2 or 3 times more massive than the RR Lyr L. Baldacci, G. Clementini, E.V. Held, M. Marconi, L. Rizzi 31 stars, but we still lack precise estimates (Nemec et al. 1988 and references therein). Masses could allow us to disentangle between the two possible scenarios proposed for the origin of ACs: they are relatively young and massive stars (∼ 1 Gyr, Norris & Zinn 1975, M< 2.5 M¯) or they resulted from mass transfer in binary systems formed by old stars (∼ 10 Gyrs, Renzini et al. 1977). In the latter case their masses could not exceed twice the turn-off mass of the system (∼ 1.6M¯ for Spheroidal galaxies, see Wallerstein & Cox 1984 for details). The question about the origin of the ACs in dSphs remains unsettled because none of these two hypotheses could be definitely ruled out (Da Costa 1988). P2Cs are very common in Galactic GCs. They are very old, metal-poor, low mass (M≤ 0.6 M¯) stars that cross the instability strip while evolving from the blue tail of the HB towards the Asymptotic Giant Branch (see Wallerstein & Cox, 1984). With the exception of Ursa Minor, dSphs generally do not have HBs extending to the blue enough to produce P2Cs, but they are found in the dSphs that host globular clusters, namely Fornax and Sagittarius. Two further types of pulsating variables lie in the portion of the HR diagram brighter than the HB of the LG dwarf Irregular (dIrr) galaxies, they are the short period Cepheids (SPCs) and the low luminosity (LL) Cepheids. Smith et al. (1992) defined SPCs as a conspicuous population of variables in the Small Magellanic Cloud with periods between 0.6 d to 10 d, that did not follow the ACs P/L relations and fell instead on the extension to short periods of the Classical Cepheids’ P/L relations. SPCs have been found in many dIrrs since, they extend to longer periods and are brighter than the ACs. Both ACs and SPCs are helium burning stars, but the former have experienced the helium flash (namely have masses M ≤ 2.5M¯), while the latter are blue loop stars that have ignited helium in non degenerate conditions (M ≥ 2.5M¯). SPCs should represent the low mass tail of the Classical Cepheids in low metallicity systems (Gallart et al. 1999, Dolphin et al. 2002). LL Cepheids were observed for the first time in the dIrr galaxy NGC6822 by Clementini et al. (2003a). They have small amplitudes (0.1 - 0.4 mag in V), are fainter and have shorter periods than the SPCs: they seem to merge in magnitude with the RR Lyr stars forming a continuum in the classical instability strip. Due to their small amplitudes, LL Cepheids are difficult to detect, thus they may have been missed in dIrr galaxies where crowding is severe. In the P/L plane the LL Cepheids occupy the short-period low-luminosity region where ACs and Classic Cepheids P/L relations merge (see fig.2) and where the 4 ACs detected in the LMC by Clementini et al. (2003b), and the SPCs recently found in Phoenix by Gallart et al. (2003) are also located. Because of their low luminosities LL Cepheids could be the counterpart of ACs in dIrrs, indeed models for ACs predict variables with such small amplitudes and low luminosities (Fiorentino et al. 2003).

Dwarf Spheroidal Galaxies

All dwarf Spheroidals studied so far are found to host ACs, although not in very large numbers (And VI: Pritzl et al. 2002; Leo II: Siegel & Majewski 2000; Draco: Zinn & Searle 1976, Kinemuchi et al. 2002; Ursa Minor: Nemec et al 1988; Carina: Saha et al. 1986, Dall’Ora et al. 2003; Sculptor: Swope 1968, Kaluzny et al. 1995; Sextans: Mateo et al. 1995a, Sagittarius: Mateo et al. 1995b, Layden & Sarajedini 2000; AndIII: Da Costa et al. 2002; And II: Pritzl et al. 2003; Leo I: Hodge & Wright 1978; Fornax: Light et al. 1986, Bersier & Wood 2002, Clementini et al. 2003c, Mackey & Gilmore 2003). Figure 1 shows the P/L relation of the ACs in the V band, drawn from the above literature data generally selecting only variables with accurate data. We have adopted the distance scale of Pritzl et al. (2002) which is consistent with a distance modulus of 18.5 for the LMC. The distance scale has a fundamental role both in the slope and zero point of the ACs P/L relations (slanted solid lines in ﬁg. 1), and in the pulsation mode determination. The horizontal lines mark the mean level of RR Lyr stars in the metal poorer (Ursa Minor) and the metal richer (Fornax) galaxies and show that there is no clear separation between the distributions of ACs and HB 32 A continuous population of variable stars up to about 1.5 mag above the horizontal branch?

Figure 1: P/L distribution of the ACs in various dSphs. The slanted solid lines are the ACs P/L relations by Pritzl et al. (2002), the horizontal solid lines mark the RR Lyr average luminosity in Ursa Minor and Fornax. Theoretical boundaries of the ACs instability strips are from Marconi et al. (2004).

variables. Also shown in the figure are the boundaries of the theoretical instability strip of ACs models with different masses computed by Marconi et al. (2004). The Leo I ACs are not displayed and are discussed more in detail in the next section. The Galactic GCs P2Cs collected by Nemec et al. (1994) are also shown in Figure 1. Fornax and Sagittarius are so far the only dSphs known to host GCs, and found to contain both ACs and P2Cs. Two of the variables in Sagittarius are in the cluster M54 (Layden & Sarajedini 2000). They had been originally classified as a candidate AC and a candidate P2C, but clearly lie both in the P2Cs region. Fornax variables present a more complex scenario since many of the field variables classified as ACs by Bersier & Wood (2000) lie instead on the P/L relation of the P2Cs. If confirmed when more accurate photometric data will become available, this would thus be the first identification of P2Cs in the field of a dSph. LeoI Leo I has a dominant young and intermediate-age stellar population. The galaxy has a bulk of candidate variables 2.4 mag brighter than the HB, and about 1 mag brighter than the ACs found in the other dSphs (Lee et al. 1993, Baldacci et al. 2003). Caputo et al. (1999) demonstrate that they are still consistent with ACs models, but Gallart et al. (1999) claim that they are bright enough to be SPCs. The published light curves for these variables (Hodge & Wright 1978) are affected by a large scatter, thus the presence of variables more massive than the ACs in Leo I is a hypothesis that needs to be confirmed. L. Baldacci, G. Clementini, E.V. Held, M. Marconi, L. Rizzi 33

Figure 2: P/L distribution of Cepheids with period shorter than 20 d found in LG Irregular galaxies.

Dwarf Irregular Galaxies

Figure 2 shows the P/L distribution of Cepheids with period shorter than 20 d found in the LG Irregular galaxies (IC1613: Dolphin et al. 2001; Leo A: Dolphin et al. 2002; Sextans A: Dolphin et al. 2003; SMC: Udalski et al. 1999; LMC: Udalski et al. 1999, Clementini et al. 2003b; NGC6822: Antonello et al. 2002, Clementini et al. 2003a; Phoenix: Gallart et al. 2003). The dashed-dotted lines are the P/L relations followed by the SPCs with periods shorter than 2 days in the SMC (see Dolphin et al. 2003 for details). We have extended them to larger periods (up to ∼ 10 d) since they very well represent the general distributions shown in Figure 2. The solid lines are the P/L relations for ACs in dSphs by Pritzl et al. (2002). The P/L relations of the ﬁrst overtone ACs and Cepheids are similar to each other, the fundamental mode relations show instead some diﬀerences. The LL Cepheids in NGC6822 appear to be consistent both with the ACs and SPCs relations.

Conclusion

The classical instability strip appears to be continuously populated in the dIrrs with the LL Cepheids ﬁlling the gap between RR Lyr stars and SPCs. An instability strip uniformly 34 A continuous population of variable stars up to about 1.5 mag above the horizontal branch? populated as observed in NGC 6822 or in Phoenix probably reﬂects the continuous star formation process occurring in these galaxies. On the other side, ACs with luminosities close to the RR Lyr stars have been found in some dSphs but they are only a few. Thus they may represent the the tail at low masses of the ACs mass distribution, more than a continuity in the star formation process. The actual nature of the LL Cepheids still remains unclear since they cannot be distinguished from ACs and SPCs on the basis of the P/L relations.

Acknowledgments. We are grateful to C. Gallart for providing us the data for the SPCs in Phoenix, and to D. Bersier for helpful discussions on the ACs and P2Cs in Fornax. References Alcock, C. et al. 1996, AJ 111, 1146 Antonello, E., Fugazza, D., Mantegazza, L., Stefanon, M., Covino, S. 2002, A&A 386, 860 Baade, W., Swope, H.H. 1961, AJ 66, 300 Baldacci, L. et al. 2003, in “Stars in Galaxies”, in press (astro-ph/0305506) Bersier, D., Wood, P.R. 2002, AJ 123, 840 Bono, G., Caputo, F., Santolamazza, P., Cassisi, S., Piersimoni, A. 1997, AJ 113, 2209 Caputo, F., Cassisi, S., Castellani, M., Marconi, G., Santolamazza, P. 1999, AJ 117, 2199 Clementini, G., Held, E.V., Baldacci, L., Rizzi, L. 2003a, ApJ 588L, 85 Clementini, G. et al. 2003b, AJ 125, 1309 Clementini, G. et al. 2003c, in “Variable stars in the Local Group”, in press (astro-ph/0310545) Da Costa, G.S. 1988, IAU Symp. 126, 217 Da Costa, G.S., Armandroff, T.E., Caldwell, N. 2002, AJ 124, 332 Dall’Ora, M. et al. 2003, AJ 126, 197 Dolphin, A.E. et al. 2001, ApJ 550, 554 Dolphin, A.E. et al. 2002, AJ 123, 3154 Dolphin, A.E. et al. 2003, AJ 125, 1261 Fiorentino, G., Caputo, F., Marconi, M. 2003, in “Stars in Galaxies”, in press Gallart, C., Freedman, W.L., Aparicio, A., Bertelli, G., Chiosi, C., 1999, AJ 118, 2245 Gallart, C. et al. 2003, in “Variable stars in the Local Group”, in press Hodge, P.W., Wright, F.W. 1978, AJ 83, 228 Kaluzny, J. et al. 1995, A&AS 112, 407 Kinemuchi, K. et al. 2002, ASP Conf. Ser. 259, 130 Layden, A.C., Sarajedini, A., 2000, AJ 119, 1760 Lee, M.G. et al. 1993, AJ 106, 1420 Light, R.M., Armandroff, T.E., Zinn, R. 1986, AJ 92, 43 Mackey, A.D., Gilmore, G.F., 2003, MNRAS, in press (astro-ph/0307275) Marconi, M., Fiorentino, G., Caputo, F. 2004, A&A, in press (astro-ph/0401332) Mateo, M., Fischer, P., Krzeminski, W. 1995a, AJ 110, 2166 Mateo, M. et al. 1995b, AJ 110, 1141 Nemec, J.M., Wehlau, A., Mendes de Oliveira, C. 1988, AJ 96, 528 Nemec, J.M., Nemec, A.F.L., Lutz, T.E. 1994, AJ 108, 222 Norris, J., Zinn, R. 1975, ApJ 202, 335 Pritzl, B.J., Armandroff, T.E., Jacoby, G.H., Da Costa, G.S. 2002, AJ 124, 1464 Pritzl, B.J., Armandroff, T.E., Jacoby, G.H., Da Costa, G.S. 2003, AJ, in press (astro-ph 0310620) Renzini, A., Mengel, J.G., Sweigart, A.V. 1977, A&A 56, 369 Saha, A., Monet, D.G., Seitzer, P. 1986, AJ 92, 302 Siegel, M.H., Majewski, S.R 2000, AJ 120, 284 Swope, H.H. 1968, AJS 73, 204 Smith, H.A., Silbermann, N.A., Baird, S.R., Graham, J.A. 1992, AJ 104, 1430 Udalski, A., Kubiak, M., Szymanski, M. 1997, AcA 47, 319 Udalski, A. et al. 1999, AcA 49, 201 Wallerstein, G., Cox, A.N. 1984, PASP 96, 677 Zinn, R., Dahn, C.C. 1976, AJ 81,527 Zinn, R., Searle, L. 1976, ApJ 209, 734 Comm. in Asteroseismology Vol. 145, 2004

The core/envelope asymmetry in p-mode pulsating stars

A. Miglio1,2, E. Antonello1

1 INAF, Osservatorio Astronomico di Brera, via E. Bianchi 46, 23807 Merate, Italy 2 Institut d’Astrophysique et de Géophysique de l’Université de Liège, Allèe du 6 Aout,ˆ 17 B-4000 Liège, Belgium

Abstract

It has been shown that there is a potential ambiguity in the asteroseismic determination of the location of internal structures in a pulsating star (Montgomery et al. 2003). We show how, in the case of high-order non-radial acoustic modes, we can possibly remove this ambiguity by considering modes of diﬀerent degree. To support our conclusions we have investigated the seismic signatures of sharp density variations in the structure of quasi-homogeneous models.

Aliasing

It is known that a sharp variation in the equilibrium structure of a star gives rise to a periodic component in the frequencies of oscillation (see for example Monteiro et al. 2000). A way to isolate these components, in high order modes, is to consider deviations from asymptotic expressions for period (frequency) spacings in g-mode (p-mode) pulsators. Montgomery et al. (2003) reported that in the case of white dwarfs, where only high order gravity modes have been detected, there is a potential ambiguity in determining where in the stellar interior the variation that generates the periodic signal is located. With the aim of extending the analysis to acoustic modes, we present how we could possibly remove such an ambiguity by considering modes of diﬀerent degree. A general form for the periodic signal generated by a sharp variation located at an acoustic depth τd could be approximated by

δν ' A(ν) sin (2π ν 2τd + φ) (1) where A(ν) is a slowly decreasing function of frequency which depends on the characteristics of the sharp variation (Monteiro et al., 2000). When looking for such a periodic signal in the frequencies of an acoustic oscillation spectrum it is clear that the signal can be evaluated only in a discrete set of frequencies νn,`, solutions of the oscillation equations. Let us consider modes of some degree ` and a periodic signal as in Eq. (1). Having deﬁned the acoustic radius as r dr0 θ(r) = Z0 c and remembering the simple ﬁrst order asymptotic relation (Tassoul, 1980)

0 νn ' ∆ν n + φ (2) ¡ ¢ and T ≡ τ(0) ≡ θ(R) ' 1/(2∆ν) (3) 36 The core/envelope asymmetry in p-mode pulsating stars it is straightforward to show that δν (Eq. (1)) can be also written as

00 δν = A(ν) sin (2π ν 2θd + φ ) (4)

This means that we cannot distinguish whether a variation is located at an acoustic depth τd or θd = T − τd (see Mazumdar & Antia (2001) and Montgomery et al. (2003) in the case of g modes).

Figure 1: (a) If the discontinuity is located near the surface, the periodic signal can be described as slowly changing and independent from ` with a period ∼ 1/(2τd) (continuous line) or as a signal with a short period (1/(2θd)) with a phase which depends on ` being even or odd (dashed and dotted lines). The signal evaluated at the discrete frequencies in Eq. (5) is represented by asterisks (` = 0) and diamonds (` = 1). The values on the axes are arbitrary. (b) The discontinuity is located near the center of the star.

Since we would like to include in our treatment modes of diﬀerent degree ` we generalized the previous argument considering, instead of Eq. (2), an asymptotic expression which includes the dependence on ` (Tassoul, 1980):

` 0 νn,l ' ∆ν n + + φ (5) µ 2 ¶

It follows therefore that the signal in Eq. (1) is equivalent to

` 00 δν = (−1) A(ν) sin (2π ν 2θd + φ ) (6)

We can then conclude that, to this very ﬁrst degree of approximation, it is equivalent to consider a periodic signal independent from ` with a “frequency” twice the acoustic depth or signals that have a “frequency” twice the acoustic radius of the discontinuity and depend on ` through the multiplicative factor (−1)`. This can be applied both to periodic signals generated by discontinuities located near the surface and the center of the star (see Fig. 1). A. Miglio and E. Antonello 37

Signatures of density variations in quasi-homogeneous models

As a first investigation we considered models with simple density profiles, then found analyti- cally the pressure profile and calculated acoustic oscillation spectra using the Aarhus Adiabatic 1 Pulsation Package . We looked for oscillatory signals in Dn` = (νn,` − νn−1,`+2)/(4` + 6). As presented in Fig. 2, if we consider a homogeneous model, Dn` does not depend on the degree ` and has a smooth behaviour throughout the range of frequencies considered. If we introduce a density variation in the equilibrium model (a step function in the derivative of the density profile) we notice the appearance in Dn` of a periodic signal whose phase depends on the degree, as qualitatively predicted by Eq. (6).

Figure 2: Small separation as a function of frequency. The continuous line is Dn0 (=Dn1) for the homogeneous model; the dashed and dotted lines represent respectively Dn0 and Dn1 for models with a sharp density variation at (a) r/R = 0.1 and (b) r/R = 0.3.

Conclusion

Using a simple argument we have shown how, in stars that show non-radial acoustic oscillations, we could break the core/envelope symmetry found for g-modes in white dwarfs. It is just a ﬁrst approximation and has to be thoroughly analyzed and applied to realistic models. References Montgomery M. H., Metcalfe T. S. and Winget, D. E. 2003, MNRAS, 344,657 Monteiro M. J. P. F. G., Christensen-Dalsgaard J. and Thompson M. 2000, MNRAS, 316, 165 Mazumdar A. & Antia, H. M. 2001, A&A 377, 192 Tassoul M., 1980, ApJS, 43, 469

1http://astro.phys.au.dk/~jcd/adipack.n/ Comm. in Asteroseismology Vol. 145, 2004

Mapping non-radial pulsation using surface imaging techniques

S.V. Berdyugina1,2, H. Korhonen3, J.H. Telting4, C. Schrijvers5

1 Institute of Astronomy, ETHZ, CH-8092 Zurich, Switzerland 2 Astronomy Division, University of Oulu, P.O. Box 3000, FIN-90401 Oulu, Finland 3 Astrophysikalisches Institut Potsdam, An der Sternwarte 16, D-14482 Potsdam, Germany 4 Nordic Optical Telescope, Apartado 474, E-38700 S/C de La Palma, Canarias, Spain 5 Astronomical Institute Anton Pannekoek, University of Amsterdam, Kruislaan 403, NL-1098 SJ Amsterdam, Netherlands

Abstract

We apply stellar surface imaging techniques for studying non-radial pulsations. Stellar surface imaging is based on inversions of time series of variable spectral line profiles without making assumptions on the specific shape of the pulsations. The inversion results in an image of the stellar surface in which the sectoral and tesseral modes can in many cases be distinguished, and the pulsational degree l and the azimuthal order |m| can be determined. We apply this method to simulated data for testing the method (Berdyugina et al. 2003a). The tests show that the tesseral modes with l − |m| = 2 (or any even number) can be successfully recovered. Pulsation modes that are antisymmetric with respect to the equator, i.e. when l − |m| = 1 (or any odd number), are difficult to recover accurately.

Figure 1: The image of ω1 Sco and ﬁts to the observed line proﬁles.

The method was also applied to high-resolution spectra of the rapidly rotating Beta Cep- type star ω1 Sco (Berdyugina et al. 2003b). In ω1 Sco we ﬁnd a sectoral mode of l = |m| = 9 or l = |m| = 8, also the tesseral mode l = 8 with |m| = 7 is possible. The surface map of the S.V. Berdyugina, H. Korhonen, J.H. Telting, C. Schrijvers 39 dominant pulsation mode (Fig. 1) shows amplitude modulation in the opposite hemispheres. This suggest the presence of another sectoral mode with a frequency close to that of the dominant mode. References Berdyugina S.V., Telting J.H., Korhonen H., 2003a, A&A 406, 273 Berdyugina S.V., Telting J.H., Korhonen H., Schrijvers C., 2003b, A&A 406, 281 Comm. in Asteroseismology Vol. 145, 2004

High Amplitude δ Sct-type variables

E. Rodr´ıguez

1 Instituto de Astrof´ısica de Andaluc´ıa, CSIC, P.O. Box 3004, E-18080 Granada, Spain, E-mail:[email protected]

Abstract

Historically, the high amplitude δ Sct-type variables (δ Sct pulsators with full amplitudes larger than 0.m3) have been considered as a separated group from the “normal” low amplitude δ Sct variables on the basis, mainly, of their pulsation amplitudes. This has been a subject of controversy by a number of authors. After the review papers by Breger (1979, 1980), the commonly accepted idea is that, independently of the amplitude, the δ Sct variables are normal Population I stars in, or evolving oﬀ, the main sequence according to standard stellar evolution theory. This excludes the recently discovered pre-main sequence δ Sct pulsators. Nevertheless, some diﬀerences remain and some interesting aspects make these high amplitude objects very useful.

Introduction

High amplitude δ Sct (HADS) stars are a subgroup of the δ Sct-type variables formed by those stars with full amplitudes larger than about 0.m3, peak to peak. Presently, there are about 150 members catalogued in this group (Rodr´ıguez et al. 2000). Similar to the δ Sct variables with lower amplitudes, they are of Population I. However, by tradition, a few variables of Population II showing similar light curves have also been included into the same group for a long time. They are known as SX Phe variables. Only 13 of these objects are catalogued in the list of Rodr´ıguez et al. (2000) and all belong to the ﬁeld. Some of them (8) display also high pulsational amplitudes. During the last few years, a great number of these Population II variables were discovered in globular clusters. The subject of the present work is to review the present status of the HADS variables, however some aspects dealt here with will also be applicable to the ﬁeld high amplitude (HA) SX Phe stars. Similar to the normal δ Sct variables, the HADS stars represent evolutionary stages of normal Population I stars in main sequence or just post-main sequence phases with radii of about 2-3 R¯ and masses of 1.5-2.5 M¯, with solar abundances and low spatial motions typical of Population I. The HADS variables also show period distributions, period-gravity relations and period ratios similar to the δ Sct variables with low amplitudes. However, their rotational velocities are very low (vsini≤45 Km/s in all cases) as compared with the values (=109 Km/s) derived from the δ Sct pulsators with amplitudes smaller than 0.m03 (Rodr´ıguez et al. 2000). In the following, we consider the term low amplitude δ Sct (LADS) stars for those stars with full amplitudes lower than about 0.m1 and the term medium amplitude δ Sct (MADS) stars for those variables with amplitudes between about 0.1 and 0.3 mag. E. Rodr´ıguez 41

Light curves

Concerning stability of the light curves, it is well known that multiperiodic LADS variables commonly show variations in the amplitude of a number of modes over long time scales (years). This is also shown in some monoperiodic (or nearly monoperiodic) LADS stars as τ Peg (Breger 1991), BP Phe (Poretti et al. 1996) or 28 And (Rodr´ıguez et al. 1993, 1998). Figure 1 shows the case of 28 And where strong amplitude variations take place. Extreme amplitude variations are also found in the multiperiodic LADS star V663 Cas (Mantegazza & Poretti 1990, Poretti et al. 1996) where no detectable or very small variations were found in the period 1999-2003 (Rodr´ıguez et al. 2003). Amplitude variations are also seen in some multiperiodic MADS variables as AN Lyn (∆V∼0.m20) (Rodr´ıguez et al. 1997) and V1162 Ori (∆V∼0.m20) (Arentoft et al. 2001). However, no significant amplitude variations are found in any HADS variable (Rodr´ıguez 1999). Possible exceptions are: the double-mode HADS star AE UMa (Zhou 2001, but not confirmed by Pócs & Szeidl 2001) and the monoperiodic field HA SX Phe variable XX Cyg (Zhou et al. 2002, but not confirmed by Blake et al. 2003). Concerning multiperiodicity, the LADS stars present very complex pulsational spectra with many independent frequencies and commonly nonradial modes. One example is XX Pyx where 30 frequencies were detected with 22 of them being independent (Handler et al. 2000). In the case of some MADS stars as AN Lyn, 3 independent frequencies were detected by Rodr´ıguez et al. (1997), with at least one being nonradial or V1162 Ori where 6 independent frequencies were detected with most of them likely nonradial (Arentoft et al. 2001). However, if we are dealing with HADS pulsators, they are always monoperiodic or double-mode variables with only radial modes mostly pulsating in the fundamental mode or/and first overtone of radial pulsation. The unique exception seems to be V974 Oph (∆V∼0.m5) where Poretti (2003) finds five independent frequencies with several likely nonradial modes. On the other hand, microvariability takes also place in HADS variables. Besides the main periodicities which come from the radial modes, their harmonics and combinations, additional modes with very small amplitudes have also been detected in some HADS stars when analysing the residuals. Commonly, these modes are nonradial. Some examples are the cases of AI Vel (Walraven et al. 1992) where three of such modes were detected with at least one being nonradial or SX Phe (Garrido & Rodr´ıguez 1996) with two additional frequencies and at least one being nonradial. Recently, such kind of microvariability has also been discovered in RV Ari (Pócs et al. 2002) and BL Cam (Zhou et al. 1999).

Figure 1: B amplitudes of 28 And in diﬀerent years. 42 High Amplitude δ Sct-type variables

Phase shifts between light curves

Elst (1978) found phase shifts between light curves collected in different filters, using Johnson UBV photometry, for the variable SX Phe itself. This author found that the light maxima occur later when the corresponding wavelength is longer. Later, phase shifts have also been detected in a number of δ Sct variables. In particular this effect is observed in a large sample of HADS stars, including some field HA SX Phe variables, using both Johnson UBV and Strömgren uvby photometry. In the case of Strömgren photometry, it is also found that the “amplitude ratios versus phase shifts” diagrams for the (v,y) and (b,y) pairs of bands are discriminant between radial and low order nonradial pulsation (Garrido et al. 1990). This discrimination is also valid for the pair ((b-y),y). However, the expected phase shifts, in the case of radial pulsation, are very small (only a few thousandths of period in the case of vb filters with respect to the y filter). Therefore, very good precision is necessary in order to get reliable mode identifications. In this way, the HADS variables are very good targets for this kind of mode identification because they present very simple spectra and also the precision in “phase” is much better than in LADS variables (this is inversely proportional to the pulsation amplitude). In this sense, an investigation was carried out by Rodr´ıguez et al. (1996) for all the HADS and field HA SX Phe variables with reliable multicolor Johnson and Strömgren photometry available in the bibliography, concluding that, in all the cases (at least the main periodicities), they are radial pulsators. m1-index curve

In Strömgren photometry, the m1 index is related to metallicity. Moreover, in some pulsating stars in the lower part of the Instability Strip, this index shows variation along the pulsation cycle which is connected with the location of the variable in the Hertzsprung-Russell (H-R) diagram and with its metal content. This offers a possibility to check the atmosphere grids using pulsating variables, but only objects with large amplitudes of luminosity are suitable for this task because of the commonly very small variation taking place in the m1 index. This is the case of the RR Lyr, HADS and HA SX Phe variables. The HA SX Phe variables always show a large variation of the m1 index in the same sense of the light curve (that is, m1 increases when temperature also increases), but no homogeneity is found for the HADS and RR Lyr stars. This behaviour can be explained when the (β, m1) versus (Te, log g) grids are taken into account for different metallicities, in the sense that the β−m1 slopes are larger when the metal content is lower (Rodr´ıguez et al. 1991). Moreover, the temperature and surface gravity of the star have to be also taken into consideration, specially for solar abundances or cool objects in the case of low abundances. Figure 2 shows the observed and predicted m1 index curves for several HADS and field HA SX Phe variables. This allows to build grids relating directly the observations (β-index and ∆m1) with the metal content [Me/H] of the variables.

Period changes

It is well known for HADS variables, from classical O-C analyses of the times of light maximum, that their periods are not constant. The same is true for the known ﬁeld HA SX Phe pulsators. These variables are very good targets for this analysis because of their very simple spectra and high amplitudes and, hence, very good precision in determining the times of maximum. On the other hand, period changes are expected to reﬂect the evolutionary changes in radius. Thus, it is a good tool to test the evolutionary status of these stars and the evolutionary tracks across the H-R diagram. E. Rodr´ıguez 43

Figure 2: Observed (+) and predicted (*) variations of the m1-index over the pulsation cycle for several stars using the grids of Kurucz (1979) at the corresponding metal abundances: BL Cam, [Me/H]=−1.5; KZ Hya, [Me/H]=−1.0; CY Aqr, [Me/H]=−0.5; HD 79889 and RY Lep, [Me/H]=−0.0; HD 200925, [Me/H]=+0.5.

The period changes predicted by evolution models within the boundaries of the δ Sct instability strip are always positive, except in the zone of the overall contraction phase where the evolutionary periods are decreasing. However, the evolution in this zone is very quick and, hence, the probability of finding a star there is very small. In the rest of the δ Sct region, typical period increases of ∼10−9y−1, in units of dP/Pdt, are predicted for main sequence stars and of ∼10−7y−1 for post-main sequence stars. However, these predictions are not in good agreement with the changes derived from the observations (Rodr´ıguez et al. 1995, Breger & Pamyatnykh 1998). In fact, the observational characteristics can be summarized as follows: a) positive and large period changes in HADS stars with the shortest periods, b) negative changes in HADS stars with long periods, c) negative changes in HA SX Phe variables, d) possible sudden jumps in a number of stars and e) different rates of variation for different modes of the same star. None of these observational features are explained by evolution. Hence, the observed period changes are not caused by stellar evolution alone. It should be very interesting to study the period changes taking place in pre-main sequence 44 High Amplitude δ Sct-type variables

δ Sct variables because the predicted evolutionary period changes are negative with rates of 10-100 times larger than those occurring in main sequence and post-main sequence stars. Thus, the period changes caused by evolution should not be hidden by other effects. However some caution is necessary for these stars because none of them is, up-to-date, known to be of high amplitude and the frequency spectra are, in general, more complex. Moreover, the evolution within the instability strip as a pre-main sequence star is very rapid. Hence, the probability of finding a star in this phase of evolution is very small as compared with that of finding it in a main-sequence stage. Multiplicity can also be derived through the residuals remaining from the O-C analysis of light maxima. Sometimes, these residuals can be attributed to the light-time effect produced in a binary system. Nevertheless, such detections are very difficult and only analyses with data of high quality and very long time baseline are reliable for this task. Therefore, only pulsators with high luminosity amplitudes and simple frequency spectra (only one or two periods) are good candidates for such studies.

Period-Luminosity relation

Period-Luminosity-Colour (P-L-C) relations are very important as they provide distance scales into the Universe. In the case of the HADS stars, only a P-L relation is needed because the width of the HADS strip is very small, less than 500 K (McNamara 1997). Another advantage of these stars concerns the fact that they are mostly known as radial pulsators with very simple spectra (monoperiodic or double-mode pulsators) and that they are pulsating in the fundamental mode and/or first overtone of radial pulsation. Then, the pulsational mode identification is relatively easy. Moreover, the HADS variables provide a new distance scale which is independent from the classical existing ones, such as from classical Cepheids and RR Lyr stars. However, there is some problem because of the faintness of a lot of these variables, which implies that only very few of them are known with accurate luminosities. This will be solved, for example, with the parallaxes to be obtained by the GAIA satellite to be launched in a few years. Nevertheless, precise P-L and P-R (radius) relations have recently been obtained for HADS or HADS/classical Cepheids variables (McNamara 2002; Laney et al. 2002, 2003). References Arentoft T., Sterken C., Handler G. et al. 2001, A&A 374, 1056 Blake R.M., Delaney P., Khosravani H., Tome J., Lightman M. 2003, PASP 115, 212 Breger M. 1979, PASP 91, 5 Breger M. 1980, ApJ 235, 153 Breger M. 1991, A&A 250, 107 Breger M., Pamyatnykh A.A. 1998, A&A 332, 958 Elst E.W. 1978, ApJ 223, 959 Garrido R., Rodr´ıguez E. 1996, MNRAS 281, 696 Garrido R., Garc´ıa-Lobo E., Rodr´ıguez E. 1990, A&A 234, 262 Handler G., Arentoft T., Shobbrook R.R. et al. 2000, MNRAS 318, 511 Kurucz R.L. 1979, Dudley Obs. Rep. 14, 271 Laney C.D., Joner M.D., Schwendiman L. 2002, PASPC 259, 112 Laney C.D., Joner M., Rodr´ıguez E. 2003, PASPC 292, 203 Mantegazza L, Poretti E. 1990, A&A 230, 91 McNamara D.H. 1997, PASP 109, 1221 McNamara D.H. 2002, PASPC 259, 116 Paparó M., Szeidl B., Mahdy H.A. 1988, Ap&SS 149, 73 Pócs M.D., Szeidl B., Virághalmy G. 2002, A&A 393, 555 Pócs M.D., Szeidl B. 2001, A&A 368, 880 Poretti E. 2003, A&A 409, 1031 Poretti E., Mantegazza L., Bossi M. 1996, A&A 312, 912 Rodr´ıguez E. 1999, PASP 111, 709 E. Rodr´ıguez 45

Rodr´ıguez E., Rolland A., López de Coca P., Garrido R. 1991, A&A 247, 77 Rodr´ıguez E., Rolland A., López de Coca P., Garrido R., Mendoza E.E. 1993, A&A 273, 473 Rodr´ıguez E., López de Coca P., Costa V., Mart´ın S. 1995, A&A 299, 108 Rodr´ıguez E., Rolland A., López de Coca P., Mart´ın S. 1996, A&A 307, 539 Rodr´ıguez E., González-Bedolla S.F., Rolland A. et al. 1997, A&A 328, 235 Rodr´ıguez E., Rolland A., López-González M.J., Costa V. 1998, A&A 338, 905 Rodr´ıguez E., López-González M.J., López de Coca P. 2000, A&AS 144, 469 Rodr´ıguez et al. 2003, in preparation Walraven Th., Walraven J., Balona L.A. 1992, MNRAS 254, 59 Zhou A.Y. 2001, A&A 374, 235 Zhou A.Y., Rodr´ıguez E., Jiang S.Y., Rolland A., Costa V. 1999, MNRAS 308, 631 Zhou A.Y., Jiang S.Y., Chayan B., Du B.T. 2002, Ap&SS 281, 699 Comm. in Asteroseismology Vol. 145, 2004

Pulsational behaviour of the HADS RY Lep

E. Rodr´ıguez1, C.D. Laney2, P.J. Amado1, M.J. L´opez-Gonz´alez1, M. Joner3

1 Instituto de Astrof´ısica de Andaluc´ıa, CSIC, P.O. Box 3004, E-18080 Granada, Spain 2 South African Astronomical Observatory, P.O. Box 9, Observatory 7935, Cape Town, South Africa 3Department of Physics and Astronomy, Brigham Young University, Provo, Utah 84602, USA

RY Lep is a long-period High Amplitude δ Sct-type pulsator (V=8.m21, ∆V=0.m35) with a main period of 0.d2254 (Diethelm 1985). This star was assumed to be monoperiodic with stable light curves for a long time. However, some disturbances have recently been discovered by Laney et al. (2002). New observations were collected at Sierra Nevada Observatory (SNO), Spain, with simultaneous uvby photometry, from 1998 to 2002, but only the two data sets collected in 1998 and 2002 are good enough to perform individual Fourier analyses. Additional VJHK data were collected at South African Astronomical Observatory (SAAO), South Africa, during the same epoch. −1 Besides the main periodicity at f1=4.4416 cd , the existence of a secondary frequency −1 at f2=6.60 cd was confirmed when Fourier analyses were performed for each of the reliable data sets available: our 1998 and 2002 SNO data sets, those of Hipparcos satellite (ESA 1997) and those of Diethelm (1985). Moreover, in some sets it seems that combinations of f1 and f2 are also present (f2+f1 in 1998; f2+f1 and f2-f1 in the Hipparcos data). This corroborates the existence and pulsational nature of f2 together with the observed amplitude ratios and phase shifts between different filters obtained for f2 and uvby and BV photometry. Amplitude variations from season to season are also evident for f2, however there are no significant variations for f1. On the other hand, the derived phase shifts in uvby and BV photometry suggest radial pulsation for f1 and nonradial for f2. In the case of f1, it also agrees with the d results of Rodr´ıguez et al. (1995). Moreover, a Q value of 0. 033 is found for f1, which is indication of pulsation in the fundamental mode. This suggests that f2 corresponds to a nonradial p2 mode. The analysis of the VJHK data collected at SAAO confirmed the existence of f2 and the nature of the modes. Although the expected pulsational amplitude in the infrared filters is very small (about 30% and 20% in J and K relative to the amplitude observed in the v filter (Balona & Evers 1999)), f2 was detected in the J filter of the data set collected during the year 2000. As compared with the vby filters, the phase shifts confirm the radial nature of f1 and the nonradial one for f2 with an angular quantum number of l=2. In summary, the pulsational behaviour of RY Lep can be well described by a main frequency f1, stable in amplitude and being the fundamental radial mode, and a secondary frequency f2, variable in amplitude from season to season and corresponding to nonradial pulsation with p2 and l=2. Moreover, binarity is also suggested from our study when an O-C analysis is performed with the derived times of light maximum. References Balona L.A., Evers E.A. 1999, MNRAS 302, 349 Diethelm R. 1985, A&A 149, 465 ESA 1997, The Hipparcos and Tycho Catalogues, ESA SP-1200 Laney C.D., Joner M., Schwendiman L. 2002, PASPC 256, 173 Rodr´ıguez E., Rolland A., Costa V., Mart´ın S. 1995, MNRAS 277, 965 Comm. in Asteroseismology Vol. 145, 2004

SZ Lyn: New pulsational and orbital elements based on old and recent photometric observations

K.D. Gazeas, P.G. Niarchos, K.A. Boutsia Department of Astrophysics, Astronomy and Mechanics, University of Athens, GR 157 84 Zographou, Athens, Greece SZ Lyncis (=HD 67390) is a high amplitude δ Scuti star, discovered by Hoffmeister in 1949. Van Genderen (1967) noticed that the residuals in the O-C diagrams followed a sinusoidal variation with a period of Porb = 3.091 years. Several years later, Barnes & Moffett (1975) improved this period to Porb = 3.138 years and suggested that the sinusoidal variations in the O-C diagrams, observed by van Genderen (1967), originate from the light travel time effect, since SZ Lyn is a member of a binary system. This hypothesis was confirmed by Bardin & Imbert (1984) with measurements of radial velocities. Soliman et al. (1986) found the pulsation period to be 0.120534896 days and the orbital period 1173.5 days. From BVRI observations during the period January 1975 - March 1979, Moffett et al. (1988) estimated the pulsational period as 0.12052115 days, which is shorter than earlier determinations. The latest research was made by Paparo et al. (1988), who determined the pulsational and orbital elements of the system even better, using all available data from 1961 until 1988. In this paper we present the results of new CCD time-series photometry carried out at the University of Athens Observatory. Our new BVRI CCD photometric observations and those obtained by Derekas et al. (2003) and Hipparcos (ESA 1997) extended the time base of the data from 27 to 42 years (or from 8 to 14 revolutions of the system). The 165 times of maxima observed between 1961 and 2003 were used to calculate the pulsational and orbital elements of the binary system. A new ephemeris was calculated with the new times of maxima, d derived from our light curves: tmax(HJD) = 2452776.289(10) + 0 .1205349(41)×E; From a least squares fit to all available O-C values we were able to calculate more precise values of the following parameters: the linear change in the star’s pulsational period −12 (β=2.90§0.22 × 10 days/cycle), the orbital period (Porb=1179.3§2 days), the semima- jor axis (a sin i=0.998§0.04 AU), the eccentricity (e=0.205§0.010), the longitude and time of the periastron passage (ω=87.6§1.1 degrees and T (HJD)=2445699.8436§0.022) and the mass function f(M)=0.095§0.008.

Acknowledgments. It is a pleasure to thank E. Fragoulopoulos for his help with the numerical computations of the present work. References Bardin, C., Imbert, M., 1984, A&AS, 57, 249 Barnes, T. G. III, Moffett, T. J., 1975, AJ, 80, 48 Derekas, A, et al., 2003, A&A, 402, 733 ESA, 1997, The Hipparcos and Tycho Catalogues, ESA SP-1200 Hoffmeister, C., 1949, Astron. Abhand, 12, 1 Moffett, T.J., Barnes, T.G. III, Fekel, F.C. Jr., Jefferys, W. H., Achtermann Jeffrey, M., 1988, AJ, 95 Paparo, M., Szeidl, B., Mahdy Hamid, A., 1988, Ap&SS, 149 Soliman, M.A., Hamdy, M.A., Szeidl, B., Szabados, L., 1986, Comm. Konkoly Obs. Hung. Acad. Sci., Budapest, No 88 (Vol. 10, part 2) Van Genderen, A.M., 1967, Bull. Astron. Inst. Neth., 19, 74 Comm. in Asteroseismology Vol. 145, 2004

Short–Period Variables in ASAS Photometry

J. Molenda–Zak˙ owicz1

1 Institute of Astronomy, Kopernika 11, 51-622 WrocÃlaw

Abstract

We present results of our study of short–period variables in ASAS photometry. We focus on slowly pulsating B stars (SPBs), most of which were discovered by the Hipparcos satellite. We discuss the problem of aliasing in the ASAS photometry and its influence on the identification of frequencies of SPBs. Finally, we show that the ASAS photometry can be used not only to confirm the Hipparcos frequencies and amplitudes but it can also give new results for selected SPBs.

Introduction

The ASAS (All Sky Automatic Survey) project aims for monitoring variability of all objects in the sky brighter that 14 mag. Its prototype instrument and data pipeline were developed by Dr. Pojmanski´ (Pojmanski´ 1997). In 1997–2000 ASAS observed in the I–band (ASAS– 2 project) and since 2001 in V (ASAS–3 project). It succeeded in discovering more than 5 500 new variables (Pojmanski´ 2000 and 2002) and was used for studying Cepheids in the Magellanic Clouds (Pietrukowicz 2001, 2002) and the Galaxy (Beltrame & Poretti 2002). In this work, we analyze ASAS–3 photometry of stars classiﬁed as SPB in the Hipparcos Catalogue (ESA 1997). We discuss ASAS observing and spectral window and present results obtained for selected stars.

Observing and Spectral Windows

In the ASAS–3 observing schedule each of the preselected fields is observed once per night. However, the fields overlap so that many stars are observed several times per night. We show a typical ASAS observing window in the left panel of Fig. 2. This window (compiled for HD 52057 from three separate data sets) covers a time span of 2.3 years and consists of 152 observations indicated by impulses. In this figure, Observations are gathered in three clumps inside which sampling is close to one per night. Observations sampled more frequently are rare but also present. Such sampling produces significant daily aliases in the spectral window; in the left panel of Fig. 1 we show an example – the spectral window computed for IS Lup. Windows of this shape, with daily aliases getting lower for higher frequencies, can be computed for ∼ 50% stars observed by ASAS. The other stars have spectral windows with a 2 c/d peak higher than the one at 1 c/d. We find such spectral windows for stars which were observed at the beginning and then at the end of the majority of observing nights. As an example, we show the spectral window for HD 52057 in the middle panel of Fig. 1 . For few stars we find spectral windows with the 3 c/d peak higher than the 1 and 2 c/d ones. Windows of this shape occur for stars which are observed sparsely and for which observations are clumped in 8.96 '032101.hp'

8.95

8.94

8.93

8.92

8.91

8.9 9 8.89'025394.29'

8.88 p(f)

8.87 8 1884 188618881890 189218941896 189819001902 190419061908 191019121914 191619181920 192219241926 192819301932 193419361938 194019421944 194619481950 195219541956 195819601962 196419661968 197019721974 197619781980 198219841986 198819901992 199419961998 200020022004 200620082010 201220142016 201820202022 202420262028 203020322034 203620382040 204220442046 204820502052 205420562058 206020622064 206620682070 207220742076 207820802082 208420862088 209020922094 209620982100 210221042106 210821102112 211421162118 212021222124 212621282130 213221342136 213821402142 214421462148 215021522154 215621582160 216221642166 216821702172 217421762178 218021822184 218621882190 219221942196 219822002202 220422062208 221022122214 221622182220 222222242226 222822302232 223422362238 224022422244 224622482250 225222542256 225822602262 226422662268 227022722274 227622782280 228222842286 228822902292 229422962298 230023022304 230623082310 231223142316 231823202322 232423262328 233023322334 233623382340 234223442346 234823502352 235423562358 236023622364 236623682370 237223742376 237823802382 238423862388 239023922394 239623982400 240224042406 240824102412 241424162418 242024222424 242624282430 243224342436 243824402442 244424462448 245024522454 245624582460 246224642466 246824702472 247424762478 248024822484 248624882490 249224942496 249825002502 250425062508 251025122514 251625182520 252225242526 252825302532 253425362538 254025422544 254625482550 255225542556 255825602562 256425662568 257025722574 257625782580 258225842586 258825902592 259425962598 260026022604 260626082610 261226142616 261826202622 262426262628 263026322634 263626382640 264226442646 264826502652 265426562658 266026622664 266626682670 267226742676 267826802682 268426862688 269026922694 269626982700 270227042706270827102712271427162718272027222724 8.86 0frequency 0.2 c/d 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2

J. Molenda–Zak˙ owicz 49

p(f)

0 -4 -2 0 2 4 -4 -2 0 2 4 -4 -2 0 2 4 frequency c/d frequency c/d frequency c/d

Figure 1: Spectral windows of ASAS photometry. left: IS Lup, middle: HD 52057, right: V 1370 Ori.

Table 1: Number of observations, frequencies and amplitudes detected in ASAS photometry for 17 stars classiﬁed as SPB in the Hipparcos Catalogue. Asterisks indicate that the highest peak in periodogram indicated is an alias of the correct frequency.

Name Nobs f A Name Nobs f A (c/d) (mmag) (c/d) (mmag) CG Hyi 123 1.33482 * 18.19 V386 Pup 39 1.21260 * 64.66 1.44480 9.66 V1370 Ori 45 1.11300 * 22.98 MY Vel 100 0.80769 25.43 V726 Mon 65 2.32456 * 23.04 V363 Vel 119 0.40717 26.04 NZ CMa 117 0.88972 * 11.68 PR Vel 116 0.80727 18.25 KP CMa 106 0.93566 22.02 0.87613 11.99 LM CMa 121 0.43212 24.03 PZ Vel 158 1.17949 17.05 HD52057 152 0.98423 14.25 LY Vel 147 1.34908 10.18 0.79958 12.37 V483 Car 151 1.22191 15.46 V375 Pup 122 0.58761 24.29 IS Lup 185 1.16974 16.42 LZ TrA 193 1.75355 * 20.82 very narrow time spans at the beginning and at the end of observing nights. An example is the spectral window of V 1370 Ori shown in the right panel of Fig. 1.

Results for SPBs

We analyzed ASAS photometry of 72 stars classified as SPB in the Hipparcos Catalogue. We downloaded observations of southern SPBs form the ASAS home page (http://www. astrouw.edu.pl/∼gp/asas/asas.html) while for the northern ones we used data kindly provided by Dr. Pojmanski.´ In case of 55 stars we could not perform analysis of variability. Most of these stars are too bright for ASAS and their magnitudes are saturated, show high scatter and significant trends. We did not analyze stars with a number of observations less than ∼ 40. Eventually, we were left with 17 stars in whose photometry we sought periodic variability. We list the stars in Table 1. In the first column we give the names or HD numbers of the stars, then we list the number of observations used for analysis, the values of detected frequencies and fitted amplitudes. Frequencies of six stars are indicated with an asterisk. We indicated in this way stars, for which the highest peak in periodogram occurred at an alias of the correct frequency. (We identified correct frequencies using Hipparcos photometry which does not show daily aliases.) As we found, the problem of aliasing is most severe for stars with a small number of observations (V 1370 Ori, V 726 Mon and V 386 Pup) or/and a spectral window with the highest peak at 2 (CG Cyg) or 3 c/d (V 1370 Ori). The ASAS photometry reproduces quite well also amplitudes known from Hipparcos pho- 8.96 '032101.hp'

8.95

8.94

8.93

8.92

8.91

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50 Short–Period Variables in ASAS Photometry

-0.05 9.3

0 9.35

ASAS mag 0.05 9.4 1800 2100 2400 2700 0 0.5 1 1.5 2 0 0.5 1 1.5 2 HJD-2450000 phase phase

Figure 2: HD 52057: left: observing window, middle: ASAS magnitudes phased with frequency f1 = 0.98423 c/d, right residuals of ASAS magnitudes phased with frequency f2 = 0.79958 c/d. tometry. However, due to the scatter in the two photometric data sets and because of the probability of imperfect fits of amplitudes, a detailed comparison can not be performed. The frequencies present in the ASAS photometry agree with the Hipparcos ones much better. We confirmed frequencies known from Hipparcos photometry for 11 monoperiodic and two doubly–periodic stars, namely, CG Hyi and PR Vel. For three other doubly–periodic Hipparcos SPBs, namely KP CMa, PZ Vel and V 483 Car, we confirm only the first frequencies. For one star, HD 52057, we detected two frequencies, f1=0.98423 and f2=0.79958 c/d, none of which is present in the Hipparcos photometry. We show the phase diagrams con- structed for the two frequencies in Fig. 2. In the Hipparcos Catalogue this star is not classified as variable but Waelkens et al. (1998) find in its Hp magnitudes one frequency, f = 0.90872 c/d and classify it as SPB. We show that this star is in fact a doubly–periodic variable with both frequencies typical for SPBs.

Acknowledgments. We are indebted to Dr. Pojmanski´ for providing ASAS observations of the northern SPBs. This work was supported by a KBN grant 5 P03D 014 20. References Beltrame, M., Poretti, E. 2002, A&A 386, L9 ESA 1997, The Hipparcos and Tycho Catalogues, ESA SP–1200, NOORDWIJK, ESA Pietrukowicz, P. 2001, Acta Astron. 51, 247 Pietrukowicz, P. 2002, Acta Astron. 52, 177 Pojmanski,´ G. 1997, Acta Astron. 47, 467 Pojmanski,´ G. 2000, Acta Astron. 50, 177 Pojmanski,´ G. 2002, Acta Astron. 52, 397 Waelkens, C., Aerts, C., Kestens, E., Grenon, M., Eyer, L. 1998, A&A 330, 215 Comm. in Asteroseismology Vol. 145, 2004

Asteroseismology of Procyon: Preliminary results from SARG

R.U. Claudi1, A. Bonanno2, R. Ventura2, G. Bonanno2,R. Cosentino2,3, S. Desidera1, R. Gratton1, S. Scuderi2, Endl M.4

1 I.N.A.F. – Oss. Astronomico di Padova, Vicolo Osservatorio,5 35122 Padova, Italy 2 I.N.A.F. – Oss. Astroﬁsico di Catania, Via S. Soﬁa, 78, Catania, Italy 3 I.N.A.F. – Centro Galileo Galilei, Calle Alvarez de Abreu 70, 38700 Santa Cruz de La Palma (TF), Spain 4 McDonald Observatory, The University of Texas, Austin, TX 78712, USA

The F5 IV-V subgiant Procyon was observed over 6 nights with SARG at TNG. We took sequences of 10 s exposures with an average dead time in between of 127 s. In total, 956 spectra were collected with a typical signal-to-noise ratio ranging between 250-330. Data reduction was performed using IRAF tasks devoted to echelle spectra. Successively the modelling of the star plus iodine absorption spectra was performed by using AUSTRAL code (Endl et al. 2000, A&A, 362, 585) in order to obtain the radial velocities time series. The Scargle and Lomb modiﬁed periodogram (Lomb 1976, Ap&SS, 39, 447, Scargle 1982, ApJ, 263, 835) shows two prominent frequencies: ν1 = 0.2346 mHz and ν2 = 0.8387 mHz both with a signiﬁcance level greater than 99% . Frequency ν2 corresponds to the 20 min period found by Brown et al. (1991 ApJ, 368, 599).

Figure 1: Power spectrum of Procyon SARG time series 52 Asteroseismology of Procyon: Preliminary results from SARG

In particular we were able to fit data with a sinusoidal signal with a period corresponding to ν1. It seems very probable that the Doppler signals detected result from p-mode oscillations of Procyon. In fact in our power spectra it is possible to see an excess of power about frequency ν2 that survive also after a filtering of ν1. Moreover the power spectrum seems to have a cut-off for frequencies greater than 1.6 mHz almost equal to the acoustic cut-off frequency predictions for Procyon. In order to confirm these preliminary results we have to perform the reduction of the remaining 5 observing nights, but now we are confident that SARG is one of the promising instruments for the challenging task of the solar like p-mode detection. References Brown et al., 1991, ApJ, 368, 599 Endl et al., 2000,A&A, 362, 585 Lomb, 1976, Ap&SS, 39, 447 Scargle, 1982, ApJ, 263, 835 Comm. in Asteroseismology Vol. 145, 2004

The use of Petersen diagrams and period ratios in investigating the pulsational content of stars in the classical Instability Strip

E. Poretti and M. Beltrame

INAF - Osservatorio Astronomico di Brera, Via E. Bianchi, 46 – 23807 Merate (LC), Italy

Abstract

The aspects of the analysis of photometric time series obtained on double–mode or multiperiodic pulsating stars are brieﬂy reviewed. In particular, the ratios between frequencies are used to pin cases revealing peculiarities. In addition to the Petersen diagrams, we also demonstrated that the period ratios can single out interesting objects. In particular, new results are obtained on High–Amplitude Delta Scuti stars contained in the OGLE-II database.

Introduction

In the recent years a huge collection of time series has been obtained on variable stars, as a noticeable by–product of several microlensing projects. Therefore, the investigation of thousands of light curves is carried out by detecting the frequencies present in the time series. It is not easy to give astrophysical depth to this kind of analysis, as we have monochromatic photometric data only at our disposal. Diﬀerent classes of variable stars can show very diﬀerent physical processes with very similar light curves. Moreover, instrumental terms are often superimposed to physical ones in the same frequency range. In this paper we will try to review some of these aspects.

The Petersen diagrams

When multiperiodicity is detected, it is quite an obvious procedure to calculate the frequency ratios. In case of double–mode pulsation, we deal with a short (PS ) and a long (PL) period. The plot of the PS /PL ratio versus PL is now known as the Petersen diagram (Petersen 1973). Small variations of temperature, mass, metallicity or luminosity push the PL, PS /PL points into different directions: as an example, see Fig. 2 in Popielski et al. (2001). The mass capable to reproduce the observed PS /PL ratio is called the beat mass. There have been several astrophysical applications of the Petersen diagrams. The most relevant one has been the reconciliation of pulsational, evolutionary and beat masses of Double Mode Cepheids after having introduced the new opacities (Christensen-Dalsgaard & Petersen 1995). Let us indicate the fundamental radial mode as F , the first overtone radial mode as 1O, the second one as 2O. Recently, Beltrame & Poretti (2002) demonstrated that HD 304373 is the second case of 1O/2O double–mode Cepheid in the Galaxy. Its position in the Petersen diagram is very similar to that of some LMC stars. In general, all the 2O/1O values are very close to each other and only the different range of periods allows us to separate the different environments (Fig. 1, left panel). On the contrary, the 1O/F ratios show a strong dependence on metallicity 54 The use of Petersen diagrams and period ratios

(Fig. 1, right panel). It seems that the 1O/2O ratios are less sensitive than the 1O/F ratios to the difference in metallicity: the latter values comprise a five time larger interval than the former ones. Christensen-Dalsgaard & Petersen (1995) pointed out that the match between the F/1O ratios for galactic pulsators and the theoretical models occurs for metallicities smaller than the solar value of 0.017–0.020; if that applies for the 1O/2O pulsators too, a metallicity close to 0.010 allows the P2/P1 = 0.8058 and P1=0.922405 d values to reasonably fit the theoretical models (Christensen-Dalsgaard & Petersen 1995). We also note that assuming P1/P0=0.70, we obtain P0=1.32 d, i.e., the fundamental period of HD 304373 is really one of the shortest among galactic Cepheids.

Figure 1: The Petersen diagrams for double–mode Cepheids in the Milky Way, the Small and Large Magellanic Clouds. The P0/P1 pulsators belonging to the three diﬀerent galaxies are well separated, while the P2/P1 ones are not.

As in the case of CO Aur, there is no signiﬁcant contribution of the 2f2, harmonic in the light curve of HD 304373, i.e., it is perfectly sine–shaped within the error bars. Only small or marginal deviations from a sine wave have been found in the LMC and SMC 2O samples.

The distinction between pulsating stars and geometric variables

The analysis of the 82 periodic pulsating stars included in the OGLE II database (Mizerski & Beijger 2002) revealed that pulsating and geometric variables can be confused by some automatic routines, but they can be more easily separated by more clever methods (Beltrame 2002). As a first step, we decided to perform frequency analyses of all the stars, to avoid any possible misinterpretation. Using the least-squares iterative sine wave fitting (Vaniˇcek 1971), we obtained the power spectrum for every variable star of our sample, thus being able to compare the highest peaks with their aliases. No discrepancy was found as respects the values reported by Mizerski & Beijger (2002). The following step was to refine the periods of all the stars and to analyze their residual power spectrum, looking for the presence of multiperiodicity or other peculiar effects (such as the Blazhko effect for RRab and RRc). Therefore, we considered the preliminary solutions and the fit order found in the previous step. The solution was given as input parameters to a code keeping locked the relationships between the main frequency and the harmonic terms (Multiple Trigonometric Analysis Program; Carpino et al. 1987); the best fit was searched for E. Poretti and M. Beltrame 55 around the preliminary solution. Once the refined period was obtained, we started searching for additional terms. Only the frequency values of the main term and its harmonics were considered as input values; no prewhitening was done. A few multiperiodic stars (RRab and RRc showing Blazhko stars, a new multimode pulsator) have been discovered. Moreover, the results of the period refinement shows that we have ∆P ∼ 10−7 for 14 stars, ∆P ∼ 10−6 for 43 stars. The rest of the sample (24 stars) showed a more significant refinement, with ∆P ∼ 10−5–10−4.

Figure 2: The true nature of bul1.686: the star is not a pulsating variable with a period of 0.191 d (left panel), but a geometric one with a period twice the “pulsational” one (right panel): note the diﬀerent depths of minima.

Having obtained the correct periods for every star, we started with a preliminary fit up to the eighth order, in order to obtain the correct Fourier parameters. Therefore, we discarded all harmonics with amplitudes less than 3 times their error estimate. During this procedure, three stars (bul1.2457, bul1.1323, bul1.686), classified as HADS by Mizerski & Beijger (2002), showed a notable spread of points at the minimum light of their light curves. Therefore, we checked the possibility for them being W UMa variables, doubling the period found. We found that bul1.686 is clearly a W UMa variable, since the light curve on the doubled period shows two minima having different depths (Fig. 2). In the other cases, there is still some dispersion at minima and a certain classification cannot be made. However, the power spectra always detected a pair of terms, in the ratio 2:1, with the higher amplitude related to the shorter period. A conservative approach would strongly suggest that in presence of the 2:1 ratio the variable should be considered a geometric one (eclipsing or rotational). Indeed, to explain such a ratio by the excitation of resonant modes seems an “ad hoc” solution, even if very attractive for theoreticians. We also note that stars showing a sine–shaped light curve (i.e., no significant contribution from the harmonics of the main frequency) can be geometric variables having minima of equal amplitudes. In case of monoperiodicity, this fact makes it quite delicate to distinguish the sine–shaped light curves of 2O pulsators (see previous section) from those of geometric variables.

The frequency ratios in High Amplitude Delta Sct stars

Poretti (2003) recently pointed out that HADS can show frequency spectra much more complicated than the ones considered some years ago. Figure 3 (which is an update of Fig. 5 56 The use of Petersen diagrams and period ratios by Poretti 2003) illustrates how several stars deviate from the canonical 0.77 ratio between the F − and the 1O modes. Values higher than 0.77 can be caused by very low metallicities (Z <0.0005). Since most cases are actually much higher than 0.77, the metal shortage should be very relevant and this seems unlikely for Pop. I stars. Also fast rotation can strongly modify the ratio, but it is quite uncommon in HADS stars, which are evolved ones. If we also consider the variety of ratios visible in Fig. 3, the excitation of nonradial modes is indicated as the natural explanation for such a diﬀerent pulsational content. To corroborate the excitation of nonradial modes in HADS, high–resolution spectroscopy is strongly recommended to detect the signature of line proﬁle variations.

Figure 3: Observed (ﬁlled dots) frequency ratios among HADS stars showing possible nonradial modes. Vertical lines indicate the theoretical ratio between fundamental (F) and overtone (ﬁrst, 1O; second, 2O) radial modes. Note also the ratios around 1.0, i.e., the presence of modes close to the fundamental radial one.

As discussed above, the 0.800 ratio is found in double mode Cepheids pulsating in the 1O and 2O modes. Such a value is also observed in some double–mode HADS stars (Musazzi et al. 1998) and it is attributed to the same modes, but there are some unclear points. In particular, the 0.800 ratio is related to an unusual shape of the PL light curve: the descending branch is steeper than the ascending one. This feature still remains unique in the zoo of the light curves of pulsating variables. The large databases did not supply any new stars simultaneously showing the 0.800 ratio and the asymmetric–in–the–bad–sense light curve. When looking at frequency ratios it is interesting to search for the 0.620 value, which should be the signature of the excitation of the F and 2O modes. Performing the search E. Poretti and M. Beltrame 57

Phase

Figure 4: The phased light curves of two frequencies detected in the bul1.3074 time series: they give f1/f2=0.62 described above in the OGLE-II database, we discovered that bul1.3074 is a new multiperiodic HADS star. Three independent frequencies have been detected, i.e., f1=5.275, f2=8.672 −1 and f3=8.618 cd . In addition to the close doublet composed of f2 and f3, the ratio f1/f2 is intriguing, as it results in 0.61. The presence of aliases could have interfered in determining the correct frequencies, but even considering the peaks at f + 1, f − 1 cd−1 we were not able to solve the problem detecting the usual 0.77 ratio. Also in this case a possible explanation could be the excitation of a nonradial mode of pulsation. However, if F/2O pulsators do exist among HADS, bul1.3074 should be considered a promising candidate. Figure 4 shows the light curves of the f1 and f2 terms: they look very well deﬁned, strongly supporting their reality.

Acknowledgments. This paper was partly prepared during EP’s stay at Konkoly Obser- vatory in the framework of the Italian–Hungarian T´eT cooperation (project I–24/1999).

References

Beltrame, M., 2002, Laurea Thesis, Universit`a di Milano (in Italian) Beltrame, M., Poretti, E., 2002, A&A 286, L9 Carpino, M., Milani, A., Nobili, A.M. 1987, A&A 181, 182 Christensen-Dalsgaard, J., Petersen, J.O., 1995, A&A 229, L17 Mizerski, T., Beijger, M., 2002, Acta Astron. 52, 61 Musazzi, F., Poretti, E., Covino, S., Arellano Ferro, A., 1998, PASP 110, 1156 Petersen, J.O., 1973, A&A 27, 89 Popielski, B. L., Dziembowski, W. A., Cassisi, S., 2000, Acta Astron. 50, 491 Poretti, E., 2003, A&A 409, 1031 Vaniˇcek, P. 1971, Ap&SS 12, 10 Comm. in Asteroseismology Vol. 145, 2004

Period–radius relation for semiregular and Mira stars

K. Szatm´ary

Dept. of Exp. Physics and Astronomical Observatory, University of Szeged, D´om t´er 9, Szeged, Hungary

There is a number of works in which the log P vs log R relation for radially pulsating variable stars have been studied (mainly for Cepheids and RR Lyrae stars, with some efforts on δ Scuti and long-period stars). This relation might serve to test whether the pulsation is radial or nonradial, similarly to the log P vs log g relation (Szatmáry & Kiss 2002). Furthermore, if the observed period and radius do not fit the relation but the pulsation is evidently radial, the shift from the relation would indicate the presence of overtone pulsation. There is a possibility of mode discrimination and mass estimation based on this relation. Previous analyses covered a wide period range from the δ Scuti stars (0.06 days) to the classical Cepheids (120 days). The main goal of our study is to extend the relation into the domain of semiregular (SR) and Mira variables. For this, we have collected a few tens of long period pulsators with published radii. They were determined via Baade-Wesselink analysis, surface-brightness method and infrared interferometry. We presented and compared earlier results and a new log P − log R diagram for 233 pulsating variables, from δ Scuti stars to Miras (more details can be found at http://astro.u-szeged.hu). We note the large uncertainty of the radii caused by many problematic aspects of radius determinations for red giant SR and Mira stars: the radius depends on the pulsational phase; the limb darkening is wavelength-dependent; the presence of strong molecular absorption in IR bands and gas and dust envelopes around the star, deviations from the spherical symmetry or duplicity can have hardly accountable systematic effects.

Acknowledgments. This work was supported by OTKA grant T042509. References Szatm´ary, K., Kiss, L.L. 2002, Proc. ”Radial and Nonradial Pulsations as Probes of Stellar Physics”, eds. C. Aerts, T.R. Bedding and J. Christensen-Dalsgaard, ASP Conf. Ser. 259, 566 Comm. in Asteroseismology Vol. 145, 2004

Relevant issues in the study of Pre-Main Sequence δ Scuti stars

M. Marconi1, V. Ripepi1, F. Palla2, A. Ruoppo1

1 INAF - Osservatorio Astronomico di Capodimonte, Via Moiariello 16, 80131 Napoli, Italy 2 INAF - Osservatorio Astroﬁsico di Arcetri, Largo E. Fermi, 5, I-50125 Firenze, Italy

Abstract

We will review the theoretical and observational developments in the study of Pre-Main Sequence (PMS) δ Scuti stars and point out some current open problems. In particular, we stress the strong need for multi-site and/or space-based observations and for nonradial pulsation modelling. The most recent observations of the best studied object, V351 Ori, and the preliminary results of the application of a nonradial code to PMS δ Scuti stars will also be discussed.

Introduction

The PMS evolutionary phase starts when a stellar structure becomes optically visible at the end of the protostellar phase and ends with the arrival on the Main Sequence. Usually, PMS stars are characterized by a high degree of surface activity and mass loss which is the manifestation of the interaction with the circumstellar environment (disks, envelopes) and by photometric and spectroscopic variability occurring on time scales from minutes to years. The first PMS stars discovered were the low-mass T Tauri stars (0.1 ≤ M/M¯ ≤ 1.5). The more massive (1.5≤ M/M¯ ≤8.0) counterparts were identified in the 1960s by G. Herbig who searched for stars of spectral type A or B with emission lines, located in obscured regions and associated with reflection nebulosities. A modern classification of these Herbig Ae/Be stars requires: 1) Spectral type A or B with emission lines and variable Hα; 2) infrared excess due to hot or cool circumstellar dust or both; 3) luminosity class from III to V; 4) association with molecular clouds and/or young stellar clusters. During the contraction phase toward the Main Sequence, intermediate-mass stars cross the pulsation instability strip of more evolved variables, suggesting that, in spite of the relatively short time spent in the strip (∼ 105-106 years), at least part of the observed activity could be due to intrinsic variability. The first observational evidence for such variability is due to Breger (1972) who detected δ Scuti-like pulsations in two Herbig stars of the young cluster NGC2264, namely V588 Mon and V589 Mon. More than 20 years later the topic was reconsidered by Kurtz & Marang (1995) and Donati et al. (1997) who observed δ Scuti-like variability in the Herbig stars HR5999 and HD104237. Since then there has been a renewed interest in the study of these young pulsators, both from the observational and theoretical point of view. For the latter, using convective nonlinear models, Marconi & Palla (1998) computed the first theoretical instability strip for PMS δ Scuti stars. They also identified a list of candidates with spectral types in the range of the predicted instability region. This theoretical investigation stimulated new observational programs carried out by various groups with the result that the current number of known or suspected candidates amounts to at least 13 objects. 60 Relevant issues in the study of Pre-Main Sequence δ Scuti stars

There are at least three reasons for studying pulsation in young stars. 1) The relation between the pulsation period and the intrinsic stellar parameters allows to independently constrain the evolutionary properties and in particular the stellar mass of observed objects1. 2) On the basis of experience with other classes of variable stars, we know that asteroseismological techniques allow to derive information on the inner structure of observed pulsators; for example, Suran et al. (2001) made a comparative analysis of the seismology of pre- and post-MS stars of the same mass (1.8 M¯) and found that some non-radial unstable modes are very sensitive to the deep internal structure that is profoundly different in the two evolutionary phases (see also Templeton & Basu 2003). 3) At least in principle, PMS stars could be used to search for mode frequency changes due to the rapid evolution of their interior (Breger and Pamyatnykh 1998 and Catala 2003). A census of PMS δ Scuti stars is given in Sect. 2, whereas the comparison with the prediction of pulsation models is shown in Sect. 3. In Sect. 4 we discuss the observational and theoretical limitations affecting our results and show the specific case of V351 Ori.

The observed PMS δ Scuti stars

In Table 1 we show the present census of known (or suspected) PMS δ Scuti stars. The first column reports the identification, whereas frequencies are given in the following five columns. The last three columns give the visual amplitudes, the visual magnitudes and the spectral types. We note that many pulsators show multifrequency behaviour and that for the monoperiodic objects data are often affected by uncertainties due to the short time coverage, so that other frequencies could be discovered with more accurate observations. This means that asteroseismological techniques are in principle useful for these variables.

Table 1: Observed pulsational properties for all the 13 known or suspected PMS δ Scuti stars. Note that, in order to save space, the sixth frequency (27 c/d) found for IP Per has not been reported in the table. VAR f1 f2 f3 f4 f5 ∆V V S.T. c/d c/d c/d c/d c/d mag mag

V588 Mon1 7.1865 ? 0.04 9.7 A7 V589 Mon1 7.4385 ? 0.04 10.3 F2 HR59992 4.812 0.02 7.0 A7 HD1042373 33 0.02 6.6 A7 HD359294 5.10 0.02 8.1 A5 V351 Ori5 15.687 13.331 12.754 15.885 12.817 0.045 8.9 A7 BL 506 13.9175 9.8878 0.02 14.5 HP 576 12.72557 15.52437 0.03 14.6 HD1426667 21.43 0.01 8.8 A8 V346 Ori8 35.3 22.6 45.5 18.3 0.015 10.1 A5 H2549 7.41 0.02 10.6 F0 NGC6383 410 14.376 19.436 13.766 8.295 17.653 0.014 12.61 A7 IP Per11 30.45 22.88 34.64 42.27 48.31 0.006 10.4 A7 Sources: (1) Breger (1972), Pena˜ et al. (2002); (2) Kurtz & Marang (1995), Kurtz & Catala (2001); (3) Donati et al. (1997), Kurtz & Muller (1999); (4) Marconi et al. (2000); (5) Ripepi et al. (2003); (6) Pigulski et al. (2000); (7) Kurtz & Muller¨ (2001); (8) Pinheiro et al. (2003); (9) Ripepi et al. (2002); (10) Zwintz & Weiss (2002); (11) Ripepi et al. in preparation.

1The other direct way to infer the stellar mass is based on the small number of spectroscopic eclipsing binaries that are young enough to contain Herbig stars. M. Marconi, V. Ripepi, F. Palla and A. Ruoppo 61

Comparison with the pulsation models

The pulsation periods can be predicted by radial linear nonadiabatic pulsation models for each selected mode (Marconi & Palla 1998, 2003) as a function of mass, luminosity and effective temperature. In addition, the evolutionary prescriptions provide constraints on the luminosity level for each mass and effective temperature. This implies that the comparison between empirical and theoretical periods, for a given set of evolutionary tracks, allows to estimate the mass, luminosity and effective temperature of the pulsators. However, if only one period is observed, different combinations of luminosity and effective temperature can simultaneously reproduce the pulsation relation for the period and the evolutionary properties. In this case, independent information (e.g. empirical values from the literature) is needed in order to remove the degeneracy. If more than one period is observed, and the accuracy is high enough, the comparison with model predictions should be able to provide a unique solution for the position of the star in the HR diagram.

Figure 1: Position in the HR diagram of known PMS δ Scuti stars. The predicted instability strip is represented by the shaded region, whereas solid and dotted lines are PMS and post-MS evolutionary tracks respectively. The dashed line represents the birthline (see Marconi & Palla 1998 for details)

By comparing the observed frequencies of the PMS δ Scuti stars reported in Table 1 with the predictions of linear nonadiabatic pulsation models (see Marconi & Palla 1998 and references therein for details on the models), we can derive their position in the H-R diagram 62 Relevant issues in the study of Pre-Main Sequence δ Scuti stars and make a comparison with the predictions of the nonlinear instability strip (see Fig. 1). Even if this result is heavily dependent on the assumption of radial pulsation, the agreement is quite satisfactory: only three pulsators are found to be bluer than the second overtone blue edge and indeed they are predicted to pulsate in higher overtones.

Open problems: the case of V351 Ori

The main limitations of the method illustrated in the previous section are: 1) the uncertainties still affecting many of the observed frequencies, due to poor data quality and/or the aliasing problem; 2) the difficulty to discriminate between PMS and post-MS evolutionary phases on the basis of models with radial modes only, in particular for pulsators that are predicted to be located close to the MS; 3) the fact that the likely presence of nonradial modes is not taken into account. Concerning the first point, significant improvements can be obtained by means of multisite campaigns and will be obtained with future satellite missions (e.g. EDDINGTON and COROT). As for the last two issues, it is clear that both radially and nonradially pulsating models should be computed in order to understand the intrinsic properties of the rather unexplored class of young variable stars better. To illustrate how the observational and theoretical limitations affect a specific case, we discuss the best studied PMS δ Scuti star, V351 Ori. This is a Herbig Ae star that has been discovered to pulsate as a δ Scuti PMS star by Marconi et al. (2000) and confirmed to be a multiperiodic pulsator by Marconi et al. (2001, hereinafter M01) and by the more accurate photometric and spectroscopic investigation of Balona et al. (2002, hereinafter B02). Even if it has been suggested in the literature that V351 Ori is not a PMS star (e.g. Koval’chuk & Pugach 1998), the spectroscopic study by B02 has shown the presence of characteristic features of Herbig stars in its spectrum (Hα emission, sharp and broad NaII absorption components and weak HeI absorption). From the theoretic al point of view, it is difficult to establish the evolutionary phase of this object on the basis of radial pulsation analysis, given its position near the MS in the HR diagram, in a region where PMS and post-MS evolutionary tracks tend to intersect each other (see Fig. 1). On the other hand, a comparative asteroseismological analysis, such as the one performed by Suran et al. (2001), should allow to confirm the PMS nature of this star. For this purpose, accurate frequency measurements are critical. In order to confirm the frequencies found by M01 and B02, a multisite campaign on V351 Ori has been recently organized (see Ripepi et al. 2003, hereinafter R03), involving 7 telescopes and 180 hours of observation distributed over 29 nights in a 2 year period. The Fourier analysis of this data set (Fig. 2) confirms the multiperiodic nature of V351 Ori. The five frequencies of pulsation reported in Table 1 are measured (four of them with high accuracy). The last one is more uncertain even if it results to be “good” according to the Scargle (1982) test and the Breger et al. (1993) criterion (see R03 for details). The comparison of these frequencies with the predictions of linear nonadiabatic pulsation models indicates that no solution can match simultaneously all the observed periodicities, while only two solutions can reproduce f1 and f3. The latter correspond to a double mode pulsation either in the first and second (2M¯ PMS model) or in the second and third overtone modes (2.3M¯ PMS model, see open circles in Fig. 1 and R03 for details). The inability to fit all the frequencies with radial pulsation models clearly points out to the need for a nonradial analysis of V351 Ori. In order to cope with this problem, we have applied Christensen-Dalsgaard’s adiabatic nonradial code (Christensen-Dalsgaard 1982) to the same PMS evolutionary models for which we reproduce f1 and f3 by means of radial pulsation analysis. As a result, we find that, at least in the case of the 2M¯ model, f2 can be associated to a nonradial l=1 mode, whereas f1 and f3 could be radial modes of consecutive radial order. For the 2.3M¯ model the interpretation M. Marconi, V. Ripepi, F. Palla and A. Ruoppo 63

Figure 2: Frequency analysis of the multisite campaign dataset. Each panel shows the Fourier Transform after the subtraction of a pulsation frequency. The solid line corresponds to S/N=4. The dotted and dashed lines show the 99% and 90% signiﬁcance levels, resp., calculated from the Scargle (1982) test.

is more diﬃcult and no clear identiﬁcation of f2 with a nonradial mode is possible. A detailed analysis of the dependence of the nonradial mode analysis on the stellar mass is in progress.

Acknowledgments. It is a pleasure to thank J. M. Alcal´a, M. J. P. F. G. Monteiro and E. Poretti for useful discussions. References Balona, L. A., Koen, C., van Wyk, F. 2002, MNRAS, 333, 923 (B02) Breger, M. 1972 ApJ, 171, 539 Breger, M., Pamyatnykh, A.A. 1998, A&A, 332, 958 Breger, M., Stich, J., Garrido, R., et al. 1993, A&A, 271, 482 Catala, C. 2003, Ap&SS 284, 53 Christensen-Dalsgaard, J., 1982, MNRAS, 199, 735 Donati, J.-F., Semel, M., Carter, B. D., Rees, D. E., Cameron, A. C. 1997, MNRAS, 291, 658 Koval’chuk, G. U., & Pugach, A. F. 1998, AstL 24, 106 Kurtz, D.W., Catala, C. 2001, A&A, 369, 981 Kurtz, D. W., & Marang, F. 1995, MNRAS, 276, 191 Kurtz, D.W., Muller,¨ M. 1999, MNRAS, 310, 1071 Kurtz, D.W., Muller,¨ M. 2001, MNRAS, 325, 1341 64 Relevant issues in the study of Pre-Main Sequence δ Scuti stars

Marconi, M., Palla, F. 1998, ApJ, 507, L141 Marconi, M., Palla, F. 2003, Ap&SS 284, 245 Marconi, M., Ripepi, V., Alcal´a, J.M. et al. 2000, A&A, 355, L35 Marconi, M., Ripepi, V., Bernabei, S. et al. 2001, A&A, 372, L21 (M01) Pena,˜ J. H., Peniche, R., Cervantes, F., Parrao, L. 2002, RMxAA, 38, 31 Pigulski, A., KoÃlaczkowski, Z., Kopacki, G. 2000a, AcA, 50, 113 Pinheiro, F.J.G., Folha, D.F.M., Marconi,M. et al. 2003 A&A, 399, 271 Ripepi, V., Palla, F., Marconi, M. et al. 2002 A&A, 391, 587 Ripepi, V., Marconi, M., Bernabei, S. et al. 2003, A&A, 408, 1047 (R03) Scargle, J. D. 1982, ApJ, 263, 835 Suran M., Goupil, M., Baglin, A., Lebreton, Y., Catala, C. 2001, A&A, 372, 233 Templeton, M.R., Basu, S., 2003, in:“Asteroseismology across the HR Diagram”, M.J. Thompson, M.S. Cunha and M.J.P.F.G. Monteiro eds., Kluwer Academic Publishers Zwintz, K. & Weiss, W.W., 2003, in “Asteroseismology across the HR diagram”, M.J. Thompson, M.S. Cunha and M.J.P.F.G. Monteiro, eds., Kluwer Academic Publishers Comm. in Asteroseismology Vol. 145, 2004

Pulsating stars in open clusters

T. Arentoft1, L.M. Freyhammer2,3, M.Y. Bouzid2, C. Sterken2and S. Frandsen1 1 Aarhus University, Ny Munkegade, Bldg. 520, DK-8000 Aarhus C, Denmark 2 Vrije Universiteit Brussel, Pleinlaan 2, B-1050 Brussels, Belgium 3 Royal Observatory of Belgium, Ringlaan 3, B-1180 Uccle, Belgium

Abstract

We report studies that are carried out with the aim of searching for and studying short-period variable stars in northern open clusters. The background for these studies is described along with the results that have been obtained up to now.

Introduction

The overall goal of studying short-period pulsating stars, such as δ Scuti or β Cep stars, is to do asteroseismology – i.e. to use the pulsational frequencies to constrain stellar models. Such constraints become even tighter if parameters like age and distance can be determined independently, as is the case in clusters. Furthermore, studying pulsating stars in clusters using CCD photometry has the advantage that several variables can be observed simultaneously, making the observations very efficient. Large numbers of pulsating stars can be found in globular clusters (see e.g. Bono et al. 2003), but the photometric precision is limited by crowding and therefore, in general, only high-amplitude variables are studied. In open clusters, on the other hand, the number of variables is much smaller, but the fields are typically only semi-crowded although still containing a significant number of constant stars, making high-precision (mmag) photometry possible. In such systems, low-amplitude, multi-periodic variables like δ Scuti or β Cep stars can be studied to high precision. Several very interesting open clusters are known. An excellent example is NGC 6231 (e.g. Arentoft et al. 2001, Sterken et al. 2002). This cluster contains, apart from a set of eclipsing binaries, 7–8 β Cep stars, 3 SPB candidates, 4 δ Scuti stars and 3 γ Dor candidates as well as several variables of presently unknown type. This rich variety of variables makes NGC 6231 one of the most attractive clusters to study as it ultimately will offer the possibility for comparative studies of variables of different types formed under the same conditions. Further, extensive studies are underway on this cluster, as it is the main subject of the PhD studies of M.Y. Bouzid. Among other interesting clusters are NGC 6134 (Frandsen et al. 1996) which contains 6–7 δ Scuti stars or NGC 3293 (Balona & Engelbrecht 1983) and NGC 4755 (Stankov et al. 2002) which both contain a number of β Cep stars. However, these clusters are positioned in the southern skies while most small (1–2 m) telescopes are situated in the northern hemisphere. Such telescopes are the optimal instruments for obtaining cluster time series because of their typical field of view (FoV) (several arcmin) and availability for long, uninterrupted time series. For this reason, a part of the work related to STACC (an observing network focusing on studying cluster variables, Frandsen (1992)) has in recent years been to search for northern open clusters with a population (> 5) of pulsating stars within a small FoV (a few arcmin). The strategy for this project along with the results that have been obtained so far are summarized in the two following Sections. 66 Pulsating stars in open clusters

Observing strategy

The search has mainly focused on finding multi-periodic δ Scuti stars in the open clusters. To do so, target clusters were carefully selected in order, obviously, to make the search efficient. The selection criteria are mainly the cluster distance (1–2 kpc is preferred) and age (0.3–1.0 Gyr). The former ensures relatively compact, semi-crowded fields with many stars but few crowding problems as well as the possibility to do spectroscopy with medium sized telescopes, the latter that many stars are in the δ Scuti instability strip. This is because the cluster turn-off from the main-sequence for these clusters will be located in the δ Scuti instability region of the HR-diagram. A number of clusters that fits this description are compiled by Frandsen & Arentoft (1998a), who also discuss three steps in the observations of δ Scuti stars in open clusters: step I is locating interesting targets by obtaining a few (3–4) nights of high-quality time-series to identify pulsating stars, in step II target information is collected (membership information, physical parameters from spectroscopy and photometry). Step III is a coordinated multisite campaign using telescopes around the globe in order to secure continuous monitoring and abundant data (500+ hours of photometry). Then follows the confrontation with the models (asteroseismology). Below we describe the progress on two clusters – NGC 7062 and NGC 1817 – for both of which step II has been reached.

Results on NGC 7062 and NGC 1817

NGC 7062 was observed with the 2.54-m Nordic Optical Telescope in August 2000. Four nights had been allocated to the project, but only two were clear while the remaining two nights had poor conditions. The data reduction was carried out with the programme MOMF (Kjeldsen & Frandsen 1992) which combines PSF and aperture photometry and therefore is very robust towards variable observing conditions. Despite the mixed weather conditions, suﬃcient high-quality data was obtained to allow > 4σ detections of pulsational frequencies with amplitudes as low as 1.2 mmag. From these observations, Freyhammer et al. (2001) detected 15 variable stars within a FoV of only 6.5 × 6.5 arcmin. Of these variables, at least 13 are δ Scuti stars and of those, 10 were found to pulsate in two or more frequencies and are thus multiperiodic. Another cluster that has been studied is NGC 1817. This cluster has a relatively large extent in the sky of almost half a degree and only a part of the cluster has been searched for pulsating stars so far. However, the part that has been investigated has turned out to be extremely interesting. First, Frandsen & Arentoft (1998b) found 7 potential δ Scuti stars from two nights of observations with the IAC 80-cm telescope at Tenerife, Spain. This was then followed up by new observations in December 2002, again with the Nordic Optical Telescope. The observations were collected during 5 nights and included both time-series observations in B and V and uvby standard data. Preliminary results from the analysis of these observations were presented by Arentoft et al. (2004) where the detection of 14 new variable stars was announced. This brings the total number of known variable stars in NGC 1817 to 19, of which 12 are multi-periodic δ Scuti stars. An example of a newly detected δ Scuti star is shown in Fig. 1. Furthermore, Balaguer-Nunez´ et al. (1998) carried out a proper motion study of NGC 1817. Based on their results (and for some stars that are not included in their study, on the position in the HR-diagram) 11 of the 12 δ Scuti stars are probable cluster members.

These ﬁndings make both NGC 7062 and NGC 1817 prime targets for further investigations within the STACC network. It is therefore time now to stop searching for target clusters and instead to complete step II and start planning step III for these two clusters. Indeed, we are contemplating to launch a multi-site campaign on NGC 1817 in one of the coming observing seasons, probably in the northern winter 2004–2005. T. Arentoft, L.M Freyhammer, M.Y Bouzid, C. Sterken and S. Frandsen 67

Figure 1: A new multiperiodic δ Scuti star detected with the new NGC 1817 data. The data are less abundant during the last night because alternating B and V images were obtained.

Acknowledgments. TA acknowledges financial support from The Danish Natural Sci- ence Research Council, partly through the project “Stellar structure and evolution – new challenges from ground and space observations” carried out at Aarhus University and Copen- hagen University. LMF and CS acknowledge support from the project IUAP P5/36 financed by the Belgian State, Federal Office for Scientific, Technical and Cultural Affairs. MYB and CS acknowledge financial support from the Belgian Fund for Scientific Research (FWO). References Arentoft, T., Freyhammer, L.M., Bouzid, M.Y., Sterken, C., Frandsen, S. 2004, to appear in ”Variable Stars in the Local Group“, ASP Conf. Ser., D.W. Kurtz & K. Pollard, eds. Arentoft, T., Sterken, C., Knudsen, M.R. et al. 2001, A&A 380, 599 Balaguer-Nunez,´ L., Tian, K.P., Zhao, J.L. 1998, AAS 133, 387 Balona, L.A., Engelbrecht, C.A. 1983, MNRAS 202, 293 Bono, G., Petroni, S., Marconi, M. 2003, ASP. Conf. Ser. 292, ”Interplay of Periodic, Cyclic and Stochastic Variability in Selected Areas of the H-R Diagram“, ed. C. Sterken, 71 Frandsen, S. 1992, Delta Scuti Star Newsletter (Univ. of Vienna) 5, 12 Frandsen, S., Balona, L.A., Viskum, M. et al. 1996, A&A 308, 132 Frandsen, S., Arentoft, T. 1998a, J. Astron. Data 4, 6 Frandsen, S., Arentoft, T. 1998b, A&A 333, 524 Freyhammer, L.M., Arentoft, T., Sterken, C. 2001, A&A 368, 580 Kjeldsen, H., Frandsen, S. 1992, PASP 104, 413 Stankov, A., Handler, G., Hempel, M., Mittermayer, P. 2002, MNRAS 336, 189 Sterken, C., Knudsen, M.R., Duerbeck, H.W. et al. 2002, ASP Conf. Ser. Vol. 256, ”Observational Aspects of Pulsating B- and A Stars“, eds. C. Sterken and D.W. Kurtz, 183 Comm. in Asteroseismology Vol. 145, 2004

A Variable Star Survey of the Open Cluster NGC 2126

A. Gáspár1, L. L. Kiss2, A. Derekas2, T. R. Bedding2, S. Kaspi3, Cs. Kiss4, K. Sárneczky5, Gy. M. Szabó1, M. Váradi1

1Dept. of Experimental Physics, University of Szeged, Szeged, Hungary 2School of Physics, University of Sydney, Australia 3School of Physics and Astronomy and the Wise Observatory, Tel-Aviv University, Tel-Aviv 69978, Israel 4Konkoly Observatory of the Hungarian Academy of Sciences, Budapest, Hungary 5 Astronomical Observatory, Szeged, Hungary

We present the first CCD photometric observations of the northern open cluster NGC 2126 in the constellation Auriga. Johnson-Cousins V(RI)C data (with a total time span of ∼57 hours) were taken on eight nights in 2002 February and December at the Piszkéstet˝o Station of the Konkoly Observatory, using the 60/90/180-cm Schmidt telescope. We have discovered six new variable stars and have estimated the main characteristics of the cluster. The results of the project can be summarized as follows. Cluster parameters were estimated by fitting isochrones (Bertelli et al. 1994) to the colour-magnitude diagrams. In order to decrease foreground contamination, we have examined the proper motion distribution of stars in the field using data taken from the USNO B-1.0 catalogue (the cluster itself has undetected proper motion). To minimize the effects of background stars, we used only the inner 80 of the cluster. The resulting physical parameters are: m − M = 11m. 0 § 0m. 5, E(B − V ) = 0m. 2 § 0m. 15, d = 1.3 § 0.6kpc. Of the six variables, V1 and V2 showed clear variability, however, our dataset is too short to determine types or periods. V3 and V5 showed rapid oscillations with full amplitudes of a few tens of mmag. The periods and period ratios (V3: f1/f2 = 0.81, V5: f1/f2 = 0.94) suggest low-order radial overtone (V3) and non-radial (V5) δ Scuti-type pulsations for the two stars. We also discovered an Algol-type eclipse for V4. The most interesting variable star is V6. We observed well-defined minima and steady oscillations outside eclipses with amplitude and cycle length characteristic of δ Sct pulsation. With these properties V6 seems to be an eclipsing binary with at least one pulsating component. The period analysis resulted in Porb = 1.17320(3) d. The oscillations outside eclipses seemed to be stable, with a period of Ppul = 0.12936(24) d. An interesting result is that Porb/Ppul = 9.07 § 0.02, suggesting that there might be a 1:9 resonance between the orbital motion and pulsation. A low-resolution optical spectrum is consistent with an F-type star, so that the oscillations may be attributed to δ Sct pulsation. From the astrometric study its cluster membership can be excluded; it is a foreground object.

Acknowledgments. This work has been supported by the FKFP Grant 0010/2001, OTKA Grant #F043203 and the Australian Research Council. References Bertelli, G., Bressan, A., Chiosi, C., et al., 1994, A&AS, 106, 27 Comm. in Asteroseismology Vol. 145, 2004

Amplitude and frequency variability of pulsating stars

G. Handler

Institut fur¨ Astronomie, Turk¨ enschanzstrasse 17, 1180 Vienna, Austria

Abstract

We review the observations of amplitude and frequency variability of pulsating stars and interpretations thereof. Most of these changes do not seem to be connected to effects of global stellar evolution, and different classes of pulsating star show different behaviour. It is attempted to single out objects for which evolutionary period changes can be measured, and some suggestions that may help the understanding of non-evolutionary amplitude and frequency variations are made.

Introduction

Many regularly pulsating stars change their pulsational frequencies and amplitudes over time. The time scales involved are often shorter than those connected with stellar evolution. The question now arises, what is the reason for those variations and (where) can we use period changes to study stellar evolution?

Amplitude variability

The Blazhko effect is the most widely known case of amplitude variability, occurring in about one fourth of all RRab stars and in some RRc stars. The light curves of these pulsators are modulated in amplitude on time scales of a few weeks to a few months, and the most promising explanation for the Blazhko effect to date is beating of the high-amplitude radial modes with some nonradial pulsation modes. We refer to Kolenberg (these proceedings) for a review. Some other explanations for the occurrence of amplitude variations would be pulsational damping if a star is about to leave its instability strip (e.g. Dall et al. 2003), resonant mode interaction (Moskalik 1985), or the excitation and damping of new pulsation modes as the star evolves. All these mechanisms would create a modulation of the intrinsic amplitude of the stellar pulsation modes, whereas others, like the Blazhko effect, or precession of the stellar pulsation axis to the line of sight (Balona 1985) modifying the apparent amplitudes of nonradial modes, only affect the apparent amplitudes of a star. What is required to understand amplitude variability of pulsating stars? The different physical mechanisms mentioned above would operate on different time scales. Resonant mode interaction or excitation of new modes would modulate the amplitudes on a time scale consistent with the inverse growth rate of a given mode, beating of close frequencies produces a variation with the inverse frequency difference and a predictable phase behaviour, precession would also yield predictable changes, and other mechanisms may introduce rather stochastic modulations. 70 Amplitude and frequency variability of pulsating stars

The solution would then lie within long-term monitoring with good time coverage of several selected stars, to follow the amplitude (and phase) modulations over several cycles (if any). Unfortunately, such a project seems rather diﬃcult to justify to time allocation committees as the required extent of the observations and expected scientiﬁc results are hard to predict.

Period changes

The study of pulsational period changes appears more fruitful, in particular if they would result in measurement of evolutionary period changes. In the following, we will discuss for which classes of pulsating star determinations for evolutionary period changes seem possible.

δ Cephei stars

The rates of period change measured for Cepheids are roughly consistent with evolutionary effects, although some disagreement was noted (see Pietrukowicz 2003 and references therein): besides some unusual objects, Cepheids with periods longer than 10 days show period changes that are slower than predicted by stellar evolutionary models. Pietrukowicz (2003) suggests that this may be due to the stars burning a larger fraction of their Helium than predicted by model calculations.

RR Lyrae stars

The situation for RR Lyrae stars appears different. For instance, Paparó et al.’s (1998) study of RRd variables in M 15 resulted in a variety of observed behaviour. Some stars even exhibit period change rates with different signs for the fundamental mode and for the first overtone. It therefore seems that period changes of most RR Lyrae variables are not of evolutionary origin.

δ Scuti stars

Breger & Pamyatnykh (1998) have extensively reviewed the period change behaviour of the δ Scuti stars. They ﬁnd no evidence that evolutionary period changes were observed so far, but pointed out that pre-main sequence objects may oﬀer good chances for such a determination. Very recently, Handler et al. (2004) measured the rates of period change for the three radial modes of an evolved massive star just crossing the δ Scuti instability strip, V823 Cas, and found them to be consistent with those predicted from stellar evolution. roAp stars

The well-studied members of this group show large, sometimes cyclic, period changes, which are not compatible with evolutionary eﬀects, but are probably dominated by magnetic variations. See Kurtz et al. (1997) for details.

β Cephei stars

The period changes of the β Cephei stars seem to be similar to those of the δ Scuti stars, and have been reviewed by Jerzykiewicz & Pigulski (1998). In many cases, the observed period changes are too large to be compatible with eﬀects from stellar evolution only. It is interesting to note that β Cephei stars tend to pulsate in the same modes as the δ Scuti stars. G. Handler 71

Pulsating white dwarf stars The period change behaviour of the pulsating white dwarf stars is extremely diverse. However, it can be noted that the shortest periods of these stars change consistently with stellar evolution (e.g. see Kepler et al. 2000), whereas the longer-period variables can show gross frequency changes (e.g. Kleinman et al. 1998). Interestingly, period changes of some of the hottest pulsating white dwarfs could be used to infer the neutrino cooling rate (O’Brien & Kawaler 2000).

Discussion Which stars are most promising for determining evolutionary period changes? Unfortunately, not many seem to be. In our view, only the hottest DA and DB as well as cool DO white dwarfs and short-period Cepheids offer good prospects for such measurements. Some RR Lyrae and β Cephei stars as well some more “exotic” cases like evolved massive δ Scuti stars or pre-main sequence objects may be suitable as well. The case of the pulsating sdB stars, discovered only a few years ago, still remains to be examined when measurements over a longer time baseline become available. What happens in the stars that show non-evolutionary period changes? It is clear that something in the pulsation cavity must change to modify the mode periods. In this context it is important to remember that nonradial modes are often “weighted” in the stellar interior, i.e. their kinetic energy is dominated by a certain part of the star. For instance, the high- overtone gravity modes of pulsating white dwarf stars are mostly confined to regions close to the stellar surface, and hence it requires less energy to modify their cavity than that of low-overtone modes that penetrate in the deep interior - and this is exactly what’s observed: the low-overtone modes are much more stable in time. It would be interesting if observations of consistent behaviour in the period changes of and between other groups of pulsating star could be made and connected. After all, the different classes of pulsator still obey the same basic physics. Consequently, some similarities between them should be expected.

Acknowledgments. This work has been supported by the Austrian Fonds zur F¨orderung der wissenschaftlichen Forschung under grant R12-N02. References Balona, L. A., 1985, MNRAS 217, 17P Breger, M., Pamyatnykh, A. A., 1998, A&A 332, 958 Dall, T. H., Handler, G. Moalusi, M. B., Frandsen, S., 2003, A&A, in press Handler, G., Rodr´ıguez, E., Ezhkova, O. V., Costa, V., Krzesinski, J., Antipin, S. V., 2004, MNRAS, in preparation Jerzykiewicz, M., Pigulski, A., 1998, in A Half Century of Stellar Pulsation Interpretations: A Tribute to Arthur N. Cox, ed. P. A. Bradley & J. A. Guzik, ASP Conf. Ser. 135, p. 43 Kepler, S. O., Mukadam, A., Winget, D. E., Nather, R. E., Metcalfe, T. S., Reed, M. D., Kawaler, S. D., Bradley, P. A., 2000, ApJ 534, L185 Kleinman, S. J., et al., 1998, ApJ 495, 424 Kurtz, D. W., van Wyk, F., Roberts, G., Marang, F., Handler, G., Medupe, R., Kilkenny, D., 1997, MNRAS 287, 69 Moskalik, P., 1985, Acta Astron. 35, 229 O’Brien, M. S., Kawaler, S. D., 2000, ApJ 539, 372 Papar´o, M., Saad, S. M., Szeidl, B., et al., 1998, A&A 332, 102 Pietrukowicz, P., 2003, Acta Astron. 53, 63 Comm. in Asteroseismology Vol. 145, 2004

New observational results on pulsating B stars

A. Pigulski

WrocÃlaw University Observatory, Kopernika 11, 51-622 WrocÃlaw, Poland

Abstract

The paper summarizes recent observational results concerning pulsating main-sequence B- type stars: β Cephei and SPB. In particular, recent studies of Galactic open clusters and Magellanic Clouds led to the discovery of many β Cephei stars. These results conﬁrm observationally the strong dependence of the pulsation mechanism of β Cephei stars on metallicity, predicted by theory. New ﬁndings in the follow-up observations of SPB stars and asteroseismology of β Cephei stars are also described.

Introduction

Theory and observations support each other in bringing new ideas which lead to a better understanding of stars and their evolution. The pulsations of main-sequence B-type pulsators, β Cephei and SPB, were explained successfully a decade ago. The success of theory enabled some detailed predictions which could be now tested observationally. In particular, the eﬀect of metallicity on pulsations can be checked in a great detail. In this context, there are actually two main trends in the observational eﬀorts concerning the two types of variable stars mentioned above: (i) search for new variable stars, (ii) detailed studies of selected stars. This short paper summarizes recent observational results in these areas.

Galactic β Cephei stars

In 1993, Sterken & Jerzykiewicz published a list of 59 certain β Cephei stars supplemented by a list of 79 suspects. Out of the former list, 17 stars were members of three southern clusters (NGC 3293, NGC 4755, and NGC 6231) that in the past helped to establish that β Cephei stars are main-sequence objects (Balona & Engelbrecht 1981, Balona & Shobbrook 1983). The remaining stars from the list could be assigned either to Galactic OB associations or the Galactic field. At that time not a single certain β Cephei-type star was known in an open cluster of the northern hemisphere. Since the publication of that paper, twelve new β Cephei stars were found in the three famous southern clusters (Koen 1993; Balona & Koen 1994; Balona 1994; Arentoft et al. 2001; Stankov et al. 2002) bringing the total number of their member β Cephei stars to 29, roughly one third of all Galactic stars of this type. During the last decade, about 15 β Cephei stars were also discovered in the northern open clusters. It was mainly the result of the observing programs undertaken in the WrocÃlaw University Observatory and other Polish observatories. Among others, β Cephei stars were discovered in h & χ Persei (Krzesinski´ & Pigulski 1997, Krzesinski´ et al. 1999, Gomez- Forrellad 2000), NGC 663 (Pietrzynski´ 1997; Pigulski et al. 2001), NGC 7235 (Pigulski et al. 1997), NGC 7419 (KoÃlaczkowski et al. 2002), Cygnus OB2 (Pigulski & KoÃlaczkowski 1998), and recently, in NGC 6910 (KoÃlaczkowski et al. 2004b). In addition, six stars were A. Pigulski 73 found by Waelkens et al. (1998) and Aerts (2000) in the Hipparcos photometry. Adding a few other found/confirmed in the Galactic field (Telting & Schrijvers 1998; Robb et al. 2000, Paardekooper et al. 2002), we actually know over 90 β Cephei stars in the Galaxy. Having searched some northern clusters for the presence of early-type variables, we can make some comparisons. In particular, the number of β Cephei stars with respect to the number of all B-type stars in a certain range of absolute magnitude can be calculated. This study (Pigulski et al. 2002) revealed a striking difference in the incidence of this type of variability that cannot be explained as a result of differences in age or the detection threshold. Namely, while in the three southern clusters located along the Sagittarius-Carina spiral arm, 35 § 7% stars with −4.5 < MV < −1.5 are β Cephei pulsators, in 13 clusters of the Local and Perseus arms this number amounts to 6 § 2% (see Fig. 1). Since the presence of an overall metallicity gradient in the Galaxy seems to be well established (see, e.g., Chen et al. 2003), this result can be explained as observational evidence for the strong dependence of the pulsation mechanism of β Cephei stars on metallicity.

Per

Local

Sgr-Car

To GC 1 kpc

Figure 1: Location of young open clusters searched for the presence of β Cephei stars in the Galactic plane. Direction to the Galactic center is shown by the arrow. Three nearby spiral arms are labelled. The Sun (¯) is in the center of the ﬁgure.

β Cephei stars in the LMC

In view of the strong dependence of the pulsations of β Cephei and SPB stars on metallicity, it is interesting to answer the question whether these variables can be found in objects of low metallicity. From the theoretical point of view (Pamyatnykh 1999), β Cephei-type pulsations practically cease at Z = 0.01. With the average Z ' 0.008 in the Large (LMC) and Z ' 0.004 in the Small Magellanic Cloud (SMC), pulsations should not be observed. In fact, first attempts failed to find β Cephei stars in the Clouds. However, thanks to the microlensing surveys, huge photometric databases, OGLE-II and MACHO, are now available for the Clouds. The analysis of short-period variables from the OGLE-II catalogue of Zeb˙ run´ et al. (2001) supplemented by MACHO data, allowed us to find the first three β Cephei stars in the LMC (Pigulski & KoÃlaczkowski 2002). After reprocessing the OGLE-II data, this work has been repeated. As a result of the analysis of the photometry of over 75 000 early B-type stars, 64 short-period, presumably β Cephei-type stars, were found in the LMC. This discovery nearly doubles the number of known β Cephei stars. A preliminary report of this work has been 74 New observational results on pulsating B stars recently published by KoÃlaczkowski et al. (2004a). In the colour-magnitude diagram of the LMC, the stars occupy mainly the range 16 < V < 17.5, with only a few brighter stars (Fig. 2).

18 V [mag] 19

-1.0 0.0 1.0 2.0 3.0 (V - IC ) [mag]

Figure 2: The colour-magnitude diagram of one of the OGLE-II LMC ﬁelds showing the positions of 64 β Cephei stars (grey dots) found in the LMC. [Adopted from KoÃlaczkowski et al. (2004a)]

45 GALAXY: median P = 0.17 d 0.7 40 LMC: median P = 0.27 d 0.6 35 0.5 30

25 0.4

20 Period [d] 0.3 15 Number of periods 0.2 10 0.1 5

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 14.5 15.0 15.5 16.0 16.5 17.0 17.5 Period [d] V magnitude

Figure 3: Left: The distribution of periods in the Galactic (solid line) and the LMC (dashed line) β Cephei stars. Right: Periods detected in the LMC β Cephei stars plotted against the V magnitude. Periods in monoperiodic stars are shown as ﬁlled circles, those found in multiperiodic stars, as open circles (short periods) and open squares (long periods). The grey strip covers the range of periods observed in Galactic β Cephei stars. [Adopted from KoÃlaczkowski et al. (2004a)]

The β Cephei stars found in the LMC diﬀer from the Galactic ones. First, their periods are generally longer: while the median period for Galactic stars is 0.17 d, it reaches 0.27 d for the LMC objects (Fig. 3). At least partly, this can be explained by lower metallicity, because at lower metallicities the instability strip becomes narrower and conﬁned to regions very close to the end of the hydrogen-core burning phase of evolution (Pamyatnykh 1999). However, even more exciting is the fact that out of 64 β Cephei stars in the LMC, twenty (∼30%) A. Pigulski 75 show additional period(s) longer than ∼0.35 d (Fig. 3). So far, such long periods were not observed in the Galactic β Cephei stars. These periods need to be explained theoretically; they can be probably attributed to low-order g modes.

Asteroseismology of β Cephei stars

Asteroseismology of β Cephei stars is still in its infancy. Using this promising tool we would like to investigate the internal chemical and rotation profiles, presence of magnetic field, core overshooting, etc. In order to get this information, we first need to detect modes and then identify them properly. The first attempts have been already made for some well-studied β Cephei stars: 16 (EN) Lac (Dziembowski & Jerzykiewicz 1996), β Cep (Shibahashi & Aerts 1998), 12 (DD) Lac (Dziembowski & Jerzykiewicz 1999), V836 Cen (Aerts et al. 2003), IL Vel, V433 Car, and KZ Mus (Handler et al. 2003), and finally, ν Eri. The latter star was observed within a large international campaign (Handler & Aerts 2003a,b) and actually has the largest number of independent modes detected: nine. As yet, the asteroseismology of β Cephei stars did not teach us much about these stars. Simply the number of modes is too small, too few rotationally split multiplets are observed, we still lack reliable mode identifications. It also happens that the models we use are too simple or inadequate. The models help in many cases to reject some identification and constrain global stellar parameters, but we are still far from the real asteroseismological work. There is probably only an indication for faster core rotation coming from some papers mentioned above (Dziembowski & Jerzykiewicz 1996, Aerts et al. 2003).

New photometry and spectroscopy of SPB stars

About a dozen of slowly pulsating B stars (SPB, Waelkens 1991), showing high-order g modes, were known before the Hipparcos mission. Hipparcos increased this number to about a hundred (Waelkens et al. 1998). It soon became clear, however, that with Hipparcos photometry alone, only a limited number of modes can be detected. Moreover, misidentifications are quite possible, so that follow-up observations are highly desirable. This is also because SPB stars are not easy to observe. The periods of the order of 1 day, small amplitudes and a dense spectrum of excited modes, make the mode detection a challenging task. Also, some other kinds of variability are indistinguishable in photometry from single-mode SPB-type pulsations. With about a hundred data points from Hipparcos distributed unevenly over three years, the study of multiperiodicity becomes very difficult (see, e.g., Molenda-Zak˙ owicz 2002). For this reason, Aerts et al. (1999) initiated a program of follow-up spectroscopic and photometric observations of brightest southern SPB stars found by Hipparcos, extended later to the North- ern hemisphere (Mathias et al. 2001). As a result, many spectroscopic binaries were found (De Cat et al. 2000) and some stars were reclassified as ellipsoidal or chemically peculiar stars (De Cat & Aerts 2002). At present, about 40 SPB stars have a secure classification (De Cat 2003). SPB stars were also detected in the photometric studies of open clusters. For example, they were found in NGC 7654 (Choi et al. 1999), h Per (Krzesinski´ et al. 1999), NGC 3293 (Arentoft et al. 2001), and NGC 4755 (Stankov et al. 2002). At present, about 20 SPB stars are known in Galactic clusters. Finally, SPB stars were discovered in the LMC. First examples were reported by KoÃlacz- kowski et al. (2003), but a comprehensive study that is now in progress will surely bring a bulk of new discoveries. For the study of these stars, the microlensing databases, covering presently about 10 years and having no large gaps, constitute an ideal source of photometry. 76 New observational results on pulsating B stars

Final comments

Undoubtedly, there are great prospects in studying β Cephei and SPB stars in Galactic clusters and nearby galaxies, especially in the Magellanic Clouds. The studies of this kind will help to understand the role of metallicity in the pulsations and will allow us to find the observational limits of metallicity required to get driving. It is obvious that spectroscopic determinations of abundances will be needed to establish this quantitatively. In an even broader context, some difficult and important questions on the stability and mode selection could be answered. On the other hand, photometric campaigns on selected objects are highly desirable as they, by means of the asteroseismological methods, would at least allow some constraints to be put on global stellar parameters and mode identification of these variable stars.

Acknowledgments. This paper has been supported by the KBN grant 5 P03D 014 20. References Aerts, C. 2000, A&A 361, 245 Aerts, C., De Cat, P., Peeters, E. et al. 1999, A&A 343, 872 Aerts, C., Thoul, A., Daszynsk´ a, J. et al. 2003, Science 300, 1926 Arentoft, T., Sterken, C., Knudsen, M.R. et al. 2001, A&A 380, 599 Balona, L.A. 1994, MNRAS 268, 119 Balona, L.A., Engelbrecht, C. 1981, Workshop on pulsating B stars, p. 195, eds. G.E.V.O.N. & C.Sterken Balona, L.A., Koen, C. 1994, MNRAS 267, 1071 Balona, L.A., Shobbrook, R.R. 1983, MNRAS 205, 309 Chen, L., Hou, J.L., Wang, J.J. 2003, A&A 401, 939 Choi, H.S., Kim, S.-L., Kang, Y.H., Park, B.-G. 1999, A&A 348, 789 De Cat, P. 2003, Proc. IAU Coll. 193, in press De Cat, P., Aerts, C. 2002, A&A 393, 965 De Cat, P., Aerts, C., De Ridder, J. 2000, A&A 355, 1015 Dziembowski, W., Jerzykiewicz, M. 1996, A&A 306, 436 Dziembowski, W., Jerzykiewicz, M. 1999, A&A 341, 480 Gomez-Forrellad, J.M. 2000, IBVS No. 4924 Handler, G., Aerts, C. 2003a, Comm. in Asteroseismology 142, 20 Handler, G., Aerts, C. 2003b, Proc. IAU Coll. 193, in press Handler, G., Shobbrook, R.R., Vuthela, F.F. et al. 2003, MNRAS 341, 1005 Koen, C. 1993, MNRAS 264, 165 KoÃlaczkowski, Z., Pigulski, A., Kopacki, G. 2002, A.S.P. Conf. Ser. 259, 150 KoÃlaczkowski, Z., Pigulski, A., Soszynski,´ I. et al. 2004a, ASP Conf. Ser., in press (astro-ph/0310582) KoÃlaczkowski, Z., Kopacki, G., Pigulski, A., Michalska, G., 2004b, Acta Astron., submitted Krzesinski,´ J., Pigulski, A. 1997, A&A 325, 987 Krzesinski,´ J., Pigulski, A., KoÃlaczkowski, Z. 1999, A&A 345, 505 Mathias, P., Aerts, C., Briquet, M. et al. 2001, A&A 379, 905 Molenda-Zak˙ owicz, J. 2002, Ph.D. thesis, University of WrocÃlaw Paardekooper, S.J., Veen, P.M., van Genderen, A.M., van der Hucht, K.A. 2002, A&A 384, 1012 Pamyatnykh, A.A. 1999, AcA 49, 119 Pietrzynski,´ G. 1997, AcA 47, 211 Pigulski, A., KoÃlaczkowski, Z. 1998, MNRAS 298, 753 Pigulski, A., KoÃlaczkowski, Z. 2002, A&A 388, 88 Pigulski, A., Jerzykiewicz, M., Kopacki, G. 1997, AcA 47, 365 Pigulski, A., Kopacki, G., KoÃlaczkowski, Z. 2001, AcA 51, 159 Pigulski, A., Kopacki, G., KoÃlaczkowski, Z., Jerzykiewicz, M. 2002, A.S.P. Conf. Ser. 259, 146 Robb, R.M., Delaney, P.A., Cardinal, R.D. et al., 2000, IBVS No. 4913 Shibahashi, H., Aerts, C. 2000, ApJ 531, L143 Stankov, A., Handler, G., Hempel, M., Mittermayer, P. 2002, MNRAS 336, 189 Sterken, C., Jerzykiewicz, M. 1993, Space Science Rev. 62, 95 Telting, J.H., Schrijvers, C. 1998, A&A 339, 150 Waelkens, C. 1991, A&A 246, 453 Waelkens, C., Aerts, C., Kestens, E., Grenon, M., Eyer, L. 1998, A&A 330, 215 Zeb˙ run,´ K., Soszynski,´ I., Wo´zniak, P.R. et al. 2001, AcA 51, 317. Comm. in Asteroseismology Vol. 145, 2004

Radial Velocity variations of the roAp-star HD122970: new results

A. Gamarova1,3, A. Hatzes1 and D. Mkrtichian2,3 1 Thuringer¨ Landessternwarte Tautenburg, Sternwarte 5, 07778 Tautenburg, Germany 2 Astrophysical Research Center of the Structure and Evolution of the Cosmos, Sejong University, Seoul 143-747, Korea 3 Astronomical Observatory, Odessa National University, Shevchenko Park, Odessa 65014, Ukraine

Abstract

In this paper we present new results on the precise relative radial velocity (RV) measurements for the roAp star HD122970. The RV line-by-line frequency analysis revealed the dependence of the pulsational amplitudes on the line strength and a bi-modal phase distribution. These new results can be considered as a signiﬁcant evidence of the presence of a radial node in the atmosphere of HD122970.

The roAp nature of the cool Ap star HD122970 was established by Handler & Paunzen (1999), who found a main pulsational period of 11.09 min (f = 129.81427 c/d). Pulsational RV variations were detected by Hatzes et al. (2000). For the present investigation we used 150 high resolution (R=60,000) spectra of HD122970 taken with an iodine cell as a wavelength reference (Hatzes et al., 2000). The RVs were determined over the spectral region between 5000–6300 A.˚ The analysis of the “broad-band” (∆λ = 10 A)˚ RV series showed that the signal, corresponding to the main photometric frequency, was present only in several spectral ranges and with diﬀerent RV amplitudes. Spectral regions dominated by strong lines had amplitudes of around 100 m s−1, while regions containing mostly weak lines had amplitudes up to 400 m s−1. The RV analysis of individual lines revealed the presence of the pulsational signal only in 21 spectral lines dominated by rare-earth elements. The weaker spectral lines tend to show higher RV amplitudes with the largest amplitude being 1.5 km s−1. The lowest pulsational amplitudes tend to occur among relatively strong lines and these are consistent to within the error of the RV amplitude derived using the “broad-band” measurements. Such an amplitude behaviour has been explained as an atmospheric height eﬀect (Kanaan & Hatzes 1998). The pulsational phase distribution appears to be bi-modal with 6 lines having a phase shifted by about 180o relative to the mean phase of other lines. This is consistent with the presence of a radial node in the stellar atmosphere of HD 122970, similar to what we found in our study of the roAp star 33 Lib (Mkrtichian et al. 2003) and in α Cir by Baldry et al. (1998). Our results on HD 122970 show the similarities in acoustic structures of roAp stars’ atmospheres, giving us the great possibility to investigate the vertical structure of the stellar atmosphere by the acoustic cross-section method (Mkrtichian et al., 2003).

References Baldry I. K., Bedding T.R., Viskum M. et al. 1998, MNRAS, 295,33 Handler G., Paunzen E. 1999, A&AS 135, 57 Hatzes A., Mkrtichian D. & Kanaan A. 2000, NATO Science Series C. 544, 405 Kanaan A. & Hatzes A. 1998, ApJ 503, 848 Mkrtichian, D., Hatzes A. & Kanaan A., MNRAS 2003, in press. Comm. in Asteroseismology Vol. 145, 2004

Pulsation and Binarity in RZ Cas

E. Rodr´ıguez1, J.M. Garc´ıa2, D.E. Mkrtichian3,4, V. Costa1, S.-L. Kim5, M.J. L´opez-Gonz´alez1, E. Hintz6, A.V. Kusakin7,8, A.Y. Gamarova4, J.W. Lee5, J.-H. Youn5, E.B. Janiashvili9, R. Garrido1, A. Moya1, Y.W. Kang3

1 Instituto de Astrof´ısica de Andaluc´ıa, CSIC, P.O. Box 3004, E-18080 Granada, Spain, E-mail:[email protected] 2 Departamento de F´ısica, E.U.I.T. Industrial, UPM, Ronda de Valencia 3, E-28012 Madrid, Spain 3 Astrophysical Research Center for the Structure and Evolution of the Cosmos (ARCSEC), Sejong University, Seoul 143-747, Korea 4 Astronomical Observatory, Odessa National University, Shevchenko Park, Odessa, 65014, Ukraine 5 Korea Astronomy Observatory, Daejeon, 305-348, Korea 6 Department of Physics and Astronomy, Brigham Young University, Provo, UT 84602, USA 7 Sternberg State Astronomical Institute, Universitetsky prospect, 13, Moscow, 119899, Russia 8 Isaak Newton Institute in Chile, Kazakhstan Branch 9 Abastumani Astrophysical Observatory, Abastumani, 383763, Georgia

Abstract

We present here a study of the Algol-type system RZ Cas from both points of view, pulsational and binary, based on a multisite photometric campaign carried out in the year 1999. Moreover, a review of the pulsational behaviour of its primary component over time (decades) is performed leading to very interesting results.

Introduction

RZ Cas is a bright Algol-type eclipsing binary system (V=6.m26, A3V+K0IV) where the d primary component is a δ Sct-type pulsator. This system has an orbital period of Pb=1. 1953 and eclipse depths of about ∆V∼1.m50 and 0.m07 for the primary and secondary minima, respectively. The pulsational amplitude is very small in comparison (∼0.m015, peak to peak) with a very short main period (22 minutes) (Ohshima et al. 1998, 2001). In fact, this is the δ Sct variable with the shortest main period known (Rodr´ıguez et al. 2000). Despite its very low pulsational amplitude, the oscillations of RZ Cas are directly seen in the observed light curves, even during the secondary minimum and at the beginning and the end of the primary minimum, as shown in Fig. 1 for some light curves collected in the present work. Nevertheless, the history of the study of the pulsations in this system is very short. RZ Cas was discovered as eclipsing binary by Muller in 1906 and Dugan (1916) published the first complete light curve deriving the orbital elements of the system. Since then, the system has been widely observed both photometrically and spectroscopically by many authors, but the δ Sct-type variability was only recently announced by Ohshima et al. (1998). During several decades, one very important subject of controversy in this system has been the type of primary minimum taking place, because different shapes for the light curves were found at different minima. The analyses of a number of photometric light curves carried out by different authors indicate that the primary minimum corresponds to a partial eclipse. However, partial eclipses with different shapes have been reported. Furthermore, flat bottoms in some minima were detected at other times. This has led to a number of E. Rodr´ıguez, J.M. Garc´ıa, D.E. Mkrtichian et al. 79 different interpretations based, in all cases, on the particular characteristics of the eclipsing system: activity, starspots, etc. were deemed responsible for modifying the light curve during the primary eclipse. However, Ohshima et al. (2001) showed that the existing short-period pulsations in the primary component can be responsible for these discrepancies.

Figure 1: Some examples of nightly observed y light curves of RZ Cas: a,c,d) out and during the primary eclipse and b) out and during the secondary eclipse.

Observations

In order to make a detailed study of the pulsational behaviour of RZ Cas, a coordinated multisite photometric campaign was carried out from four observatories: Sobaeksan Optical As- tronomy Observatory (SOAO), South Korea; Tien-Shan Astronomical Observatory (TSAO), Kazakhstan; Sierra Nevada Observatory (SNO), Spain and Orson Pratt Observatory (OPO), USA. In total, 171 hours on 34 nights of useful data were collected over a time span of 141 days from July to December of 1999. Different detectors were used at different observatories. In particular, simultaneous observations in the four uvby filters of the Strömgren photometric system were collected at SNO along with a few Hβ measurements obtained around orbital phase of 0.25 for purposes of calibration.

Results

Our main results can be summarised as follows: a) RZ Cas is a semi-detached system where the secondary component ﬁlls its Roche lobe, with a circular orbit and with no sign of third light in the system. The appearance of the light curves reveals the presence of a hot spot on the surface of the primary as result of the mass stream coming from the secondary. There are also some indications of chromospheric activity of the secondary. 80 Pulsation and Binarity in RZ Cas

b) The existence of pulsations of the δ Sct-type in the primary component is confirmed. It can explain the existing distortions, reported by earlier authors, in the light curves during the primary minima. This can also explain some disturbances found out-of-eclipse by other authors. c) For data collected between 1997 (Ohshima et al. 2001) to 1999 (present work), the pulsational behaviour can be well described in a similar way: with only one frequency and constant amplitude. d) Our results indicate that nonradial pulsation in a high radial order (n=6), with l=2, |m|=1,2 is the most suitable mode identification. The theoretical solutions were modelled using the method of Spatial Filtration (Gamarova et al. 2003), by predicting the distortions in the pulsational light curves when the primary component is being partially hidden by the secondary. e) The pulsation amplitude in the u band is larger than in both the b and v bands, which is unusual among the δ Sct-type variables. Using new improvements in multicolor photometry, this can be explained as due to pulsation in a high n-value of a star close to the blue edge of the δ Sct region. f) A revision of all the photometric out-of-eclipse data sets available in the literature was carried out. From this, we find: the existence of amplitude variations in the pulsations from season to season except in the interval mentioned in point c), possible multiperiodicity in some epochs and possible variations in the frequencies themselves. In fact, in a number of epochs the pulsation is not detected. If existing, it is below the photometric limit of detectability. This limit is in some cases very small (∼3 mmag). References Dugan R.S. 1916, Contr. Princeton University Obs. No. 4 Gamarova A.Y., Mkrtichian D.E., Rodr´ıguez E., Costa V., López-González M.J. 2003, PASPC 292, 369 Ohshima O., Narusawa S.Y., Azakawa H. et al. 1998, Inf. Bull. Var. Stars. No. 4581 Ohshima O., Narusawa S.Y., Azakawa H. et al. 2001, AJ 122, 418 Rodr´ıguez E., López-González M.J., López de Coca P. 2000, A&AS 144, 469 Comm. in Asteroseismology Vol. 145, 2004

AB Cas revisited

E. Rodr´ıguez1, P.J. Amado1, J.M. Garc´ıa2, V. Costa1, M.J. L´opez-Gonz´alez1

1 Instituto de Astrof´ısica de Andaluc´ıa, CSIC, P.O. Box 3004, E-18080 Granada, Spain 2 Dep. de F´ısica, E.U.I.T. Industrial, UPM, Ronda de Valencia 3, E-28012 Madrid, Spain

AB Cas is a very good example of an eclipsing binary system where the light curves show simultaneously two types of variation: binarity of the Algol-type and pulsation of δ Sct-type. In fact, this system belongs to the very small group of “A-F spectral type main-sequence mass- accreting pulsating stars in semi-detached Algol-type eclipsing binary systems” proposed by Mkrtichian et al. (2002). d In the case of AB Cas, the orbital period is of Porb=1. 3668 with eclipse depths of ∆V∼1.m6 and 0.m1 (primary and secondary, respectively), whereas the main pulsational d m period is Ppul=0. 0583 with an amplitude of about 0. 05 (from peak to peak). The most complete study was carried out by Rodr´ıguez et al. (1998) by using simultaneous uvby observations collected from 1987 to 1988. They found only one pulsational frequency in the amplitude spectra which was suggested as radial in the fundamental mode. New observations have been carried out during the years 1998-1999 with simultaneous uvby photometry using the six-channel uvbyβ spectrograph photometer attached to the 90 cm telescope at Sierra Nevada Observatory, Spain. About 90 hours of data were collected and nearly all of the orbital phases were covered twice. The short period oscillations are directly seen in the collected light curves in all the orbital phases, except during the primary eclipses. In order to analyse the pulsational behaviour of the primary component, the binary contribution was first removed from the light curves. For this purpose, the orbital solution obtained by Rodr´ıguez et al. (1998) was adopted as a preliminary solution. Now, the pulsation is also visible during the primary minima as confirmation that the eclipse is partial. Then, the residuals O-C were analysed and, similar to that paper, they show some disturbances during the orbital phases corresponding to the primary eclipses. They will be investigated in more detail when a definitive binary solution has been obtained. Thus, phases corresponding to the primary eclipses were not taken into account in our frequency analysis. The data sets corresponding to each year 1998 and 1999 were analysed −1 separately. Our results indicate the existence of a main frequency f1=17.1564 cd in very good agreement with that found by Rodr´ıguez et al. (1998) with data collected one decade before. Within the observational uncertainties, the phase shifts for data collected in the different filters agree well with those reported in that paper. Nevertheless, it seems that the amplitude of f1 presents changes from season to season and there are also some insights on −1 the existence of a secondary frequency at f2=14.961 cd . References Rodr´ıguez E., Claret A., Sedano J.L., Garc´ıa J.M., Garrido R. 1998, A&A 340, 196 Mkrtichian D.E., Kusakin A.V., Gamarova A.Y., Nazarenko V. 2002, PASPC 259, 96 Comm. in Asteroseismology Vol. 145, 2004

A few concluding remarks

A. Baglin1

1 LESIA, Observatoire de Paris, 92195 MEUDON, France

Abstract

Since the discovery of time variability in observed stellar quantities, as apparent magnitude and spectral characteristics, this phenomenon has been considered as a very important source of information to understand stars. Indeed, the global surface parameters as effective temperature, luminosity, and surface chemical composition tell a lot and have been extensively used in building internal structure theory. But this information is generally not sufficient as it is ”degenerate”, different internal physical conditions producing identical surface parameters. Dynamical phenomena, as intrinsic oscillations are the ideal indicators of these internal properties. They are present in many types of stars, with very different characteristics. The method and tools to observe them, as well as their potential of diagnostics in terms of internal structure are then very diverse. In this symposium, the different aspects of variability studies and seismology have been presented, from the discovery of new objects and new effects, to the inference of the physical parameters of the interiors, with particularly difficult steps such as mode identification.

The large population of variable stars

Many classes of variables have been revisited, leading to new members of existing classes, to the discovery of new effects, based on progress of instrumentation, of time coverage, of the use of extensive data mining. Variable stars as members of groups provide more complete information and can help interpretation. Several clusters have been revisited or studied for the first time. Some open clusters are very promising by their large content of Delta Scuti stars. It is more and more easy to compare variables in galaxies of the local group to our own, allowing to study the effect of metallicity for instance, which is particularly important for classes of variables where it is predicted that metallicity is the driving factor of the oscillations, as e.g. in β Cephei stars and SPBs. Statistical studies provide also some hints for interpretation. They benefit from large surveys, essentially MACHO on the Magellanic Clouds and OGLE for the galactic bulge. Observations over long periods allow to detect variations of pulsational properties on different time scales, which are not yet understood in general. Using large telescopes with high resolution spectrographs, detailed spectroscopic studies are revisiting well known behaviors like for instance the Blazhko effect in RR Lyrae stars. The long standing question about the coexistence of both variable and non variable stars in the same region of the HR diagram is still pending in most cases. For instance, abundance differences observed in λ Bootis stars do not provide all the necessary clues. A. Baglin 83

Mode identiﬁcation

One of the key issues to extract the information from any seismic data is the ability to identify the mode of pulsation corresponding to an observed frequency. Unfortunately, the structure of the power spectrum is generally much more complicated than the solar comb. Spectra are often coarse and non equidistant. Except in white dwarfs where rotational splitting allows to determine the l value, there is no indisputable identification, even in the very famous δ Scuti star FG Vir, where more than 20 modes have been detected. Since many years it has been proposed to use the phase differences and amplitude ratios of the oscillation in different colours to test the horizontal structure of the modes (l and m values). It is now recognized that this method requires a comparison to refined modelling of the outer layers, including non-adiabatic effects and convection/pulsation interaction in cool stars. In δ Scuti and γ Doradus stars, the perturbation of the eigenfunctions due to rotation has also to be taken into account. This technique is very promising, but a lot more work has to be done to be able to perform an unambiguous determination of the l value; the quality of the data has also to be improved. In eclipsing binaries, the transit phase can be used to map the stellar surface and detect the geometrical properties of the oscillation. In rapidly rotating stars with wide line profiles, surface imaging techniques are promising tools to map the oscillation on the disk.

Seismic interpretation

Stellar seismology is in general more difficult to handle than helioseismology. The old slowly rotating Sun, with its radiative core has the simplest oscillation behavior one can think of! The generalization of techniques used in the solar case to slightly different types of models gives valuable tools to understand the variation of the stellar structure with mass and age in the solar vicinity. But, it is already possible to generalize the seismology techniques to quite different classes of stars. The discovery of a few pulsating pre-main sequence Delta Scuti stars stimulated both observational and theoretical studies, aiming at determining the behavior of stars in their contraction phase. Also, in large amplitude pulsators (HADS), with a few modes, the classical method consisting in using period ratios to determine some global properties can nicely be used. In white dwarfs, long term variations of frequencies interpreted as a signature of the cooling process provide some insight on the state of matter in the central regions and test the existence of axions. Among the wide efforts aiming at using the seismic signatures (frequency, amplitude, and eventually life-time of the detected modes) to infer stellar properties, hydrodynamical simulations will bring some new insight in mode selection effects, in excitation processes, in surface effects... Another important difficulty in seismic interpretation is due to the uncertainties on the fundamental parameters of distant stars. This problem evidently and thankfully did not exist for the Sun. Efforts have to be made on that subject, dealing with detailed physics of the stellar atmospheres, to be able for instance to compare measured and computed ”effective temperatures” at the level of a few tens of degrees. In this respect, the advent of interferometry with large telescopes may lead, at least for bright stars, to radius determinations of sufficient accuracy to be useful in seismic studies. Working with homogeneous groups as clusters will help, but will not cover all types of stars. 84 A few concluding remarks

Ground based observations and networks

Europe has a wide variety of instruments and the number of astronomers involved in these activities is quite large. In photometry, long duration coordinated campaigns have proven to be very efficient in deciphering the spectra of White dwarfs, for instance. And it is evidently this type of observations which is required to progress in the improvement of our knowledge of the pulsation behavior of many objects. As one of the major requirements is a high duty cycle over many days, it implies coordinated networks with a reasonable coverage in longitude in very good photometric sites. Each such a campaign is a huge effort. Robotic telescopes are developing rapidly. Coordinated in networks and equipped with instrumentation as homogeneous as possible, they can help in reducing the work load. However it remains necessary to select carefully the targets, and to coordinate activities of many countries in order not to waste efforts and telescope time. The spectroscopic technique has already been very successful in detecting solar-like oscillations in a few bright stars. Surface imaging in fast rotators is able to detect oscillations with large m values. It requires access to large telescopes, equipped with stable and precise spectrographs. Once again the ideal situation would be to operate a world-wide homogeneous network, but presently it is out of the possibilities.

Space observations

Space, in principle, overcomes many of the diﬃculties of the ground observations: trans- parency, stability and continuity though it is clear that it will never supersede them. Space projects dedicated to stellar variability have been proposed since more than 20 years and only recently selection committees have considered them positively. Due to the required size of the instrument, and the need to access all types of stars, including fast rotators, the photometric technique has been preferred up to now.

MOST: the pioneer

Figure 1: First image of the MOST star tracker

The Canadian suitcase-sized microsatellite MOST has been launched successfully on June 30th by Rockot into a heliosynchronous low earth orbit at 820 km. Its 15 cm collector will observe a few bright stars (mv ≤ 6) , of diﬀerent characteristics for continuous periods of 30 up to 58 days. News can be found at http://www.astro.ubc.ca/MOST/index.html A. Baglin 85

COROT and EDDINGTON

It is in Europe, and particularly in France, that the ﬁrst space projects have been proposed in the 80s. Unfortunately after the crash of the MARS96 spacecraft, with the small experiment EVRIS on board, new opportunities were scarce. In the framework of the national Danish program the Roemer/Mons project has been studied till the end of Phase B, but then stopped. The CNES programme of ”small missions” preselected COROT in 1994, which since then has succeeded to overcome all the selections and budget diﬃculties.

Figure 2: A preliminary set of candidates for the principal targets of the seismology programme of COROT, as seen on the sky, with the focal plane, and in the HR diagram. These targets are the brightest ones, and will be followed continuously for 150 days. Ten times more objects around these ones will be observed at the same time.

COROT is now in phase C, to be launched in early 2006. It has a specific seismology programme of very high accuracy, observing 50 stars for 150 days and 100 for 20 days. A very large number of faint stars (180 000) will be observed with a lower accuracy and lower time sampling, but providing continuous time series of extreme importance for variability studies. More information can be found at http://corot.astrsp-mrs.fr With COROT, France and Europe take the floor. But this European leadership has to be maintained, through a second generation project, using the expertise acquired for COROT. The project EDDINGTON is this second step in ultra-high precision photometry from space. As Corot it will have two major programmes: one dedicated to a general survey of the seismic properties of stars, the other one to the discovery of planetary systems. When writing this paper, the decision to implement Eddington has not been taken. The financial difficulties of the science Programme of ESA have lead the Science Programme Committee to propose an affordable version of the ”Cosmic Vision” programme which does not include Eddington, though considering its extreme scientific importance. Let’s hope that a solution will be found to be able to overcome this disastrous situation and allow the development of Eddington in due time to remain a major actor in the international game of ultra-high precision stellar photometry, after COROT. 86 A few concluding remarks

Figure 3: An artistic view of Eddington

The European Network ENEAS

As demonstrated in this symposium and also browsing literature, Europe plays a major role in stellar variability and seismology studies. As the different steps of a seismic study need strong efforts, very broad and different expertise, the European community has created a network of scientists and laboratories called ENEAS in October 2002. As described by Aerts et al. (2003), ENEAS is a tool to strengthen Europe’s position in this field, to prepare the European community to exploit the new ground based instrumentation and the space missions by exchange of expertise and training, and to coordinate efforts. Presently 256 scientists from 43 Institutions have joined the group. A web site http://www.eneas.info has been set up to provide a natural and vivid link between the participants, even before any formal support is obtained. References Aerts, C., Baglin, A. et al. 2003, Second Eddington Workshop ESA-SP, in press.

Figure 4: The ENEAS logo