Intrinsic Variability in Multiple Systems and Clusters

Astrophysics of Variable Stars ASP Conference Series, Vol. 349, 2006 C. Sterken & C. Aerts

Intrinsic Variability in Multiple Systems and Clusters: an Overview A. Pigulski Instytut Astronomiczny Uniwersytetu WrocÃlawskiego, Kopernika 11, 51-622 WrocÃlaw, Poland Abstract. We present a brief overview of the present knowledge of the intrinsic variability of stars in binary/multiple systems and clusters of different age. Using examples taken from the literature, we discuss which stellar parameters of a binary component or cluster member can be constrained and then used in better modelling and understanding of its variability and evolution.

1.

Introduction

Variable stars are usually divided into two groups, intrinsic and non-intrinsic. The latter variability results from purely geometrical effects like rotation or orbital motion in a binary, whereas the rotating star or binary component itself does not vary in brightness. Eclipsing binaries, ellipsoidal variables and rotating stars with surface inhomogeneities belong to this category. On the other hand, we have two main types of intrinsically variable stars. The first one includes binary-induced variability in cataclysmic variables, supernovae eruptions, variability due to flares and fast evolutionary phases. The second group contains about 20 different types of stars which vary in brightness due to pulsations. A variety of astrophysical processes can be studied using pulsating stars and we will focus on this kind of intrinsic variability in this overview. In order to better understand the phenomenon of stellar oscillations and other kinds of intrinsic variability, the stars need to be modelled. The modelling, however, requires the knowledge of stellar parameters. In this context, the fact that a pulsating star belongs to a binary system or stellar cluster has a great advantage as both the binarity and cluster membership provides stellar parameters. Modelling of the internal structure of a star requires at least the knowledge of its mass and initial chemical composition. We know, however, that the Vogt-Russell theorem is not valid in a general case, so that to model a star in an advanced stage of evolution, one needs to know not only its mass, chemical composition and age, but also the radius, effective temperature or luminosity. Reliable models include a very good physics including complications as rotation, mass loss, convective overshooting, magnetic fields, etc. The prediction of the output flux, i.e. the model of the stellar atmosphere, requires a different set of parameters, namely effective temperature, surface gravity (which can be derived from radius and mass), and surface chemical composition. Some stellar parameters, like effective temperature or surface chemical composition, can be obtained from spectral analysis. However, as mentioned above, we can benefit from the fact that a given star belongs to a multiple system or a 137

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cluster. In the two sections below, we explain which stellar parameters can be derived for such systems and give a short overview of pulsating stars that are currently known in eclipsing binaries (Sect. 2) and clusters (Sect. 3). 2.

Intrinsic Variables in Multiple Systems

Since over 50% of stars reside in binaries, it is reasonable to claim that many pulsating stars are components of binary and multiple systems as well. Pulsating stars are spread over the whole Hertzsprung-Russell diagram (hereafter HRD), and are found at different stages of stellar evolution. The instability of a given type is usually restricted to a well-defined area in the HRD called instability strip. If we have a pulsating star which is the component of a binary, we have to consider the possible influence of its companion. If the system is well detached, we may safely assume that the components followed single-star evolution. This is a good assumption for most of the main-sequence pulsators, as the changes of stellar radii are not large at this stage. On the other hand, if we have a close binary, the binary-star evolution has to be taken into account. In this case, it is possible that one of the components entered a given instability strip already after the mass transfer. If so, the internal composition of such component might be quite different from that of a single star located in the same place of the HRD. It is interesting to ask, how the fact that a star underwent mass transfer influences its pulsational properties? Some δ Scuti stars of this kind are known (see Sect. 2.1 below). There are at least two other examples of pulsating stars in post-mass transfer systems. The first one includes pulsating white dwarfs and subdwarfs in close binary systems which had to pass through the commonenvelope stage of evolution (Paczy´ nski 1976). Such close binaries are sometimes called pre-cataclysmic stars (see, e.g., Ritter & Kolb 1998). The other example concerns SX Phœnicis stars which are found in the blue stragglers region in globular clusters and therefore are believed to be stellar mergers (Hills & Day 1976; Benz & Hills 1987). It is well known that eclipsing binaries are crucial as far as the knowledge of stellar masses and radii is concerned. The best combination is a system which is both eclipsing and double-lined in spectroscopy (see Maceroni, these Proceedings; Ribas, these Proceedings). In this case, both masses and radii of the components can be derived. The masses can be also obtained from a noneclipsing system provided that it is a double-lined spectroscopic and visual one. This requirement, however, restricts the systems to relatively nearby ones. Since from the point of view of modelling pulsations, the radius is a very important parameter, we will concentrate on pulsating stars which are components of eclipsing systems. However, some interesting examples of non-eclipsing systems with a pulsating component will also be given. We start our review from the main-sequence pulsators; then the pulsating giants and stars at the late stages of stellar evolution will be discussed. 2.1.

Main-sequence pulsators

There are six main types of pulsating stars which reside along the main sequence. Going from largest to smallest masses these are: β Cephei stars (Stankov & Handler 2005), slowly pulsating B-type (SPB) stars (De Cat et al. 2004), δ Scuti stars

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(Breger 2000), rapidly-oscillating Ap (roAp) stars (Martinez & Kurtz 1995), γ Doradus stars (Henry et al. 2005), and stars showing solar-like oscillations (Christensen-Dalsgaard 2004). Table 1 summarises currently known numbers of main-sequence pulsators in the Galaxy. The stars of a given type which are known to be members of eclipsing binaries are also listed. Finally, the numbers of stars known in clusters are given as well; they will be discussed in Sect. 3. The first three types of main-sequence pulsators (β Cephei, SPB, and δ Scuti) are also known outside the Galaxy (Mateo et al. 1998; Pigulski & KoÃlaczkowski 2002; KoÃlaczkowski et al. 2004a, 2005; ?). Table 1. Numbers of currently known pulsating stars of six types located in the main sequence. The names of stars in eclipsing binaries are given in parentheses. Number of stars Type of variable

known

β Cephei SPB δ Scuti/SX Phe roAp γ Doradus solar-like

∼110 ∼120 ∼1200 ∼35 ∼50 11

in eclipsing binaries [names] 4 1 24 none none none

[16 Lac, V381 Car, η Ori, λ Sco] [V539 Ara] see Table 2 — — —

in clusters ∼40 ∼20 ∼250 none a few cand. none

β Cephei-type stars. The first eclipsing β Cephei star we discuss here is 16 (EN) Lacertae. The primary eclipses in this single-lined, 12.1-day spectroscopic binary system with a pulsating primary were discovered by Jerzykiewicz et al. (1978). A detailed analysis of the available photometry yielded the inclination, the ratio of the radii and the relative radius of the primary in terms of the binary separation (Pigulski & Jerzykiewicz 1988). These parameters, combined with the mass function equal to 0.0160 ± 0.0008 M⊙ derived from the spectroscopic elements provided by le Contel et al. (1983), led to the mass-radius and then, with the use of effective temperatures, to the mass-luminosity (M − L) relations for both components. The second M −L relation was obtained by Pigulski & Jerzykiewicz (1988) from the evolutionary models. Since the two relations intersected under a reasonable angle, quite accurate masses (M1 = 10.2 ± 0.5 M⊙ , M2 = 1.29 ± 0.06 M⊙ ) and radii of the components could be derived. The result was slightly model-dependent, but it is a good illustration that even a single-line spectroscopic binary can be used to yield useful stellar parameters if eclipses are observed. The primary’s mass was later used by Dziembowski & Jerzykiewicz (1996) for seismic modelling of the star and compare very well with the value of 9.62 ± 0.11 M⊙ derived by Thoul et al. (2003) from a similar kind of modelling, but without a priori assumption of the mass. The next β Cephei star in an eclipsing binary, V381 Car, is even more interesting. Likewise 16 Lac, it is the primary in a single-lined spectroscopic and well-detached system. The orbital period amounts to about 8.23 d. In addition, it is a member of the young open cluster NGC 3293. The cluster is very

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rich in β Cephei-type stars; eleven stars of this type are known in it (Balona 1994). The secondary in V381 Car system is of earlier type than in 16 Lac, hence both eclipses are observed. The star was discovered as an eclipsing binary by Engelbrecht & Balona (1986) and then studied by Jerzykiewicz & Sterken (1992). Recently, Freyhammer et al. (2005) obtained spectroscopic observations and yielded masses and radii of the components. The stellar parameters for the components allowed to derive the distance of the system D = 2.8 ± 0.3 kpc which agrees very well with the value of 2.75 ± 0.25 kpc derived by Baume et al. (2003) from the cluster main-sequence fitting. The next eclipsing β Cephei star, η Ori, is quintuple in a classical hierarchical system. The closest Aa-Ab pair is double-lined and eclipsing binary consisting of two early-B components in a 7.989-day orbit (Adams 1903). The third component, Ac, also quite massive, revolves the pair in a 9.51-yr eccentric orbit ˇ zka & Beardsley 1981). Two other, visual components, B and (Pogo 1928; Ziˇ C, at separations of about 1.′′ 5 and 115′′ are known, although the latter may be not physically related to the close quadruple. The two pairs, Aab-Ac and A-B are resolved by means of the speckle interferometry (McAlister 1976). This combination of different observable orbits allows determination of masses of the three components and the radii of the two, Aa and Ab. This was already done by several investigators, including the latest studies of De Mey et al. (1996) and Balega et al. (1999). The masses of all three closest components amount to 10–13 M⊙ , well within the range covered by β Cephei stars. Relatively little photometry was made for η Ori after the discovery that it is an eclipsing system (Kuntz & Stebbins 1916). The newest observations (Waelkens & Lampens 1988; Lee et al. 1993) revealed total eclipses in the system. There is however, a controversy related to the nature of the short-period variability attributed usually to the Ab component. Koch et al. (1980) and Waelkens & Rufener (1983) reported a period of 0.301 d, while Waelkens & Lampens (1988) and Lee et al. (1993) opted for its daily alias, 0.432 d. The latter authors proposed the interpretation of the short-period variations by means of the eclipsing or ellipsoidal changes in B or Ac component. On the other hand, De Mey et al. (1996) revealed 0.13-day variations in the line profiles of the Ab component attributing it to the β Cephei-type variability. Concluding, the star deserves a comprehensive photometric and spectroscopic study to resolve the nature of the short-period variability of all its components. The fourth β Cephei star known in an eclipsing system is λ Scorpii. It is hierarchical triple system with orbital periods of 5.953 and 1082 d for the close and wide pair, respectively (De Mey et al. 1997; Uytterhoeven et al. 2004). Its pulsating nature was discovered by Shobbrook & Lomb (1972), who indicated that the system might be eclipsing as the star was fainter than usual by 0.04 mag during one night. This was confirmed by Uytterhoeven et al. (2004) who analysed Hipparcos data for this star. However, the final confirmation with a clear evidence of total eclipses and the eccentricity of the orbit came from the WIRE satellite observations of this star (Bruntt & Buzasi 2005). A thorough analysis of the light variations will be published soon (Bruntt, private communication). There is another β Cephei-type star worth mentioning in this context, although it is not an eclipsing binary. This is bright star β Centauri which is a double-lined spectroscopic system consisting of two twin early B-type stars in a very eccentric orbit with e = 0.81 and an orbital period of about 357 days

Intrinsic Variability in Multiple Systems and Clusters

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(Ausseloos et al. 2002). It is possible that both components are β Cephei-type stars. In addition, the visual orbit of the star was observed interferometrically by Davis et al. (2005). A combination of the visual and spectroscopic elements led these authors to a very accurate masses, M1 = M2 = 9.1 ± 0.3 M⊙ , and the distance to the system, D = 102.3 ± 1.7 pc. SPB-type stars. Although many SPB-type stars are known in binary systems (e.g., De Cat et al. 2000), there is only one that was found in an eclipsing binary. It is V539 Arae, a detached double-lined system with Porb ≈ 3.17 d and the Algol-type eclipses, discovered by Strohmeier (1964). The apsidal motion is observed in this star as well (Clausen 1996; Wolf & Zejda 2005). The outof-eclipse variations were reported earlier (Knipe 1971; Sch¨ offel 1973), but it was Clausen (1996), who first derived coherent variations in the out-of-eclipse photometry of this star and attributed them to the SPB-type pulsations of the B4 V-type secondary. The star has accurately determined masses (6.24 ± 0.07, 5.31 ± 0.06 M⊙ ) and radii (4.50, 3.41 ± 0.08 R⊙ ) that can be used in the future modelling. δ Scuti-type stars. There is a growing interest in studying δ Scuti stars in binary systems. The first δ Scuti-type pulsations in an eclipsing binary were discovered in AB Cas by Tempesti (1971), but most of 24 such stars known at present (Table 2) were discovered during the last five years. Several other stars are suspected members of this group. In some systems, the pulsating star is the main-sequence star accreting mass in a classical semi-detached Algol-type binary and therefore did not follow a single-star evolution in the past. These pulsating components were called oscillating EA (oEA) stars (Mkrtichian et al. 2004). An important question that have to be asked is whether the oEA stars differ by some way from ‘normal’ δ Scuti stars? One possible difference is that some of them (RZ Cas, AS Eri, CT Her, IU Per, and VV UMa, see Table 2) show periods much shorter than usually observed in δ Scuti stars. It is, however, an open question whether this fact might be explained by the differences in evolution. Some other open questions related to δ Scuti stars in eclipsing binaries are discussed by Lampens (these proceedings). γ Doradus stars, roAp stars, and stars showing solar-like oscillations. As shown in Table 1, we do not know a single star of these three types which is a component of an eclipsing binary. However, some are members of non-eclipsing binaries. One of these systems merits special attention, because it is the nearest star, α Centauri. In both main components of this system, α Cen A and α Cen B, solar-like oscillations were successfully detected (Bouchy & Carrier 2001; Carrier & Bourban 2003). The system is a double-lined spectroscopic and visual binary and its parallax is measured with a very good accuracy. Moreover, the angular diameters of both components were determined interferometrically (Kervella et al. 2003). Table 3 summarises the present knowledge of the parameters of the α Cen system. The observed frequencies of the pulsating modes and, in particular, the values of the large and small separations listed in Table 3, provide very rigorous constraints on the models. The modelling may provide an estimation of the age of the components and the values of the initial chemical composition. Two such

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Pigulski Table 2. Main characteristics of δ Scuti stars that are components of eclipsing binaries. Porb stands for the orbital period, Npuls for the number of detected periodic terms attributed to pulsations.

Name

Porb [d]

Npuls

Freq. range [d−1 ]

References/notes

Y Cam AB Cas RZ Cas

3.306 1.367 1.195

4 1 2

15.0 – 18.3 17.2 56.6 – 64.2

RS Cha

1.670

?

(10 – 13)

R CMa V346 Cyg V469 Cyg GK Dra TW Dra

1.136 2.743 1.313 9.974 2.807

1 2 1 1 1

21.2 19.9 – 22.6 36 8.8 18.0

AS Eri

2.664

3

59.0 – 61.7

CT Her EF Her TU Her AI Hya RX Hya V577 Oph

1.786 4.729 2.267 8.290 2.282 6.079

1 1 1 1 1 1

52 9.6 18 7.2 19.4 14.4

AB Per IU Per AO Ser V1178 Tau VV UMa

7.160 0.857 0.879 unkn. 0.687

1 2 1 4 2(3)

5.1 42.1 – 45.8 21.5 6.2 – 15.0 47.5 – 51.2

HD 172189 HD 232486 NGC 2126-V6

5.702 2.372 1.173

1 1 1

19.6 24.5 7.7

Kim et al. (2002) Tempesti (1971), Rodr´ıguez et al. (2004b) Ohshima et al. (1998), Rodr´ıguez et al. (2004a), Lehmann & Mkrtichian (2004) McInally & Austin (1977), Clausen & Nordstr¨ om (1980) Mkrtichian & Gamarova (2000) Kim et al. (2005b) Caton (2004) Dallaporta et al. (2002) Kusakin et al. (2001), Kim et al. (2003) Gamarova et al. (2001), Mkrtichian et al. (2004) Kim et al. (2004a) Kim et al. (2004a) Lampens et al. (2004) Jørgensen & Grønbech (1978) Kim et al. (2003) Volkov (1990), Diethelm (1993), Zhou (2001) Kim et al. (2003) Kim et al. (2005c) Kim et al. (2004b) Arentoft et al. (2005), in NGC 1817 L´ azaro et al. (2001, 2002), Kim et al. (2005a) Mart´ın-Ruiz et al. (2005), in IC 4756? Escol` a-Sirisi et al. (2005) G´ asp´ ar et al. (2003)

studies, by Eggenberger et al. (2004) and Miglio & Montalb´ an (2005), yielded similar values of these parameters: an age of about 6.6 Gyr, a helium initial abundance equal to Yinit = 0.276 and a heavy elements abundance Zinit = 0.031. 2.2.

Pulsators in the giant phase

Since pulsating giants have, on average, much larger diameters than main-sequence stars, the orbital periods of the systems they belong to, are much longer. Of many types of pulsating giants, Cepheids and RR Lyrae stars are of greatest importance due to their role in the distance determination. Knowing such stars in eclipsing systems would lead us to get their accurate distances. Subsequently, they could be used to calibrate the distance determination methods that rely on absolute magnitudes of these stars. In fact, many Galactic Cepheids are known in binaries (Evans 1995; Szabados 2003). Unfortunately, none of these systems is known as an eclipsing one!

Intrinsic Variability in Multiple Systems and Clusters Table 3.

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Some parameters of the components of α Centauri system

Parameter

α Centauri A

α Centauri B

Parallax [mas] Major semi-axis [′′ ] Orbital period [yr] Masses [M⊙ ] Ang. diameters [mas] Radii [R⊙ ] Eff. temp. [K] Large separation [µHz] Small sep., δν02 [µHz]

747.1 ± 0.2 17.57 ± 0.02 79.91 ± 0.01 1.105 ± 0.007 0.934 ± 0.006 8.511 ± 0.020 6.001 ± 0.034 1.224 ± 0.003 0.863 ± 0.005 5810 ± 50 5260 ± 50 105.5 ± 0.1 162 5.6 ± 0.7 ∼10

Source, notes Hipparcos, S¨ oderhjelm (1999) Pourbaix et al. (2002) Pourbaix et al. (2002) Pourbaix et al. (2002) Kervella et al. (2003) Kervella et al. (2003) Eggenberger et al. (2004) A: Bouchy & Carrier (2002) B: Kjeldsen et al. (2005)

Cepheids. Favourably, owing to the microlensing surveys and other large projects focused on extragalactic variable stars, we now know more Cepheids outside the Galaxy than inside it (Table 4). Among them, three Cepheids in the Large Magellanic Cloud (LMC) were found in eclipsing systems (Udalski et al. 1999; Alcock et al. 2002; Lepischak et al. 2004). OGLE SC16-119952 = MACHO 81.8997.87 is a 2.035-day overtone Cepheid, so that it is potentially useful for calibrating the zero point of Cepheid period-luminosity (PL) relation. However, we definitely need more such systems to do it well. Of the two remaining stars, MACHO 78.6338.24 is a Population II Cepheid, while MACHO 6.6454.7 is a puzzle as in the PL diagram for LMC Cepheids it lies between relations for Population II and fundamental classical Cepheids. Table 4. Numbers of currently known Galactic/extragalactic pulsating stars which are subgiants, giants or supergiants. ‘EB’ stands for eclipsing binaries. Number of stars Type of variable Cepheid (incl. Pop. II) RR Lyrae Mira semi-regular

known

known in EB

known in clusters

∼800 / ∼5 000 ∼14 000 / ∼12 000 ∼10 000 / ∼5 000 ∼10 000 / ∼60 000

0/3 0 / (3) ∼10 / 0 ∼20 / 0

∼40 / ∼350 ∼2 500 / ∼500 ∼50 / 0 ∼100 / 0

RR Lyrae stars. The situation with RR Lyrae stars resembles that with Cepheids: we do not know any RR Lyrae star in an eclipsing system in the Galaxy, but three candidates were found in the OGLE-II data by Soszy´ nski et al. (2003). The orbital periods for these three stars are, however, quite short. It is, therefore, very likely that they are not real binaries, but blends of two different variable stars. Long-period variables. Microlensing surveys provided photometry for millions of stars in and outside the Galaxy. With these data, a huge amount of new long-period variables were discovered. The numbers given in Table 4 are only indicative. Many studies were devoted to these stars during the last years (Kiss

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& Lah 2005, and references therein), but their light curves were rather not searched for eclipses and this still need to be done. Some eclipsing binaries with long-period pulsators as companions are known, however. Many can be found among symbiotic stars (MikoÃlajewska 2003) as they are, by definition, binaries. Good examples of such systems are: AX Per (Skopal et al. 2001), AR Pav (Skopal et al. 2000), CH Cyg (Iijima 1998), and PU Vul (Nussbaumer & Vogel 1996). 2.3.

Pulsators at the late stages of stellar evolution

We know three (or four, if DOV and DBV stars are distinguished) ‘variability islands’ in the white dwarf cooling sequence. These are pulsating nuclei of planetary nebulae (PNNV), pulsating DO (DOV), DB (DBV), and DA-type (DAV = ZZ Ceti) white dwarfs (Table 5). In addition, there are two types of pulsating hot subdwarfs, EC 14026 stars called also sdBV or V361 Hya-type stars (Kilkenny et al. 1997) and PG 1716+426 known also as ‘Betsy stars’ (Green et al. 2003). Table 5. Numbers of currently known pulsating white dwarfs and subdwarfs. The names of stars in eclipsing binaries are given in parentheses. Number of stars Type of variable PNNV DOV/DBV (GW Vir) DAV (ZZ Ceti) EC 14026 (sdBV) PG 1617+426 (Betsy stars)

known 10 37 71 32 ∼20

in eclipsing binaries [names] none none 1 1 none

[HS 2331+3905] [NY Vir = PG 1338-018]

in clusters none none none none none

Pulsating white dwarfs. At present, only one pulsating ZZ Ceti star is known in an eclipsing binary. It is the hot component of the cataclysmic variable HS 2331+3905 (Araujo-Betancor et al. 2005). The light variations in the system are quite complicated because ZZ Ceti-type pulsations are superimposed on the periodic 81.1-minute light curve with a pronounced reflection effect and well-seen eclipses. In addition, variations due probably to the permanent superhumps are observed. There are two other ZZ Ceti stars known in cataclysmic variables, GW Lib (van Zyl et al. 2004) and SDSS J161033.64-010223.3 (Woudt & Warner 2004). These two stars, however, are not eclipsing. Pulsating hot subdwarfs. Many hot subdwarfs are binary members, it is even possible that the binary evolution is responsible for one of the evolutionary channels that leads to the origin of these stars (Han et al. 2002). The searches for pulsating subdwarfs brought the discovery of one such the star in the eclipsing binary NY Vir = PG 1338−018 (Kilkenny et al. 1998, 2003). The orbital period is very short, only barely exceeding 0.1 d.

Intrinsic Variability in Multiple Systems and Clusters 3.

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Intrinsic Variables in Clusters

Studying pulsating stars in clusters is a very active area of research which has sped up in the recent years mainly due to the two factors: (i) development of good CCD cameras with large field of view, and (ii) inventing the new methods that allow effective searches for variables even in very dense fields (Alard & Lupton 1998; Alard 2000). The profits from studying variables in clusters are manifold. This is primarily a consequence of the fact that stars in a cluster were formed almost coevally. In addition to sharing the same age, stars in a cluster are at the same distance or at least the spread of their distances is small in comparison with the mean distance of the cluster. Moreover, they usually have the same initial chemical composition and the same reddening. The latter is not always true, especially for young clusters, where the remnants of the cloud the cluster was formed of, induce large scatter of reddening. Some other complications occur, mainly due to the contamination of foreground and background stars, which pose problems in establishing the membership of some stars. Nevertheless, the fact that a given intrinsic variable is a cluster member, allows to derive its age, mass, reddening, distance modulus and conclude on its evolutionary status. These parameters are derived by means of main-sequence fitting or rather the isochrone fitting method. Going back to pulsating stars, it is obvious that, as far as the variability contents of clusters is concerned, it is principally defined by the cluster age. This is a consequence of the way in which stellar evolution works and the fact that pulsating stars occupy well-defined instability strips in the HRD. The other parameters that may influence the variable star contents are metallicity and the shape of the initial mass function. For example, the differences in the number of RR Lyrae stars in globular clusters are primarily due to differences in metallicities. The detection (or non-detection) depends also on observational selection effects that are related to the accuracy of photometry and time resolution of the observations. For some types of pulsating stars, a very tight constraint on age can be given from observations in clusters. For example, β Cephei-type pulsations are not expected to be found in stars (which means also in clusters) older than ∼30 Myr. Similar upper limits for age can be given for all main-sequence pulsators. On the other hand, some regions of pulsational instability can be reached only after some age. For example, RR Lyrae stars are not known in Galactic open clusters, even in the oldest ones with ages of about 5 Gyr, but are very abundant in globular clusters which are older than 10 Gyr. This allows to conclude on the masses of the progenitors of RR Lyrae stars and helps to understand the evolution of low-mass stars. Below we make a brief review of the variability contents of clusters at different ages, again focusing on the pulsating stars. The numbers of pulsating stars of different types were already given in Tables 1, 4, and 5. 3.1.

Very young open clusters

In a very young cluster, there are no evolved stars. Massive stars populate the main-sequence while those with small masses might still be contracting towards it. Surprisingly, some pre-main sequence (PMS) δ Scuti-type pulsators were found in young clusters. The first two candidates were discovered by Breger

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(1972a) in NGC 2264, although their PMS status is not certain. Two next stars were found in NGC 6823 by Pigulski et al. (2000) and recently two (or three) in NGC 6383 by Zwinz et al. (2005). Some PMS δ Scuti stars in the field are known as well. Since some searches for such stars are underway (Ripepi et al. 2005), new members of this group which now counts about a dozen stars will probably be found. Therefore, δ Scuti stars are probably the only pulsators that can be studied at the PMS stage, during the main-sequence evolution and at the post-main sequence stage. There is little chance to find SPB or β Cephei pulsators in the PMS stage. They are more massive than δ Scuti stars and therefore could be found only in clusters younger than ∼1 Myr. At this age, clusters are usually still embodied in the cloud the cluster was formed of. 3.2.

Young open clusters

Clusters in the range of ages between 5 and 25 Myr are best for studying β Cephei-type stars. In fact, about half of the known β Cephei-type stars belongs to such open clusters. Among them, there are four where at least four members were found to pulsate: NGC 3293 (Balona & Engelbrecht 1983; Balona 1994), NGC 4755 (Jakate 1978; Koen 1993; Balona & Koen 1994; Stankov et al. 2002), NGC 6231 (Shobbrook 1979; Balona 1983; Balona & Engelbrecht 1985; Arentoft, Sterken & Handler 2001), and NGC 6910 (KoÃlaczkowski et al. 2004b). However, β Cephei stars were found in several other open clusters: NGC 663 (Pietrzy´ nski 1997; Pigulski et al. 2001), h & χ Persei (Krzesi´ nski & Pigulski 1997; Krzesi´ nski et al. 1999; Gomez-Forellad 2000), NGC 1502 (St¸e´slicki, these proceedings), NGC 7235 (Pigulski et al. 1997), NGC 6200 and Hogg 22 (Pigulski 2005). Since OB associations are also in the considered range of ages, β Cephei stars are also found in some of them. This is also valid for extragalactic stars of this type (Pigulski & KoÃlaczkowski 2002). 3.3.

Intermediate-age open clusters

In the intermediate-age open clusters, evolved stars are already present, so that it is more convenient to describe different types of pulsators separately. SPB stars. The upper limit for the age of a star showing this kind of pulsations corresponds roughly to the main-sequence lifetime of a 3 M⊙ star, i.e., 200 Myr. So far, however, SPB stars were detected mainly in young open clusters: NGC 7654 (Choi et al. 1999), h Persei (Krzesi´ nski et al. 1999), NGC 3293 (Arentoft, Sterken & Handler 2001), NGC 4755 (Stankov et al. 2002), and others (Mart´ın et al. 2003; Mart´ın 2004). Classical Cepheids. Classical Cepheids in open clusters were intensively studied for many years. The main motivation for this work was the necessity of the knowledge of accurate value of the zero-point of the PL relation for these pulsators (Fernie 1969; Feast & Walker 1978; Walker 1998; Hoyle et al. 2003). One of the best studied clusters containing Cepheids was NGC 7790 (Sandage 1958; Smak 1966; Romeo et al. 1989; Matthews et al. 1995; Gupta et al. 2000), where three Cepheids, CF Cas, CE Cas a, and CE Cas b, are known. The ages of clusters which contain classical Cepheids range between 20 and 120 Myr.

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Cepheids are also known in the Small and Large Magellanic Clouds clusters (Hodge & Lee 1984; Pietrzy´ nski & Udalski 1999; Storm et al. 2005). δ Scuti stars. There is no lower limit in age for pulsations of δ Scuti-type stars. However, from the point of view of the detection, it is most convenient to search for δ Scuti stars in those clusters, in which the cluster turn-off point lies slightly above or in the instability strip. This means that the clusters are typically a few hundred Myr old. The clusters known to harbour the largest numbers of δ Scuti stars are (see also Li & Michel 1999): Hyades (Horan 1979), Pleiades (Breger 1972b; Fox Machado et al. 2000), Praesepe (Michel et al. 1999), NGC 6134 (Frandsen et al. 1996), NGC 7062 (Freyhammer et al. 2001) and NGC 1817 (Arentoft et al. 2005). However, there are many others known (see Rodr´ıguez 2002). γ Doradus stars. Some γ Doradus candidates are known in Galactic open clusters (Krisciunas & Patten 1999; Sterken et al. 2002; Mart´ın et al. 2003; Mart´ın 2004), but to confirm their status, additional information like the MK spectral types are necessary. This is because some other types of variability can mimic γ Doradus star, especially when only a single periodicity is detected. Moreover, at the lower parts of the colour-magnitude diagrams of studied clusters, where γ Doradus candidates are likely to occur, the contamination by foreground and background stars is usually large. For this reason, independent confirmation of the membership, preferably from proper motion studies, is highly desirable. 3.4.

Old open clusters

In the old open clusters, stars that could pulsate as δ Scuti or γ Doradus stars already evolved off the main sequence leaving the instability strip, and the only pulsators that could be expected in such the clusters are located in the giant branch. One can say that solar-like oscillations could be observed as well. In principle, this is true, but these stars are, at present, undetectable. The reason is the following. The variability searches are usually optimised for brightest stars in a cluster, so that variations in stars which are intrinsically faint and have very small amplitudes will not be detected. This is not only the question of the accuracy of the photometry, but also the temporal resolution of the observations. The same effects, at least nowadays, do not allow to detect pulsating white dwarfs and subdwarfs in globular clusters. This, however, will surely be possible in the future. 3.5.

Globular clusters

Globular clusters have a very well defined variability contents that includes several types of pulsators. A very good summary of this contents has been given a few years ago by Clement et al. (2001). The most abundant type of pulsators in clusters are RR Lyrae stars: they constitute more than 2/3 of all variable stars known in globular clusters. For this reason, they were in the past called ‘cluster variables’. RR Lyrae stars populate horizontal branch and are very useful in the studies of metallicity and age differences between globular clusters. They are also used as distance indicators, at least for globular clusters, satellite dwarf galaxies and Magellanic Clouds.

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The second group of pulsators observed in globular clusters are population II Cepheids which enter the main instability strip when they are making loops during the asymptotic giant branch evolution. Those with periods shorter than ∼10 days are called BL Herculis stars (e.g., Kopacki et al. 2003), but anomalous Cepheids and RV Tauri stars are observed as well. The third well-defined group of pulsators in globular clusters is formed by SX Phœnicis stars, which are Population II counterparts of the high-amplitude δ Scuti stars. They locate above the turn-off point of globular clusters, in the blue straggler region. Thus, the most convenient explanation of this location is that they are stellar mergers. Clement et al. (2001) listed 117 SX Phe stars in globular clusters, but this number is growing rapidly due to the searches devoted to the study of these stars and the application of new methods of analysis (Jeon et al. 2003, 2004; Olech et al. 2005; Kopacki 2005). Finally, globular clusters contain long-period variables. They populate the tip of the red giant branch. Typically, they show semi-regular variability (e.g., Frogel & Whitelock 1998). 4.

Final Remarks

We hope that this short overview illustrates that the study of these objects in binaries and clusters is very important and fruitful. However, we still need much better statistics for these stars, so that the searches should be continued. Fortunately, there are data at hand, as the huge photometric searches provided and will provide excellent photometric time-series for millions of stars. Moreover, there are many opportunities to obtain new photometry, because a small telescope equipped with a CCD camera is sufficient to do this work. Next, the large databases of archival data can be reanalysed with the new methods that were developed during the last years. The scientific perspectives for the astrophysics of variable stars seem therefore very promising. Acknowledgments. P03D 016 27.

This work was supported by the MNiI grant No. 1

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