In the two centuries since the discovery of δ Cephei and η Aquilae, the study of Cepheids, and of pulsating stars in general, has become a very important field in astronomy. The usefulness of Cepheids, both as distance indicators and as test objects for stellar astrophysics, has been amply demonstrated, and if one just looks at the flood of papers on Cepheids that appears each year, it is clear that the subject is not only old and respectable, but also still very much alive. This twohundredth anniversary is therefore an appropriate occasion to evaluate what we have learnt about Cepheids, and where the remaining problems lie.

Recent observations of double-mode Cepheids and proposed candidates are reviewed. It appears that the change of modal content reported in some stars may not be real. Observations show that the double-mode Cepheids are indistinguishable from normal Cepheids of similar period. This poses a severe problem for pulsation theory which predicts very low masses from the ratio of first overtone to fundamental period. Attempts to resolve this problem and the problem of modal selection are discussed.

A number of previous studies of the relation between observed colors and temperatures of Cephelds have been done (Kraft 1961; Johnson 1966; Parsons 1971; Bohm-Vitense 1972; Schmidt 1972; Pel 1978). It was the discrepancies between these various temperature scales, especially at the cooler end, that led us to undertake the present recalibration. We felt some improvement on the previous work would result from our access to better scan data, reddening information, and model atmospheres. The results presented here are preliminary, as they represent only a sample of the data we have obtained.

Approximately 2000 radial velocities of 88 classical Cepheids have been observed using a photoelectric radial velocity meter. During the same time interval, these same Cepheids were intensively observed in the BVRI bandpasses, as reported elsewhere in these proceedings. This provides a homogeneous set of phase-locked radial velocity and photometric data which are useful in several contexts. We present here a sample of these results which will be published in their entirety elsewhere.

From November, 1981 to March, 1982, nine Pop I and Pop II cepheids of periods between 1.5 and 4.2 days have been monitored, in Geneva photometry from La Silla Observatory (Chile) and in radial velocities from the Haute-Provence Observatory (France). These cepheids are listed in Table 1. Figure 1 shows an example of the light, colour and velocity curves for EU Tau, a small amplitude cepheid with a period of 2.10 days.

Recently Gieren (1984) has derived accurate radii and distances of a sample of short-period classical Cepheids using the surface brightness (SB) method introduced by Barnes & Evans (1976). The results indicated that the period-radius (P-R) relationship obtained from SB radii might possess a slope close to the value of 0.82 defined by the Cepheids in clusters and associations (Fernie, 1983) and in conflict with the values obtained from Baade-Wesselink radii and from theoretical models (see Fernie, 1983). Since this finding would lend considerable support to the presently accepted absolute magnitudes of the cluster Cepheids, it was decided to obtain SB radii and distances of well-observed long-period Cepheids in order to strengthen the P-R relationship obtained from the SB technique.

The CORS method for the empirical determination of the radii of pulsating variables (Caccin et al., 1981; Sollazzo et al., 1981) is discussed in the framework of the quasistatlc approximation to the variations of the atmospheric parameters (Unno, 1965) and reformulated in a way that does not make direct use of theoretical calibrations of the photometric system in terms of model atmospheres. The radii calculated with this approach are in good agreement with those previously obtained by means of Pel's calibrations of the VBLUW system (Sollazzo et al.,1981) which lead to a period-radius relation coinciding, within the errors, with the theoretical one (Cogan, 1978) and, consequently, mass determinations consistent with pulsational masses (Cox, 1979). The method can be immediately applied to any other multicolour system, and very promising preliminary results are obtained by using recent UBV data by Gieren (1982).

The radii of Galactic Cepheids as determined from a version of the Baade-Wesselink technique are shown to depend upon the colour index used to define the temperature scale. The (V-l) radii are systematically larger than the commonly used (B-V) radii and are probably better estimators of the true radii. There still remains a problem, however, in reconciling the period-radius relation with the period-luminosity-colour relation.

We have determined radii for Cepheids using nearinfrared K(2.2 µm) photometry and Balona’s approach to the Baade-Wesselink method of radius determination. The lower sensitivity of the K flux to temperature variations results in improved sensitivity to radius changes. We present the results of maximum-likelihood radius solutions for Cepheids with modern radial velocity curves. We point out limitations of the Balona technique as it is currently applied in the optical and suggest improvements.

We have used new BVRI photometry and radial velocities of a selection of bright classical Cepheids to determine their distances and radii through the surface brightness method. The improved photometry permitted, through the visual surface brightness relation, high-quality angular-diameter values for each Cepheid throughout its pulsation. The simultaneous radial velocities permitted the linear displacement curve to be phase-locked to the angular diameter variation. The results are individual distances and radii with considerably smaller uncertainty than could be obtained previously.

The BVRI light-curve parameters of 112 galactic Cepheids are determined by Fourier analysis using over 4,000 differential photoelectric observations. This catalog is similar to Schaltenbrand and Tammann's except that it is based on a homogeneous data set and the Fourier coefficients are given.

Infrared photometry enables radii, and hence absolute magnitudes, to be derived more accurately than is possible using purely optical photometry. In this paper we present BVJHK observations of the galactic cepheids T Vul, U Vul and T Mon. Using this data we find reasonable agreement with current versions of the Period-Luminosity relations, in both the optical and infrared.

From these relations and existing optical and infrared data for LMC Cepheids we find for the LMC (i) Av = 0.35 and (ii) a distance modulus of 18.50. In addition we show that the P-L-C relation has the form

<Mv> = – 3.10 log P + 1.70 (<B>–<V>) – 2.37

The question of apparent mass anomalies in classical cepheids was first brought up by Christy (1968) and Stobie (1969), but 15 years later there is still no definite picture concerning the reality and the possible cause of these mass anomalies. The masses obtained from application of standard evolutionary theory were always sensibly larger than the masses derived from pulsation theory using both linear and nonlinear codes. Since for various reasons few people have accepted the idea that mass loss could play an important role in cepheids a number of elaborate scenarios have been proposed to account for the mass discrepancies. Among these are helium enriched outer layers and tangled magnetic fields. It is difficult, however, to see how significant mass loss can be avoided during the evolution of the more massive cepheids. In fact, practically all supergiants lose mass over the whole HR diagram, a process frequently manifesting itself in photometric microvariability. Little hope can be placed in attempts to solve the problem by means of improved determinations of the physical parameters of cepheids; intrinsic colours, luminosities, radii, effective temperatures, and the width of the instability strip have been disputed for years with no definite results yet. Only independent observational evidence will make it possible to confirm - or reject - the mass anomalies. On account of the large number observed and because of the fairly complete sample they represent, the cepheids in the LMC, SMC and in our Galaxy are best suited for this kind of investigation.

The period is an ideal parameter for monitoring minute changes in the structure of a star passing through the instability strip, as it can be measured with an accuracy of up to one part per million. The view of Parenago (1956) that only abrupt period changes occur in cepheids is no longer prevalent, and it is generally accepted that random period changes are superposed on the secular variation due to evolution. One possible mechanism for the random fluctuations in period or phase is convection or semiconvection, which Sweigert & Renzini (1979) showed could account for the period changes of RR Lyrae stars. Other mechanisms include the influence of binary companions and mass loss. The latter mechanism forms the basis for a separate study involving the use of IUE spectra to search for evidence of matter being ejected from cepheids.

The rate of binaries among cepheid stars is 25 - 35% (Burki, 1984a), a value which is in agreement with the rate among F-M supergiants (31-38%) obtained by Burki and Mayor (1983) from a radial velocity survey.

For binary cepheids, the Wesselink radius RW is affected by the light of the companion. Balona (1977) found that RW is too small if the companion is a blue main sequence star and too large if it is a red giant star. This effect has been quantitatively examined by Burki (1984a). For example, it was found that, in the case of a cepheid of period P = 32d with a companion fainter by 2 mag., RW is 70% of its correct value if we are dealing with a main sequence companion and 130% in the case of a companion redder by 0.6 in B-V. The bias on RW becomes negligible when the companion is fainter than the cepheid by more than 4 mag.

Cepheid variables in binaries are important from various points of view. These objects can in some cases provide direct information about the physical parameters of the system, can be used as tracers of stellar evolution, and the effect of the companions may influence the form of various relations (e.g. P-L-C, P-R) derived for Cepheids. While the first two advantages mentioned concern individual stars, the third involves the question of the frequency of binaries among the Cepheids. Systematic searches for binaries containing this kind of variable resulted in increasingly higher frequency of incidence: 2% (Abt 1959), 15% (Lloyd Evans 1968), >20% (Madore 1977), 25% (Pel 1978), 20%-40% (DeYoreo & Karp 1979), 35% (Madore & Fernie 1980). It was only in the early eighties that this trend ceased. The recent determinations of the incidence of binaries among the Cepheids are: 20%-40% (Gieren 1982), 18% (lower limit, Lloyd Evans 1982), 25% (Russo 1982), 25%-35% (Burki 1984). At the same time we have been going over to a qualitative era from the quantitative one, i.e. very thorough studies are now available on some individual cases of binary Cepheids (e.g. McNamara & Feltz 1981; Coulson 1983; Evans 1983; Bohm-Vitense et al. 1984).

A survey of 24 classical Cepheids has been made to search for blue companions using the Call H and K lines. It is shown that this technique can detect an early A companion for a typical Cepheid. A blue companion of SU Cas was discovered and upper limits for the companions for a number of previously suspected binaries were established.

The radial velocities of 89 Herculis (89 Her) between 1977 and 1981 show a clear periodicity of about 285 days. This periodic variation is interpreted as the orbital variation of 89 Her around an unseen companion. From the orbital elements no support is found for a low mass (M ~ 2Mʘ ) for 89 Her, but rather a high mass (13 < M/Mʘ < 24) is preferred.

The question of whether non-Cepheids populate the cepheid instability strip has been the subject of much recent interest. Several investigators (see especially Fernie and Hube 1971 and Fernie 1976) have concluded that indeed there are an appreciable number of objects not presently recognized as Cepheids within the strip, though both the size and position of the strip and the placement of supergiants in the H-R diagram are subject to considerable uncertainty. In view of the interest in this matter, I have attempted to shed some light on this situation by simply considering the nature of the stars spectroscopically classified as of high luminosity in spectral classes F and G. For this one needs, of course, a complete sample of the relevant stars, which fortunately is now to some extent available.