Recent general observations pertaining to the masses and pulsation modes of classical Cepheids are reviewed. Certain special ones of these variables that display unusual behavior such as long term amplitude variations, overtone pulsations, and double-mode behavior, including one Cepheid in the first and second overtones as well as those in the fundamental and first overtone, are discussed in some detail. I suggest that the amplitude varying supergiant Cepheid HR 7308, which seems to be pulsating in the second radial overtone, is alternating between states where there is enough helium to barely give kappa and gamma effect driving, and where the helium has settled too deep for this driving. Reestablishment of the helium may be due to rapid levitation of the CNONe elements which cause convection and which then dredge-up the helium again to suppress the convection and also to drive pulsations. The use of Fourier fitting to the light and velocity curves have revealed some features that are interesting and are discussed, such as the pulsation mode discrimination and the derivation of accurate Wesselink radii. The seven methods of determining the masses of these stars are presented with a short critique of each. Evolution and pulsation masses depend on uncertain observed luminosities, and these have been revised recently. Evolution masses also depend on the blue looping yellow giant evolution tracks that may need revision because of convective core overshooting and possible opacity, Z, or Y abundance increases. The most discrepant masses, however, are those that depend on period ratios – the “bump” and “beat” masses. The possibility that the Cepheid internal structure can be modified enough by doubling the material opacity seems unlikely. It is suggested, though, that perhaps the period ratio mass anomaly solution can be found in CNONe element enhancement by radiation absorption levitation that would give higher opacities by abundance effects instead of any revisions in the opacity calculations. Some details for this mass anomaly “solution” are presented.

The main properties of the evolution of low, intermediate, and high mass stars are reviewed focusing on a few issues tightly related to the interpretation of Pop I Cepheid stars. After a summary discussion of the physical mechanism responsible for the Cepheid pulsation, the classical results of stellar evolution theory for the main evolutionary phases (main sequence, core He-burning, and later) all over the HR diagram are presented, putting into evidence the various points of disagreement with current observational data. We then review the models incorporating the effect of convective overshoot, and present in some detail a study on the rich, young cluster NGC 1866 in the Large Magellanic Cloud, in which they are compared with the observational data. Arguments are given to favour the adoption of models with convective overshoot instead of the classical ones. The topics of the mass discrepancy and frequency-period distribution of Cepheid stars are then discussed in the light of models with convective overshoot, showing how they can better account for the observational data. Finally, we address the question of the enhancement in the radiative opacity of heavy elements in the middle temperature region (approximately where the ultimate ionization of the CNO group of elements occurs), which has been suggested to explain the mass anomalies and period ratios encountered in double-mode and bump Cepheids. Evolutionary models for intermediate mass stars incorporating the above modification in the radiative opacity are then presented and discussed in some detail.

A brief description is given of a large international project for computing new stellar envelope opacities and equation of state data.

Mass loss at rates sufficient to alter the evolution of stars is known to occur during the pre-main sequence evolution of most stars, on the main sequence for massive stars, and during advanced evolutionary phases when the luminosity is high and the effective temperature is low. While most investigations of the effects of mass loss on stellar evolution have assumed continuous (parametrized) mass loss laws apply, there is increasing evidence that mass loss rates are substantially higher for stars that are pulsating with large amplitude and/or in selected modes. Some new insights into the mass loss that terminates the AGB evolution of intermediate mass stars, and leads to the formation of planetary nebulae, come from recent detailed studies of the mass loss process from the Mira variables.

The combination of chemical abundance, kinematic, and age data for stars near the sun provides important information about the early evolution of the Galaxy. We review available data, with some new analysis, to show that the sum of all available information strongly suggests that the extreme population II subdwarf system formed during a period of rapid collapse of the proto-Galaxy. This subdwarf system now forms a flattened, pressure-supported distribution, with axial ratio ∼2:1. The thick disk formed subsequent to the subdwarf system. At least the metal-poor tail of the thick disk is comparable in age to the globular cluster system. The thick disk is probably kinematically discrete from the Galactic old disk, though the data remain inadequate for robust conclusions.

In 1973 the outstanding problems confronting the theory of horizontal branch evolution were the “second parameter” problem and the Oosterhoff Effect. Despite significant progress, particularly in the observations and in the observation/theory interface, they remain as the outstanding problems of 1988. The Oosterhoff Effect is now discussed primarily in the guise of the Sandage Period Shift Effect. The morphology of the HB seems more complicated than ever. E.g., many clusters show bimodal distributions along the HB. Here we will tentatively consider those to be manifestations of the second parameter problem. We will indicate why we feel that all previously suggested solutions have all been chimeras.

It is shown that the intrinsic spread in the absolute magnitudes of the RR Lyrae variables in a given globular cluster can reach 0.5 magnitudes at a given period or at a given color, due to luminosity evolution away from the zero age horizontal (ZAHB). The size of this intrinsic luminosity spread is largest in clusters of the highest metallicity.

The absolute magnitude of the ZAHB itself also differs from cluster to cluster as a function of metallicity, being brightest in clusters of the lowest metallicity. Three independent methods of calibrating the ZAHB RR Lyrae luminosities each show a strong variation of MV(RR) with [Fe/H]. The pulsation equation of P<ρ>0.5 = Q(M,Te, L) used with the observed periods, temperatures, and masses of field and of cluster RR Lyraes gives the very steep luminosity-metallicity dependence of dMv(RR)/d[Fe/H] = 0.42. Main sequence fitting of the color-magnitude diagrams of clusters which have modern main-sequence photometry gives a confirming steep slope of 0.39. A summary of Baade-Wesselink MV(RR) values for field stars determined in four independent recent studies also shows a luminosity-metallicity dependence, but less steep with a slope of dMV(RR)/d[Fe/H] = 0.21.

Observations show that the magnitude difference between the main sequence turn-off point and the ZAHB in a number of well observed globular clusters is independent of [Fe/H], and has a stable value of dV = 3.54 with a disperion of only 0.1 magnitudes. Using this fact, the absolute magnitude of the main sequence turn-off is determined in any given globular cluster from the observed apparent magnitude of the ZAHB by adopting any particular MV(RR) = f([Fe/H]) calibration.

Ages of the clusters are shown to vary with [Fe/H] by amounts that depend upon the slopes of the MV(RR) = f([Fe/H]) calibrations. The calibrations show that there would be a steep dependence of the age on [Fe/H] if MV(RR) does not depend on [Fe/H]. No dependence of age on metallicity exists if the RR Lyrae luminosities depend on [Fe/H] as dMV(RR)/d[Fe/H] = 0.37. If Oxygen is not enhanced as [Fe/H] decreases, the absolute average age of the globular cluster system is 16 Gyr, independent of [Fe/H], using the steep MV(RR)/[Fe/H] calibration that is favored. If Oxygen is enhanced by [O/Fe] = – 0.14 [Fe/H] + 0.40 for [Fe/H] < –1.0, as suggested from the observations of field subdwarfs, then the age of the globular cluster system decreases to 13 Gyr, again independent of [Fe/H], if the RR Lyrae ZAHB luminosities have a metallicity dependence of dMV(RR)/d[Fe/H] = 0.37.

The significance of some of the unusual characteristics of the globular cluster ω Centauri in various fundamental problems is explored. Interest is centred on the properties of the cluster RR Lyraes, and what they can contribute to studies of early cluster chemical enrichment, stellar pulsation, the distance scale, stellar evolution, stellar ages and the Oosterhoff period-shift problem. This article, which is intended to highlight problems and progress rather than give a comprehensive review, includes new results based on photometry of the RR Lyraes, red giants, subgiants, horizontal-branch and main sequence stars in the cluster.

For three quarters of a century pulsating variable stars have lain at the foundation of the extragalactic distance scale. The construction of larger telescopes, advances in detector technology, hard work by observers, and our understanding of stellar structure have all contributed to the expansion of the realm of the Cepheids to the distance of M101. Now, with the advent of Hubble Space Telescope (HST), we can look forward to the detection of Cepheids in the Virgo cluster and the removal of much of the remaining uncertainty in the Hubble constant.

A program is underway to obtain accurate, well sampled light curves for Cepheids in several Local Group galaxies. We have succeeded in attaining accuracies adequate for light curve analysis for stars with periods as short as about 12 days. Photometry for six known Cepheids in NGC 6822 is discussed. Although better sampling in phase is needed to allow full light curve analysis, a Fourier decomposition was performed for one star and it appears to show some differences from galactic Cepheids. A preliminary comparison of some of the gross properties of the light curves with galactic Cepheids shows both similarities and interesting differences.

The historical foundations of the Baade-Wesselink (BW) method were established through the work of Baade (1926), Becker (1940), and Wesselink (1947). All modern versions of the BW-method are constructed upon these foundations. Since the radii of pulsating stars are fundamental to many areas of astronomical research (theories of stellar structure and evolution, galactic structure, and the cosmic distance scale), it is paramount that we strive to improve their observational determination. At the present time, the BW-technique is the only “direct” method for determining the radii of pulsating stars. Until a new technique is devised, better determinations of this important physical parameter will only occur through improvements in the BW-method.

The Mira variables make important contributions to four of the main problems under discussion at this meeting, (1) stellar pulsation, (2) stellar evolution, (3) the morphology and history of the Galaxy, (4) the comparative study of different galaxies. The Miras also show how these rather different fields of study overlap, so that it is no longer possible to deal with any one field in isolation.

Recent studies of anomalous Cepheids (ACs) and Pop II blue stragglers (BSs), including photometrically variable BSs (VBSs), are reviewed. The VBSs represent about 25% of the BSs, the majority of which are SX Phe short-period variables in the Cepheid instability strip. Mass estimates derived using various techniques suggest that both ACs and BSs are relatively massive (about 1.0–1.6 Me). The recent discovery that two BSs in the globular cluster NGC 5466 are contact binaries, and the earlier discovery that one of the BSs in ω Cen is an eclipsing binary, provide direct evidence that at least some BSs are binary systems. If all BSs are binaries, and the time scale for coalescence is a few Gyr, then the majority are likely to be coalesced. Because ACs and BSs are found in the same stellar systems, and are probably related through their evolution, it is highly likely that most ACs are also coalesced binary systems. The fact that ACs and BSs are found only in low density environments, suggests that they were primordial binaries.

We investigate the cause of the transition from limit cycles to chaotic oscillations in pulsation of less-massive supergiant stars. For this purpose, we examine one of the models which has a limit cycle but is very close to the transition to the type I intermittency (Aikawa 1988, Astrophys. & Space Sci., 139, 214). It is shown that the pulsational driving by the hydrogen ionization with the M type ionization front, which becomes very effective at amplitudes beyond the limit cycle, is responsible for the existence of another unstable fixed point beyond the limit cycle (see Aikawa, 1988, in press Astrophys. & Space Sci.) A merging process of these two fixed points makes the transition.

The basic physical properties of double mode Cepheids and double mode δ Scuti stars are still highly controversial. Based on results of very recent opacity calculations a detailed consistent, possible solution of the problem of the nature of double mode variable stars has been developed. Extensive studies have been performed to establish the rules governing the morphology of the period ratio diagrams. An ideal reproduction of the period ratio data for both stellar types are obtained assuming an increase of the Cox-Steward opacity by a factor of about 2.5 in the temperature range from 1.5 X 105K to 8.0 X 105K. Consequences for the mass calibration of Petersen diagrams are evaluated.

Among the δ Scuti stars with large amplitude there are a few stars with unusual light curve shape and multiperiodicity. These stars are V1719 Cyg, V798 Cyg, V974 Oph and δ Scuti. The Fourier phase difference for the main pulsation mode is very different from that typical of the other large amplitude δ Scuti, SX Phe and RR Lyrae stars. The period ratio is generally high, ≧0.80. Two of the stars (δ Scuti and V1719 Cyg) have known spectral type or Stromgren indices, and these indicate high metallicity which should be related to the δ Delphini type (evolved Am/Fm stars). Some tests with the one-zone model show that the unusual light curve shape could be related to a poor He content in the envelope, while the application of model atmosphere grids shows that the anomalous behavior of the metallicity photometric index of V1719 Cyg is simply due to the high metal abundance of its atmosphere. The conclusion is that diffusion phenomena such as the He settling and the metal enhancement should be able to explain all the observed characteristics of these pulsating stars.

It is well known that the Baade-Wesselink method leads to different radii for Cepheids depending on which colors are used to determine the effective temperatures. We try to find the reasons for this discrepancy. We employ yet another version of this method using only maximum and minimum radii, thereby circumventing uncertainties in the phase relations between radial velocities and colors. This has essentially no influence on the derived radii. One major uncertainty is the relation between the photospheric expansion velocity and the measured radial velocity. The main reason for the discrepant results obtained by using different colors appears to be an inconsistency in the difference in the applied temperature-color calibrations. Small changes in the d(log Teff)/d(color) can cause major changes in the derived radii.

Multisite photoelectric b and V photometry of the δ Scuti variable θ2(78) Tau has been obtained on three continents. Five close pulsation frequencies (13.22965, 13.48073, 13.69360, 14.31764 and 14.61454 cycles per day) with visual amplitudes between 0.001 and 0.007 mag were found. The four frequencies found in the previous campaign were confirmed. All three main data sets (1982-1986) are in excellent agreement with each other and fit the solution to ±0.0028 mag per single measurement. Over the four years the amplitudes and frequencies of pulsation were constant.

We have studied the effects of a pulsationally-driven wind on Cepheid evolution. Mass loss due to the wind, which occurs only when the star is crossing the Cepheid instability strip, is a function of luminosity and radius. We have investigated the evolution of 4, 5, 6, 7 and 8 M⊙ stars using the updated 12C(α,γ) 16O rates.

Using optical and infrared photometry and echelle spectroscopy of variable V8 in the globular cluster M5, we derive a cluster distance of 6.8 kpc using the Baade-Wesselink method. This agrees with the prediction obtained for the cluster’s metallicity using a sample of 19 field stars studied by us and by Liu and Janes (this volume). It also agrees well with estimates for Mv obtained from statistical parallaxes of field stars. It agrees as well with the main sequence fitting procedure where we have used only HD 103095, the field halo dwarf with the most accurate trigonometric parallax (3% error), and which has a metallicity almost identical to that of M5. The star is also cool, hence unevolved, and is not a binary. Using the luminosity of the cluster’s main sequence, both Yale and Victoria isochrones yield a cluster age of 18 ± 3 Gyrs.