The characteristics of the RR Lyrae stars in the Magellanic Clouds are discussed. The existence of numerous RR Lyrae variables in the Large Magellanic Cloud (LMC) cluster NGC 1835 is noted. The variables indicate that this cluster is of Oosterhoff type I. No cluster of Oosterhoff type II has yet been recognized in the Clouds. Some new results of a study of the RRLyrae variables in an LMC field 1° x 1.°3 are discussed. Periods have been determined for 50 out of 72 probable RR lyraes in this field. RR Lyrae ab stars with periods less than 0.d46 are absent. The time averaged and are 19.m56 and 19.m20 with surprisingly small dispersion. First impressions of results for a similar field in the Small Magellanic Cloud (SMC) suggest that the old stellar population of the SMC may have a slightly lower metal abundance than that of the LMC. The best available distance moduli for the Magellanic Clouds indicate a mean absolute visual magnitude M of +0.m5 ±0.2 for the RR Lyrae stars in these systems.

There are up to 14 known Mira variables in seven globular clusters, though several have not yet been confirmed as radial velocity members. The periods of only 5 are known, all near 200 days. The clusters seem to form a compact group of relatively metal rich clusters. In 3 or 4 cases spectroscopy shows that the giant branches of these clusters penetrate into the M types. The Mira-containing clusters also contain red variables of shorter period and smaller amplitude which are generally also M type stars. Stars apparently evolve to the red of the giant tip as variables of increasing amplitude and period. Effects of TiO blanketing on the (B — V) colours may be anticipated in these clusters.

Besides variables at the red giant tip the metal poor globular cluster ω Cen contains variables with strong TiO bands. Photometry, including recent J, H, K, L photometry by Glass shows that these stars are very cool objects. They indicate an extension of the giant branch considerably cooler than previously considered for metal poor clusters.

V1, NGC 121 in the Small Magellanic Cloud has a spectrum indicative of an SRd variable. It is not yet clear whether galactic stars similar to this star exist or not.

Investigations in recent years have shown that there may be two mechanisms which place stars in the W Virginis instability region (Kraft, 1972). The variables with periods less than 8 days seem to be in the stage of ‘above horizontal branch’ evolution discussed by Strom et al. (1970). The longer period group apparently results when thermal instabilities in the helium burning shell of an asymptotic red giant branch star cause it to loop to the left in the HR diagram. This longer period group has been investigated by Schwarzschild and Härm (1970) and Mengel (1972). The present study has been undertaken to see if there are any notable differences between the period changes of variables belonging to the two groups.

Photographic B and V light curves are determined for six variables, with periods longer than one day, in and near NGC 1751, NGC 1953, and NGC 2121. New photoelectric sequences are used to calibrate the plates. The mean magnitudes and colours of these variables are similar to the magnitudes and colours of Classical Cepheids of the same period. The photometric properties of these variables are unlike Population II Cepheids in the Galaxy but are comparable to field Cepheids of the Large Magellanic Cloud.

The globular clusters contain sufficiently large numbers of stars to permit a systematic study of the intrinsically rare variable stars which lie near the tip of the red giant branch. The position of the smaller amplitude stars in the colour magnitude diagram is of particular interest. Eggen (1972) has published photoelectric observations of such stars in several globular clusters, most of intermediate or low metal abundance. The mean colour of 14 stars in 5 clusters is (V-IK) = 1.40, with a spread from 1.60 to 1.12 (or 0.75 if V8 in M22 is of this type) which Eggen regards as indicating a range of temperature. The red variable stars in the metal rich globular cluster 47 Tucanae are much redder and show a considerable range of colour.

Fourteen red variables in the southern globular clusters 47 Tuc, ω Cen, and NGC 362 have been observed on an eight-color system of narrow-band photometry in the near infrared. Temperatures are derived from blackbody fits to the calibrated fluxes, and spectral types are given for the M stars. The types observed for the three Mira variables in 47 Tuc range from M3.1 to M7.5; two small-range variables in the same cluster are later than M4. The variables in ω Cen are mostly earlier than K5, but spectra of types M3 and MO were also encountered among radial-velocity members. In both the metal-rich 47 Tuc and the metal-poor ω Cen, the relation between TiO band strength and temperature is approximately normal. Several of these stars fall well above or below the red giant branches of their clusters in diagrams of infrared magnitude against temperature. Comparisons are made with recent results obtained at Radcliffe Observatory on some of the same stars.

A study has been made of the variables in the Southern Hemisphere globular cluster NGC 6723, which is suspected of being relatively metal-rich on the basis of its colour-magnitude diagram and of its integrated spectral type of G3. Seven new RR Lyrae stars and two bright red, probably semiregular, variables have been found and the suspected variable of Fourcade and Laborde has been confirmed. The complement of RR Lyrae stars is now 27, consisting of 4 c-type and 23 ab-type variables, the mean periods being Pc = 0.d292 and Pab = 0.d537. On the basis of the two-colour diagram of the horizontal branch stars the cluster is considered to be virtually un-reddened. Applying Christy’s models to the data from this study we find the following parameters for the variables: Mv= 1.m10, mass = 0.42 M⊙, and Y=0.4.

The period-luminosity relation for Cepheids in globular clusters has been investigated many times (e.g. Fernie, 1964; Kwee, 1968; Frolov, 1970; Demers, 1971).

The method of determination of the apparent distance moduli was recently revised by Kukarkin and Russev (1972). Instead of using a single absolute magnitude for RR Lyrae variables, the magnitudes according to pulsation theory (Christy, 1966, 1971) were adopted. The inhomogeneity of the absolute magnitudes of the RR Lyrae variables had already been established long ago (Pavlovskaya, 1953), but it attracted attention only recently. The different methods for determining the distance moduli of globular clusters were calibrated according to the new absolute magnitudes of the RR Lyrae variables. The problem consisted in the determination of the absolute magnitudes of the Cepheids in globular clusters according to the apparent distance moduli.

Traditionally, cluster variables have been used as distance indicators and have in this sense played an important role in our understanding of stellar evolution. In particular, the determination of the distance moduli of globular clusters and of the absolute magnitude of the main sequence turnoff, thus yielding the ages of the cluster, have relied heavily in the past on observations of RR Lyrae stars.

The observational evidence leading to the classification, following Oosterhoff, of globular clusters containing RR Lyrae stars into two distinct groups, is summarized and discussed in the light of results of stellar evolution theory and pulsation theory. The dichotomy is caused, at least in part, by a dichotomy in the ‘transition period’ between the type-ab and type-c stars which reflects a difference in effective temperature at the transition point. When this difference is accounted for, there remains a smaller average difference between the groups, though no longer a clear dichotomy, that is probably a mass and luminosity effect. If this remaining difference is interpreted as a luminosity effect the average difference in luminosity between the two Oosterhoff groups is at most 0.1 mag. It is suggested that Christy’s theoretical relationship between transition period and luminosity cannot be valid, at least not for clusters of different Oosterhoff groups. It is conjectured that the transition-temperature dichotomy may be a reflection of different predominant directions of evolution along the horizontal branch, accompanied by a hysteresis effect in the pulsations.

The differences in observational parameters of the RR Lyrae variables and horizontal branch stars of globular clusters and other population II systems are considered. A discontinuous behaviour of some parameters is outlined. The Oosterhoff dichotomy and the HB morphology are discussed with regard to a conjecture of mass loss in the pre-HB phase.

The separation of RRab variables into two sequences on the amplitude-period diagram was found by Belserene (1954) for globular cluster variables, and by Detre (1965) for field variables. It is significant that the sequence of short period variables is steeper on this diagram than that for stars of longer period. Szeidl (1965) pointed out that other characteristics of the light curves and photometric quantities such as the asymmetry of light curve ε, mean color index B—V, median magnitude mmed, maximum magnitude mmax are also separated into distinct sequences. Figures 1, 2 and 3 show these sequences on the colour-magnitude, colour-period, period-amplitude (or period-maximum magnitude, minimum magnitude) diagrams for RRab variables in the globular clusters M3, ω Cen and in the dwarf galaxy in Draco. On these figures RRab variables of the long period sequence are marked by crosses. The colour-magnitude and colour-period diagrams for M3 were obtained by Roberts and Sandage (1955); the period-maximum magnitude, minimum magnitude diagram obtained by Szeidl (1965) is constructed for stars measured by Roberts and Sandage. To get the most accurate F-magnitudes and colour indices for variables in ω Cen the data of Dickens and Saunders (1965) and Geyer and Szeidl (1970) have been averaged. The diagrams for RR Lyr variables in the Draco system were obtained by Baade and Swope (1961). The variables which show the Blazhko effect were excluded.

Schwarzschild and Härm (1970, hereafter abbreviated SH) have suggested that the presence of Cepheids in globular clusters can be explained by the occurrence of ‘flashes’ in the thermally unstable helium-burning shells of post-horizontal-branch, or ‘asymptotic-branch’ stars. These flashes in the deep interior of the star produce large changes in the energy flux at the base of the envelope, which in turn cause the position of the model in the Mbol — logTe diagram to move. For most values of the total stellar mass and envelope composition studied by SH, the models simply moved up and down the asymptotic branch in response to a helium shell flash. However in a few cases, characterized by low total mass and a relatively high value of the envelope helium abundance, the models left the asymptotic branch and described loops extending into the region of pulsational instability. The Cepheids of Population II were thus tentatively identified by SH as asymptotic-branch stars that had recently undergone a helium shell flash and whose tracks were as a result describing a loop extending into the instability strip.

Theoretical computations (Hoyle and Schwarzschild, 1955; Faulkner, 1966; Iben and Rood, 1970; Demarque and Mengel, 1971a, b) have identified the horizontal-branch stars in globular clusters with the evolution phase in which helium burns within a convective core and hydrogen burns in a shell outside the convective core. Most computations for such double-energy-source models have indicated that the evolution proceeds smoothly on a nuclear time scale during the horizontal-branch phase, leading to small predicted rates of change in the RR Lyrae pulsation period (Iben and Rood, 1970). Sweigart and Demarque (1972) have recently considered the effects of semiconvection on the horizontal-branch evolution of typical Population II stars and have suggested that changes in the composition distribution within the core may occur on a time scale considerably shorter than the nuclear time scale during the phase immediately preceding core-helium exhaustion. It has been found that the composition distribution generated by the growth of a semiconvective zone in the layers surrounding the convective core can become unstable when Yc, the helium abundance within the convective core, decreases below roughly 0.12. The changes in the internal structure caused by this instability result in relatively rapid movement of the models in the HR diagram and consequently produce large predicted rates of change in the RR Lyrae pulsation period. The possibility that RR Lyrae period changes may be associated with the behavior of the semiconvective zone has been previously suggested by Schwarzschild (1970). A similar instability may occur in the late core-hydrogen burning phase for stars around 10 M⊙. Percy (1970) has noted the coincidence of β Cephei stars with stellar models containing semiconvective zones. It is tempting to suggest that such an instability in the semiconvective zone could also be related to the β Cephei phenomenon.

The helium abundance Y in the envelopes of RR Lyrae stars in globular clusters has been estimated. The values of Y range from 0.07 to 0.59. The properties of variable stars in globular clusters of two types distinguished by a type of dependence of the horizontal branch form on the chemical composition are compared. The clusters of type I are shown to be on the average poorer in RR Lyrae stars than those of type II. The RR Lyrae stars in type I clusters are on the average brighter by 0.1 mag. It is found that as Y increases, the cluster richness in W Virginis variables decreases.