The Oosterhoff division of globular clusters into two dichotomous mean period groups is a result of the variation with metallicity of the combined effects of (1) a mean increase in period with decreasing metallicity, and (2) the change of globular cluster horizontal branch (HB) morphology from the M3 to the M13 HB type within the instability strip in the metallicity range of [Fe/H] between -1.7 and -1.9. A new representation of the Oosterhoff period effect showing this property is made from the individual cluster data in Figure 1. The relation between period and metallicity for cluster and for field RR Lyraes at the blue fundamental edge of the instability strip in the HR diagram as read from this figure is

log Pab = -0.122(±0.02)([Fe/H]) - 0.500(±0.01)

using the metallicity scale of Butler.

The high slope coefficient is consistent with the extant models of the HB when they are read at the varing temperature of the fundamental blue edge given by equation (3) of the text. Most of the current literature treats only the constant temperature condition, which is manifestly incorrect. It is this temperature effect that reconciles the observations and the models.

A new calibration of the absolute magnitudes of RR Lyrae stars as a function of metallicity, combined with new oxygen enhanced isochrones for globular clusters (Bergbusch & VandenBerg 1992) reduces the age of the Galactic globular cluster system to 14.1 ± 0.3 Gyr (internal error). The resulting lower age of the universe which, when combined with a Hubble constant near 50 km s-1 Mpc-1 determined from type I supernovae, shows that the cosmological expansion has been decelerated by an amount consistent with the closure density, permitting Ω ∼ 1 now from the timing test.

Recent work on the Magellanic Cloud RR Lyrae stars is reviewed. The absolute magnitudes of LMC RR Lyraes, when calibrated from a distance modulus of 18.5 mag, disagrees with the Galactic calibration. The revised distance scale makes distances greater, and ages younger, within our galaxy. Field star studies show that the “halo” population of the LMC is very similar to that of our own Galaxy outside of the solar circle. This result supports a Searle and Zinn model of galaxy formation.

The observational and theoretical basis for the log P vs. K-mag relation is reviewed. The observed gradient in all well observed globular clusters agrees well with the theoretical prediction. An indistinguishable result is found for field RR Lyrae stars whose absolute magnitudes have been determined from infrared Baade-Wesselink analyses. A full reference list is given for the source of these magnitudes. Application of the results to find the distance to globular clusters and the Galactic Centre is discussed.

We have carried out K band photometric observations of RR Lyrae stars in two globular clusters which both have large populations of RR Lyraes but different characteristics: the moderately metal-rich cluster M5 ([Fe/H] = –1.40) and the metal-poor one M15 ([Fe/H] = –2.15). The purpose is to accurately calibrate the linear relationship between RR Lyrae infrared (K) absolute magnitudes and their periods that has been confirmed by recent Baade-Wesselink type studies of RR Lyraes and IR photometry of cluster variables. A total of 47 RR Lyraes in M15 was observed and each has more than 8 measures on the average, which allows the accurate determination of a mean K magnitude for each star. In M5 44 stars have been observed with each RR Lyrae having 4 measurements. Our preliminary results show that the RR Lyrae infrared period-luminosity relations for the two clusters have roughly the same slope, despite the fact that they have a large metallicity difference. This suggests that the metallicity effect on the (MK)-log P relation is indeed small as one would expect. The M5 and M15 RR Lyrae IR photometry gives a reliable determination for the slope of the infrared period-luminosity relation because of the large number of stars measured. A well-calibrated (MK)-log P relation will be very useful in distance determinations to heavily reddened star regions such as the Galactic center and globular clusters in the Galactic bulge.

New period-luminosity-metallicity (P-L-[Fe/H]) relationships for Pop. II Cepheids, RR Lyrae stars, anomalous Cepheids and SX Phe (variable-blue straggler) stars are presented. These were computed by fitting regression lines to observed pulsation periods and mean B, V, K magnitudes for over 1200 stars in ∼40 stellar systems. The stars were assumed to be pulsating in either the fundamental (F) or first-overtone (H) modes (excluding double-mode and other multi-periodic variables). Eight P-L-[Fe/H] relationships (one for each of the two pulsation modes for the four kinds of stars) were simultaneously fitted for each filter. After accounting for the metal abundance differences, the slopes of the P-L relations were tested for departures from equality. The results are consistent with the assumption that, for each kind of star, the relations for the F and H stars are vertically offset, with a family of lines corresponding to the different metallicities. In the case of the globular cluster Cepheids, the available B, V data support Arp's 1955 contention that the Cepheids are oscillating in the F and H modes; moreover, the majority of the short-period Cepheids (BL Her stars) appear to be first-overtone pulsators, while most of the Cepheids with periods between 10 and 30 days (W Vir stars) appear to be fundamental-mode pulsators. For the RR Lyrae stars, the slopes of the P-L-[Fe/H] relations in B, V and K show a clear trend with filter type, namely, the absolute values of the slopes increase from B to K. Finally, for the SX Phe stars the differences between the P-L-[Fe/H] relations in B and V for the F and H stars are found to be consistent with the known period-ratio for the double-mode star SX Phe.

Observations with the Wide Field Camera on HST were examined, and 27 Cepheids were discovered. Photometry and period analysis have produced unambiguous light curves free of alias. The observed P-L relation has a slope consistent with seminal calibration studies of Galactic and LMC Cepheids. An apparent distance modulus (in V) of 28.47 ± 0.10 to IC 4182 is derived. This implies that Mv(max) for SNIa 1937C is -19.92 ± 0.2 mag, independent of everything except differential absorption between the Cepheids and the supernova. Using this to calibrate Hubble diagrams for SNIa by several authors, and allowing for a 1-σ uncertainty in the absolute magnitude from the calibration of only one SNIa, we obtain H0 = 45 ± 14kms-1Mpc-1.

In the course of the last decade significant advances have been made in the observations of Cepheid variables and in their successful application to the extragalactic distance scale. Much of this progress has come about as a result of new CCD and near-infrared photometry. These recent improvements are discussed, and a comparison is given of Population I Cepheids and Population II distances. The correspondence is good, with the zero points agreeing at a level of better than 15% in distance. At this same level of significance, a systematic difference between these distances scales may exist, in the sense that the RR Lyrae distances appear to be smaller than the Cepheid distances (if it is assumed, as has generally been done for extragalactic studies of RR Lyraes, that Mv(RR) = 0.77 mag, independent of [Fe/H]). However, several recently-published calibrations of Mv(RR) significantly reduce this discrepancy. Finally, new Cepheid data for the nearby galaxy M81 are presented based on recent Hubble Space Telescope observations.

The absolute calibration of the Cepheid period-luminosity (PL) relation with galactic Cepheids is discussed. Various methods, most importantly the cluster ZAMS-fitting scale and the Baade-Wesselink scale are found to yield PL zero points which agree within ∼ ± 0.1 mag. The present Cepheid calibration sets the Large Magellanic Cloud at μ0 (LMC) = 18.6 ± 0.1 mag, in good agreement with the distance derived from SN 1987A and other methods except RR Lyrae stars which seem to give a shorter distance scale.

We are currently undertaking a ground-based imaging survey which attempts to discover and determine periods for variable stars in Virgo Cluster galaxies. Such a survey is now feasible thanks to the high resolution imaging (FWHM ≤ 0.50 arcsec) routinely obtained with the High Resolution Camera on the Canada-France-Hawaii Telescope. The Virgo Cluster has long been considered a crucial “stepping-stone” in the extragalactic distance scale problem given that the cluster is at a “cosmologically interesting” distance and that there is little controversy in the relative distance between Virgo and more distant clusters, such as Coma. Consequently, much of the controversy regarding the extragalactic distance scale and the Hubble Constant can be eliminated with a determination of the Virgo Cluster distance. Some preliminary results and the prospects for establishing the distance to the Virgo Cluster using Cepheids and LPVs are discussed.

Current progress is described for an ongoing program to secure new observational data (star counts, photoelectric, photographic & CCD photometry, and spectroscopy) for stars in the large sample of potential Cepheid calibrating clusters and associations.

NGC 6822 was the first galaxy outside the Galaxy where the Cepheid period-luminosity relation was applied as a distance indicator (Hubble 1925, ApJ, 62, 409). Later, thirteen Cepheids in this galaxy were studied by Kayser (1967, AJ, 72, 134) using BV photographic photometry. We have obtained BVRI CCD photometry of stars in two 2.2' X 3.5' fields of NGC 6822. Field 3) using Figure 1 shows an I – (V – I) diagram of ∼ 6,400 measured stars in NGC 6822 including seven known Cepheids. The reddening is estimated to E(B – V) = 0.28 ± 0.03 from the (B – V)-(V – I) diagram of the stars with V < 20 mag. The distance to NGC 6822 has been estimated using the random-phase I band photometry of seven Cepheids (V7(I=16.31), V5(I=18.97), V6(I=18.44), V3(I=17.88), V1(I=18.05), V28(I=17.61), and V2(I=17.29)) combined with their periods given by Kayser.

WLM (DD0221) is a highly resolved dwarf irregular galaxy in the Local Group. Fifteen Cepheids in this galaxy have been studied by Sandage & Carlson (1985, AJ, 90, 1464) using photographic photometry. We have obtained BVRI CCD photometry of stars in the central area (2.2' x 3.5') of WLM. Figure 1 shows an I–(V – I) diagram of ∼ 2,600 measured stars including five known Cepheids. The distance to WLM has been estimated using the random-phase I band photometr y of five Cepheids (V7(I=20.52), V29(I=20.77), V48(I=20.43), V66(I=21.19), V67(I=21.14)) combined with their periods given by Sandage & Carlson. We have obtained Δ(m - M)II(WLM – LMC) = 6.25 ± 0.11 and (m - M)0 = 24.92 ± 0.21, adopting (m - M)o(LMC) = 18.5 and AI(WLM) = 0.04.

We present a new distance determination to the Small Magellanic Cloud from the surface brightness technique applied to the Cepheid variable HV 829. Although this is a preliminary distance based on only one star, it illustrates the power of the surface brightness technique to extragalactic Cepheid distances, it develops the technique which we will apply to additional SMC and LMC Cepheids, and the distance is of intrinsic interest because of the current controvery concerning distances for the Magellanic Clouds.

For HV 829 itself we obtain a distance modulus of 18.91 ± 0.20 mag. From other evidence we infer that HV 829 is slightly in front of the SMC centroid distance. Correcting to the SMC centroid yields a distance to the SMC of 19.05 ± 0.20 mag. We stress that this distance modulus is fully independent of any other distance modulus for the SMC, including those based upon Cepheids. Even so, our result agrees more closely with other, independent Cepheid distances than with RR Lyrae distances and main sequence fitting distances.

Hindsley and Bell (1989, Ap. J., 341, 1004) determined distances for 23 Cepheids using the surface brightness method. The color V – IC on the Cousins system or V – RJ on the Johnson system was used to measure visual surface brightness. Combined with the observed visual magnitudes, angular diameters were then calculated. Comparison of angular diameters with radius differences in linear units, obtained by integrating the radial velocity curve, yielded each Cepheid's distance.

Hindsley and Bell calibrated the relationship between color and surface brightness using model atmospheres. The zero point of the relationship was found using observations of Vega and an appropriate model. More recently the spectral scans of Gunn and Strycker (1983, Ap. J. Suppl., 52, 121) and the Cousins filter response curves of Hindsley and Bell were used to calculate colors and these were compared to the corresponding observed colors.

We investigate whether the currently available Galactic Cepheid kinematic data can put interesting constraints on large scale low amplitude non-axisymmetry of the Galactic plane rotation pattern. In this connection we address the experimental design problem of where in the Galactic plane additional Cepheids would prove the most useful for the axisymmetric and the non-axisymmetric modeling of the kinematics.

Supergiant Long-Period Variables (LPVs) are both more luminous and more common than Cepheids. The fact that a P – L relation exists at K (e.g. Wood et al. 1983 ApJ, 272, 99; Mould et al. 1990 ApJ, 349, 503) and not at visible wavelengths is usually attributed to the strong temperature sensitivity of TiO, which dominates the spectra of these stars in the visible. This has led us to apply a narrow bandpass (λ0 = 8250Å, BW = 350Å), avoiding TiO, in the hopes that an optical P – L relation can be found.

The data for Per OB1, the LMC, and M 33 are shown in figure 1. The small dispersion (σLMC = 0.22 mag.) and flat slope are evident. Combining the data we find:

(1)

with the absolute calibration from the ten LPVs in Per OBI, assuming m – M = 11.8±0.2 (Garmany & Stencel 1992 AAS, 94, 211).

Feast et al. (1989) obtained observationally a period-luminosity (P-L) relation of Mira variables in LMC. Basically, fundamental periods of stellar pulsation should be determined by two quantities —a mass and a radius of the star. The existence of a P-L relation implies a special condition that reduces a function of two variables into a function of only a single variable. Though the AGB appears as a thin line in the HR diagram like the Cepheid instability strip, it is an “asymptotically” merged line of evolutionary tracks of stars in a range of about 0.5-3 solar masses. This fact means that the masses of stars on a point of the AGB are not unique though the radii and the effective temperatures are unique, respectively. Therefore we cannot expect, in the case of AGB stars, that a period is reduced to a function of a single variable.