We demonstrate that the Oosterhoff II (Oo II) RR Lyrae ab variables are hotter by ~270 K, at the same period, than Oo I variables. Or, at the same (B– V)₀ value the Oo II variables have larger radii than Oo I variables. This accounts for the reason Oo II variables are brighter (0.12-0.20 mag) than Oo I variables. The dependence of the light amplitude of RR Lyrae variables on temperature is independent of Oo type. This makes it possible to derive an accurate set of equations to relate intrinsic (B – V)₀ color indices to light amplitudes, which in turn can be used to determine the interstellar reddening (E (B – V)). With just a few variables (~5), it is possible to determine the E (B – V) to an accuracy of <0.01 mag in the absence of systematic photometric errors. We discuss the errors introduced in color excess determinations by including the Blazhko stars in a solution. A comparison of color excess values of 23 globular clusters and two regions of the Large Magellanic Cloud (LMC), determined with the aid of our newly developed equations, are found to compare favorably (~0.01 mag) with color excess values found in the literature. Four new Oo III variables, some found in metal-poor clusters, are discussed. An analysis of the galactic-field variables indicates the majority are Oo I and Oo II variables, but a few short-period (log P < –0.36) metal-strong variables, so far not found in galactic globular clusters are evidently ~0.30 mag fainter than Oo I variables. Oo III variables may also be present in the field. We conclude that the RR Lyrae ab variables are primarily restricted to four sequences or groups. If we assume that the Oo I variables' mean absolute magnitude is Mv = 0.61, the mean absolute magnitudes of the other three sequences are: short-period variables Mv ~ 0.89 mag, Oo II Mv ~ 0.43 mag, and Oo III Mv ~ 0.29 mag. The Oo I fundamental RR Lyrae ab red edge (FRE) and fundamental blue edge (FBE) occur at approximately the following temperatures: FRE T ~ 6180 K and FBE T ~ 6750 K. There is a strong dependence of Mv on [Fe/H] as we proceed from the short-period variables to the Oo I variables and to the Oo II variables, but there seems to be little or no dependence of Mv on [Fe/H] for stars within a group, at least for the Oo I and Oo II groups. The Oo II variables exhibit a weak period luminosity relation in V in many globular clusters unlike the Oo II-like variables in Oo I clusters which do not exhibit a P-L relation. The properties of some intermediate LMC clusters are discussed.

The distances to four galaxies and two globular clusters which are derived with the aid of period-luminosity and period-color relations of delta Scuti and SX Phe stars are compared to the distances derived by other methods, in particular RR Lyrae stars. We examine the luminosities of horizontal branch or RR Lyrae stars in Oosterhoff I and II globular clusters. Observational data from a variety of sources indicate a discontinuous jump of similar to 0.2 mag in the luminosities of RR Lyrae variables at [Fe/H] approximate to -1.5 as we transition from Oosterhoff I to Oosterhoff II clusters. If Oosterhoff I clusters have RR Lyrae variables with average M-V values of M-V = 0.53 mag at [Fe/H] = -1.5, it implies that RR Lyrae stars in Oosterhoff II clusters average M-V values are similar to 0.34 mag. Unlike the Oosterhoff I clusters which show an increase in the V luminosity of RR Lyrae stars as [Fe/H] becomes smaller, little or no change in the V luminosity of RR Lyrae variables is evident in Oosterhoff II clusters in the interval of [Fe/H] from -1.5 to -2.2. We find distance moduli found with RR Lyrae variables agree to <= 0.04 mag with those found with the delta Scuti and/or SX Phe variables if the M-V values of RR Lyrae stars above are adopted. We find evidence of recent star formation (presence of near solar-metallicity delta Scuti stars with ages of 150 Myr to 1 Gyr) in the Large Magellanic Cloud (LMC), Small Magellanic Cloud, and the central region of the Fornax (dSph) galaxies. We also find an older population of metal-poor delta Scuti variables (SX Phe stars) in the LMC and Fornax galaxies. The Carina dSph is unique in that only an old population of metal-poor delta Scuti variables is evident. No evidence of recent delta Scuti star formation is found. The minimum periods observed for the SX Phe variables (blue stragglers) in the globular clusters M55 and omega Cen indicate that they could have been formed in a burst of metal-poor single star formation in the last 2.9-6 Gyr. If formed by the more acceptable scenario of stellar mergers, it is likely that the merged remnant resembles a normal star in a relatively advanced stage of main-sequence evolution with an enriched He core and ordinary He envelope. We present equations to calculate intrinsic-color indices for delta Scuti, SX Phe, and RR Lyrae stars at mean light. Finally, we show that the fundamental-radial-pulsating stars (delta Sct and SX Phe variables) have larger average light amplitudes than the first-overtone pulsating variables. The fundamental metal-poor variables (SX Phe stars) have the largest average and individual amplitudes.

We present results from a well-studied delta Scuti star discovered in the Large Magellanic Cloud ( LMC). The absolute magnitude of the variable was determined from the period-luminosity ( P-L) relation for Galactic delta Scuti stars and from theoretical modeling of the observed B; V; I light curves with nonlinear pulsation models. The two methods give distance moduli for the LMC of 18.46 +/- 0.19 and 18.48 +/- 0.15, respectively, for a consistent value of the stellar reddening of E( B-V) 0.08 +/- 0.02. We have also analyzed 24 delta Scuti candidates discovered in the OGLE II survey of the LMC, and seven variables identified in the open cluster LW 55 and in the galaxy disk by Kaluzny and coworkers. We find that the LMC delta Scuti stars define a P-L relation whose slope is very similar to that defined by the Galactic delta Scuti variables, and yield a distance modulus for the LMC of 18.50 +/- 0.22 mag. We compare the results obtained from the delta Scuti variables with those derived from the LMC RR Lyrae stars and Cepheids. The corresponding distance moduli are as follows: delta Scuti stars, 18.48 +/- 0.02 mag ( standard deviation of the weighted average of the three above solutions); RR Lyrae stars, 18.49 +/- 0.06 mag; and Cepheids, 18.53 +/- 0.02 mag. We have assumed an average color excess of E( B-V) 0.08 +/- 0.02 mag for both delta Scuti stars and Cepheids. Within the observational uncertainties, the three groups of pulsating stars yield very similar distance moduli. These moduli are all consistent with the "long'' astronomical distance scale for the Large Magellanic Cloud.

We examine the luminosity levels of the main-sequence turnoffs, M-v(TO), and horizontal branches, M-v(HB), in 16 globular clusters. An entirely new approach of inferring the luminosity levels by utilizing high-amplitude delta Scuti variables (HADS) is introduced. When the M-v(TO) values are compared with theoretical values inferred from models, we find all 16 clusters (metal-strong to metal-poor) are coeval with an average age of similar to 11.3 Gyr. A considerable scatter of M-v(HB) values of clusters at similar [Fe/H] values is found. A trend for clusters with blue horizontal branches to have brighter M-v(HB) than clusters with blue-red horizontal branches is suggested by the data. The M-v(HB) values appear to depend on another or other parameters in addition to the [Fe/H] values. In spite of this problem, we derive an equation relating M-v(HB) values of globular clusters to their [Fe/H] values. We also derive an equation relating the M-v(TO) values of clusters to their [Fe/H] values. Both of these equations can be utilized to find cluster distances. The distance modulus of the LMC is found to be 18.66 from the V(TO)values of three LMC globular clusters; RR Lyrae stars in seven globular clusters yield 18.61, and RR Lyrae stars in the LMC bar yield 18.64.

We analyze photometric observations of high-amplitude delta Scuti stars (HADS) in the globular cluster omega Cen and the Carina galaxy. The pulsation modes of the HADS are inferred primarily from their positions in V, log P diagrams. For omega Cen we identify nine fundamental pulsators (F), 22 first-overtone (1, O), one second-overtone (2, O), and probably two third-overtone (3, O) stars. The majority of the F pulsators have light amplitudes Delta V greater than or equal to 0.15 mag, but two have Delta V < 0.15 mag. Four of the 1, O pulsators have Delta V > 0.15 mag, but the majority have smaller amplitudes. We find that the F pulsators tend to have more asymmetric light curves. The Carina variables are all large-amplitude variables. Fourteen are F pulsators and six are 1, O pulsators. At least one and possibly two 1, O stars appear to have asymmetric light curves unlike those found in omega Cen. The data are very uncertain, so the asymmetry may be an artifact of observational uncertainty. The HADS data along with their P-L relation are utilized to find the distances to omega Cen and the Carina galaxy and absolute magnitudes of their horizontal branches (HB) or RR Lyrae stars. We find the distances to be d = 6370 pc to omega Cen and d = 124,000 pc to the Carina galaxy. The M-v(RR)-values for the omega Cen RR Lyrae stars are M-v(RR) = 0.14 (Oost II variables) and M-v(RR) = 0.28 (Oost I stars); M-v(HB) = 0.29 for the Carina galaxy.

The Optical Gravitational Lensing Experiment (OGLE) data on high-amplitude delta Scuti stars (HADS) and RR Lyrae stars have been analyzed to determine the distance to the Galactic bulge. Individual color excesses and V absorption for each individual variable star have been computed, which lead to accurate [V-0] magnitudes. The period-luminosity relation of the HADS is utilized to calculate distance moduli. We find that the metal-strong HADS are concentrated strongly to the bulge. The best distance modulus to the bulge from the HADS data is 14.49 +/- 0.06 mag. The dependence of M-v on period for the bulge RR Lyrae stars can be found from the reddening-free magnitude TV-I. The zero point of the M-v-log P relation is set with the horizontal branches of Oosterhoff type I globular clusters. M-v congruent to 0.44 mag (long-distance scale) in the log P interval -0.29 to -0.22 as inferred by main-sequence fitting of the clusters to local subdwarfs and utilizing short-period HADS in the clusters. The best distance modulus to the bulge from the RR Lyrae (ab) stars is 14.45 mag, which compares favorably with the distance modulus of 14.49 mag found from the MADS. We adopt the mean value 14.47 +/- 0.08 mag for the bulge distance modulus. A small additive correction leads to 7.9 +/- 0.3 kpc as the best distance to the Galactic center.