Luminosities of SX Phoenicis, Large-Amplitude Delta Scuti, and RR Lyrae Stars

Strömgren uvby β photometry of SX Phoenicis and large-amplitude δ Scuti variables is analyzed to determine the mean temperatures, metal abundances, and surface gravities of the stars. The mean temperatures and fundamental periods are used in conjunction with the pulsation equation and stellar models to derive masses, radii, surface gravities, and M bol of the variables. The stars exhibit a period-luminosity relation. With the aid of Hipparcos trigonometric parallaxes the zero-point of the M v , p is set. We find M v = -3.725 log P - 1.933. This P-L relation is utilized to find the M-v values of RR Lyrae stars or horizontal-branch stars in globular clusters and the Carina galaxy-objects that contain both SX Phe, and RR Lyrae variables, or horizontal-branch stars. The M v values of the metal-poor RR Lyrae stars are found to be consistent with M v [Fe/H] calibrations derived by Sandage (1993) and by McNamara (1997) from revised Baade- Wesselink M v values. At [Fe/H] = -1.9 M v is 0.42. Feast and Catchpole (1997) suggestion that M v = 0.25 at [Fe/H] = -1.9 for RR Lyrae is discussed. This M v value is too luminous because it makes the (T eff ) of RR Lyraes too high-well off any (T eff ) = f (color index) calibration.