Luminosities of SX Phoenicis, large-amplitude delta Scuti, and RR Lyrae stars

Stromgren uvby beta photometry of SX Phoenicis and large-amplitude delta 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 relation is set. We find (Eq. 1) 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 (AJ, 106, 703, 1993) and by McNamara (PASP, 109, 857, 1997). The latter is based on revised Baade-Wesselink M-v values. At [Fe/H]= -1.9 M-v is 0.42. Feast and Catchpole's (MNRAS, 286, L1, 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. The distance to the Large Magellanic Cloud is discussed. The ''best'' distance modulus based on recent determinations is 18.57 +/- 0.03.