The period-magnitude diagram of RR Lyrae stars .1. The controversy about the distance scale

Convective pulsating models with surface helium abundances of Y=0.24 and total masses of M=0.58, 0.65 and 0.75 M(circle dot) are used to predict the limits of the distribution of RR Lyrae stars with a given mass in the period-absolute magnitude (log P, M(v)) plane. On this basis, data of RR Lyrae stars in well-studied Galactic globular clusters clearly contradict the so-called 'long distance scale' for calibrating the RR Lyrae absolute magnitude in terms of metal content {M(v)(RR) = 0.94 + 0.30[Fe/H]}, in that most c-type variables turn out to fall in the hot stable region, outside the RR Lyrae instability strip. Conversely, if the calibration of M(v) (RR) follows the precepts of stellar evolution theory, then a close agreement with the pulsational constraints is obtained. Furthermore, this new approach is adopted to derive the distance to the Large Magellanic Cloud from RR Lyrae rich globular clusters. The resulting true distance modulus (d(0) = 18.44 +/- 0.10 for scaled solar chemical composition and d(0) = 18.37 +/- 0.10 if the alpha elements are enhanced by a factor of 3) is in close agreement with the distances derived from supernova 1987A and planetary nebulae, and only marginally smaller than that derived from Cepheids.