On the reliability of the semi-empirical RR Lyrae period–V-band luminosity–blue amplitude relation

We investigate the accuracy and reliability of the semi-empirical period–V-band luminosity–blue amplitude (PLA) relationship for ab-type RR Lyrae stars originally obtained by Castellani and De Santis in the mid-1990s. We infer that the zero-point of this relationship depends on the metallicity, by studying a sample of both field and cluster variables. We also show that the use of this relationship can still be useful for those stellar systems showing an intrinsic metallicity spread, since in this case the metallicity has a negligible effect on the final distance modulus estimate. We compare the adopted semi-empirical relationship with the fully empirical one recently provided by Kovács & Walker. When the zero-point of the latter relation is fixed consistently with the former one, the two equations are equivalent.By applying the semi-empirical period–V-band luminosity–blue amplitude relation, as well as the technique proposed recently by Cassisi, De Santis & Piersimoni, to the globular cluster ω Cen, we show that the empirical slope of the relationship between the mass of the fundamental RR Lyrae pulsators and their metallicity is in fair agreement with the one predicted by updated evolutionary models for horizontal branch stars.