On the Normalization of Cepheid Period-Luminosity Relationships

Abstract

Results of stellar evolution calculations and results of non-adiabatic stellar pulsation calculations can be used to construct theoretical, composition-dependent short-period boundaries (or “blue edges”) of the instability strip in the period-luminosity plane for Cepheids pulsating in the fundamental and first overtone radial modes. The slopes of these blue edges are very similar to the slopes of the blue edges of instability strips defined by observed Cepheids in external galaxies. By insisting that the theoretical and observed blue edges coincide for any chosen galaxy, one may estimate the distance to that galaxy. The result is very similar to a distance estimated with the help of an empirical period-magnitude relationship normalized by main-sequence fitting. In addition, masses of Cepheids obtained using the periods, surface temperatures, and luminosities (consistent with the derived distance modulus) in a relationship between these quantities derived by pulsation theory defines a semiempirical mass-luminosity relationship which is consistent with the one defined by the theoretical evolution calculations which have been used to construct the theoretical blue edges. Even so, given existing uncertainties in the theoretical evolutionary models, there is no guarantee that the distance moduli and the mass-luminosity relationships derived in this way are correct. However, most remarkably, a forced change in the adopted distance to a group of extragalactic Cepheids does not destroy the coincidence between theoretical blue edges and blue edges defined by the observed Cepheids. When, with the help of pulsation theory, the revised mass-luminosity relationship defined by the observed Cepheids (at the new distance) is inserted into the equation for the theoretical blue edge, this edge moves in such a way as to remain in contact with the blue edge defined by the Cepheids at the new distance. This means that results of calculations using pulsation theory are consistent with the observations, whatever the distance modulus.