Pulsation Constants and Densities for Double-Mode Variables in the Cepheid Instability Strip

Pulsation constants and period ratios are given for the first six radial pulsation modes of a set of seven polytropes with indices ranging from n = 2.25 to n = 4.00. The polytrope results are combined with published theoretical data from pulsation calculations for stellar models and observational data on thirteen double-mode variables in the Cepheid instability strip to obtain four interpolation formulae relating fundamental periods P0, pulsation constants Qo, and period ratios P1/P0 and P2!P1. The derived relations are used to obtain accurate densities for the thirteen observed variables, which include six dwarf Cepheids or Al Velorum stars, one Scuti star, one RR Lyrae star, and five Cepheids. Approximate masses and luminosities are obtained for some of these stars. The probable connection between massluminosity ratios and the existence of double-mode variables is discussed.