Fourier decompositions are performed for the V magnitude variations of a sample of 57 Cepheids ranging in period from 2 to 17 days. The coefficients have been tabulated to allow rapid reconstruction of the light curves. It is shown that combinations of the low-order coefficients quantitatively describe the progression of curve shape with period. The pulsation amplitude plays only a minor role. Sharp breaks in the progression, occurring at around 10 days, are attributed to the resonance PdPo =0.5. It is suggested that the Fourier decompositions provide a straightforward method for resolving a number of controversies concerning theoretical interpretations of the Hertzsprung sequence. The paper closes 'With a brief discussion of three short-period stars which seem to occupy a unique position in our sample.

No abstract

Fourier decompositions have been made of the light curves of a large sample of RR Lyrae field stars. The coefficients have been tabulated. Following the scheme of an earlier investigation of classical Cepheids, certain combinations of the low-order coefficients-21' R 21' and 31-are plotted against period. The Bailey-type c pulsators stand out from the type ab stars, particularly on the R21 plot which is found to be a more sensitive discriminator of Bailey type than is the traditionally employed amplitude-period diagram. We compare the RR Lyrae plots of 21' R 21 , and 31 with those previously obtained for classical Cepheids. It is noted that, while the Cepheid plots display a tightly defined progression with period, reflecting the influence of a modal resonance, in the RR Lyrae case there is much more scatter. However, some evidence is shown to exist for a Cepheid-like progression appearing among the longer period RR Lyrae pulsators and culminating in the unique small-amplitude variable XZ Ceti. New observations will be required to confirm the reality of such a progression.

No abstract

It is shown that increasing the opacity due to heavy elements by a factor of 2-3 leads to classical Cepheid models which reproduce observed period ratios at evolutionary masses and luminosities. Thus the mass anomalies are removed in both the double-mode and bump Cepheid regimes. The proposed increases may also serve to energize {3 Cephei variables, thus solving yet another important problem in the theory of pulsating stars. We argue that opacity changes of this order are not implausible and urge further work in this important area.