The Fourier Decomposition Technique: Interpreting the Variations of Pulsating Stars

Abstract

We review the application of the Fourier decomposition technique to Type I and Type II Cepheids as well as RR Lyrae stars both in clusters and in the field. We show how the Fourier coefficients may be used to discern a star’s pulsation mode and to detect resonances in the normal mode spectrum. Observed Fourier quantities are compared with those generated by nonlinear pulsation calculations and some serious shortcomings are found in the theoretical models. Comparison of galactic and extragalactic Cepheid data shows both similarities and differences among Local Group pulsators. Applied to RR Lyrae stars, the Fourier decomposition technique reveals a relation between light curve structure and metallicity among the shorter period field stars. We also study both Osterhoff I and II type globular clusters and the unique cluster ω Cen. The short-period Type II Cepheids provide another fertile ground for the Fourier method. We show resonance effects in the light curves of these stars and pose some provocative riddles regarding the origin of disk and halo pulsators. Observed and calculated Fourier phases are compared in an attempt to derive the mass of the Type II field Cepheid, BL Her. Finally, we argue that if a reliable hydrodynamic pulsation code were available, the Fourier technique would be capable of determining masses, luminosities and temperatures of individual stars, in many cases using observations already in hand.