RESONANCE EFFECTS IN FUNDAMENTAL, 1ST OVERTONE AND DOUBLE-MODE CEPHEIDS

The paper deals with models and observed properties of Cepheids with p eriod less than about 10 days. Linear adiabatic periods and period rat ios (or frequency ratios) of Cepheid models with augmented and new opa cities have been computed taking into account standard and nonstandard mass-luminosity relations. A comparison of the results with the obser ved properties of fundamental, first overtone and double-mode Cepheids has yielded the following results: (a) The linear model results obtai ned for a nonstandard mass-luminosity relation predict the following r esonances among pulsation modes with frequency f(i): the well known f2 /f0 = 2 at P0 about 10 days, and f4/f0 = 3 at P0 about 6.7 days; f4/f1 = 2 at P1 about 3.2 days; f1 + f0 = f3 at P0 about 6.5 days. (b) Prob able effects produced by these resonances have been detected in the li ght curves of Cepheids at the expected periods: f2/f0 = 2 and f4/f0 = 3 in classical Cepheids; f4/f1 = 2 in first overtone Cepheids; f4/f1 = 2 and f1 + f0 = f3 in double-mode Cepheids. (c) A nonstandard mass-lu minosity relation is needed in order to compare fruitfully observed st ars and models on the temperature-period (or luminosity) diagram, taki ng the resonance condition periods as reference points. It is not poss ible to get a similar agreement using the standard mass-luminosity rel ation, because the models have a lower luminosity and a much lower tem perature than real stars.