On Period Ratios and Resonance Sequences

Extract

Basic features of calibrations of period ratio diagrams in terms of mass or radius can be understood from two facts: (1) The pulsation Q-parameter for the fundamental mode of Cepheid-type models increases by a factor of about 3 from periods of about 0.05 days to 100 days, whereas Q for overtones vary much less. Therefore period ratios usually decrease with increasing pulsation period in a group of variable stars or in a model sequence (calibration curve). (2) Mass over radius (M/R) is a good pulsation parameter determining Q-values and therefore also period ratios (e.g. Cogan 1970). Using the pulsation criterion with constant Q, it is easy to show that this implies that periods of models with a fixed period ratio, e.g. 0.70, to a first approximation is proportional to both M and R. Thus all calibration curves in period ratio diagrams should move towards increasing period with increasing M or R. This is confirmed in numerous cases.