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On Period Ratios and Resonance Sequences

Published online by Cambridge University Press:  15 February 2018

J.O. Petersen*
Affiliation:
Copenhagen University Observatory, Denmark

Extract

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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.

Type
Windows on the Instability Strip
Copyright
Copyright © Cambridge University Press 1993

References

Cogan, B.C., 1970, Astrophys. J., 162, 139.Google Scholar
Petersen, J.O., 1984, Astron. Astrophys. 139, 496.Google Scholar
Petersen, J.O., Diethelm, R., 1986, Astron. Astrophys. 156, 337.Google Scholar