On properties of the Fourier harmonics in the limit-cycle models of classical Cepheids

Details On properties of the Fourier harmonics in the limit-cycle models of classical Cepheids On properties of the Fourier harmonics in the limit-cycle models of classical Cepheids

Mar 1994

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1994ap%26ss.213...75f&link_type=abstract

Astrophysics and Space Science (ISSN 0004-640X), vol. 213, no. 1, p. 75-101

Astronomy and Astrophysics

Astrophysics

4

Cepheid Variables, Fourier Analysis, Harmonics, Standing Waves, Amplitudes, Fourier Series, Phase Shift, Radial Distribution, Thermodynamic Properties

Scientific paper

The Fourier coefficients of the hydrodynamic variables are calculated for the limit-cycle models of classical Cepheids having periods from 7.2 to 10.9 days. In adiabatically pulsating layers of the stellar envelope, each Fourier harmonic of order k less than or equal to 8 is shown to be identified with a corresponding standing wave, so that the pulsation motions of the adiabatic layers may be represented as a superposition of standing waves. Each Fourier harmonic of order k may also be identified with the eigenfunction of order l of the linear adiabatic wave equation when the resonance condition OMEGA l / OMEGA 0 = k is fulfilled. The spectra of the oscillatory moment of inertia and the spectra of kinetic energy obey the power law for the Fourier harmonics of order k less than or equal to 15, the spectrum slope being steeper for shorter pulsation periods. In the helium and hydrogen ionizing regions all of the Fourier harmonics drive the pulsation instability, whereas in the radiative damping region the mechanical work done by each Fourier harmonic is negative. In classical Cepheids having periods shorter than 10 days the period dependence of the secondary bump is due to phase changes of the second order Fourier harmonic in the outer nonadiabatic layers of the stellar envelope. At a pulsation period of PI approximately equals 9.7 days the second order Fourier harmonic is identified with the second overtone. At periods PI greater than 10 days the second order Fourier harmonic tends to be attracted by the fundamental mode in such a way that their phases coincide in the outer layers of the stellar envelope.

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