Cepheid stars

Cepheids have different cases comparing to the lenght of the observing run. The expected periods located in the 10 - 100 days period range. In some cases not more than one, two cycles will be observed. Single and double mode Cepheids were involved in the test cases. Later possibility of finding a much lower amplitude non-radial mode was also investigated.

Single mode Cepheids:

The step of the frequency search:

Peaks in the residual spectrum:

The doublet at 3.4 c/d is also present as in some cases of the critical separation.

Spectra and light curves:

• Spectra: (PS)
• Original light curve: (PS)
• Residual light curve, prewhitened with 1 frequencies: (PS)

Double mode Cepheids:

The steps of the frequency search:

Peaks in the residual spectrum:

The doublet at 3.4 and 1.7 c/d are also present.

The reason of systematic behaviour:

- I used FFT but with an algorythm usable with unequally spaced data, although the synthetic data set was generated with an equal sampling.

- I used the data as a single segment. It creates not errors in the solution.

Solution:

- The data sets has to be cut into more segment. The systematic behaviour of the residual spectrum created by the error will decrease.

- The classic way of Fast Fourier Transform (with equally spaced data) is suggested.

- Discrete Fast Fourier Transformation is slower but it gives more precise result.

Spectra and light curves:

• Spectra: (PS)
• Original light curve: (PS)
• Light curve, prewhitened with 1 frequency: (PS)
• Residual light curve, prewhitened with 2 frequencies: (PS)

Non-radial modes in Cepheids:

The speciality of the non-radial modes in Cepheids is the same as in RR Lyrae stars. The amplitude of the non-radial mode is much lower than the amplitude the fundamental mode and first overtone. In the generation one order of magnitude lower amplitude was used. The distant non-radial mode in frequency to the main radial modes has not been investigated because no problem seems to appear in that case. Close non-radial mode was tested.

Close non-radial mode:

The steps of the frequency search:

Peaks in the residual spectrum:

The location of the non-radial mode is closer that the halfwidth of the mean peak in the spectral window, exactly it is half of it. It means that the two frequencies are not well-separated. Even in this case, the algorythm is working, the precise values of the frequencies were found.

Spectra and light curves:

• Spectra: (PS)
• Original light curve: (PS)
• Light curve, prewhitened with 1 frequency: (PS)
• Residual light curve, prewhitened with 2 frequencies: (PS)

Webmaster: Zsófia Sódorné Bognár; Design: András Bognár

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