Critical frequency separations

As we presented in the description of the spectral window the halfwidth of the main peak is 0.00416 c/d. The independent frequencies further than this separation can be easily resolve by our analysis. A systematic check was carried out that what is the frequency separation that we can resolve on the COROT data sets.

Separation 0.01 c/d

The frequencies are well-separated in the original spectrum:

The steps of frequency search:

Peaks in the residual spectrum:

There are doublets around 3.4, 2.5 and 4.2 c/d.

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)

Separation 0.005 c/d

This frequency separation represents a slightly higher value comparing to the halfwidth of the mean peak:

The steps of frequency search:

Peaks in the residual spectrum:

The solution of the two frequencies is unique although the original spectrum is slightly asyimmetric. The same doublets at 3.4, 2.5 and 4.2 are found in this residual spectrum as in the previous case.

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)

Separation 0.001 c/d:

This separation is slightly less than the halfwidth of the original spectrum, which means that the two frequencies are not well-separated. There is no distinct sign of the second frequency with lower amplitude:

The steps of frequency search:

Peaks in the residual spectrum:

The frequency values applied are precisely obtained, although the two frequencies are not well-separated. After the first step all the amplitude content of the two frequencies are concentrated in a single frequency. The residual spectrum after prewhitening with a single frequency has the next frequency with a doublet structure. There are doublets around 3.4 and 2.5.

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)

Separation 0.0001 c/d:

This separation is much less than the halfwidth of the original spectrum, which means that the two frequencies are can not be separated in the original spectrum:

The steps of frequency search:

Peaks in the residual spectrum:

The frequency values applied are precisely obtained, although the two frequencies are not separated. After the first step all the amplitude content of the two frequencies are concentrated in a single frequency. The structure of the residual spectrum is quite different when the other frequency of the doublet is used in the second step.

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)

Separation 0.00001 c/d:

This separation is much less than the halfwidth of the original spectrum, which means that the two frequencies are can not be separated in the original spectrum:

The steps of frequency search:

The search can not find the second frequency.

Peaks in the residual spectrum:

After the first step all the amplitude content of the two frequencies are concentrated in a single frequency. The second frequency can not be found.

Spectra and light curves:

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

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