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RR Lyr - Fourier spectrum

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RR Lyr - Fourier spectrum

Hi everyone,

We know that there are three main types of RR Lyrae stars: RRab, RRc and RRd.

RRab stars pulsate in the fundamental  mode, RRc in the first overtone and RRd in both fundamental mode and first overtone. 

I can't understand how the fourier spectrum of RRc and RRd stars will look like.

I know that RRab stars show the fundamental frequency and its harmonics in the fourier spectrum and after prewhitening no signal remains. What about other types? 


Thank you in advance!


SHA's picture
Fourier spectra

RRc stars will also show the main frequency (the first overtone in their case) and its harmonics, but usually fewer harmonic terms are needed to adequately describe the light curve than for RRab stars because RRc light curves are closer to sinusoids to begin with.  RRd stars will show the fundamental mode and first overtone mode frequencies, their harmonics, and also possibly some cross-mode terms, such as the sum or difference of the fundamental and first overtone frequencies.  RRab and RRc stars that exhibit the Blazhko effect will have more complex Fourier spectra, with additional frequencies present near the main frequency and its harmonics.  The Fourier spectra of observed light curves can also be made more complex by gaps in the time series of the observations and by noise in the data.  Sometimes spurious peaks can be introduced.  Kepler mission observations of RR Lyrae have been prized because they often include long time-series without important gaps and with high signal-to-noise.  Ground-based observations are often messier, but combining observations from observers at several longitudes (or from Antarctica) can help with the gap problem. -- Horace

So if you just see a spectrum

So if you just see a spectrum with a main frequency and the harmonics, how can you recognise if this is the fundamental mode or the 1st overtone?

Or you can't and you need to take also into consideration the shape of the light curve?

SHA's picture
Light curve shape

While one can often make a good guess from period alone, since RRc stars usually have shorter periods than RRab stars, you are right that it is better to take into account the shape of the light curve.  This can be done by inspection, but there are also quantitative ways of describing the light curve, for example so-called Fourier decomposition parameters or, more simply, plots of period versus amplitude.

Nodal surfaces

Thank you very much! One last question.

Since RRc stars are 1st overtone stars means that they pulsate radially (may also exist non radial modes) and there is a nodal surface where gas moves in different directions. While in RRab stars, gas moves in one way, from the stellar center to the surface (only radial pulsation). What about RRd stars? Is there also one nodal surface?

pkneipp's picture
WebObs PEP Data

Encountered a problem with uploading unreduced PEP observation using WebObs today. The error message stated a problem with the page after serveral attemps to submit observations. I also noticed that I haven't received my weekly usage report as well.


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