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Watching the sky on a starry night seems like a painting. A lot of black paint, a splash of blue and tiny specs of white and yellow in between.  But the image of starlight being a still picture is not true for all stars. Variable stars pulsate, varying in light intensity as much as a factor 4 over a period of half a day. In this story, we are taking a deeper look into RR Lyrae stars. Why are they different from other stars?

Variable stars can exist because of helium in their outer layer that is hot enough to partially ionise. This triggers a mechanism in which this layer is repeatedly compressed and expanded. In the compressed state, photons from inside the star cannot pass through, and the star will appear dark. The trapped photons will build up pressure from inside, making the helium expand, and letting light through once again. You can see this oscillating behaviour clearly in the measured flux:

This dataset was captured as part of NASA's K2 mission. If we zoom deeper, we can see the individual periods clearly. The star (called ktwo246272964-C12) makes a full cycle after 0.6 Barycentric Julian Days, or what a non-astronomer would call roughly 14 hours:

The shape of the curve is consistent through each cycle, and also between different stars. It can serve as a fingerprint to recognise the type of star. Star ktwo246300909-C12, for example, has a different shape than the one above:

This periodic behaviour is even more interesting to look at in the frequency domain. If we take a Fast Fourier Transform (FFT) of the flux, we get an idea of what frequencies are in the signal. In this case, we can clearly see a peak in the frequency domain at 0.00002 Hz. This corresponds to the primary variation of the signal of 14 hours:

Other frequencies are present too, each a multiple of the primary frequency. The second star has different frequencies, but showing a similar repetition of frequencies. The main frequency is now around 0.00003 Hz. The frequency is higher, because the period in the time domain is shorter.

This is a beautiful pattern. Is this what Van Gogh saw on a Starry Night?


Based on Jort Van Den Kieboom's master thesis (UAntwerpen, 2020). Raw data from the Mikulski Archive for Space Telescopes, available at https://archive.stsci.edu/. Visualisations done in Marple.

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