Planets, Pulsations and the Discrete Fourier Transform, Professor Don Kurtz (UCLAN)
Abstract
One of the biggest questions humans can ask is, “Are we alone?” Does Earth harbour the only life in the universe? Everyone has an opinion on this question, but as scientists, we want to know. A first step is to find other planets like the Earth, planets with rocky surfaces and liquid water where conditions are similar to home. The Kepler Space Mission has done this. With the discovery of nearly 5000 planets, orbiting other stars Kepler has revolutionised our view.
The Kepler mission measured the brightnesses of nearly 200,000 stars for four years and astronomers use Fourier analysis to extract the signals of sound waves reverberating through these stars, allowing them to characterise the stars, the exoplanets that orbit them, and to see inside the stars to what Sir Arthur Stanley Eddington called “the most inaccessible place in the universe”.
In this talk, the speaker will derive the simple mathematics of the Discrete Fourier Transform for unequally spaced data, and show how astronomers use it for time series analysis. We will learn about the window function, and the Nyquist frequency; the latter is richer and more interesting in Kepler Mission data than what you may expect from purely mathematical considerations. Finally, we will look at some real Kepler Mission data in Fourier space using a freely downloadable time series analysis program, PERIOD04.
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