What are Fourier Coefficients?

Fourier coefficients are terms found by fitting a periodic sequence to a sin and/or cosine function. In the case of variable stars, the current form of the Fourier fitting formula was introduced by Simon and Lee (1981), who used the formula


to describe the light curve variation of Cepheids. In this formula, V is the observed magnitude at time t (which can be measured from some epoch), and is 2 /period. The coefficients are the Ai terms and the i terms.

The Ai terms and i terms are often combined to produce useful values,

Rij = Ai/Aj
ij = i - i j

These values are often graphed relative to the pulsation period of the variable, or the Log (period) value. A collection of graphs can be found here. Often the j value in the formulas is 1, so that all other terms are compared to the first or most dominant element of the light curve.

The Rij and ij values are valuable in discerning various aspects of stellar properties. These include pulsation mode, resonance effects, metallicity effects, temperature, and luminosity values. Fourier coefficients have been derived for a wide variety of stars, including Cepheids, RR Lyrae, Delta Scutis, Miras and SX Phe stars.

You may want to check the authors list for the many references to these coefficients.

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