FM stars: A Fourier view of pulsating binary stars, a new technique for measuring radial velocities photometrically

TL;DR

This paper introduces a novel photometric method to determine binary star parameters and radial velocities using Fourier analysis of pulsating stars' light curves, eliminating the need for spectroscopic data.

Contribution

It develops a theoretical framework to extract binary system parameters from light curves alone, including the mass function, by analyzing frequency multiplets caused by orbital motion.

Findings

Successfully derived binary parameters from artificial data.

Applied method to Kepler data of KIC 4150611, demonstrating practical viability.

Showed potential to detect Jupiter-mass planets around pulsating stars.

Abstract

Some pulsating stars are good clocks. When they are found in binary stars, the frequencies of their luminosity variations are modulated by the Doppler effect caused by orbital motion. For each pulsation frequency this manifests itself as a multiplet separated by the orbital frequency in the Fourier transform of the light curve of the star. We derive the theoretical relations to exploit data from the Fourier transform to derive all the parameters of a binary system traditionally extracted from spectroscopic radial velocities, including the mass function which is easily derived from the amplitude ratio of the first orbital sidelobes to the central frequency for each pulsation frequency. This is a new technique that yields radial velocities from the Doppler shift of a pulsation frequency, thus eliminates the need to obtain spectra. For binary stars with pulsating components, an orbital solution can be obtained from the light curve alone. We give a complete derivation of this and demonstrate it both with artificial data, and with a case of a hierarchical eclipsing binary with {\it Kepler} mission data, KIC 4150611 (HD 181469). We show that it is possible to detect Jupiter-mass planets orbiting $\delta$ Sct and other pulsating stars with our technique. We also show how to distinguish orbital frequency multiplets from potentially similar nonradial $m$-mode multiplets and from oblique pulsation multiplets.