Hiromoto Shibahashi, Donald W. Kurtz
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.
View original:
http://arxiv.org/abs/1202.0105
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