FM stars II: a Fourier view of pulsating binary stars -- determining binary orbital parameters photometrically for highly eccentric cases

TL;DR

This paper introduces a photometric method to determine binary orbital parameters, including eccentricity and periapsis argument, from pulsating stars' frequency multiplets, eliminating the need for spectroscopic data.

Contribution

It provides an analytical framework and a practical method to extract orbital parameters from photometric data alone, especially for highly eccentric binary systems.

Findings

Successfully applied to Kepler data of three stars with eccentricity > 0.5

Derived orbital parameters consistent with spectroscopic methods

Demonstrated the method's effectiveness for highly eccentric binaries

Abstract

Continuous and precise space-based photometry has made it possible to measure the orbital frequency modulation of pulsating stars in binary systems with extremely high precision over long time spans. Frequency modulation caused by binary orbital motion manifests itself as a multiplet with equal spacing of the orbital frequency in the Fourier transform. The amplitudes and phases of the peaks in these multiplets reflect the orbital properties, hence the orbital parameters can be extracted by analysing such precise photometric data alone. We derive analytically the theoretical relations between the multiplet properties and the orbital parameters, and present a method for determining these parameters, including the eccentricity and the argument of periapsis, from a quintuplet or a higher order multiplet. This is achievable with the photometry alone, without spectroscopic radial velocity measurements. We apply this method to Kepler mission data of KIC8264492, KIC9651065, and KIC10990452, each of which is shown to have an eccentricity exceeding 0.5. Radial velocity curves are also derived from the Kepler photometric data. We demonstrate that the results are in good agreement with those obtained by another technique based on the analysis of the pulsation phases.