Asteroseismic search for invisible binary companions

Abstract

AbstractContinuous 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. We present the phase modulation (PM) method for finding binaries among pulsating stars. We demonstrate how the orbital elements of a pulsating binary star can be obtained analytically from photometry alone, without spectroscopic radial velocity measurement. Frequency modulation (FM) caused by binary orbital motion also manifests itself in the Fourier transform, as a multiplet with equal spacing of the orbital frequency. The orbital parameters can also be extracted by analysing the amplitudes and phases of the peaks in these multiplets. 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. This, too, is achievable with the photometry alone, without spectroscopic radial velocity measurements. We apply these two methods to Kepler mission data and demonstrate that the results are in good agreement with each other. These methods are used to search for invisible binary companions, including planets and invisible massive objects such as neutron stars and stellar-mass black holes.