Binary star detectability in $Kepler$ data from phase modulation of different types of oscillations

Detecting binary stars in photometric time series is traditionally done by measuring eclipses. This requires the orbital plane to be aligned with the observer. A new method without that requirement uses stellar oscillations to measure delays in the light arrival time and has been successfully applied to $\delta$ Scuti stars. However, application to other types of stars has not been explored. To investigate this we simulated light curves with a range of input parameters. We find a correlation between the signal-to-noise of the pulsation modes and the time delay required to detect binary motion. The detectability of the binarity in the simulations and in real $Kepler$ data shows strong agreement, hence, we describe the factors that have prevented this method from discovering binary companions to stars belonging to various classes of pulsating stars.