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We explore the detection limits of the phase modulation (PM) method offinding binary systems among multi-periodic pulsating stars. The method is anattractive way of finding non-transiting planets in the habitable zones ofintermediate mass stars, whose rapid rotation inhibits detections via theradial velocity (RV) method. While oscillation amplitudes of a few mmag arerequired to find planets, many $\delta$ Scuti stars have these amplitudes. Insub-optimal cases where the signal-to-noise of the oscillations is lower,low-mass brown dwarfs ($\sim$13 M$_{\rm Jup}$) are detectable at orbitalperiods longer than about 1 yr, and the lowest mass main-sequence stars(0.1-0.2 M$_{\odot}$) are detectable at all orbital periods where the PM methodcan be applied. We use purpose-written Markov chain Monte Carlo (MCMC) softwarefor the calculation of the PM orbits, which offers robust uncertainties forcomparison with RV solutions. Using Kepler data and ground-based RVs, we verifythat these two methods are in agreement, even at short orbital periods wherethe PM method undersamples the orbit. We develop new theory to account for theundersampling of the time delays, which is also necessary for the inclusion ofRVs as observational data in the MCMC software. We show that combining RVs withtime delays substantially refines the orbits because of the complementarity ofworking in both the spatial (PM) and velocity (RV) domains simultaneously.Software outputs were tested through an extensive hare and hounds exercise,covering a wide range of orbital configurations including binaries containingtwo pulsators.

Finding binaries from phase modulation of pulsating stars with Kepler. IV. Detection limits and radial velocity verification