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

TL;DR

This paper assesses the detection limits of the phase modulation method for finding binary systems among pulsating stars using Kepler data, and verifies its effectiveness with radial velocity measurements, enhancing orbit determination accuracy.

Contribution

It introduces a robust MCMC-based approach for combining phase modulation and radial velocity data, improving binary detection and orbit characterization among pulsating stars.

Findings

PM method detects low-mass brown dwarfs at long periods.

Combining RVs with PM refines orbital parameters.

Verification shows agreement between PM and RV methods.

Abstract

We explore the detection limits of the phase modulation (PM) method of finding binary systems among multi-periodic pulsating stars. The method is an attractive way of finding non-transiting planets in the habitable zones of intermediate mass stars, whose rapid rotation inhibits detections via the radial velocity (RV) method. While oscillation amplitudes of a few mmag are required to find planets, many $\delta$ Scuti stars have these amplitudes. In sub-optimal cases where the signal-to-noise of the oscillations is lower, low-mass brown dwarfs ($\sim$13 M$_{\rm Jup}$) are detectable at orbital periods longer than about 1 yr, and the lowest mass main-sequence stars (0.1-0.2 M$_{\odot}$) are detectable at all orbital periods where the PM method can be applied. We use purpose-written Markov chain Monte Carlo (MCMC) software for the calculation of the PM orbits, which offers robust uncertainties for comparison with RV solutions. Using Kepler data and ground-based RVs, we verify that these two methods are in agreement, even at short orbital periods where the PM method undersamples the orbit. We develop new theory to account for the undersampling of the time delays, which is also necessary for the inclusion of RVs as observational data in the MCMC software. We show that combining RVs with time delays substantially refines the orbits because of the complementarity of working 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 containing two pulsators.