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

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$13 M${}_{\mathrm{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.

13 pages, 14 figures (most of which are in colour). Accepted for publication in MNRAS. v2: there was a missing '/' in eq (16). We have reformulated the equation

References in corpus (4)

• Finding binaries among Kepler pulsating stars from phase modulation of their pulsations
• Kepler and the seven dwarfs: detection of low-level day-timescale periodic photometric variations in white dwarfs
• Deriving the orbital properties of pulsators in binary systems through their light arrival time delays
• Validation of the Frequency Modulation technique applied to the pulsating delta Sct - gamma Dor eclipsing binary star KIC 8569819

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• Nonradial and radial period changes of the Delta Scuti star 4 CVn II. Systematic behavior over 40 years
• A binary with a $\delta$~Scuti star and an oscillating red giant: orbit and asteroseismology of KIC9773821
• Spectroscopic confirmation of the binary nature of the hybrid pulsator KIC 5709664 found with the frequency modulation method
• Orbital solutions derived from radial velocities and time delays for four {\it Kepler} systems with A/F-type (candidate) hybrid pulsators
• KIC 10855535: An elegant Delta Scuti pulsator with Amplitude and Phase Modulation
• The $\beta$ Pictoris b Hill sphere transit campaign. Paper II: Searching for the signatures of the $\beta$ Pictoris exoplanets through time delay analysis of the $\delta$ Scuti pulsations