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.

arXiv comment13 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 (13)

• Rotational velocities of A-type stars. III. Velocity distributions
• FM stars: A Fourier view of pulsating binary stars, a new technique for measuring radial velocities photometrically
• Super-Nyquist asteroseismology with the Kepler Space Telescope
• Finding binaries among Kepler pulsating stars from phase modulation of their pulsations
• Three ways to solve the orbit of KIC11558725: a 10 day beaming sdB+WD binary with a pulsating subdwarf
• KIC 10080943: a binary star with two $\gamma$ Doradus/$\delta$ Scuti hybrid pulsators. Analysis of the g modes
• Kepler and the seven dwarfs: detection of low-level day-timescale periodic photometric variations in white dwarfs
• KIC 10080943: An eccentric binary system containing two pressure- and gravity-mode hybrid pulsators
• Deriving the orbital properties of pulsators in binary systems through their light arrival time delays
• Toward mode selection in Delta Scuti stars: Regularities in observed and theoretical frequency spectra
• Asteroseismology of KIC 11754974: a high-amplitude SX Phe pulsator in a 343-day binary system
• Validation of the Frequency Modulation technique applied to the pulsating delta Sct - gamma Dor eclipsing binary star KIC 8569819
• Binary star detectability in $Kepler$ data from phase modulation of different types of oscillations

Cited by in corpus (19)

• Angular Momentum Transport in Stellar Interiors
• Finding binaries from phase modulation of pulsating stars with Kepler: V. Orbital parameters, with eccentricity and mass-ratio distributions of 341 new binaries
• The astrophysics of visible-light orbital phase curves in the space age
• The effect of tides on near-core rotation: analysis of 35 Kepler $\gamma$ Doradus stars in eclipsing and spectroscopic binaries
• A planet in an 840-d orbit around a Kepler main-sequence A star found from phase modulation of its pulsations
• Multi-technique investigation of the binary fraction among A-F type candidate hybrid variable stars discovered by Kepler
• Metal-Rich SX Phe stars in the Kepler Field
• The sdB pulsating star V391 Peg and its putative giant planet revisited after 13 years of time-series photometric data
• Forward modeling the orbits of companions to pulsating stars from their light travel time variations
• TIC 308396022: a $\delta$ Scuti--$\gamma$ Doradus hybrid with large-amplitude radial fundamental mode and regular g-mode period spacing
• 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
• Finding binaries from phase modulation of pulsating stars with \textit{Kepler}: VI. Orbits for 10 new binaries with mischaracterised primaries
• Spectroscopic confirmation of the binary nature of the hybrid pulsator KIC 5709664 found with the frequency modulation method
• Anomalous Orbital Characteristics of the AQ Col (EC 05217-3914) System
• Orbital solutions derived from radial velocities and time delays for four {\it Kepler} systems with A/F-type (candidate) hybrid pulsators
• Constraining stellar physics from red-giant stars in binaries - stellar rotation, mixing processes and stellar activity
• 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