Precision Orbit of $\delta$ Delphini and Prospects for Astrometric Detection of Exoplanets

Abstract

Combining visual and spectroscopic orbits of binary stars leads to a determination of the full 3D orbit, individual masses, and distance to the system. We present a full analysis of the evolved binary system $\delta$ Delphini using astrometric data from the MIRC and PAVO instruments on the CHARA long-baseline interferometer, 97 new spectra from the Fairborn Observatory, and 87 unpublished spectra from Lick Observatory. We determine the full set of orbital elements for $\delta$ Del, along with masses of $1.78\pm 0.07$ $M_{\odot }$ and $1.62\pm 0.07$ $M_{\odot }$ for each component, and a distance of $63.61\pm 0.89$ pc. These results are important in two contexts: for testing stellar evolution models and defining the detection capabilities for future planet searches. We find that the evolutionary state of this system is puzzling, as our measured flux ratios, radii, and masses imply a $\sim$ 200 Myr age difference between the components using standard stellar evolution models. Possible explanations for this age discrepancy include mass transfer scenarios with a now ejected tertiary companion. For individual measurements taken over a span of 2 years we achieve $<10$ $\mu$-arcsecond precision on differential position with 10-minute observations. The high precision of our astrometric orbit suggests that exoplanet detection capabilities are within reach of MIRC at CHARA. We compute exoplanet detection limits around $\delta$ Del, and conclude that if this precision is extended to wider systems we should be able to detect most exoplanets $>2$ M${}_J$ on orbits $>0.75$ AU around individual components of hot binary stars via differential astrometry.

arXiv comment28 pages, 14 figures, accepted for publication in ApJ

References in corpus (31)

• Astropy: A Community Python Package for Astronomy
• emcee: The MCMC Hammer
• Modules for Experiments in Stellar Astrophysics (MESA)
• Validation of the new Hipparcos reduction
• Modules for Experiments in Stellar Astrophysics (MESA): Giant Planets, Oscillations, Rotation, and Massive Stars
• Modules for Experiments in Stellar Astrophysics (MESA): Binaries, Pulsations, and Explosions
• MESA Isochrones and Stellar Tracks (MIST). I: Solar-Scaled Models
• MESA Isochrones and Stellar Tracks (MIST) 0: Methods for the construction of stellar isochrones
• Accurate masses and radii of normal stars: modern results and applications
• Information criteria for astrophysical model selection
• First Results from the CHARA Array. II. A Description of the Instrument
• The angular size of dwarf stars and subgiants - Surface brightness relations calibrated by interferometry
• The incidence of stellar mergers and mass gainers among massive stars
• Astrometric exoplanet detection with Gaia
• The VAST Survey - III. The multiplicity of A-type stars within 75 pc
• Medium-resolution Isaac Newton Telescope library of empirical spectra - II. The stellar atmospheric parameters
• Efficient fitting of multiplanet Keplerian models to radial velocity and astrometry data
• Interferometric radii of bright Kepler stars with the CHARA Array: θ Cygni and 16 Cygni A and B
• The HARPS-N Rocky Planet Search I. HD219134b: A transiting rocky planet in a multi-planet system at 6.5 pc from the Sun
• Double-blind test program for astrometric planet detection with Gaia
• Resolving Vega and the inclination controversy with CHARA/MIRC
• Pseudomagnitudes and Differential Surface Brightness: Application to the apparent diameter of stars
• Astrometric Detection of Giant Planets Around Nearby M Dwarfs: The Gaia Potential
• A Data Exchange Standard for Optical (Visible/IR) Interferometry
• The PHASES Differential Astrometry Data Archive. V. Candidate Substellar Companions to Binary Systems
• Spectral and spatial imaging of the Be+sdO binary phi Persei
• A Goldilocks principle for modeling radial velocity noise
• Mass estimates for visual binaries with incomplete orbits
• Precise Radial Velocity Measurements for Kepler Giants Hosting Planetary Candidates: Kepler-91 and KOI-1894
• AE Ursae Majoris -- a $\delta$ Scuti Star in the Hertzsprung Gap
• Enabling science with Gaia observations of naked-eye stars

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• $\nu$ Gem: a hierarchical triple system with an outer Be star
• ARMADA II: Further Detections of Inner Companions to Intermediate Mass Binaries with Micro-Arcsecond Astrometry at CHARA and VLTI
• ARMADA I: Triple Companions Detected in B-Type Binaries alpha Del and nu Gem
• Weighing stars from birth to death: mass determination methods across the HRD
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