[Paper Review] Triple Stars Observed by Kepler

Jerome A. Orosz|arXiv (Cornell University)|Mar 25, 2015

Stellar, planetary, and galactic studies3 citations

TL;DR

This paper analyzes triple-star systems detected by the Kepler space telescope using eclipse timing variations (ETVs) and photodynamical modeling. It demonstrates that 15–20% of Kepler eclipsing binaries host close-in tertiary companions, with detailed modeling of systems like KIC 10319590 and KIC 7668648 revealing complex orbital dynamics, mutual inclinations near 40°, and even eclipse role reversals due to Kozai cycles and tidal effects.

ABSTRACT

The Kepler mission has provided high quality light curves for more than 2000 eclipsing binaries. Tertiary companions to these binaries can be detected if they transit one or both stars in the binary or if they perturb the binary enough to cause deviations in the observed times of the primary and secondary eclipses (in a few cases both effects are observed in the same eclipsing binary). From the study of eclipse timing variations, it is estimated that 15 to 20% of the Kepler eclipsing binaries have close-in tertiary companions. I will give an overview of recent results and discuss some specific systems of interest.

Motivation & Objective

• To determine the frequency of close-in tertiary companions in Kepler eclipsing binaries using eclipse timing variations (ETVs).
• To model complex photodynamical systems with multiple transits, occultations, and ETVs to derive precise orbital and stellar parameters.
• To test the Kozai cycle and tidal friction model in compact triple systems by analyzing mutual inclinations and orbital evolution.
• To resolve discrepancies between light curve solutions and radial velocity data by distinguishing light travel time effects from dynamical perturbations.
• To provide high-precision mass and radius measurements for low-mass stars in hierarchical triple systems using combined photometric and spectroscopic data.

Proposed method

• Utilized high-precision Kepler light curves to detect eclipse timing variations (ETVs) in over 2000 eclipsing binaries.
• Applied light travel time (LTT) models to infer minimum masses of tertiary companions using the modified ephemeris equation (2) and mass function (4).
• Modified the ELC light curve synthesis code with a Newtonian N-body integrator to model non-Keplerian orbits in triple systems.
• Combined photometric light curves with radial velocity measurements from the Kitt Peak 4m telescope echelle spectrograph to constrain stellar masses and radii.
• Fitted photodynamical models to systems exhibiting transits, occultations, and ETVs, including eclipse role reversals and depth variations.
• Used the Kozai cycle and tidal friction model to interpret mutual inclinations and orbital evolution, particularly in systems with eccentric outer orbits.

Experimental results

Research questions

• RQ1 What fraction of Kepler eclipsing binaries host close-in tertiary companions, as inferred from eclipse timing variations?
• RQ2 How do dynamical perturbations from a third body affect the observed eclipse timing and depth variations in compact triple systems?
• RQ3 To what extent do light travel time effects alone explain the observed ETVs, or are dynamical effects necessary to reconcile mass estimates with observations?
• RQ4 Can photodynamical modeling resolve eclipse role reversals and complex transit/occultation patterns in systems like KIC 7668648?
• RQ5 What is the significance of mutual orbital inclinations near 40° or 140° in triple systems, and how do they support the Kozai cycle and tidal friction model?

Key findings

• Approximately 15–20% of Kepler eclipsing binaries exhibit significant eclipse timing variations, indicating the presence of close-in tertiary companions.
• The system KIC 10319590 has an inner binary period of 21.31 days and an outer orbital period of 457.6 days with an eccentricity of 0.142 and mutual inclination of 43.1°, consistent with Kozai cycle predictions.
• In KIC 7668648, the primary and secondary eclipses reversed roles after 51 orbital cycles, with the deeper eclipse switching from primary to secondary, indicating strong dynamical modulation.
• The system KIC 7668648 hosts a low-mass tertiary star (0.278 M☉) that transits both components of the inner binary and is itself occulted, with a 206.4-day outer orbital period.
• Masses for KIC 10319590 were determined as M₁ = 0.95 M☉, M₂ = 0.71 M☉, and M₃ = 0.84 M☉, with high-precision radii and orbital parameters derived from photodynamical modeling.
• The study confirms that dynamical effects—beyond light travel time—dominate in systems like IU Aurigae and SS Lac, where LTT-only mass estimates are inconsistent with observed third-light and radial velocity data.