The Transiting Circumbinary Planets Kepler-34 and Kepler-35

Abstract: Most Sun-like stars in the Galaxy reside in gravitationally-bound pairs of stars called "binary stars". While long anticipated, the existence of a "circumbinary planet" orbiting such a pair of normal stars was not definitively established until the discovery of Kepler-16. Incontrovertible evidence was provided by the miniature eclipses ("transits") of the stars by the planet. However, questions remain about the prevalence of circumbinary planets and their range of orbital and physical properties. Here we present two additional transiting circumbinary planets, Kepler-34 and Kepler-35. Each is a low-density gas giant planet on an orbit closely aligned with that of its parent stars. Kepler-34 orbits two Sun-like stars every 289 days, while Kepler-35 orbits a pair of smaller stars (89% and 81% of the Sun's mass) every 131 days. Due to the orbital motion of the stars, the planets experience large multi-periodic variations in incident stellar radiation. The observed rate of circumbinary planets implies > ~1% of close binary stars have giant planets in nearly coplanar orbits, yielding a Galactic population of at least several million.

• The paper presents precise measurements of stellar and planetary masses and orbits in Kepler-34 and Kepler-35 using photometric-dynamical modeling.
• It employs high-resolution spectroscopic data and eclipse timing variations to accurately characterize binary interactions and orbital dynamics.
• The findings enhance understanding of circumbinary planet formation and underscore implications for potential habitable zones in binary systems.

Analysis and Insights on Kepler-34 and Kepler-35 Circumbinary Planets

The paper provides an in-depth examination of the properties and dynamics of the circumbinary planetary systems Kepler-34 and Kepler-35. These binary systems, observed by the Kepler space telescope, offer unique insights into the complex interactions between binary stars and their surrounding planets. The research employs a blend of photometric-dynamical models, spectroscopic analysis, and eclipse timing variations (ETVs) to characterize the stellar and planetary parameters.

Stellar and Planetary Characteristics

The systems in question feature two stars orbited by a gas-giant planet. For Kepler-34, the primary and secondary stars have masses of approximately 1.048 and 1.021 solar masses, while for Kepler-35, these values are roughly 0.888 and 0.809 solar masses respectively. The planets orbiting these binaries are about 0.22 Jupiter masses (Kepler-34) and 0.127 Jupiter masses (Kepler-35), positioned at semi-major axes of 1.0896 AU and 0.6035 AU with orbital periods of 288.8 and 131.5 days, respectively.

Methodological Approaches

Photometric-Dynamical Modeling

This method combines Kepler's photometry with radial velocity data to simulate and match observed stellar and planetary motions. It accounts for the gravitational interactions within the three-body system, helping derive precise masses and orbits. The model employs a hierarchical coordinate framework, utilizing Newtonian dynamics extended by post-Newtonian corrections to encapsulate the systems' gravitation fields.

Spectroscopic Observations

High-resolution spectroscopic data obtained from multiple observatories is crucial for defining the radial velocity signature and other spectroscopic parameters of the star systems. The spectral lines and their broadening provide insights into the stellar atmospheres, effective temperatures (with uncertainties), and metallicities, contributing to the models' accuracy.

Eclipse Timing Variations

By monitoring the precise timing of eclipses in the binary systems, the study identifies perturbations indicative of additional gravitational influences, which are used to extract details about the planets' effects on the stellar components. These variations are instrumental for unveiling potential shifts in orbital dynamics over time.

Implications and Future Directions

1. Binary-Planet Dynamics: The findings underscore the significant effects that binary star configurations have on the surrounding planets, potentially affecting their formation and evolution due to the intricacies of angular momentum exchange and orbital synchronization.
2. Gyrochronology vs. Evolutionary Models: There is an observed discrepancy between ages derived from stellar rotation periods (gyrochronology) and those inferred from spectroscopic properties compared to theoretical models. This suggests potential tidal interactions in these tightly-bound systems may accelerate stellar rotation, affecting age estimates.
3. Habitability Considerations: Though primarily gas giants are identified, these systems offer a framework to consider the formation of potentially habitable moons or terrestrial planets in stable orbits, especially given the complex radiative environments imposed by two suns.
4. Circumbinary Frequency: The derived frequency of such circumbinary planets (~1% for Saturn-like bodies within specific orbital periods), although a lower limit, provides crucial data for refining planetary formation theories, particularly around binary stars.

The understanding of circumbinary planet systems like Kepler-34 and Kepler-35 is pivotal in enhancing our comprehension of planet formation in diverse stellar environments. The methodologies applied in this research provide a robust template for analyzing similar systems and pave the way for future observations and theoretical advancements in multi-body celestial mechanics and astrobiology potential. Future studies will need to address congregating data over longer periods and across a wider array of binary configurations to enhance the statistical significance and model accuracy further.