Abstract
Many exoplanets are discovered in binary star systems in internal or in circumbinary orbits. Whether the planet can be habitable or not depends on the possibility to maintain liquid water on its surface, and therefore on the luminosity of its host stars and on the dynamical properties of the planetary orbit. The trajectory of a planet in a double star system can be determined, approximating stars and planet with point masses, by solving numerically the equations of motion of the classical three-body system. In this study, we analyze a large data set of planetary orbits, made up with high precision long integration at varying: the mass of the planet, its distance from the primary star, the mass ratio for the two stars in the binary system, and the eccentricity of the star motion. To simulate the gravitational dynamics, we use a 15th order integration scheme (IAS15, available within the REBOUND framework), that provides an optimal solution for long-term integration. In our data analysis, we evaluate if an orbit is stable or not and also provide the statistics of different types of instability: collisions with the primary or secondary star and planets ejected away from the binary star system. Concerning the stability, we find a significant number of orbits that are only marginally stable, according to the classification introduced by Musielak et al. (Astron. Astrophys. 434:355, 2005). For planets of negligible mass, we estimate the critical semi-major axis a_{c} as a function of the mass ratio and the eccentricity of the binary, in agreement with the results of Holman and Wiegert (Astron. J. 117:621, 1999). However we find that for very massive planets (Super-Jupiters) the critical semi-major axis decrease in some cases by a few percent, compared to cases in which the mass of the planet is negligible.
Highlights
The first possible observational evidence of a Jupiter-like planet in the binary star system gamma Cephei was reported by Campbell et al (1988), based on the measurements of the radial velocity variations in a sample of stars
We report how the stability depend on the mass of the planet, the initial semi-major axis of the planetary orbit, and on the mass ratio and eccentricity of the binary star system
We introduce with some examples2 the statistics of possible collisions of the planet with one of the two stars of the binary and of ejections from the binary system
Summary
The first possible observational evidence of a Jupiter-like planet in the binary star system gamma Cephei was reported by Campbell et al (1988), based on the measurements of the radial velocity variations in a sample of stars. Due to possibility that the low signal was due to chromospheric activities of the star, the existence of a planet in this system was subsequently questioned (Walker et al 1992). It was thanks to more accurate measurements that the true nature of the gamma Cephei planet was confirmed (Hatzes et al 2003), fifteen years after the first observation. The catalogue maintained by Schwarz et al (2016) reports 103 binary and 26 multiple confirmed star systems hosting planets, and 28 candidates.
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