2017MNRAS.466.1555B

We present a survey on exoplanetary systems of binary stars with stellar separations less than 100 au. For a sample of 11 binaries that harbour detected circumstellar giant planets, we investigate the frequency of systems with secular resonances (SR) affecting the habitable zone (HZ). SR are connected to dynamically unstable or chaotic regions by enforcing highly eccentric motion. We apply a semi-analytical method to determine the locations of linear SR, which is based on finding the apsidal precession frequencies of the massive bodies. For configurations where the giant planet is located exterior to the HZ, we find that there is always an SR interior to its orbit; the exact location of the SR strongly depends on the system's architecture. In systems with the giant planet interior to the HZ, no SR can occur in the Newtonian framework. Taking into account the general relativistic precession of the perihelion, which increases the precession frequencies, planets with a < 0.1 au can cause SR in the HZ. We find two cases where the SR is located inside the HZ and some more where it is close to the HZ. Generally, giant planets interior to the HZ are more favourable than exterior planets to avoid SR in the HZ. Around the location of the SR weaker mean-motion resonances are excited and resonance overlap is possible. Existing analytical models are not as accurate as the semi-analytical method in locating the SR and deviate by ∼0.1 au or more.