The impact of secular resonances on habitable zones in circumstellar planetary systems of known binary stars

We present a survey on binary star systems with stellar separations less than 100 astronomical units. a selection of 11 binaries with a detected (giant) planet in circumstellar motion we determine the conditions that would allow additional planets to be present inside or nearby the habitable zone (HZ) of the host star. First we calculate the three-body HZ for these systems, in order to investigate the dynamics of bodies in those regions. After adding the giant planetu0027s influence the final HZ is considerably modified in particular by mean motion and secular resonances. We apply a semi-analytical method to determine the locations of linear secular resonances, which is based on finding the apsidal precession frequencies of the massive bodies. For very close-in giant planets we also take the general relativistic precession of the pericenter into account. Our results demonstrate that there is a qualitative difference in the dynamics whether the giant planet is located exterior or interior to the HZ. An exterior giant planet is more likely to cause a secular resonance than an interior planet. Exterior planets play an important role for the HZ by enforcing highly eccentric orbits on potentially habitable planets. interior planets generally we do not find a secular resonance in the Newtonian framework, but the general relativistic precession introduces another source for a secular resonance. In 7 out of 11 systems secular resonances play a role. We compare our semi-analytical method to various purely analytical models, and show that it is more accurate in determining the location of secular resonances.