Secular resonances in circumstellar systems in binary stars

Planet formation around single stars is already a complicated matter, but extrasolar planets are also present in binary and multiple star systems. We investigate circumstellar planets in binary star systems with stellar separations below 100 astronomical units. For a selection of 11 systems with at least one detected giant planet we determine the location and extension of the habitable zone (HZ), subject to the incident stellar flux from both stars. We work out the stability of additional hypothetical terrestrial planets in or close to the HZ in these systems. To study the secular dynamics we apply a semi-analytical method. This method employs a first-order perturbation theory to determine the secular frequencies of objects moving under the gravitational influence of two much more massive perturbers. The other part uses a single numerical integration of the equations of motion and a frequency analysis of the obtained time-series to determine the apsidal precession frequencies of the massive bodies. By combining these two parts we are able to find the location of the most important secular resonances and the regions of chaotic motion. We demonstrate that terrestrial planets interior to the giant planet’s orbit may suffer from a linear secular resonance that could prevent the existence of habitable planets. Contrary to this, close-in giant planets are
less of a problem, but one has to take into account the general relativistic precession of the pericenter that can also lead to resonances.