Planet-planet scattering in presence of a companion star

Planet-planet (P-P) scattering is a leading dynamical mechanism invoked to explain the present orbital distribution of exoplanets. Many stars belong to binary systems; therefore, it is important to understand how this mechanism works in the presence of a companion star. We focus on systems of three planets orbiting the primary star and estimate the time-scale for instability, finding that it scales with the Keplerian period for systems that have the same ratio between inner planet and binary semimajor axes. An empirical formula is also derived from simulations to estimate how the binary eccentricity affects the extent of the stability region. The presence of the secondary star affects the P-P scattering outcomes, causing a broadening of the final distribution in semimajor axis of the inner planet as some of the orbital energy of the planets is absorbed by the companion star. Repeated approaches to the secondary star also cause a significant reduction in the frequency of surviving two-planet systems in particular for larger values of the inner planet semimajor axis. The formation of Kozai states with the companion star increases the number of planets that may be tidally circularized. To predict the possible final distribution of planets in binaries, we have performed a large number of simulations where the initial semimajor axis of the inner planets is chosen randomly. For small values of the binary semimajor axis, the higher frequency of collision alters the final planet orbital distributions that, however, beyond 50 au appear to be scalable to wider binary separations.