Stability of planets in double star systems

In this work we investigate the problem of orbital stability of planetary orbits in stellar binaries. We carry out  a large number of numerical simulations of  planets on circumbinary (p-type) and circumstellar (s-type) orbits over long timescales.  We cover the whole parameter space by considering three dimensional and eccentric orbits for all bodies in the system, while exploring a wide range of mass ratios.  The results of the numerical integrations provide us with two critical borders: i) for the p-type case, an outer border beyond which all planetary orbits are stable and an inner border closer to the binary below which all planetary orbits are unstable. In between the two borders, a mixture of stable and unstable planetary orbits is observed.  ii) For the s-type case, an inner border closer to the planet hosting star below which all planetary orbits are stable and an outer border beyond which all planetary orbits are unstable. Again, between the two borders, a mixture of stable and unstable planetary orbits is observed. We provide empirical expressions in the form of easy to use fits for these two critical borders. Application of our results to known planetary systems are presented and comparison is made with past results on the subject.