Orbital stability of the unseen solar companion linked to periodic extinction events

Evidence from three-dimensional numerical modelling is presented that only cometary orbits with a limited range in inclination with respect to the galactic plane are formally stable for the length of time required to cause periodic extinction events. The calculations were done using Cowell's method employing a fourth-order Runge-Kutta integration scheme in an inertial reference frame in orbit about the Galaxy. Tidal perturbations in the radial direction due to the Galaxy and the Coriolis forces are included. The vertical component of the gravitational field of the galactic disk is superimposed on these forces. The results indicate that orbits for Nemesis that are inclined at more than 30 deg to the galactic plane are not allowed and suggests that the search for Nemesis should be concentrated toward the plane of the Galaxy. Perturbations by passing stars or molecular clouds may make even the low-inclination orbits unstable.