Stability of Triple Star Systems with Highly Inclined Orbits

It is well established that certain detached eclipsing binary stars exhibitapsidal motions whose value is in disagreement with with calculated deviationsfrom Keplerian motion based on tidal effects and the general theory ofrelativity. Although many theoretical senarios have been demonstrated to bringcalculations into line with observations, all have seemed unlikely for variousreasons. In particular, it has been established that the hypothesis of a thirdstar in an orbit almost perpendicular to the orbital plane of the close binarysystem can explain the anomalous motion in at least some cases. The stabilityof triple star systems with highly inclined orbits has been in doubt, however. We have found conditions which allow the long term stability of such systemsso that the third body hypothesis now seems a likely resolution of the apsidalmotion problem. We apply our stability criteria to the cases of AS Cam and DIHer and recommend observations at the new Keck interferometer which should beable to directly observe the third bodies in these systems.Comment: edited to match published versio