SCATTER Common Envelope Formalism for Triples

Many stars are components of triple-star systems, or of higher-order multiples. In such systems mass transfer is common, and when the transfer is dynamically unstable, a common envelope forms. As such, it is important to be able to compute the post-common-envelope orbital separations among the various stars comprising the system, and to determine whether the common envelope induces mergers or makes later mergers inevitable. In this paper we compute the results of common-envelope evolution for triples. We employ the SCATTER formalism, a new approach to the computation of post-common-envelope separations. This work has applications to gravitational-wave mergers, Type Ia supernovae, and a broad range of other highly energetic phenomena.