A statistical view on stable and unstable Roche lobe overflow of a tertiary star onto the inner binary in triple systems

In compact stellar triple systems, an evolved tertiary star can overflow its Roche lobe around the inner binary. Subsequently, the tertiary star can transfer mass to the inner binary in a stable manner, or Roche lobe overflow (RLOF) can be unstable and lead to common-envelope (CE) evolution. In the latter case, the inner binary enters the extended envelope of the tertiary star and spirals in towards the donor's core, potentially leading to mergers or ejections. Although studied in detail for individual systems, a comprehensive statistical view on the various outcomes of triple RLOF is lacking. Here, we carry out 10^5 population synthesis simulations of tight triples, self-consistently taking into account stellar evolution, binary interactions, and gravitational dynamics. Also included are prescriptions for the long-term evolution of stable triple mass transfer, and triple CE evolution. Although simple and ignoring hydrodynamic effects, these prescriptions allow for a qualitative statistical study. We find that triple RLOF occurs in ~0.06% of triples, with ~64% leading to stable mass transfer, and ~36% to triple CE evolution. Triple CE is most often (~76%) followed by one or multiple mergers in short succession, most likely an inner binary merger of two main-sequence stars. Other outcomes of triple CE are a binary+single system (~23%, most of which not involving exchange interactions), and a stable triple (~1%). We also estimate the rate of Type Ia supernovae involving white dwarf mergers following triple RLOF, but find only a negligible contribution.