Testing eccentricity pumping mechanisms to model eccentric long-period sdB binaries with MESA

Context. Hot subdwarf-B stars in long-period binaries are found to be on eccentric orbits, even though current binary-evolution theory predicts these objects to be circularised before the onset of Roche-lobe overflow (RLOF). Aims. We aim to find binary-evolution mechanisms that can explain these eccentric long-period orbits, and reproduce the currently observed period-eccentricity diagram. Methods. Three different processes are considered; tidally-enhanced wind mass-loss, phase-dependent RLOF on eccentric orbits and the interaction between a circumbinary disk and the binary. The binary module of the stellar-evolution code Modules for Experiments in Stellar Astrophysics (MESA) is extended to include the eccentricity-pumping processes. The effects of different input parameters on the final period and eccentricity of a binary-evolution model are tested with MESA. Results. The end products of models with only tidally-enhanced wind mass-loss can indeed be eccentric, but these models need to lose too much mass, and invariably end up with a helium white dwarf that is too light to ignite helium. Within the tested parameter space, no sdBs in eccentric systems are formed. Phase-dependent RLOF can reintroduce eccentricity during RLOF, and could help to populate the short-period part of the period-eccentricity diagram. When phase-dependent RLOF is combined with eccentricity pumping via a circumbinary disk, the higher eccentricities can be reached as well. A remaining problem is that these models favour a distribution of higher eccentricities at lower periods, while the observed systems show the opposite. Conclusions. The models presented here are potentially capable of explaining the period-eccentricity distribution of long-period sdB binaries, but further theoretical work on the physical mechanisms is necessary.