Formation of Ba stars: Impact of wind Roche lobe overflow and circumbinary disk in shaping the orbital parameters

Context. After more than three decades of investigation, the distribution of Ba stars in the e−log P diagram still defies our understanding. Recent smooth particle hydrodynamic simulations involving an asymptotic giant branch (AGB) primary have shown that a circumbinary disk (CB) can form around the binary and that the presence of dust in the wind of evolved low- and intermediate-mass stars can significantly affect the systemic angular momentum loss and mass accretion onto the companion through the wind Roche lobe overflow (WRLOF) phase. Aims. The aim of this paper is to provide a more realistic modeling of the progenitors of Ba stars and investigate the role of various processes (CB disk, WRLOF, tidally enhanced wind mass loss, and non-conservative RLOF) on the orbital evolution. Methods. We used the binary evolution code <ns0:sans-serif>BINSTAR</ns0:sans-serif>, which includes the latest prescriptions for mass transfer in the WRLOF regime. In our approach, we considered that a CB disk forms when WRLOF is activated. The coupling between the CB disk and the binary follows the standard resonant interaction theory. We constructed grids of 2.0 + 1.0 M⊙ and 1.2 + 0.8 M⊙ binaries for initial orbital parameters that result in WRLOF, and evolved these systems until the end of the primary's AGB phase. A tentative approach was made to estimate the effect of the CB disk during the post-AGB phase. Results. WRLOF resulted in a significant shrinkage of the orbital separation during the AGB phase, leading to binaries with initial periods on the order of ≲12 000 d undergoing Roche lobe overflow (RLOF). The combination of WRLOF, eccentricity pumping from the CB disk, and/or tidally enhanced wind mass loss can lead to RLOF on eccentric orbits down to periods of Porb∼3000 d. Non-conservative RLOF enabled a reduction of the period before circularization down to ∼2000 d, provided at least 50 percent of the transferred mass left the system. Conclusions. Our models still cannot account for the eccentricity distribution of Ba stars with periods shorter than Porb≲2000 d, where a common envelope evolution appears unavoidable.