The chemically peculiar barium stars, CH stars, and most CEMP stars are all believed to be the products of mass transfer in binary systems from a now extinct AGB primary star. The mass of the AGB star and the orbital parameters of the system are the key factors usually considered when determining how much mass is transferred onto the lower-mass main-sequence companion. What is usually neglected, however, is the angular momentum of the accreted material, which should spin up the accreting star. If the star reaches critical rotation, further accretion should cease until the excess angular momentum is somehow dealt with. If the star cannot redistribute or lose the angular momentum while the primary is on the AGB, the amount of mass accreted could be much lower than otherwise expected. Here we present calculations, based on detailed stellar evolution models, of the mass that can be accreted by putative progenitors of Ba and CEMP stars before they reach critical rotation under the assumption that no angular momentum loss occurs during the mass transfer. We consider different accretion rates and values of specific angular momentum. The most stringent limits on the accreted masses result from considering accretion from a Keplerian accretion disk, which is likely present during the formation of most extrinsically-polluted carbon-enriched stars. Our calculations indicate that in this scenario only about 0.05 solar masses of material can be added to the accreting star before it reaches critical rotation, which is much too low to explain the chemical enrichment of many Ba and CEMP stars. Either the specific angular momentum of the accreted material has to effectively be lower by about a factor of ten than the Keplerian value, or significant angular momentum losses must occur for substantial accretion to take place.
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