The eccentricities of the barium stars

We investigate the eccentricities of barium (Ba II) stars formed via a stel lar wind accretion model. We carry out a series of Monte Carlo simulations using a rapid binary evolution algorithm, which incorporates full tidal evo lution, mass loss and accretion, and nucleo-synthesis and dredge-up on the thermally pulsing asymptotic giant branch. We follow the enhancement of bar ium in the envelope of the accreting main-sequence companion and dilution i nto its convective envelope once the star ascends the giant branch. The observed eccentricities of Ba II stars are significantly smaller than t hose of an equivalent set of normal red giants but are nevertheless non-zer o. We show that such a distribution of eccentricities is consistent with a wind accretion model for Ba II star production with weak viscous tidal diss ipation in the convective envelopes of giant stars, We successfully model t he distribution of orbital periods and the number of observed Ba II stars. The actual distribution of eccentricities is quite sensitive to the strengt h of the tides, so that we are able to confirm that this strength is close to, but less than, what is expected theoretically and found with alternativ e observational tests. Two systems - one very short-period but eccentric, a nd one long-period and highly eccentric - still lie outside the envelope of our models, and so require a more exotic formation mechanism. All our mode ls, even those which were a good fit to the observed distributions, overpro duced the number of high-period barium stars, a problem that could not be s olved by some combination of the three parameters: tidal strength, tidal en hancement and wind accretion efficiency.