Barium & related stars and their white-dwarf companions I. Giant stars

This paper provides long-period and revised orbits for barium and S stars adding to previously published ones. The sample of barium stars with strong anomalies comprise all such stars present in the Lu et al. catalogue. We find orbital motion for all barium and extrinsic S stars monitored. We obtain the longest period known so far for a spectroscopic binary involving an S star, namely 57 Peg with a period of the order of 100 - 500 yr. We present the mass distribution for the barium stars, which ranges from 1 to 3 Msun, with a tail extending up to 5 Msun in the case of mild barium stars. This high-mass tail comprises mostly high-metallicity objects ([Fe/H] >= -0.1). Mass functions are compatible with WD companions and we derive their mass distribution which ranges from 0.5 to 1 Msun. Using the initial - final mass relationship established for field WDs, we derived the distribution of the mass ratio q' = MAGB,ini / MBa (where MAGB, ini is the WD progenitor initial mass, i.e., the mass of the system former primary component) which is a proxy for the initial mass ratio. It appears that the distribution of q' is highly non uniform, and significantly different for mild and strong barium stars, the latter being characterized by values mostly in excess of 1.4, whereas mild barium stars occupy the range 1 - 1.4. We investigate as well the correlation between abundances, orbital periods, metallicities, and masses (barium star and WD companion). The 105 orbits of post-mass-transfer systems presented in this paper pave the way for a comparison with binary-evolution models.