  Masses are one of the most difficult stellar properties to measure. In the
case of the white-dwarf companions of Barium stars, the situation is worse.
These stars are dim, cool, and difficult to observe via direct methods.
However, Ba stars were polluted by the Asymptotic Giant Branch progenitors of
these WDs with matter rich in heavy elements, and the properties of their WD
companions contain key information about binary interaction processes involving
AGB stars and about the slow-neutron-capture(s)-process of nucleosynthesis. We
aim to determine accurate and assumption-free masses for the WD companions of
as many Ba stars as possible. We want to provide new observational constraints
that can help us learn about the formation and evolution of these
post-interaction binary systems and about the nucleosynthesis processes that
took place in the interiors of their AGB progenitors. We combined archival
radial-velocity data with Hipparcos and Gaia astrometry using the software
package orvara, a code designed to simultaneously fit a single Keplerian model
to any combination of these types of data using a parallel-tempering Markov
chain Monte Carlo method. We adopted Gaussian priors for the Ba star masses and
for the parallaxes, and assumed uninformative priors for the orbital elements
and the WD masses. We determined new orbital inclinations and companion masses
for 60 Ba star systems, including a couple of new orbits and several improved
orbits for the longest-period systems. We also unravelled a triple system that
was not known before and constrained the orbits and the masses of the two
companions. (Continued in the manuscript)
