  Determining the type of matter that is inside a neutron star (NS) has been a
long-standing goal of astrophysics. Despite this, most of the NS equations of
state (EOS) that predict maximum masses in the range 1.4-2.8 solar masses are
still viable. Most of the precise NS mass measurements that have been made to
date show values close to 1.4 solar masses, but a reliable measurement of an
over-massive NS would constrain the EOS possibilities. Here, we investigate how
optical astrometry at the microarcsecond level can be used to map out the
orbits of High-Mass X-ray Binaries (HMXBs), leading to tight constraints on NS
masses. While previous studies by Unwin and co-workers and Tomsick and
co-workers discuss the fact that the future Space Interferometry Mission should
be capable of making such measurements, the current work describes detailed
simulations for 6 HMXB systems, including predicted constraints on all orbital
parameters. We find that the direct NS masses can be measured to an accuracy of
2.5% (1-sigma) in the best case (X Per), to 6.5% for Vela X-1, and to 10% for
two other HMXBs.
