  We have constructed a model which describes the optical emission from
ultraluminous X-ray sources (ULXs), and have used it to constrain the
parameters of seven ULX systems. Our model assumes a binary nature for ULXs,
and accounts for optical emission from an X-ray irradiated companion star and
accretion disk. We apply our model to six different ULX optical counterparts
observed with HST, and one observed with the ESO VLT, and determine the mass,
radius and age of the donor stars in these systems. In addition, we obtained
constraints for the black hole (BH) mass in some cases. We use the mass
accretion rate implied by the X-ray luminosity of these sources as an
additional constraint on the donor star, by assuming the mass transfer is
driven by the stellar nuclear evolution. We find that in general the donors are
older and less massive than previously thought, and are consistent with being
of spectral type B. We discuss how these results affect our understanding of
the evolution and history of ULXs. Where we can constrain the BH masses, we
find them to be consistent with stellar mass BHs or intermediate mass BHs of
order 100 solar masses. We make predictions for future observations of
optical/infrared ULX counterparts, calculating binary periods for different BH
masses in each of the seven sources.
