  Although attempts have been made to constrain the stellar types of optical
counterparts to ULXs, the detection of optical variability instead suggests
that they may be dominated by reprocessed emission from X-rays which irradiate
the outer accretion disc. Here, we report results from a combined X-ray and
optical spectral study of a sample of ULXs, which were selected for having
broadened disc-like X-ray spectra, and known optical counterparts. We
simultaneously fit optical and X-ray data from ULXs with a new spectral model
of emission from an irradiated, colour-temperature-corrected accretion disc
around a black hole, with a central Comptonising corona. We find that the ULXs
require reprocessing fractions of $\sim 10^{-3}$, which is similar to
sub-Eddington thermal dominant state BHBs, but less than has been reported for
ULXs with soft ultraluminous X-ray spectra. We suggest that the reprocessing
fraction may be due to the opposing effects of self-shielding in a
geometrically thick super-critical accretion disc, and reflection from far
above the central black hole by optically thin material ejected in a natal
super-Eddington wind. Then, the higher reprocessing fractions reported for ULXs
with wind-dominated X-ray spectra may be due to enhanced scattering onto the
outer disc via the stronger wind in these objects. Alternatively, the accretion
discs in these ULXs may not be particularly geometrically thick, rather they
may be similar in this regard to the thermal dominant state BHBs.
