  Ultraluminous supersoft sources (ULSs) are defined by a thermal spectrum with
colour temperatures ~0.1 keV, bolometric luminosities ~ a few 10^39 erg/s, and
almost no emission above 1 keV. It has never been clear how they fit into the
general scheme of accreting compact objects. To address this problem, we
studied a sample of seven ULSs with extensive Chandra and XMM-Newton coverage.
We find an anticorrelation between fitted temperatures and radii of the thermal
emitter, and no correlation between bolometric luminosity and radius or
temperature. We compare the physical parameters of ULSs with those of classical
supersoft sources, thought to be surface-nuclear-burning white dwarfs, and of
ultraluminous X-ray sources (ULXs), thought to be super-Eddington stellar-mass
black holes. We argue that ULSs are the sub-class of ULXs seen through the
densest wind, perhaps an extension of the soft-ultraluminous regime. We suggest
that in ULSs, the massive disk outflow becomes effectively optically thick and
forms a large photosphere, shrouding the inner regions from our view. Our model
predicts that when the photosphere expands to >10,000 km and the temperature
decreases below approximately 50 eV, ULSs become brighter in the far-UV but
undetectable in X-rays. Conversely, we find that harder emission components
begin to appear in ULSs when the fitted size of the thermal emitter is smallest
(interpreted as a shrinking of the photosphere). The observed short-term
variability and absorption edges are also consistent with clumpy outflows. We
suggest that the transition between ULXs (with a harder tail) and ULSs (with
only a soft thermal component) occurs at blackbody temperatures of
approximately 150 eV.
