  Although we are nearing a consensus that most ULXs are stellar-mass black
holes in a super-Eddington state, little is yet established of the physics of
this accretion mode. Here, we use a combined X-ray spectral and timing analysis
of a sample of ULXs to investigate this new accretion regime. We suggest a
spectral classification scheme that separates ULXs into three classes: a
broadened disc class, and two-component hard and soft ultraluminous regimes. At
the lowest luminosities the ULX population is dominated by sources with
broadened disc spectra, whilst two component spectra are seen at higher
luminosities, suggestive of a distinction between ~ Eddington and
super-Eddington accretion modes. We find high levels of variability are limited
to ULXs with soft ultraluminous spectra, and a few broadened disc sources.
Furthermore, the variability is strongest at high energies, suggesting it
originates in the harder spectral component. These properties are consistent
with current models of super-Eddington emission, where a wind forms a funnel
around the central regions of the accretion flow. As the wind provides the soft
component this suggests that inclination is the key determinant in the observed
X-ray spectra, which is very strongly supported by the variability results if
this originates due to clumpy material at the edge of the wind intermittently
obscuring our line-of-sight to the central regions of the ULX. The pattern of
spectral variability with luminosity in two ULXs that straddle the hard/soft
ultraluminous regime boundary is consistent with the wind increasing at higher
accretion rates, and thus narrowing the opening angle of the funnel. Hence,
this work suggests that most ULXs can be explained as stellar-mass black holes
accreting at and above the Eddington limit, with their observed characteristics
dominated by two variables: accretion rate and inclination. (abridged)
