A spectral-timing model for ULXs in the super-critical regime

Ultraluminous X-ray sources (ULXs) with luminosities lying between ~3x10^{39} - 2x10^{40} erg/s represent a contentious sample of objects as their brightness, together with a lack of unambiguous mass estimates for the vast majority of the central objects, leads to a degenerate scenario where the accretor could be a stellar remnant (black hole or neutron star) or intermediate mass black hole (IMBH). Recent, high-quality observations imply that the presence of IMBHs in the majority of these objects is unlikely unless the accretion flow somehow deviates strongly from expectation based on objects with known masses. On the other-hand, physically motivated models for super-critical inflows can re-create the observed X-ray spectra and their evolution, although have been lacking a robust explanation for their variability properties. In this paper we include the effect of a partially inhomogeneous wind that imprints variability onto the X-ray emission via two distinct methods. The model is heavily dependent on both inclination to the line-of-sight and mass accretion rate, resulting in a series of qualitative and semi-quantitative predictions. We study the time-averaged spectra and variability of a sample of well-observed ULXs, finding that the source behaviours can be explained by our model in both individual cases as well as across the entire sample, specifically in the trend of hardness-variability power. We present the covariance spectra for these sources for the first time, which shed light on the correlated variability and issues associated with modelling broad ULX spectra.