Probing extreme black-hole outflows on short timescales via high spectral-resolution x-ray imagers

We investigate outflows and the physics of super-Eddington versus sub-Eddington regimes in black hole systems. Our focus is on prospective science using next-generation high-resolution soft x-ray instruments. We highlight the properties of black hole ultraluminous x-ray source (ULX) systems in particular. Owing to scale invariance in accreting black holes, ULX accretion properties, including their outflows, inform our understanding not only of the closely related population of (similar-mass) x-ray binary systems but also of tidal disruption events (TDEs) around supermassive black holes. A subsample of TDEs are likely to transcend super-Eddington to sub-Eddington regimes as they evolve, offering an important unifying analog to ULXs and sub-Eddington x-ray binaries. We demonstrate how next-generation soft x-ray observations with resolving power $\gtrsim 1000$ and collecting area $\gtrsim 1000{\mathrm{cm}}^2$ can simultaneously identify ultrafast and more typical wind components, distinguish between different wind mechanisms, and constrain changing wind properties over characteristic variability timescales.