The high energy X-ray probe (HEX-P): studying extreme accretion with ultraluminous X-ray sources

Ultraluminous X-ray sources (ULXs) represent an extreme class of accreting compact objects: from the identification of some of the accretors as neutron stars to the detection of powerful winds travelling at 0.1-0.2 c, the increasing evidence points towards ULXs harbouring stellar-mass compact objects undergoing highly super-Eddington accretion.Measuring their intrinsic properties, such as the accretion rate onto the compact object, the outflow rate, the masses of accretor/companion -- hence their progenitors, lifetimes, and future evolution -- is challenging due to ULXs being mostly extragalactic and in crowded fields. Yet ULXs represent our best opportunity to understand super-Eddington accretion physics and the paths through binary evolution to eventual double compact object binaries and gravitational-wave sources. We describe the value of HEX-P in understanding ULXs and their associated key physics, through a combination of broadband sensitivity, timing resolution, and angular resolution, which make the mission ideal for pulsation detection and low-background, broadband spectral studies.