Frontiers in accretion physics at high X-ray spectral resolution

Microcalorimeters have shown remarkable success in delivering high-spectral-resolution observations of the hot and energetic Universe, and have paved the way to revolutionary new science possibilities in X-ray astronomy. There are several research areas in compact-object science that can only be addressed with energy resolution Δ E ≲ 5 eV at photon energies of a few kiloelectronvolts, corresponding to a velocity resolution of less than a few hundred kilometres per second, to be ushered in by microcalorimeters. Here we review some of the outstanding questions, focusing on how the research landscape is set to be transformed at the interface between accreting supermassive black holes and their host galaxies, in unravelling the structures of accretion environments, in resolving long-standing issues on the origins of energy and matter feedback, and in testing mass-scaled unification of accretion and feedback. The need to learn lessons from Hitomi and to make improvements in laboratory atomic data precision as well as plasma modelling are highlighted.