  Microcalorimeters have demonstrated success in delivering high spectral
resolution, and have paved the path to revolutionary new science possibilities
in the coming decade of X-ray astronomy. There are several research areas in
compact object science that can only be addressed with energy resolution
Delta(E)<~5 eV at photon energies of a few keV, corresponding to velocity
resolution of <~a few hundred km/s, to be ushered in by microcalorimeters.
Here, we review some of these outstanding questions, focusing on how the
research landscape is set to be transformed (i) at the interface between
accreting supermassive black holes and their host galaxies, (ii) in unravelling
the structures of accretion environments, (iii) in resolving long-standing
issues on the origins of energy and matter feedback, and (iv) to test
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 modeling are highlighted.
